If there's a philosophical/metaphysical aspect to this, it would be how or why something that is continually working should be so fundamentally difficult to describe as to its working
I watched a video where quantum physicist admits many quantum physicists (not just students) don't fully grasp quantum physics. (the study of what's known about quantum world)
This video requires some background knowledge, but I think the answer to thread title is in the video @10:30
Which is that there are infinite localized field intensities in quantum world. (hopefully I got that right), instead of single source of wave origin origin which makes it difficult to measure or to research deeper.
Also IIRC the study of quantum physics isn't fully researched and understood.
I've made the comment on several occasions that the Schrödinger equation, in its simplest form, is a concept from elementary calculus: the instantaneous rate of change of something is proportional to the amount of that thing at that instant. In calculus the solution of such an equation involves the exponential function, and in the setting of complex analysis, e^it = cos(t)+isin(t), which is a wave structure. Not a physical wave. Nice video, thanks.
Reply to tim wood Yes, I watched that yesterday. It is based on the fact that in the double-slit experiment, the wave pattern will gradually emerge even if the particles are fired one at a time. This leads to the (to my mind absurd) expression that the 'particle interferes with itself'. The way I put it:
the interference pattern arises not because the particles are behaving as classical waves, but because the probability wavefunction designated by the Greek letter psi, ?, and often referred to as the Schrödinger equation, in honour of Erwin Schrödinger who devised it describes where at any given point in time, any individual particle is likely to register. So it is wave-like, but not actually a wave, in that the wave pattern is not due to the proximity of particles to each other or their interaction, as is the case with physical waves. Consequently, the interference pattern emerges over time, irrespective of the rate at which particles are emitted, because it is tied to the wave-like form of the probability distribution, not to a physical wave passing through space. This is the key difference that separates the quantum interference pattern from physical wave phenomenon. This is what I describe as the timeless wave of quantum physics.
The reason it's metaphysically baffling is because it doesn't answer the question 'does the particle exist?' in an unambiguous, yes-no fashion. It neither exists nor does not exist - there are only degrees of possibility that it exists, right up until it is measured, which is the so-called 'wave function collapse'.
This is why the Copenhagen school says things like 'no phenomenon is a real phenomenon until it is an observed phenomena'.
Sir Roger Penrose cannot accept that - he is absolutely adamant that the wave function, and the wave function collapse, are physically real - otherwise, what kind of objects are we talking about? He and Einstein both reject quantum physics as incomplete because it can't answer that question. And, remember, here we're supposed to be dealing with 'fundamental particles', so this kind of pulls the rug from under physical realism.
The interpretation I favour is QBism. (I've written an essay on the topic.)
Assuming the particles follow a path of some kind, how is it they manage to favour some paths over others?
It's assuming too much. Paths are no more definite or real than particles. The brutal way of putting the Copenhagen attitude, is, in my view, there are no particles:
[quote=Kumar, Manjit. Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality (pp. 219-220)]The wave function itself has no physical reality; it exists in the mysterious, ghost-like realm of the possible. It deals with abstract possibilities, like all the angles by which an electron could be scattered following a collision with an atom. There is a real world of difference between the possible and the probable. Born argued that the square of the wave function, a real rather than a complex number, inhabits the world of the probable. Squaring the wave function, for example, does not give the actual position of an electron, only the probability, the odds that it will found here rather than there. For example, if the value of the wave function of an electron at X is double its value at Y, then the probability of it being found at X is four times greater than the probability of finding it at Y. The electron could be found at X, Y or somewhere else.
Niels Bohr would soon argue that until an observation or measurement is made, a microphysical object like an electron does not exist anywhere. Between one measurement and the next it has no existence outside the abstract possibilities of the wave function. It is only when an observation or measurement is made that the wave function collapses as one of the possible states of the electron becomes the actual state and the probability of all the other possibilities becomes zero.
For Born, Schrödingers equation described a probability wave. There were no real electron waves, only abstract waves of probability. From the point of view of our quantum mechanics there exists no quantity which in an individual case causally determines the effect of a collision, wrote Born. And he confessed, I myself tend to give up determinism in the atomic world. Yet while the motion of particles follows probability rules, he pointed out, probability itself propagates according to the law of causality[/quote]
I recall you writing the other day that 'science gave up talking about causation 100 years ago.' Isn't this one of the main reasons for that? The famous Fifth Solvay Conference, where all of this was first discussed, was in 1927.
Maybe there is a system of resonances that influence the particles as they pass through the slit to follow one or another of a limited number of discrete paths?
Also, more significantly, what existential or epistemological difference do the ontological interpretations of "quantum physics" make to classical beings classically living in a classical world (re: locality¹)?
Also, more significantly, what existential or epistemological difference do the ontological interpretations of "quantum physics" make to classical beings classically living in a classical world (re: locality¹)?
There is a fair bit of mathematical machinery that is used up again and again with these quantum interpretations. They are epistemologically silent, yet ontologically distinct, and sometimes even so obscure or unvisualizable in their presentations that they border on being declared as 'metaphysical nonsense'.
They are pragmatically a beast demanding some sort of Occam's razor to shave all of them away for cleaner but blander observable absolutism.
However, what if the mere mental fascination with any particular interpretation or indulgence in the 'chase' is what actually leads to the pragmatic results one desires?
When the dust settles. . . after all the epistemological external world skepticism. . . and the highest form of scientific under-determination of theories makes its appearance. . . what are you supposed to turn to in informing your 'free choice' or 'decision'? The aesthetically pleasing. . . the simplicity of theories. . . the indulgence in playful fantastical stories. . . and language attempts to put into pleasing speech the patterns we observe.
What difference does fantasy do to the 'free choice' and directing of the will of a Human being?
I'd say. . . a lot. Even if it is nothing but fantasy.
what existential or epistemological difference do the ontological interpretations of "quantum physics" make to classical beings classically living in a classical world
Three of the better popular science books on the subject:
Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science, David Lindley (2007)
Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality, Manjit Kumar (2011)
What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics, Adam Becker (2018)
Assuming the particles follow a path of some kind, how is it they manage to favour some paths over others?
The particles do not exist in the transmission of radiant energy, so there is no path. The energy moves as waves not particles. We all know about electromagnetic waves, light waves, radio waves, etc.. Those are real waves and we can see refraction (rainbows) and a variety of interference patterns associated with these waves.
The problem is that we have not identified the medium (sometimes called ether) within which the waves exist. Therefore the waves cannot be modeled or represented as they actually exist, so they are represented as a wave function. At the base of this problem is the fact that there is no adequate understanding of the photoelectric effect, which is the quantized way that fields of radiation waves interact with what are known as material objects. That is the relationship between the medium (ether) and the supposed material objects.
How does the relationship between energy and matter play a role in the nature of the wave-particle? Einstein showed that matter and energy are the same thing. It seems to me that energy of all forms come in waves. Waves on the ocean are two-dimensional while EM waves propagate across space in 3 dimensions. What if the wave in wave particle duality is propagating across 5 dimensions? If time is the fourth dimension would this play a roll in how we perceive particles making wave patterns over time?
The selection of paths followed is clearly not random. Not asking, being pretty sure there is no answer (yet). For whatever the particle is or is not, the account for the diffraction pattern is MIA - and so far a great mystery.
There is actually a mathematically rigorous theory called stochastic mechanics which shows that you can produce all quantum behavior from classical particles that undergo a non-dissipative diffusion.
What is a non-dissipative diffusion? Well a dissipative diffusion is something like a pollen particle being pushed about seemingly randomly by H2O molecules in a glass of water. As the pollen bashes into H2O molecules, they impart a drag or frictional force on the pollen meaning it leaks or dissipates energy into the environment.
In a non-dissipative diffusion, energy does not dissipate in these interactions; any energy lost would be returned on average to the pollen by the H2O molecules. The system is frictionless in some sense.
What is really unique about stochastic mechanics is its the only interpretation / formulation I know of that actually derives quantum theory de novo from other assumptions. It then suggests that it is sufficient for quantum behavior to be executed by regular classical point particles so long as you enforce the absence of dissipation in its behavior so that energy is conserved on average.
But if you want a kind of common-sense realistic ontology, it probably means you want a model similar to the pollen floating in the glass of water. There are experiments which actually produce quantum-like behavior in this kind of way:
What isn't mentioned in the article but you can find in the papers is that the reason the quantum-like behavior occurs is that vibrating the bath reduces viscous dissipation in the bath, 'viscous-ity' being related to friction due to interacting molecules in a fluid. Effectively, vibrating the bath replaces energy that is lost due to friction, and this makes the bouncing droplet (video at top of the page) exhibit behavior that looks quantum-like.
If hypothetically reality were to be like this then it implies particles are floating around in stuff. Very big assumption, but not so big considering the fact we know that space isn't really empty but filled with a vacuum energy and fluctuations. This provides a very plausible home for this mechanism and the fact particles are floating in a kind of fluid of stuff would give a mechanism for what you are talking about in the post, about how they seem to be guided along paths in a double slit experiment that appear as an interference pattern. Closing a slit then affects whats going on in the fluid which would then pass along to the particles move through it. You no longer have to think about a particle "interfering with itself".
So I think there is no reason to give up on a classical, realistic universe just yet. It is absolutely mathematically possible.
You see in the image trajectories from this approach produced by a mathematical simulation (far right image). Bohmian mechanics also uses classical particles but it effectively just takes the quantum wavefunction and puts deterministic trajectories on top - it doesn't explain anything about why quantum behavior occurs. In contrast, stochastic mechanics starts with a classical description of particles being pushed about like the pollen in a glass of water, and shows that under specific conditions related to energy conservation, as I previously described, all quantum behavior occurs for regular classical particles.
Bohmian mechanics also uses classical particles but it effectively just takes the quantum wavefunction and puts deterministic trajectories on top - it doesn't explain anything about why quantum behavior occurs. In contrast, stochastic mechanics starts with a classical description of particles being pushed about like the pollen in a glass of water, and shows that under specific conditions related to energy conservation, as I previously described, all quantum behavior occurs for regular classical particles.
The stochastic interpretation of QM isn't an interpretation of QM in the sense that Bohmian Mechanics is, i.e. in the sense of being a non-local or anti-realist account of quantum entanglement,, rather the stochastic interpretation amounts to a phenomenological interpretation of quantum statistics that doesn't explain entanglement and the origin of Bells inequalities.
Good question, to which I dont know the answer - but the wavefunction doesnt describe an electromagnetic wave. The wavefunction is a wave-like distribution of possibilities, but its not *actually* a wave. Thats something the video linked in the OP explains (he also remarks that it is a source of confusion about the importance of waves in quantum mechanics.)
the stochastic interpretation amounts to a phenomenological interpretation of quantum statistics that doesn't explain entanglement and the origin of Bells inequalities.
Right. The theory accounts for the observed statistical patterns of quantum mechanics (similar to the Born rule), but it does so by modelling outcomes, not necessarily by explaining the underlying quantum structure. So its phenomenological in the scientific sense of being descriptive, not necessarily explanatory.
Understood. But it must be "something" that changes its property at a certain frequency, so that a frequency can be detected and filtered by the receiver (to distinguish radio stations or colors). Also, as we know, the higher the frequency, the higher the energy (at the same amplitude).
In a radio receiver antenna, the electromagnetic waves induce alternating electric current. It's the same effect that occurs when you move a magnet near an electric wire quickly back and forth. The magnetic field, flux, or density changes relative to a certain place in 3D space (e.g. where a copper wire is located). However, that field, flux, or density itself is probably indescribable -- like a ghost ...
I don't think so. I think you're confusing electromagnetic waves with the wavefunction in quantum physics. This thread is about the latter, not the former.
ApustimelogistApril 21, 2025 at 23:05#9837530 likes
It is an interpretation in the sense of Bohmian mechanics, in fact their underlying mathematical structure is very similar.
Entanglement and Bell inequalities are direct consequences of the non-dissipative diffusion like all other quantum behavior. The background hypothesis gives a conceivable way in which the non-dissipative diffusion could be physically realized, albeit without specific details. This is an interpretation explicitly intended to give a physical account of quantum theory.
Right. The theory accounts for the observed statistical patterns of quantum mechanics (similar to the Born rule), but it does so by modelling outcomes, not necessarily by explaining the underlying quantum structure. So its phenomenological in the scientific sense of being descriptive, not necessarily explanatory.
As I said in my first post, it derives quantum theory from non-quantum assumptions about classical particles undergoing diffusion. It proves that in principle quantum mechanics can be instantiated in normal classical particles given the correct specifications which basically just amounts to conserving energy on average.
Reply to Apustimelogist Thanks for the clarification I take your point that stochastic mechanics aims to be a constructive theory, grounding quantum phenomena in classical-like processes with added stochastic dynamics.
It does seem to follow Bohms realist sentiment: to recover quantum statistics from an underlying deterministic mechanism. But it still relies on a hypothetical substrate diffusing particles and a non-dissipative background that isn't observable and must be posited as a metaphysical assumption (presumably subject to further investigation.)
By contrast, the Copenhagen interpretation is more circumspect. It doesnt posit unknowables, but draws a line at what can meaningfully be said more in the spirit of Wittgenstein: Whereof one cannot speak, thereof one must be silent. The Copenhagen attitude is not nearly so 'mystical' as many of its critics contend. It's a philosophical humility, not a metaphysical fog.
Are we not talking about the double slit experiment where light is sent through slits and certain interferences are observed?
Yes - but the salient question is, why does the interference pattern occur, when light is emitted at the rate of one particle at a time? How can that result in a wave pattern? That question concerns the wave function ?, not electromagnetic nature of light. It's easy to confuse the electro-magnetic waves, and the wave-function - this is discussed in the video linked in the OP at around 3:28 ('the Dirac wave for the electron IS NOT the Schrodinger wave'.)
ApustimelogistApril 22, 2025 at 00:55#9837790 likes
But it still relies on a hypothetical substrate diffusing particles and a non-dissipative background that isn't observable and must be posited as a metaphysical assumption (presumably subject to further investigation.
Sure, but I would say it is arguably still better than many other interpretations given it provides an explanation for quantum behavior, it completely deflates the measurement problem and classical limit, it returns metaphysics to what is intuitive and commonsensical. I would say from a standpoint of rationality this is a preferable theory because arguably we shouldn't update our beliefs about the universe (or anything) any more than required given the evidence. And despite the background assumption I think this theory is clearly the least ontologically radical of any alternatives in the sense of diverging as little as possible from pre-quantum beliefs about how the world is, what everyday experience suggests the world is like, what other sciences suggest the world is like.
It seems almost completely conspiratorial to me that the world would have some bizarre, inscrutable ontology when mathematically there is a theory, maybe even multiple theories, that can produce quantum behavior through the kind of common-sensical, realistic, classical-like manner thag the world otherwise presents itself to us as.
And yes, obviously the background is a big assumption; but we already know - or at least quantum field theory tells us - about a kind of background because the vacuum is not empty: vacuum energy and fluctuations. We just don't know if that kind of background could be part of or indicative of the same kind of background as you would want in stochastic mechanics. But at the very least this isn't such a big leap as something like Many Worlds where you are assuming something else radical (and a bit ridiculous) exists that we can never observe and has no basis anywhere else in science. We know a kind of background exists (or you are at least justified in believing it based on quantum field theory):
https://en.wikipedia.org/wiki/Vacuum_energy
We just don't know if it could be the stochastic mechanical one.
Even when just a single photon is sent at a time, and interference occurs, I think my question is on-topic. For example, the changing property might also lie in the photon's kind of spin etc. rather than in its location or velocity. I don't know. But I'm curious, and I still think it's on-topic.
Sure, but I would say it is arguably still better than many other interpretations given it provides an explanation for quantum behavior, it completely deflates the measurement problem and classical limit, it returns metaphysics to what is intuitive and commonsensical.
But notice that embodied unstated realist assumptions about 'what the world is like'. And as Sabine Hossenfelder points out in Lost in Math, there's this tendency in today's physics to rationalise posits on the basis that they supposedly make intuitive sense and then to devise the mathematics to make them stand up. So given your realist predilections, then this approach seems natural to you.
(As I've made clear in the other thread on this topic, I'm highly suspicious of the many-worlds theory.)
I would say from a standpoint of rationality this is a preferable theory because arguably we shouldn't update our beliefs about the universe (or anything) any more than required given the evidence.
Right - but this is because of a prior commitment to realism, right? Whereas QBism says that the wavefunction ? does not describe something that exists objectively out there in the world. Instead, it represents the observers knowledge of the probabilities of the outcomes of observations. In other words, the wavefunction provides a rule that an agent/observer follows to update their beliefs about the likely outcomes of a quantum experiment. These probabilities, much like betting odds, are not intrinsic features of the world but rather reflect the agents expectations based on their unique perspective and prior information.
In QBism, measurement outcomes are seen in terms of experiences of the agent making the observation. Each agent may confer and agree upon the consequences of a measurement, but the outcome is fundamentally the experience that each of them individually has. Accordingly the wavefunction doesnt describe the system itself but rather the agents belief about what might happen when they interact with it. So while quantum theory has extremely high predictive accuracy, no two observations are ever exactly the same, and each observation is unique to a particular observer at that moment. And this is being borne out by experimental validation of 'Wigner's Friend'-type scenarios.
(This doesn't mean that the outcome is entirely subjective, either, as it is constrained by the Born Rule to a range of possibilities. But it's not entirely determined, either.)
I'm not a physicist, what I know about it is based on readings of science and listening to lectures. But you're grasping for a simple explanation of a phenomenon which defies simple explanations. Have a look at this primer https://brilliant.org/wiki/double-slit-experiment/
It is an interpretation in the sense of Bohmian mechanics, in fact their underlying mathematical structure is very similar.
That is only true if the so-called background hypothesis, which is typically assumed to consist of a random field locally perturbing the motions of the particles, is assumed to have supplementary non-local Bohmian character as necessary to explain the statistics of quantum entanglement ... in which case your preferred interpretation becomes a variant of the Bohmian interpretation.
The stochastic interpretation provides a conception of wave-particle duality with an uncertainty principle, but without additional Bohmian mechanics it cannot explain Bells Theorem, for there is no getting around the fact that classical particle-field interactions that communicate slower than the speed of light cannot explain the 'action at a distance' of Bells inequalities; either the medium denoted by the background hypothesis is local, in which case we do not have quantum semantics, else the medium has non-local effects, in which case we have Bohmian mechanics.
I think the stochastic interpretation is pedagogically useful for providing a common-sense physical explanation for potentially classical aspects of complementarity that are often mistaken for inherently quantum phenomena, analogous to how Spekken's toy model of quantum mechanics is useful for providing common-sense epistemic intuition for understanding complementarity without assuming a physical account of the Schrodinger equation. But in neither case is there either a physical or epistemic explanation for entanglement.
ApustimelogistApril 22, 2025 at 17:53#9839220 likes
But notice that embodied unstated realist assumptions about 'what the world is like'. And as Sabine Hossenfelder points out in Lost in Math, there's this tendency in today's physics to rationalise posits on the basis that they supposedly make intuitive sense and then to devise the mathematics to make them stand up. So given your realist predilections, then this approach seems natural to you.
Very true, we all have different dispositions for intuition; albeit, I would say that the only reason these intuitions are open to us in physics is because of results like quantum theory. Consensus would have opted for a realistic interpretation had it been conceivable in the first place, so I would say a realistic interpretation should be preferable if available. There would be no QBism if a realistic interpretation has heen initially available to us.
That is only true if the so-called background hypothesis, which is typically assumed to consist of a random field locally perturbing the motions of the particles, is assumed to have supplementary non-local Bohmian character as necessary to explain the statistics of quantum entanglement ... in which case your preferred interpretation becomes a variant of the Bohmian interpretation.
If someone wants to call it a variation of Bohmian mechanics, I don't really see an inherent issue but you don't explicitly need Bohmian kind of non-locality for the theory to produce Bell violations. There is at least one version by Levy & Krener (1996) which is does not have Bohmian non-locality, produces all the correct predictons, and even explains that non-locality only comes when an artificially idealized assumption is used for constructing the theory.
quote="sime;983839"]The stochastic interpretation provides a conception of wave-particle duality with an uncertainty principle, but without additional Bohmian mechanicks it cannot explain Bells Theorem, for there is no getting around the fact that classical particle-field interactions that communicate slower than the speed of light cannot explain the 'action at a distance' of Bells inequalities; either the medium denoted by the background hypothesis is local, in which case we do not have quantum semantics, else the medium has non-local effects, in which case we have Bohmian mechanics.[/quote]
Well Levy & Krener's stochastic mechanics van in principle do so without explicit non-local communication.
I think the stochastic interpretation is pedagogically useful for providing a common-sense physical explanation for potentially classical aspects of complementarity that are often mistaken for inherently quantum phenomena, analogous to how Spekken's toy model of quantum mechanics is useful for providing common-sense epistemic intuition for understanding complementarity without assuming a physical account of the Schrodinger equation. But in neither case is there either a physical or epistemic explanation for entanglement.
False. It can produce all quantum behavior and explains it in terms of a non-dissipative diffusion. The issue is that its depiction of QM is radically different from what people are used to so ita difficult for them to imagine. For instance, on stochastic mechanics, spin is a statistical property and doesn't belong to individual particles. An interesting possible consequence is that we no longer have to think of measurement in entanglement experiments as actively changing properties of individual particles.
If someone wants to call it a variation of Bohmian mechanics, I don't really see an inherent issue but you don't explicitly need Bohmian kind of non-locality for the theory to produce Bell violations. There is at least one version by Levy & Krener (1996) which is does not have Bohmian non-locality, produces all the correct predictons, and even explains that non-locality only comes when an artificially idealized assumption is used for constructing the theory.
I have a suspicion that the authors you mention aren't intending to address foundational questions of QM ,and are instead focusing on the technicalities of constructing laws and diffusion models that cohere with the Schrodinger equation, with potential relevance to the subject of modelling quantum decoherence, by which classical diffusion can emerge in the limit of quantum diffusion, but without relevance as to the question of the nature and ontology of quantum states and quantum measurements.
A quantum stochastic process that in principle can model non-local correlations, i.e. a random vector field of a complex Hilbert Space that is interpretable as the evolution of a quantum state vector, cannot be explicated in terms of the local interactions of a regular stochastic process such as Brownian motion. The former can serve to explicate the latter, but not conversely unless one supplements entanglement relations.
ApustimelogistApril 23, 2025 at 15:22#9840740 likes
I have a suspicion that the authors you mention aren't intending to address foundational questions of QM ,and are instead focusing on the technicalities of constructing laws and diffusion models that cohere with the Schrodinger equation, with potential relevance to the subject of modelling quantum decoherence, by which classical diffusion can emerge in the limit of quantum diffusion, but without relevance as to the question of the nature and ontology of quantum states and quantum measurements.
I am pretty sure this is not the case. For instance:
"Nelsons stochastic mechanics formulation of quantum mechanics, which started it development with his article On the derivation of the Schrödinger equation from Newtonian mechanics in 1966 [6], is completely in accord with the requirements of Bells inequalities. By now, it has been developed to a mathematical rigor that completely parallels the formulation of classical analytical mechanics. It thus provides sufficient mathematical structure to suggest a clear physical picture of quantum phenomena."
I cannot access the Levy & Krener (1996) paper, so instead I asked Grok for an account of reciprocal stochastic processes, of which I am unfamiliar which gave an interesting reply.
If the papers referred to are "Dynamics and kinematics of reciprocal diffusions" and "Stochastic mechanics of reciprocal diffusions", then I can see how these papers are of relevance to foundational questions of QM, in the sense of attempting to reconstruct properties of quantum diffusion in terms of time-symmetric but otherwise classical stochastic processes that implement non-local aspects of the time-symmetric transactional interpretation of QM.
However, Grok's conclusion at the end is along the lines of my initial thoughts, namely that such processes fail to account for quantum entanglement as should be expected by the Kohen Specker Theorem.
" Reciprocal stochastic processes are compelling because they challenge the necessity of quantum mechanics formalism for describing quantum diffusion. If a classical-like stochastic model can replicate quantum behavior, it suggests that some quantum phenomena might be emergent from underlying probabilistic structures, aligning with interpretations like stochastic mechanics or hidden-variable theories. However, their inability to fully capture quantum non-locality (e.g., entanglement) reinforces the uniqueness of quantum mechanics, prompting deeper inquiry into what makes quantum systems distinct.
Specific foundational questions they address:
Can quantum non-locality be reduced to time-symmetric stochastic correlations?
Is the wave function a physical entity, or can it be replaced by a stochastic process with equivalent predictive power?
How does the time-symmetric nature of quantum mechanics relate to causality and the arrow of time?
Can the quantum-classical transition be fully understood as a shift from reciprocal to Markovian stochastic processes?
Conclusion
Reciprocal stochastic processes can reproduce many aspects of quantum diffusion, such as probability density evolution, interference-like patterns, and non-local effects, making them a powerful tool for modeling quantum dynamics in a probabilistic framework. Their time-symmetric and non-Markovian nature makes them particularly relevant to foundational questions about quantum non-locality, the quantum-classical transition, and the ontology of the wave function. While they do not fully explain quantum non-locality (e.g., entanglement), they offer a semi-classical perspective that challenges quantum mechanics uniqueness and invites exploration of alternative formulations, such as stochastic mechanics or time-symmetric interpretations."
So i stand partially corrected.
ApustimelogistApril 23, 2025 at 15:42#9840790 likes
However, their inability to fully capture quantum non-locality (e.g., entanglement) reinforces the uniqueness of quantum mechanics, prompting deeper inquiry into what makes quantum systems distinct.
This is absolutely false and A.I. do not reliably give you information. Often when I research something, I will read the A.I. summary thing on google just as to give me some indication if what the answer might be, but I absolutely cannot trust this. I look at the sources it says it gets the information from every time and I find that it's relatively common that the A.I. will mix things up or confabulate ideas from various sources that actually don't make sense together, ending up in wrong or misleading answers.
I think the A.I. can be used as a research aide, but it cannot be trusted to reliably give you answers to things.
For instance, I can tell that the following phrase came from an A.I. :
Btw, you can see a pdf download link by just searching something like "Levy & Krener (1996)" in google. The pdf link comes from the author's website associated with their university.
Stochastic mechanics shows mathematically that entanglement follows from a non-dissipative / conservative diffusion.
Well not according to your source "On the Stochastic Mechanics Foundation of Quantum Mechanics ".
There is no mention let alone explanation of entanglement anywhere in that paper, although there is a mention of the Bohm potential, indicating that the authors are perhaps imagining their stochastic mechanics supplemented with some other foundational interpretation, perhaps to account for the non-locality of their background hypothesis. As it stands, it is a metaphysical interpretation of the Schrodinger equation that reproduces a fragment of the least problematic parts of Quantum Mechanics with deafening silence on the most critical aspects of QM that the interpretation either fails to address, or helps itself to by appealing to unstated non-local premises.
As it stands, I view that paper, which I have admittedly scantly read, is a non-earth shattering exercise in using stochastic differential equations to simulate whatever one wishes.
For instance, I can tell that the following phrase came from an A.I. :
that implement non-local aspects of the time-symmetric transactional interpretation of QM.
sime
They were actually my own opinion in my own words, prompted by my understanding that the authors of the other paper you mention were reconstructing quantum diffusion out of time symmetric diffusions that is reminiscent of the symmetric casuality inherent in the transactional interpretation of QM. Personally I think that more modest paper is much more informative.
For what its worth, I'm finding vanilla ChatGPT especially helpful with regards to navigating in a sourced way the nuances of the stochastic mechanics interpretation. As an outsider to the physics research community who nevertheless has a vested interest in understanding the mathematics and logic of a wide range of theories for purposes in relation to computing and category theory, I'm generally finding LLMs particularly useful for getting to grips quickly with unfamiliar theoretical ideas and for understanding the tone and the context of research papers, without which it can be difficult to understand what authors are selling versus what they are claiming - a very common problem indeed.
For instance, I notice that certain physicists who are prominent members of the PhysicsForums.com were almost automatically dismissive of stochastic mechanics for the same obvious reasons that i opined earlier in this thread, but they also suspected that the authors selling stochastic mechanics were dishonest, doing pointless metaphysics, or failing to own up to the problem of entanglement.
On the other hand, ChatGPT focused on what Stochastic mechanics is and actually claims and spoke of the authors contributions in a more neutral and worthwhile tone, more or less summarizing the interpretation as a stochastic alternative to Bohmian mechanics that replaces the guiding wave with quantum diffusion, whilst also stressing the fact that stochastic mechanics cannot be an explanation for non-locality for obvious Cohen-Specker reasons, while pointing out that the model assumes non-locality in the form of the configuration space upon which the model places a quantum diffusion - namely the space describing the joint positions of all of the particles that cannot be decoupled into independent diffusions satisfying local causality if non-local entanglement is to be describable by the model.
As to the question regarding what "reciprocal processes" brings to the table, they apparently 'upgrade' the implicit and unexplained non-locality of the original model of stochastic mechanics (i.e the configuration space) , to a more explicit model of non-locality based on time-symmetry that is similar to the transactional interpretation, which in my words and understanding can presumably reconstruct at least some of the non-local unity of the configuration space in terms of the "retrocausal" effects of the future light-cone of the particles. How successful this approach is I don't know, and didn't care to ask.
ApustimelogistApril 23, 2025 at 23:08#9841460 likes
There is no mention let alone explanation of entanglement anywhere in that paper
I just gave you a quote earlier that says that it is in accord with Bell inequalities but they actually do have a paper where they produce the Bell violations with stochastic mechanics:
Stochastic mechanics can reproduce all behavior of quantum mechanics.
Now, the above paper has a kind of non-local behavior, but the authors interpret it epistemically. And this is completely justified imo because the Levy-Krener paper shows that this non-locality is a byproduct of using an artificial, idealized Markovian assumption. Their model alsocan reprosuce all quantum behavior without any non-locality at all in the formalism by not using the idealized Markov assumption.
for the non-locality of their background hypothesis. As it stands, it is a metaphysical interpretation of the Schrodinger equation that reproduces a fragment of the least problematic parts of Quantum Mechanics with deafening silence on the most critical aspects of QM that the interpretation either fails to address, or helps itself to by appealing to unstated non-local premises.
Because stochastic mechanics reproduces all quantum behavior under assumptions about point particles that always are in definite places at any time and move along continuous paths. The fact you can do this suggests it is metaphysically possible; and stochastic mechanics gives a very simple physical explanation: energy conservation. All quantum behavior manifests from this. You don't need a non-local background to do this. No where is it implied that explicit non-locality is needed, only this energy conservation property; it follows that non-local entanglement behavior would follow regardless of exactly how you enforce this energy conservation, aslong as it is achieved. Non-local correlations are a consequence of initial local interactions where the resulting behavior does not dissipate but maintains its initial correlations.
is a non-earth shattering exercise in using stochastic differential equations to simulate whatever one wishes.
You can't just do this though. These stochastic processes work under the same physical constraints people would normally assume are impossible in regards to producing quantum behavior. Its not an arbitrary formal reconstruction, it has strong physical interpretation implied directly by the formalism.
They were actually my own opinion in my own words, prompted by my understanding that the authors of the other paper you mention were reconstructing quantum diffusion out of time symmetric diffusions that is reminiscent of the symmetric casuality inherent in the transactional interpretation of QM. Personally I think that more modest paper is much more informative.
Well its completely polar opposite to what the transactional interpretation.
What do you mean by "modest"?
ApustimelogistApril 23, 2025 at 23:23#9841500 likes
For what its worth, I'm finding vanilla ChatGPT especially helpful with regards to navigating in a sourced way the nuances of the stochastic mechanics interpretation. As an outsider to the physics research community who nevertheless has a vested interest in understanding the mathematics and logic of a wide range of theories for purposes in relation to computing and category theory, I'm generally finding LLMs particularly useful for getting to grips quickly with unfamiliar theoretical ideas and for understanding the tone and the context of research papers, without which it can be difficult to understand what authors are selling versus what they are claiming - a very common problem indeed.
Completely disagree. I mean, what your A.I. gave me about stochastic mechanics is false in a way that can be easily checked. And I have my own experiences of sometimes using A.I. to help find some kind of an answer and finding that they were misleading or incorrect when checking sources myself.
A.I. will give you explanations that are easy to understand; it doesn't mean they are always accurate, just like in this case!
For instance, I notice that certain physicists who are prominent members of the PhysicsForums.com were almost automatically dismissive of stochastic mechanics for the same obvious reasons that i opined earlier in this thread, but they also suspected that the authors selling stochastic mechanics were dishonest, doing pointless metaphysics, or failing to own up to the problem of entanglement.
These physicists may not have reliable opinions either if they are not at all familiar with and actually understand stochastic mechanics and perhaps are even invested in their own preferred interpretation. Obviously I cannot actually evaluate their opinions if what they say isn't given.
the model assumes non-locality in the form of the configuration space upon which the model places a quantum diffusion - namely the space describing the joint positions of all of the particles that cannot be decoupled into independent diffusions satisfying local causality if non-local entanglement is to be describable by the model.
The Levy & Krener paper doesn't have this and explains why it occurs in a model which uses an artificial Markovian assumption.
These physicists may not have reliable opinions either if they are not at all familiar with and actually understand stochastic mechanics and perhaps are even invested in their own preferred interpretation. Obviously I cannot actually evaluate their opinions if what they say isn't given.
whilst also stressing the fact that stochastic mechanics cannot be an explanation for non-locality for obvious Cohen-Specker reasons
sime
The Levy & Krener paper doesn't have this and explains why it occurs in a model which uses an artificial Markovian assumption.
I'm in agreement with Levy & Krener to the extent I understand their actual claims, which is what I was pointing out; they are shifting to reciprocal processes to provide a non-classical account of non-locality , as per the explanation provided by Chat-GPT , in the hope of explicating the presupposition of non-locality in stochastic models that is hard-encoded in the latter's reliance upon configuration space.
None of this makes their revised account of stochastic mechanics a locally causal model of QM in line with the classical intuitions of Brownian motion.
Do you agree or not agree, that any theory dependent entirely on local causality cannot be a full explanation of QM? Secondly, how do you propose physically interpreting the use of time-symmetric reciprocal processes for guiding a collection of particles in a way that that is compatible with local realism?
What do reciprocal processes contribute to theories of Stochastic Mechanics that interpret Quantum Mechanics?
Reciprocal processes play a significant role in stochastic mechanics, particularly in the context of interpreting quantum mechanics through stochastic frameworks like the Nelson's stochastic quantization or the stochastic interpretation of quantum mechanics. Here's a concise explanation of their contribution:
[I]Bridging Classical and Quantum Dynamics[/i]:
Reciprocal processes are a class of stochastic processes that generalize Markov processes by allowing conditional dependencies on both past and future states. In stochastic mechanics, they provide a framework to describe quantum systems as stochastic processes while preserving time-reversal symmetry, a key feature of quantum mechanics. This helps reconcile classical stochastic dynamics with quantum behavior.
Schrödinger Equation Connection: Reciprocal processes are closely tied to the Schrödinger equation through the concept of stochastic differential equations. In Nelson's stochastic mechanics, the quantum wave function is interpreted as encoding information about a diffusion process. The forward and backward drifts of a reciprocal process correspond to the probability currents, which are derived from the wave function, thus providing a stochastic interpretation of quantum evolution.
Path Integral Interpretation: Reciprocal processes support the path integral formulation of quantum mechanics by describing trajectories that are conditioned on both initial and final states. This aligns with the Feynman path integral approach, where quantum amplitudes are sums over all possible paths. Reciprocal processes offer a probabilistic underpinning for these paths in a stochastic framework.
Non-Markovian Behavior: Unlike standard Markov processes, reciprocal processes can model non-Markovian dynamics, which are essential for capturing quantum phenomena like entanglement and superposition. This makes them suitable for describing the stochastic analogs of quantum correlations and interference effects.
Time-Symmetric Formulation: Reciprocal processes enable a time-symmetric formulation of stochastic mechanics, mirroring the time-reversal invariance of quantum mechanics. This symmetry is crucial for interpreting quantum phenomena like wave function collapse or measurement in a stochastic context.
In summary, reciprocal processes contribute to stochastic mechanics by providing a mathematical framework that captures quantum mechanical behaviorsuch as wave function dynamics, path integrals, and time symmetrywithin a probabilistic, stochastic setting. They offer an alternative lens to interpret quantum mechanics, emphasizing diffusion-like processes while maintaining consistency with quantum predictions.
Can reciprocal processes be understood in terms of the common-sense local causality of Brownian motion?
Yes, reciprocal processes can be understood in terms of the common-sense local causality of Brownian motion, but with important extensions that make them distinct and more suitable for capturing quantum mechanical phenomena in stochastic mechanics. Here's a concise explanation:
Brownian Motion and Local Causality
Brownian motion is a Markovian stochastic process characterized by local causality: the future evolution of a particle depends only on its current state (position and velocity) and is driven by random, uncorrelated increments (white noise). This aligns with a "common-sense" notion of causality where the past influences the future in a straightforward, memoryless way, and the dynamics are governed by local interactions (e.g., diffusion via random collisions).
Reciprocal Processes: Extending Brownian Motion
Reciprocal processes generalize Brownian motion by introducing a form of conditional dependence on both past and future states, which departs from the strict Markovian property but retains a sense of local causality in a broader sense. Here's how they relate to Brownian motion and local causality:
Local Dynamics with Boundary Conditions:
Reciprocal processes can be thought of as Brownian-like diffusions constrained by boundary conditions at both initial and final times. For example, in stochastic mechanics, a particle's trajectory is modeled as a diffusion process (akin to Brownian motion) but conditioned on starting at one point and ending at another. This introduces a "teleological" aspect, where the future influences the present, but the dynamics remain locally governed by stochastic differential equations (SDEs) similar to those of Brownian motion.
The local causality is preserved in the sense that the increments of the process are still driven by Gaussian noise, and the evolution at each time step depends on local drift and diffusion terms.
Forward and Backward Drifts:
In stochastic mechanics, reciprocal processes are described by forward and backward stochastic differential equations, where the drift terms are derived from the quantum wave function. These drifts are analogous to the drift in a biased Brownian motion but incorporate information about both initial and final states. The local causality is maintained because the drifts and noise act locally in time, even though they are influenced by global (boundary) conditions.
Mathematically, for a reciprocal process XtX_tX_t
, the forward SDE might look like:
dXt=bf(Xt,t)dt+2?dWt,dX_t = b_f(X_t, t) dt + \sqrt{2\nu} dW_t,dX_t = b_f(X_t, t) dt + \sqrt{2\nu} dW_t,
where bfb_fb_f
is the forward drift, ?\nu\nu
is the diffusion coefficient, and WtW_tW_t
is a Wiener process (Brownian motion). A similar backward SDE exists, ensuring compatibility with future conditions.
Non-Markovian but Locally Causal:
Unlike Brownian motion, reciprocal processes are generally non-Markovian because the probability of a trajectory depends on both past and future states. However, the local causality of Brownian motion is preserved in the sense that the process is still driven by local stochastic increments, and the non-Markovian behavior arises from the conditioning rather than nonlocal interactions.
This conditioning can be understood as a statistical constraint rather than a violation of locality, much like how a Brownian bridge (a Brownian motion conditioned to end at a specific point) remains locally causal despite its endpoint constraint.
Quantum Interpretation:
In the context of stochastic mechanics, reciprocal processes model quantum particles as undergoing Brownian-like motion with drifts determined by the wave function. The "common-sense" causality of Brownian motion is extended to account for quantum phenomena like interference and entanglement, where the conditioning on future states mimics the global correlations of quantum mechanics.
For instance, the interference patterns in the double-slit experiment can be modeled as reciprocal processes where the particle's stochastic paths are influenced by both the initial state and the final detection point, yet the paths themselves are locally diffusive, like Brownian motion.
Key Difference from Brownian Motion
While Brownian motion is purely Markovian and driven by local, memoryless noise, reciprocal processes introduce a form of global conditioning that makes them suitable for quantum mechanics. This conditioning does not violate local causality but modifies the drift terms to reflect quantum probabilities, effectively bridging the local, diffusive nature of Brownian motion with the nonlocal correlations of quantum systems.
Summary
Reciprocal processes can be understood as an extension of Brownian motion's local causality, where the random, diffusive nature of Brownian motion is preserved, but the trajectories are conditioned on both initial and final states. This conditioning introduces non-Markovian behavior while maintaining local stochastic dynamics, making reciprocal processes a natural framework for interpreting quantum mechanics in a stochastic setting. They retain the intuitive, local causality of Brownian motion but adapt it to capture the time-symmetric and globally correlated nature of quantum phenomena.
So are they locally causal at the expense of losing realism, as per the Kochen Specker theorem?
The question of whether reciprocal processes in stochastic mechanics are locally causal at the expense of losing realism, particularly in light of the Kochen-Specker (KS) theorem, is a nuanced one. To address this, we need to unpack the concepts of local causality, realism, and how the KS theorem applies in the context of stochastic interpretations of quantum mechanics (QM). Here's a concise and clear response:
Recap: Reciprocal Processes and Local Causality
Reciprocal processes, as used in stochastic mechanics (e.g., Nelson's stochastic quantization), model quantum systems as diffusion processes akin to Brownian motion, with forward and backward drifts derived from the quantum wave function. They are locally causal in the sense that:
The evolution of the process at each time step is governed by local stochastic differential equations (SDEs), driven by Gaussian noise and drift terms that depend on the local state.
The non-Markovian nature arises from conditioning on initial and final states, but this conditioning is a statistical constraint, not a nonlocal physical interaction.
This local causality aligns with the intuitive, diffusive picture of Brownian motion, extended to incorporate quantum behavior via time-symmetric drifts.
Kochen-Specker Theorem and Realism
The Kochen-Specker theorem (1967) is a no-go theorem in quantum mechanics that rules out non-contextual hidden variable theories under the assumption of realism. Realism, in this context, means that all measurable properties (observables) of a quantum system have definite values at all times, independent of measurement. The KS theorem shows that for quantum systems in dimensions d?3
, it is impossible to assign definite values to all observables simultaneously in a non-contextual way (i.e., where the value of an observable is independent of which other compatible observables are measured alongside it).
In other words, the KS theorem challenges the idea that quantum systems possess pre-existing, measurement-independent properties (realism) while respecting the structure of quantum observables.
Reciprocal Processes and Realism
To address whether reciprocal processes in stochastic mechanics sacrifice realism to maintain local causality, we need to examine how stochastic mechanics interprets quantum mechanics and whether it assumes realism in the sense challenged by the KS theorem:
Stochastic Mechanics as a Hidden Variable Theory:
Nelson's stochastic mechanics attempts to reproduce quantum mechanics by modeling particles as undergoing stochastic trajectories governed by reciprocal processes. The wave function is interpreted as encoding the probability distribution and drift of these trajectories, not as a physical field but as a statistical descriptor.
In its original formulation, stochastic mechanics can be viewed as a hidden variable theory, where the particle's position and trajectory are the hidden variables, assumed to have definite values at all times (realism). The stochastic drifts are derived from the wave function, and the randomness mimics quantum uncertainty.
Impact of the KS Theorem:
The KS theorem applies to stochastic mechanics if it assumes non-contextual realism, i.e., that all observables (e.g., position, momentum, spin) have definite values independent of the measurement context. Since stochastic mechanics assigns definite positions to particles at all times (the trajectories are well-defined), it inherently assumes realism for position. However, other observables, like momentum or spin, are not directly represented as definite values in the stochastic framework but are derived statistically from the wave function or ensemble averages.
The KS theorem implies that stochastic mechanics cannot consistently assign definite values to all quantum observables in a non-contextual way for systems with Hilbert spaces of dimension d?3.
. For example, attempting to define definite values for spin or momentum observables alongside position in a way that reproduces quantum predictions would lead to contextuality, contradicting non-contextual realism.
Local Causality vs. Realism:
Local causality in reciprocal processes is preserved because the dynamics are governed by local SDEs, and the conditioning on future states (non-Markovianity) is a statistical effect, not a nonlocal physical interaction. This avoids issues like Bell nonlocality, as stochastic mechanics can be constructed to respect Einstein locality for spatially separated systems.
However, to maintain consistency with quantum mechanics (and avoid contradicting the KS theorem), stochastic mechanics must abandon non-contextual realism for all observables. Instead, it may adopt contextual realism, where the values of observables depend on the measurement context (e.g., which compatible observables are measured). For instance, the momentum in stochastic mechanics is not a definite value but a statistical quantity derived from the drift, which depends on the wave function and measurement setup.
Alternatively, stochastic mechanics could abandon realism entirely for observables other than position, treating them as inherently probabilistic or emergent from the stochastic dynamics. This would align with quantum mechanics' rejection of pre-existing values but might undermine the "realist" motivation of stochastic mechanics as a classical-like interpretation.
Does Stochastic Mechanics Lose Realism?:
If stochastic mechanics insists on non-contextual realism (definite values for all observables, independent of measurement), it is incompatible with the KS theorem and fails to reproduce quantum mechanics fully. In this sense, maintaining local causality via reciprocal processes comes at the expense of non-contextual realism, as the KS theorem forbids such a model.
In practice, stochastic mechanics often adopts a weaker form of realism, where only the particle's position is real and definite (the stochastic trajectory), while other observables are contextual or probabilistic. This allows it to maintain local causality and reproduce quantum predictions (e.g., for position measurements) but sacrifices the strong realist picture where all observables have pre-existing values.
Some formulations of stochastic mechanics explicitly acknowledge this by focusing on position as the primary observable and treating other properties as statistical or context-dependent, sidestepping the KS theorem's constraints by not assigning definite values to incompatible observables.
Summary
Reciprocal processes in stochastic mechanics are locally causal, with dynamics resembling Brownian motion but conditioned on initial and final states. However, to be consistent with quantum mechanics and the KS theorem, stochastic mechanics cannot maintain non-contextual realism for all observables. It either adopts contextual realism (where observable values depend on measurement context) or restricts realism to position alone, treating other observables probabilistically. Thus, local causality is preserved, but at the expense of a strong realist interpretation where all quantum observables have definite, measurement-independent values.
In essence, the KS theorem forces stochastic mechanics to compromise on realism to remain viable, aligning its reciprocal processes with quantum mechanics' contextual or non-realist nature while retaining a locally causal framework.
So are particle velocities interpreted non-locally by this model, if they are considered to be real properties?
To address whether particle velocities in stochastic mechanics, when interpreted as real properties, are non-local in the context of reciprocal processes, we need to examine how velocities are defined in this framework, the role of realism, and the implications of non-locality. This response builds on our prior discussion, particularly the interplay between local causality, realism, and the Kochen-Specker (KS) theorem, and provides a concise answer tailored to your question.
Stochastic Mechanics and Reciprocal Processes: Overview
In stochastic mechanics (e.g., Nelsons formulation), quantum systems are modeled as particles undergoing diffusion processes akin to Brownian motion, described by reciprocal processes. These processes are governed by stochastic differential equations (SDEs) with forward and backward drifts derived from the quantum wave function. The particles position is treated as a real, definite property (realism), and its stochastic trajectory is well-defined. Reciprocal processes are locally causal because the dynamics at each time step depend on local drift and noise terms, with non-Markovian behavior arising from statistical conditioning on initial and final states, not nonlocal interactions.
Velocities in Stochastic Mechanics
In stochastic mechanics, the concept of velocity is more nuanced than in classical mechanics due to the stochastic nature of the trajectories. Lets clarify how velocities are defined and interpreted:
Forward and Backward Velocities:
The particles motion is described by a stochastic differential equation, such as:
dXt=bf(Xt,t)dt+2?dWt,dX_t = b_f(X_t, t) dt + \sqrt{2\nu} dW_t,dX_t = b_f(X_t, t) dt + \sqrt{2\nu} dW_t,
where XtX_tX_t
is the particles position, bf(Xt,t)b_f(X_t, t)b_f(X_t, t)
is the forward drift, ?\nu\nu
is the diffusion coefficient (related to ?/2m\hbar/2m\hbar/2m
), and WtW_tW_t
is a Wiener process (Brownian noise).
Similarly, a backward SDE exists with a backward drift bb(Xt,t)b_b(X_t, t)b_b(X_t, t)
. These drifts are derived from the wave function ? (I snipped Grok's unprintable unicode description)
The osmotic velocity u=(bf?bb)/2u = (b_f - b_b)/2u = (b_f - b_b)/2
and current velocity v=(bf+bb)/2v = (b_f + b_b)/2v = (b_f + b_b)/2
are introduced to describe the particles motion. The current velocity ( v ) is analogous to the Bohmian velocity in pilot-wave theory and is often interpreted as the physical velocity of the particle, while the osmotic velocity accounts for the diffusive component.
Realism of Velocities:
If velocities (e.g., the current velocity ( v )) are considered real properties, they are assumed to have definite values at each point along the particles trajectory, consistent with the realist assumption that the particle has a well-defined position and motion.
In stochastic mechanics, the current velocity v=?mIm(???)v = \frac{\hbar}{m} \text{Im} \left( \frac{\nabla \psi}{\psi} \right)v = \frac{\hbar}{m} \text{Im} \left( \frac{\nabla \psi}{\psi} \right)
depends on the wave function, which encodes global information about the quantum system. This raises the question of whether such a velocity, if real, implies non-locality.
Are Velocities Non-Local?
Non-locality in quantum mechanics typically refers to correlations or influences that violate Bells inequalities or Einstein locality, where the state of one system instantaneously affects another at a distance without a local mediating mechanism. To determine if velocities in stochastic mechanics are non-local when treated as real properties, we consider the following:
Dependence on the Wave Function:
The current velocity ( v ) is determined by the gradient of the phase of the wave function ?\psi\psi
. In quantum mechanics, the wave function is a global object that describes the entire system, including entangled or spatially extended states. For example, in an entangled two-particle system, the wave function ?(x1,x2)\psi(x_1, x_2)\psi(x_1, x_2)
depends on the positions of both particles, and the velocity of particle 1, v1=?m1Im(?1??)v_1 = \frac{\hbar}{m_1} \text{Im} \left( \frac{\nabla_1 \psi}{\psi} \right)v_1 = \frac{\hbar}{m_1} \text{Im} \left( \frac{\nabla_1 \psi}{\psi} \right), may depend on the position of particle 2, even if they are far apart.
If ( v ) is a real property, this dependence suggests non-locality, as the velocity of one particle is instantaneously influenced by the state or position of another, without a local physical mechanism. This is analogous to the non-locality in Bohmian mechanics, where the velocity of a particle is guided by the non-local quantum potential or wave function.
Reciprocal Processes and Local Causality:
Reciprocal processes themselves are locally causal in their dynamics: the SDEs governing the particles motion depend only on the local drift bfb_fb_f or bbb_bb_b and noise at the current position XtX_tX_t
. The non-Markovian conditioning (dependence on initial and final states) is a statistical constraint, not a dynamical non-locality.
However, the drifts (and thus the velocities) are derived from the wave function, which can encode non-local correlations. For a single particle in a non-entangled state, the velocity ( v ) depends only on the local gradient of ?\psi\psi , and the dynamics appear local. But in entangled or multi-particle systems, the wave functions global nature introduces non-local dependencies, even though the stochastic evolution of each particles position is locally governed.
Comparison to Bohmian Mechanics:
Stochastic mechanics shares similarities with Bohmian mechanics, where the particles velocity is explicitly non-local due to its dependence on the wave function. In Bohmian mechanics, the velocity v=?mIm(???)v = \frac{\hbar}{m} \text{Im} \left( \frac{\nabla \psi}{\psi} \right)v = \frac{\hbar}{m} \text{Im} \left( \frac{\nabla \psi}{\psi} \right) is a real property, and its non-locality is evident in entangled systems (e.g., EPR pairs), where measuring one particles position affects the others velocity instantaneously.
In stochastic mechanics, the current velocity plays a similar role, and if treated as a real property, it inherits the same non-local character. The stochastic noise adds randomness to the trajectories, but the drift (and thus velocity) is still tied to the non-local wave function.
Kochen-Specker Theorem and Contextuality:
As discussed previously, the KS theorem implies that stochastic mechanics cannot assign definite, non-contextual values to all observables (including velocity or momentum) while reproducing quantum mechanics. If velocity is treated as a real, definite property, it must be contextualits value depends on the measurement context or the state of the system (e.g., the wave function).
This contextuality reinforces the potential non-locality: the velocitys dependence on the global wave function means it cannot be determined solely by local properties of the particle, especially in entangled systems.
Non-Locality in Entangled Systems:
For a single particle or non-entangled system, the velocity ( v ) depends on the local gradient of ?\psi\psi
, and the dynamics may appear local. However, in entangled systems, the wave functions non-separable nature means that the velocity of one particle depends on the state of others, regardless of distance. This is a hallmark of quantum non-locality, as demonstrated by violations of Bell inequalities.
If velocities are real properties in stochastic mechanics, this dependence implies dynamical non-locality, where the motion of one particle is influenced by distant events (e.g., the position or measurement of another particle).
Conclusion
If particle velocities (e.g., the current velocity ( v )) are interpreted as real properties in stochastic mechanics, they are non-local in the sense that they depend on the global quantum wave function, which can encode non-local correlations, particularly in entangled systems. This non-locality arises because the velocity is derived from the wave functions phase gradient, which may involve the states of distant particles, mirroring the non-locality in Bohmian mechanics. While reciprocal processes themselves are locally causal in their stochastic dynamics (local SDEs with noise), the realism of velocities introduces non-locality through their dependence on the non-local wave function.
Thus, treating velocities as real properties in stochastic mechanics sacrifices locality in entangled or multi-particle systems, consistent with quantum mechanics non-local correlations. This does not conflict with the KS theorem, which addresses non-contextual realism, but it highlights that realism for velocities comes at the cost of non-locality, especially in quantum systems exhibiting entanglement.
ApustimelogistApril 24, 2025 at 15:36#9842580 likes
I linked you the EPR paper and the whole centra idea in stochastic mechanics is that you can derive the Schrodinger equation which means that all predictions can be reproduced. The diffusion process in Levy & Krener has conservation laws identical to the Schrodinger equation.
they are shifting to reciprocal processes to provide a non-classical account of non-locality , as per the explanation provided by Chat-GPT , in the hope of explicating the presupposition of non-locality in stochastic models that is hard-encoded in the latter's reliance upon configuration space.
I don't really understand where you are Chatgp is getting this which just suggests to me that this based on the aforementioned unreliability of these A.I. explanations.
What is interesting about Levy & Krener's theory is that it is based on realistic point particles but does not have the non-locality that Bohmian mechanics has, whilst fulfilling all predictions.
It is still Bell non-local which is different. It is widely believed that a kind of Bohmian non-locality is required to explain Bell non-locality in these kinds of models, but Levy & Krener direcrly refutes this thought while also explaining ehy Bohmian non-locality emerges in Markovian stochastic models.
Do you agree or not agree, that any theory dependent entirely on local causality cannot be a full explanation of QM? Secondly, how do you propose physically interpreting the use of time-symmetric reciprocal processes for guiding a collection of particles in a way that that is compatible with local realism?
A full explanation of QM need to violate Bell inequalities whoch falsify non-contextual hidden variable models. But stochastic mechanics is not a non-contextual hidden variable model. The subtlety is that the fact that the model is contextual doesn't necessarily have to mean non-local causation, but such an explanation is vwry intuitive in a scenario like spin measurements.
I think that what sets apart stochastic mechanics from other interpretations of QM is that in all other interpretations, spin is a property of individual particles. In stochastic mechanics, spin is a property of particle statistics that only describe the behavior of particles counterfactuslly under infinite repetition of an experiment.
You can then imagine an infinite ensemble of particle trajectories between some initial preparation and final spin measurement. The final spin measurement just divides the infinite ensembles into pairs of sub-ensembles with different statistics. It can be shown that the spin statistics of these sub-ensembles would have to remain constant between initial preparation and final spin measurement which means that if you introduce another spin measurement on a different ensemble of particles, you could correlate their respective final measurements by allowing them to share an initial preparation which fixed a correlation between them.
ApustimelogistApril 24, 2025 at 17:11#9842640 likes
Alternatively, stochastic mechanics could abandon realism entirely for observables other than position, treating them as inherently probabilistic or emergent from the stochastic dynamics. This would align with quantum mechanics' rejection of pre-existing values but might undermine the "realist" motivation of stochastic mechanics as a classical-like interpretation.
In essence, the KS theorem forces stochastic mechanics to compromise on realism to remain viable, aligning its reciprocal processes with quantum mechanics' contextual or non-realist nature while retaining a locally causal framework.
Realism of Velocities:
If velocities (e.g., the current velocity ( v )) are considered real properties, they are assumed to have definite values at each point along the particles trajectory, consistent with the realist assumption that the particle has a well-defined position and motion.
For example, attempting to define definite values for spin or momentum observables alongside position in a way that reproduces quantum predictions would lead to contextuality, contradicting non-contextual realism.
The realism of particle configurations in stochastic mechanics has nothing to do with the realism related to the KS theorem. From the stochastic mechanical perspective, KS theorem and similar are about statistics. Particles can then always be in definite positions but their statistics respect the KS non-realism.
I actually used to refer to realism completely in this statistical sense until someone suggested to me it is more intuitive to talk about realism in QM interpretation in realistic fundamental ontology. So I started changing my use of the word more in line with this intuitive way of thinking about what realism is. Stochastic mechanics has realistic ontology of particles but is statistically non-realistic.
The A.I. is right though in line with what I said in my previous post that in stochastic mechanics, momentum and spin are defined statistically so they are not actual properties of individual particles but statistics that could only be related to lots of particles under repetition. You actually can have definite spin or momentum at points in space or for measurement results, just it doesn't apply to any specific particle and there may be a statistical spread over all results. The inclination to call these exact same statistics in other interpretations as "indefinite" in some scenarios (e.g. measurement results indicate equal superposition of spin up and down) comes from the assumption that all this stuff is talking about the property of a single particle. If you do that you cannot help but say that momentum and spin or momentum in these situations are indefinite. But under a statistical or stochastic interpretation, no claims are being made about a single particle so the idea of "indefiniteness" doesn't necessarily hold up except for in the kind of trivial notion that statistics have a spread, which is incontroversial and mundane. Conversely, particle ontology may always take definite positions, but their statistics can have a spread which is what in conventional interpretations would seemingly look like "indefinite" position. But again, this is not about a specific particle but statistics. When you take this into account, the A.I.'s claim that stochastic mechanical definite position is linked to KS realism is false; particle positions in stochastic mechanics can be indefinite in the statistical KS sense (i.e a statistical spread or uncertainty related to measurement interactions) while being definite ontologically for each particle.
In stochastic mechanics, the current velocity v=?mIm(???)v = \frac{\hbar}{m} \text{Im} \left( \frac{\nabla \psi}{\psi} \right)v = \frac{\hbar}{m} \text{Im} \left( \frac{\nabla \psi}{\psi} \right) depends on the wave function, which encodes global information about the quantum system. This raises the question of whether such a velocity, if real, implies non-locality.
If ( v ) is a real property, this dependence suggests non-locality, as the velocity of one particle is instantaneously influenced by the state or position of another, without a local physical mechanism. This is analogous to the non-locality in Bohmian mechanics, where the velocity of a particle is guided by the non-local quantum potential or wave function
But in entangled or multi-particle systems, the wave functions global nature introduces non-local dependencies, even though the stochastic evolution of each particles position is locally governed.
Yes, wavefunction and velocity fields are global and carry global information but they are not physical things. They are epistemic descriptions of statistics.
It is right Markovian stochastic mechanics is non-local as described in terms of instantaneous influences. But the non-Markovian reciprocal process version by Levy & Krener does not have this property at all, and explains it away as an artifact of an Markovian idealization. It then reproduces the correct behaviors without explicit Bohmian non-locality also responsible for configuration space descriptions where distant particles depend on each other.
Comments (46)
I watched a video where quantum physicist admits many quantum physicists (not just students) don't fully grasp quantum physics. (the study of what's known about quantum world)
This video requires some background knowledge, but I think the answer to thread title is in the video @10:30
Which is that there are infinite localized field intensities in quantum world. (hopefully I got that right), instead of single source of wave origin origin which makes it difficult to measure or to research deeper.
Also IIRC the study of quantum physics isn't fully researched and understood.
The reason it's metaphysically baffling is because it doesn't answer the question 'does the particle exist?' in an unambiguous, yes-no fashion. It neither exists nor does not exist - there are only degrees of possibility that it exists, right up until it is measured, which is the so-called 'wave function collapse'.
This is why the Copenhagen school says things like 'no phenomenon is a real phenomenon until it is an observed phenomena'.
Sir Roger Penrose cannot accept that - he is absolutely adamant that the wave function, and the wave function collapse, are physically real - otherwise, what kind of objects are we talking about? He and Einstein both reject quantum physics as incomplete because it can't answer that question. And, remember, here we're supposed to be dealing with 'fundamental particles', so this kind of pulls the rug from under physical realism.
The interpretation I favour is QBism. (I've written an essay on the topic.)
It's assuming too much. Paths are no more definite or real than particles. The brutal way of putting the Copenhagen attitude, is, in my view, there are no particles:
[quote=Kumar, Manjit. Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality (pp. 219-220)]The wave function itself has no physical reality; it exists in the mysterious, ghost-like realm of the possible. It deals with abstract possibilities, like all the angles by which an electron could be scattered following a collision with an atom. There is a real world of difference between the possible and the probable. Born argued that the square of the wave function, a real rather than a complex number, inhabits the world of the probable. Squaring the wave function, for example, does not give the actual position of an electron, only the probability, the odds that it will found here rather than there. For example, if the value of the wave function of an electron at X is double its value at Y, then the probability of it being found at X is four times greater than the probability of finding it at Y. The electron could be found at X, Y or somewhere else.
Niels Bohr would soon argue that until an observation or measurement is made, a microphysical object like an electron does not exist anywhere. Between one measurement and the next it has no existence outside the abstract possibilities of the wave function. It is only when an observation or measurement is made that the wave function collapses as one of the possible states of the electron becomes the actual state and the probability of all the other possibilities becomes zero.
For Born, Schrödingers equation described a probability wave. There were no real electron waves, only abstract waves of probability. From the point of view of our quantum mechanics there exists no quantity which in an individual case causally determines the effect of a collision, wrote Born. And he confessed, I myself tend to give up determinism in the atomic world. Yet while the motion of particles follows probability rules, he pointed out, probability itself propagates according to the law of causality[/quote]
I recall you writing the other day that 'science gave up talking about causation 100 years ago.' Isn't this one of the main reasons for that? The famous Fifth Solvay Conference, where all of this was first discussed, was in 1927.
Quoting tim wood
Sounds like Bohm's hidden variables. See this Space-Time episode.
I don't find 'the Copenhagen interpretation', vague though many say it is, hard to take. It maps against Kant's noumena-phenomena distinction.
Also, more significantly, what existential or epistemological difference do the ontological interpretations of "quantum physics" make to classical beings classically living in a classical world (re: locality¹)?
https://en.m.wikipedia.org/wiki/Principle_of_locality [1]
They are pragmatically a beast demanding some sort of Occam's razor to shave all of them away for cleaner but blander observable absolutism.
However, what if the mere mental fascination with any particular interpretation or indulgence in the 'chase' is what actually leads to the pragmatic results one desires?
When the dust settles. . . after all the epistemological external world skepticism. . . and the highest form of scientific under-determination of theories makes its appearance. . . what are you supposed to turn to in informing your 'free choice' or 'decision'? The aesthetically pleasing. . . the simplicity of theories. . . the indulgence in playful fantastical stories. . . and language attempts to put into pleasing speech the patterns we observe.
What difference does fantasy do to the 'free choice' and directing of the will of a Human being?
I'd say. . . a lot. Even if it is nothing but fantasy.
Three of the better popular science books on the subject:
Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science, David Lindley (2007)
Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality, Manjit Kumar (2011)
What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics, Adam Becker (2018)
I mean ...
In water waves it's the variable water surface height that makes the wave.
In sound waves it's the variable air pressure that makes the wave.
What varies in an electromagnetic wave?
Is it the magnetic field density that varies at a certain frequency?
The particles do not exist in the transmission of radiant energy, so there is no path. The energy moves as waves not particles. We all know about electromagnetic waves, light waves, radio waves, etc.. Those are real waves and we can see refraction (rainbows) and a variety of interference patterns associated with these waves.
The problem is that we have not identified the medium (sometimes called ether) within which the waves exist. Therefore the waves cannot be modeled or represented as they actually exist, so they are represented as a wave function. At the base of this problem is the fact that there is no adequate understanding of the photoelectric effect, which is the quantized way that fields of radiation waves interact with what are known as material objects. That is the relationship between the medium (ether) and the supposed material objects.
That doesn't mean it's not real. It's just not physical. Likewise energy is real, even though it's a construct.
There is actually a mathematically rigorous theory called stochastic mechanics which shows that you can produce all quantum behavior from classical particles that undergo a non-dissipative diffusion.
https://en.wikipedia.org/wiki/Stochastic_quantum_mechanics
What is a non-dissipative diffusion? Well a dissipative diffusion is something like a pollen particle being pushed about seemingly randomly by H2O molecules in a glass of water. As the pollen bashes into H2O molecules, they impart a drag or frictional force on the pollen meaning it leaks or dissipates energy into the environment.
In a non-dissipative diffusion, energy does not dissipate in these interactions; any energy lost would be returned on average to the pollen by the H2O molecules. The system is frictionless in some sense.
What is really unique about stochastic mechanics is its the only interpretation / formulation I know of that actually derives quantum theory de novo from other assumptions. It then suggests that it is sufficient for quantum behavior to be executed by regular classical point particles so long as you enforce the absence of dissipation in its behavior so that energy is conserved on average.
But if you want a kind of common-sense realistic ontology, it probably means you want a model similar to the pollen floating in the glass of water. There are experiments which actually produce quantum-like behavior in this kind of way:
https://en.wikipedia.org/wiki/Hydrodynamic_quantum_analogs
What isn't mentioned in the article but you can find in the papers is that the reason the quantum-like behavior occurs is that vibrating the bath reduces viscous dissipation in the bath, 'viscous-ity' being related to friction due to interacting molecules in a fluid. Effectively, vibrating the bath replaces energy that is lost due to friction, and this makes the bouncing droplet (video at top of the page) exhibit behavior that looks quantum-like.
If hypothetically reality were to be like this then it implies particles are floating around in stuff. Very big assumption, but not so big considering the fact we know that space isn't really empty but filled with a vacuum energy and fluctuations. This provides a very plausible home for this mechanism and the fact particles are floating in a kind of fluid of stuff would give a mechanism for what you are talking about in the post, about how they seem to be guided along paths in a double slit experiment that appear as an interference pattern. Closing a slit then affects whats going on in the fluid which would then pass along to the particles move through it. You no longer have to think about a particle "interfering with itself".
So I think there is no reason to give up on a classical, realistic universe just yet. It is absolutely mathematically possible.
You see in the image trajectories from this approach produced by a mathematical simulation (far right image). Bohmian mechanics also uses classical particles but it effectively just takes the quantum wavefunction and puts deterministic trajectories on top - it doesn't explain anything about why quantum behavior occurs. In contrast, stochastic mechanics starts with a classical description of particles being pushed about like the pollen in a glass of water, and shows that under specific conditions related to energy conservation, as I previously described, all quantum behavior occurs for regular classical particles.
The stochastic interpretation of QM isn't an interpretation of QM in the sense that Bohmian Mechanics is, i.e. in the sense of being a non-local or anti-realist account of quantum entanglement,, rather the stochastic interpretation amounts to a phenomenological interpretation of quantum statistics that doesn't explain entanglement and the origin of Bells inequalities.
Good question, to which I dont know the answer - but the wavefunction doesnt describe an electromagnetic wave. The wavefunction is a wave-like distribution of possibilities, but its not *actually* a wave. Thats something the video linked in the OP explains (he also remarks that it is a source of confusion about the importance of waves in quantum mechanics.)
Quoting sime
Right. The theory accounts for the observed statistical patterns of quantum mechanics (similar to the Born rule), but it does so by modelling outcomes, not necessarily by explaining the underlying quantum structure. So its phenomenological in the scientific sense of being descriptive, not necessarily explanatory.
Is that correct?
Understood. But it must be "something" that changes its property at a certain frequency, so that a frequency can be detected and filtered by the receiver (to distinguish radio stations or colors). Also, as we know, the higher the frequency, the higher the energy (at the same amplitude).
Infrared ... red ... violet ... ultraviolet ... X-ray ... LF ... HF ... UHF ... gamma ...
In a radio receiver antenna, the electromagnetic waves induce alternating electric current. It's the same effect that occurs when you move a magnet near an electric wire quickly back and forth. The magnetic field, flux, or density changes relative to a certain place in 3D space (e.g. where a copper wire is located). However, that field, flux, or density itself is probably indescribable -- like a ghost ...
I don't think so. I think you're confusing electromagnetic waves with the wavefunction in quantum physics. This thread is about the latter, not the former.
It is an interpretation in the sense of Bohmian mechanics, in fact their underlying mathematical structure is very similar.
Entanglement and Bell inequalities are direct consequences of the non-dissipative diffusion like all other quantum behavior. The background hypothesis gives a conceivable way in which the non-dissipative diffusion could be physically realized, albeit without specific details. This is an interpretation explicitly intended to give a physical account of quantum theory.
Quoting Wayfarer
As I said in my first post, it derives quantum theory from non-quantum assumptions about classical particles undergoing diffusion. It proves that in principle quantum mechanics can be instantiated in normal classical particles given the correct specifications which basically just amounts to conserving energy on average.
It does seem to follow Bohms realist sentiment: to recover quantum statistics from an underlying deterministic mechanism. But it still relies on a hypothetical substrate diffusing particles and a non-dissipative background that isn't observable and must be posited as a metaphysical assumption (presumably subject to further investigation.)
By contrast, the Copenhagen interpretation is more circumspect. It doesnt posit unknowables, but draws a line at what can meaningfully be said more in the spirit of Wittgenstein: Whereof one cannot speak, thereof one must be silent. The Copenhagen attitude is not nearly so 'mystical' as many of its critics contend. It's a philosophical humility, not a metaphysical fog.
In my understanding, it is the strengths of the interacting electric and magnetic fields that vary. There is no medium beyond that.
Are we not talking about the double slit experiment where light is sent through slits and certain interferences are observed?
Yes - but the salient question is, why does the interference pattern occur, when light is emitted at the rate of one particle at a time? How can that result in a wave pattern? That question concerns the wave function ?, not electromagnetic nature of light. It's easy to confuse the electro-magnetic waves, and the wave-function - this is discussed in the video linked in the OP at around 3:28 ('the Dirac wave for the electron IS NOT the Schrodinger wave'.)
Sure, but I would say it is arguably still better than many other interpretations given it provides an explanation for quantum behavior, it completely deflates the measurement problem and classical limit, it returns metaphysics to what is intuitive and commonsensical. I would say from a standpoint of rationality this is a preferable theory because arguably we shouldn't update our beliefs about the universe (or anything) any more than required given the evidence. And despite the background assumption I think this theory is clearly the least ontologically radical of any alternatives in the sense of diverging as little as possible from pre-quantum beliefs about how the world is, what everyday experience suggests the world is like, what other sciences suggest the world is like.
It seems almost completely conspiratorial to me that the world would have some bizarre, inscrutable ontology when mathematically there is a theory, maybe even multiple theories, that can produce quantum behavior through the kind of common-sensical, realistic, classical-like manner thag the world otherwise presents itself to us as.
And yes, obviously the background is a big assumption; but we already know - or at least quantum field theory tells us - about a kind of background because the vacuum is not empty: vacuum energy and fluctuations. We just don't know if that kind of background could be part of or indicative of the same kind of background as you would want in stochastic mechanics. But at the very least this isn't such a big leap as something like Many Worlds where you are assuming something else radical (and a bit ridiculous) exists that we can never observe and has no basis anywhere else in science. We know a kind of background exists (or you are at least justified in believing it based on quantum field theory):
https://en.wikipedia.org/wiki/Vacuum_energy
We just don't know if it could be the stochastic mechanical one.
Even when just a single photon is sent at a time, and interference occurs, I think my question is on-topic. For example, the changing property might also lie in the photon's kind of spin etc. rather than in its location or velocity. I don't know. But I'm curious, and I still think it's on-topic.
But notice that embodied unstated realist assumptions about 'what the world is like'. And as Sabine Hossenfelder points out in Lost in Math, there's this tendency in today's physics to rationalise posits on the basis that they supposedly make intuitive sense and then to devise the mathematics to make them stand up. So given your realist predilections, then this approach seems natural to you.
(As I've made clear in the other thread on this topic, I'm highly suspicious of the many-worlds theory.)
Quoting Apustimelogist
Right - but this is because of a prior commitment to realism, right? Whereas QBism says that the wavefunction ? does not describe something that exists objectively out there in the world. Instead, it represents the observers knowledge of the probabilities of the outcomes of observations. In other words, the wavefunction provides a rule that an agent/observer follows to update their beliefs about the likely outcomes of a quantum experiment. These probabilities, much like betting odds, are not intrinsic features of the world but rather reflect the agents expectations based on their unique perspective and prior information.
In QBism, measurement outcomes are seen in terms of experiences of the agent making the observation. Each agent may confer and agree upon the consequences of a measurement, but the outcome is fundamentally the experience that each of them individually has. Accordingly the wavefunction doesnt describe the system itself but rather the agents belief about what might happen when they interact with it. So while quantum theory has extremely high predictive accuracy, no two observations are ever exactly the same, and each observation is unique to a particular observer at that moment. And this is being borne out by experimental validation of 'Wigner's Friend'-type scenarios.
(This doesn't mean that the outcome is entirely subjective, either, as it is constrained by the Born Rule to a range of possibilities. But it's not entirely determined, either.)
Quoting Quk
I'm not a physicist, what I know about it is based on readings of science and listening to lectures. But you're grasping for a simple explanation of a phenomenon which defies simple explanations. Have a look at this primer https://brilliant.org/wiki/double-slit-experiment/
That is only true if the so-called background hypothesis, which is typically assumed to consist of a random field locally perturbing the motions of the particles, is assumed to have supplementary non-local Bohmian character as necessary to explain the statistics of quantum entanglement ... in which case your preferred interpretation becomes a variant of the Bohmian interpretation.
The stochastic interpretation provides a conception of wave-particle duality with an uncertainty principle, but without additional Bohmian mechanics it cannot explain Bells Theorem, for there is no getting around the fact that classical particle-field interactions that communicate slower than the speed of light cannot explain the 'action at a distance' of Bells inequalities; either the medium denoted by the background hypothesis is local, in which case we do not have quantum semantics, else the medium has non-local effects, in which case we have Bohmian mechanics.
I think the stochastic interpretation is pedagogically useful for providing a common-sense physical explanation for potentially classical aspects of complementarity that are often mistaken for inherently quantum phenomena, analogous to how Spekken's toy model of quantum mechanics is useful for providing common-sense epistemic intuition for understanding complementarity without assuming a physical account of the Schrodinger equation. But in neither case is there either a physical or epistemic explanation for entanglement.
Very true, we all have different dispositions for intuition; albeit, I would say that the only reason these intuitions are open to us in physics is because of results like quantum theory. Consensus would have opted for a realistic interpretation had it been conceivable in the first place, so I would say a realistic interpretation should be preferable if available. There would be no QBism if a realistic interpretation has heen initially available to us.
Quoting Wayfarer
Yes, but a stochastic interpretation has its own viee of Wigner's friend which isn't subjectively perspectival.
If someone wants to call it a variation of Bohmian mechanics, I don't really see an inherent issue but you don't explicitly need Bohmian kind of non-locality for the theory to produce Bell violations. There is at least one version by Levy & Krener (1996) which is does not have Bohmian non-locality, produces all the correct predictons, and even explains that non-locality only comes when an artificially idealized assumption is used for constructing the theory.
quote="sime;983839"]The stochastic interpretation provides a conception of wave-particle duality with an uncertainty principle, but without additional Bohmian mechanicks it cannot explain Bells Theorem, for there is no getting around the fact that classical particle-field interactions that communicate slower than the speed of light cannot explain the 'action at a distance' of Bells inequalities; either the medium denoted by the background hypothesis is local, in which case we do not have quantum semantics, else the medium has non-local effects, in which case we have Bohmian mechanics.[/quote]
Well Levy & Krener's stochastic mechanics van in principle do so without explicit non-local communication.
Quoting sime
False. It can produce all quantum behavior and explains it in terms of a non-dissipative diffusion. The issue is that its depiction of QM is radically different from what people are used to so ita difficult for them to imagine. For instance, on stochastic mechanics, spin is a statistical property and doesn't belong to individual particles. An interesting possible consequence is that we no longer have to think of measurement in entanglement experiments as actively changing properties of individual particles.
I have a suspicion that the authors you mention aren't intending to address foundational questions of QM ,and are instead focusing on the technicalities of constructing laws and diffusion models that cohere with the Schrodinger equation, with potential relevance to the subject of modelling quantum decoherence, by which classical diffusion can emerge in the limit of quantum diffusion, but without relevance as to the question of the nature and ontology of quantum states and quantum measurements.
A quantum stochastic process that in principle can model non-local correlations, i.e. a random vector field of a complex Hilbert Space that is interpretable as the evolution of a quantum state vector, cannot be explicated in terms of the local interactions of a regular stochastic process such as Brownian motion. The former can serve to explicate the latter, but not conversely unless one supplements entanglement relations.
I am pretty sure this is not the case. For instance:
https://scholar.google.co.uk/scholar?cluster=856861870672922375&hl=en&as_sdt=0,5&as_vis=1
"Nelsons stochastic mechanics formulation of quantum mechanics, which started it development with his article On the derivation of the Schrödinger equation from Newtonian mechanics in 1966 [6], is completely in accord with the requirements of Bells inequalities. By now, it has been developed to a mathematical rigor that completely parallels the formulation of classical analytical mechanics. It thus provides sufficient mathematical structure to suggest a clear physical picture of quantum phenomena."
Quoting sime
Stochastic mechanics shows mathematically that entanglement follows from a non-dissipative / conservative diffusion.
I cannot access the Levy & Krener (1996) paper, so instead I asked Grok for an account of reciprocal stochastic processes, of which I am unfamiliar which gave an interesting reply.
If the papers referred to are "Dynamics and kinematics of reciprocal diffusions" and "Stochastic mechanics of reciprocal diffusions", then I can see how these papers are of relevance to foundational questions of QM, in the sense of attempting to reconstruct properties of quantum diffusion in terms of time-symmetric but otherwise classical stochastic processes that implement non-local aspects of the time-symmetric transactional interpretation of QM.
However, Grok's conclusion at the end is along the lines of my initial thoughts, namely that such processes fail to account for quantum entanglement as should be expected by the Kohen Specker Theorem.
" Reciprocal stochastic processes are compelling because they challenge the necessity of quantum mechanics formalism for describing quantum diffusion. If a classical-like stochastic model can replicate quantum behavior, it suggests that some quantum phenomena might be emergent from underlying probabilistic structures, aligning with interpretations like stochastic mechanics or hidden-variable theories. However, their inability to fully capture quantum non-locality (e.g., entanglement) reinforces the uniqueness of quantum mechanics, prompting deeper inquiry into what makes quantum systems distinct.
Specific foundational questions they address:
Can quantum non-locality be reduced to time-symmetric stochastic correlations?
Is the wave function a physical entity, or can it be replaced by a stochastic process with equivalent predictive power?
How does the time-symmetric nature of quantum mechanics relate to causality and the arrow of time?
Can the quantum-classical transition be fully understood as a shift from reciprocal to Markovian stochastic processes?
Conclusion
Reciprocal stochastic processes can reproduce many aspects of quantum diffusion, such as probability density evolution, interference-like patterns, and non-local effects, making them a powerful tool for modeling quantum dynamics in a probabilistic framework. Their time-symmetric and non-Markovian nature makes them particularly relevant to foundational questions about quantum non-locality, the quantum-classical transition, and the ontology of the wave function. While they do not fully explain quantum non-locality (e.g., entanglement), they offer a semi-classical perspective that challenges quantum mechanics uniqueness and invites exploration of alternative formulations, such as stochastic mechanics or time-symmetric interpretations."
So i stand partially corrected.
Quoting sime
This is absolutely false and A.I. do not reliably give you information. Often when I research something, I will read the A.I. summary thing on google just as to give me some indication if what the answer might be, but I absolutely cannot trust this. I look at the sources it says it gets the information from every time and I find that it's relatively common that the A.I. will mix things up or confabulate ideas from various sources that actually don't make sense together, ending up in wrong or misleading answers.
I think the A.I. can be used as a research aide, but it cannot be trusted to reliably give you answers to things.
For instance, I can tell that the following phrase came from an A.I. :
Quoting sime
Because the transactional interpretation has nothing to do with stochastic mechanics and is almost a polar opposite interpretation.
Btw, you can see a pdf download link by just searching something like "Levy & Krener (1996)" in google. The pdf link comes from the author's website associated with their university.
Well not according to your source "On the Stochastic Mechanics Foundation of Quantum Mechanics ".
There is no mention let alone explanation of entanglement anywhere in that paper, although there is a mention of the Bohm potential, indicating that the authors are perhaps imagining their stochastic mechanics supplemented with some other foundational interpretation, perhaps to account for the non-locality of their background hypothesis. As it stands, it is a metaphysical interpretation of the Schrodinger equation that reproduces a fragment of the least problematic parts of Quantum Mechanics with deafening silence on the most critical aspects of QM that the interpretation either fails to address, or helps itself to by appealing to unstated non-local premises.
As it stands, I view that paper, which I have admittedly scantly read, is a non-earth shattering exercise in using stochastic differential equations to simulate whatever one wishes.
Quoting Apustimelogist
Neither do publicity seeking authors advertising grandoise and unproven claims.
Quoting Apustimelogist
They were actually my own opinion in my own words, prompted by my understanding that the authors of the other paper you mention were reconstructing quantum diffusion out of time symmetric diffusions that is reminiscent of the symmetric casuality inherent in the transactional interpretation of QM. Personally I think that more modest paper is much more informative.
For instance, I notice that certain physicists who are prominent members of the PhysicsForums.com were almost automatically dismissive of stochastic mechanics for the same obvious reasons that i opined earlier in this thread, but they also suspected that the authors selling stochastic mechanics were dishonest, doing pointless metaphysics, or failing to own up to the problem of entanglement.
On the other hand, ChatGPT focused on what Stochastic mechanics is and actually claims and spoke of the authors contributions in a more neutral and worthwhile tone, more or less summarizing the interpretation as a stochastic alternative to Bohmian mechanics that replaces the guiding wave with quantum diffusion, whilst also stressing the fact that stochastic mechanics cannot be an explanation for non-locality for obvious Cohen-Specker reasons, while pointing out that the model assumes non-locality in the form of the configuration space upon which the model places a quantum diffusion - namely the space describing the joint positions of all of the particles that cannot be decoupled into independent diffusions satisfying local causality if non-local entanglement is to be describable by the model.
As to the question regarding what "reciprocal processes" brings to the table, they apparently 'upgrade' the implicit and unexplained non-locality of the original model of stochastic mechanics (i.e the configuration space) , to a more explicit model of non-locality based on time-symmetry that is similar to the transactional interpretation, which in my words and understanding can presumably reconstruct at least some of the non-local unity of the configuration space in terms of the "retrocausal" effects of the future light-cone of the particles. How successful this approach is I don't know, and didn't care to ask.
I just gave you a quote earlier that says that it is in accord with Bell inequalities but they actually do have a paper where they produce the Bell violations with stochastic mechanics:
https://scholar.google.co.uk/scholar?cluster=15973777865898642687&hl=en&as_sdt=0,5&as_ylo=2024&as_vis=1
Stochastic mechanics can reproduce all behavior of quantum mechanics.
Now, the above paper has a kind of non-local behavior, but the authors interpret it epistemically. And this is completely justified imo because the Levy-Krener paper shows that this non-locality is a byproduct of using an artificial, idealized Markovian assumption. Their model alsocan reprosuce all quantum behavior without any non-locality at all in the formalism by not using the idealized Markov assumption.
So your following statement is false:
Quoting sime
Because stochastic mechanics reproduces all quantum behavior under assumptions about point particles that always are in definite places at any time and move along continuous paths. The fact you can do this suggests it is metaphysically possible; and stochastic mechanics gives a very simple physical explanation: energy conservation. All quantum behavior manifests from this. You don't need a non-local background to do this. No where is it implied that explicit non-locality is needed, only this energy conservation property; it follows that non-local entanglement behavior would follow regardless of exactly how you enforce this energy conservation, aslong as it is achieved. Non-local correlations are a consequence of initial local interactions where the resulting behavior does not dissipate but maintains its initial correlations.
Quoting sime
You can't just do this though. These stochastic processes work under the same physical constraints people would normally assume are impossible in regards to producing quantum behavior. Its not an arbitrary formal reconstruction, it has strong physical interpretation implied directly by the formalism.
Quoting sime
Well its completely polar opposite to what the transactional interpretation.
What do you mean by "modest"?
Completely disagree. I mean, what your A.I. gave me about stochastic mechanics is false in a way that can be easily checked. And I have my own experiences of sometimes using A.I. to help find some kind of an answer and finding that they were misleading or incorrect when checking sources myself.
A.I. will give you explanations that are easy to understand; it doesn't mean they are always accurate, just like in this case!
Quoting sime
These physicists may not have reliable opinions either if they are not at all familiar with and actually understand stochastic mechanics and perhaps are even invested in their own preferred interpretation. Obviously I cannot actually evaluate their opinions if what they say isn't given.
Quoting sime
False.
Quoting sime
The Levy & Krener paper doesn't have this and explains why it occurs in a model which uses an artificial Markovian assumption.
You need to do better than that.
Quoting Apustimelogist
I'm in agreement with Levy & Krener to the extent I understand their actual claims, which is what I was pointing out; they are shifting to reciprocal processes to provide a non-classical account of non-locality , as per the explanation provided by Chat-GPT , in the hope of explicating the presupposition of non-locality in stochastic models that is hard-encoded in the latter's reliance upon configuration space.
None of this makes their revised account of stochastic mechanics a locally causal model of QM in line with the classical intuitions of Brownian motion.
Do you agree or not agree, that any theory dependent entirely on local causality cannot be a full explanation of QM? Secondly, how do you propose physically interpreting the use of time-symmetric reciprocal processes for guiding a collection of particles in a way that that is compatible with local realism?
What do reciprocal processes contribute to theories of Stochastic Mechanics that interpret Quantum Mechanics?
Reciprocal processes play a significant role in stochastic mechanics, particularly in the context of interpreting quantum mechanics through stochastic frameworks like the Nelson's stochastic quantization or the stochastic interpretation of quantum mechanics. Here's a concise explanation of their contribution:
[I]Bridging Classical and Quantum Dynamics[/i]:
Reciprocal processes are a class of stochastic processes that generalize Markov processes by allowing conditional dependencies on both past and future states. In stochastic mechanics, they provide a framework to describe quantum systems as stochastic processes while preserving time-reversal symmetry, a key feature of quantum mechanics. This helps reconcile classical stochastic dynamics with quantum behavior.
Schrödinger Equation Connection: Reciprocal processes are closely tied to the Schrödinger equation through the concept of stochastic differential equations. In Nelson's stochastic mechanics, the quantum wave function is interpreted as encoding information about a diffusion process. The forward and backward drifts of a reciprocal process correspond to the probability currents, which are derived from the wave function, thus providing a stochastic interpretation of quantum evolution.
Path Integral Interpretation: Reciprocal processes support the path integral formulation of quantum mechanics by describing trajectories that are conditioned on both initial and final states. This aligns with the Feynman path integral approach, where quantum amplitudes are sums over all possible paths. Reciprocal processes offer a probabilistic underpinning for these paths in a stochastic framework.
Non-Markovian Behavior: Unlike standard Markov processes, reciprocal processes can model non-Markovian dynamics, which are essential for capturing quantum phenomena like entanglement and superposition. This makes them suitable for describing the stochastic analogs of quantum correlations and interference effects.
Time-Symmetric Formulation: Reciprocal processes enable a time-symmetric formulation of stochastic mechanics, mirroring the time-reversal invariance of quantum mechanics. This symmetry is crucial for interpreting quantum phenomena like wave function collapse or measurement in a stochastic context.
In summary, reciprocal processes contribute to stochastic mechanics by providing a mathematical framework that captures quantum mechanical behaviorsuch as wave function dynamics, path integrals, and time symmetrywithin a probabilistic, stochastic setting. They offer an alternative lens to interpret quantum mechanics, emphasizing diffusion-like processes while maintaining consistency with quantum predictions.
Can reciprocal processes be understood in terms of the common-sense local causality of Brownian motion?
Yes, reciprocal processes can be understood in terms of the common-sense local causality of Brownian motion, but with important extensions that make them distinct and more suitable for capturing quantum mechanical phenomena in stochastic mechanics. Here's a concise explanation:
Brownian Motion and Local Causality
Brownian motion is a Markovian stochastic process characterized by local causality: the future evolution of a particle depends only on its current state (position and velocity) and is driven by random, uncorrelated increments (white noise). This aligns with a "common-sense" notion of causality where the past influences the future in a straightforward, memoryless way, and the dynamics are governed by local interactions (e.g., diffusion via random collisions).
Reciprocal Processes: Extending Brownian Motion
Reciprocal processes generalize Brownian motion by introducing a form of conditional dependence on both past and future states, which departs from the strict Markovian property but retains a sense of local causality in a broader sense. Here's how they relate to Brownian motion and local causality:
Local Dynamics with Boundary Conditions:
Reciprocal processes can be thought of as Brownian-like diffusions constrained by boundary conditions at both initial and final times. For example, in stochastic mechanics, a particle's trajectory is modeled as a diffusion process (akin to Brownian motion) but conditioned on starting at one point and ending at another. This introduces a "teleological" aspect, where the future influences the present, but the dynamics remain locally governed by stochastic differential equations (SDEs) similar to those of Brownian motion.
The local causality is preserved in the sense that the increments of the process are still driven by Gaussian noise, and the evolution at each time step depends on local drift and diffusion terms.
Forward and Backward Drifts:
In stochastic mechanics, reciprocal processes are described by forward and backward stochastic differential equations, where the drift terms are derived from the quantum wave function. These drifts are analogous to the drift in a biased Brownian motion but incorporate information about both initial and final states. The local causality is maintained because the drifts and noise act locally in time, even though they are influenced by global (boundary) conditions.
Mathematically, for a reciprocal process XtX_tX_t
, the forward SDE might look like:
dXt=bf(Xt,t)dt+2?dWt,dX_t = b_f(X_t, t) dt + \sqrt{2\nu} dW_t,dX_t = b_f(X_t, t) dt + \sqrt{2\nu} dW_t,
where bfb_fb_f
is the forward drift, ?\nu\nu
is the diffusion coefficient, and WtW_tW_t
is a Wiener process (Brownian motion). A similar backward SDE exists, ensuring compatibility with future conditions.
Non-Markovian but Locally Causal:
Unlike Brownian motion, reciprocal processes are generally non-Markovian because the probability of a trajectory depends on both past and future states. However, the local causality of Brownian motion is preserved in the sense that the process is still driven by local stochastic increments, and the non-Markovian behavior arises from the conditioning rather than nonlocal interactions.
This conditioning can be understood as a statistical constraint rather than a violation of locality, much like how a Brownian bridge (a Brownian motion conditioned to end at a specific point) remains locally causal despite its endpoint constraint.
Quantum Interpretation:
In the context of stochastic mechanics, reciprocal processes model quantum particles as undergoing Brownian-like motion with drifts determined by the wave function. The "common-sense" causality of Brownian motion is extended to account for quantum phenomena like interference and entanglement, where the conditioning on future states mimics the global correlations of quantum mechanics.
For instance, the interference patterns in the double-slit experiment can be modeled as reciprocal processes where the particle's stochastic paths are influenced by both the initial state and the final detection point, yet the paths themselves are locally diffusive, like Brownian motion.
Key Difference from Brownian Motion
While Brownian motion is purely Markovian and driven by local, memoryless noise, reciprocal processes introduce a form of global conditioning that makes them suitable for quantum mechanics. This conditioning does not violate local causality but modifies the drift terms to reflect quantum probabilities, effectively bridging the local, diffusive nature of Brownian motion with the nonlocal correlations of quantum systems.
Summary
Reciprocal processes can be understood as an extension of Brownian motion's local causality, where the random, diffusive nature of Brownian motion is preserved, but the trajectories are conditioned on both initial and final states. This conditioning introduces non-Markovian behavior while maintaining local stochastic dynamics, making reciprocal processes a natural framework for interpreting quantum mechanics in a stochastic setting. They retain the intuitive, local causality of Brownian motion but adapt it to capture the time-symmetric and globally correlated nature of quantum phenomena.
So are they locally causal at the expense of losing realism, as per the Kochen Specker theorem?
The question of whether reciprocal processes in stochastic mechanics are locally causal at the expense of losing realism, particularly in light of the Kochen-Specker (KS) theorem, is a nuanced one. To address this, we need to unpack the concepts of local causality, realism, and how the KS theorem applies in the context of stochastic interpretations of quantum mechanics (QM). Here's a concise and clear response:
Recap: Reciprocal Processes and Local Causality
Reciprocal processes, as used in stochastic mechanics (e.g., Nelson's stochastic quantization), model quantum systems as diffusion processes akin to Brownian motion, with forward and backward drifts derived from the quantum wave function. They are locally causal in the sense that:
The evolution of the process at each time step is governed by local stochastic differential equations (SDEs), driven by Gaussian noise and drift terms that depend on the local state.
The non-Markovian nature arises from conditioning on initial and final states, but this conditioning is a statistical constraint, not a nonlocal physical interaction.
This local causality aligns with the intuitive, diffusive picture of Brownian motion, extended to incorporate quantum behavior via time-symmetric drifts.
Kochen-Specker Theorem and Realism
The Kochen-Specker theorem (1967) is a no-go theorem in quantum mechanics that rules out non-contextual hidden variable theories under the assumption of realism. Realism, in this context, means that all measurable properties (observables) of a quantum system have definite values at all times, independent of measurement. The KS theorem shows that for quantum systems in dimensions d?3
, it is impossible to assign definite values to all observables simultaneously in a non-contextual way (i.e., where the value of an observable is independent of which other compatible observables are measured alongside it).
In other words, the KS theorem challenges the idea that quantum systems possess pre-existing, measurement-independent properties (realism) while respecting the structure of quantum observables.
Reciprocal Processes and Realism
To address whether reciprocal processes in stochastic mechanics sacrifice realism to maintain local causality, we need to examine how stochastic mechanics interprets quantum mechanics and whether it assumes realism in the sense challenged by the KS theorem:
Stochastic Mechanics as a Hidden Variable Theory:
Nelson's stochastic mechanics attempts to reproduce quantum mechanics by modeling particles as undergoing stochastic trajectories governed by reciprocal processes. The wave function is interpreted as encoding the probability distribution and drift of these trajectories, not as a physical field but as a statistical descriptor.
In its original formulation, stochastic mechanics can be viewed as a hidden variable theory, where the particle's position and trajectory are the hidden variables, assumed to have definite values at all times (realism). The stochastic drifts are derived from the wave function, and the randomness mimics quantum uncertainty.
Impact of the KS Theorem:
The KS theorem applies to stochastic mechanics if it assumes non-contextual realism, i.e., that all observables (e.g., position, momentum, spin) have definite values independent of the measurement context. Since stochastic mechanics assigns definite positions to particles at all times (the trajectories are well-defined), it inherently assumes realism for position. However, other observables, like momentum or spin, are not directly represented as definite values in the stochastic framework but are derived statistically from the wave function or ensemble averages.
The KS theorem implies that stochastic mechanics cannot consistently assign definite values to all quantum observables in a non-contextual way for systems with Hilbert spaces of dimension d?3.
. For example, attempting to define definite values for spin or momentum observables alongside position in a way that reproduces quantum predictions would lead to contextuality, contradicting non-contextual realism.
Local Causality vs. Realism:
Local causality in reciprocal processes is preserved because the dynamics are governed by local SDEs, and the conditioning on future states (non-Markovianity) is a statistical effect, not a nonlocal physical interaction. This avoids issues like Bell nonlocality, as stochastic mechanics can be constructed to respect Einstein locality for spatially separated systems.
However, to maintain consistency with quantum mechanics (and avoid contradicting the KS theorem), stochastic mechanics must abandon non-contextual realism for all observables. Instead, it may adopt contextual realism, where the values of observables depend on the measurement context (e.g., which compatible observables are measured). For instance, the momentum in stochastic mechanics is not a definite value but a statistical quantity derived from the drift, which depends on the wave function and measurement setup.
Alternatively, stochastic mechanics could abandon realism entirely for observables other than position, treating them as inherently probabilistic or emergent from the stochastic dynamics. This would align with quantum mechanics' rejection of pre-existing values but might undermine the "realist" motivation of stochastic mechanics as a classical-like interpretation.
Does Stochastic Mechanics Lose Realism?:
If stochastic mechanics insists on non-contextual realism (definite values for all observables, independent of measurement), it is incompatible with the KS theorem and fails to reproduce quantum mechanics fully. In this sense, maintaining local causality via reciprocal processes comes at the expense of non-contextual realism, as the KS theorem forbids such a model.
In practice, stochastic mechanics often adopts a weaker form of realism, where only the particle's position is real and definite (the stochastic trajectory), while other observables are contextual or probabilistic. This allows it to maintain local causality and reproduce quantum predictions (e.g., for position measurements) but sacrifices the strong realist picture where all observables have pre-existing values.
Some formulations of stochastic mechanics explicitly acknowledge this by focusing on position as the primary observable and treating other properties as statistical or context-dependent, sidestepping the KS theorem's constraints by not assigning definite values to incompatible observables.
Summary
Reciprocal processes in stochastic mechanics are locally causal, with dynamics resembling Brownian motion but conditioned on initial and final states. However, to be consistent with quantum mechanics and the KS theorem, stochastic mechanics cannot maintain non-contextual realism for all observables. It either adopts contextual realism (where observable values depend on measurement context) or restricts realism to position alone, treating other observables probabilistically. Thus, local causality is preserved, but at the expense of a strong realist interpretation where all quantum observables have definite, measurement-independent values.
In essence, the KS theorem forces stochastic mechanics to compromise on realism to remain viable, aligning its reciprocal processes with quantum mechanics' contextual or non-realist nature while retaining a locally causal framework.
So are particle velocities interpreted non-locally by this model, if they are considered to be real properties?
To address whether particle velocities in stochastic mechanics, when interpreted as real properties, are non-local in the context of reciprocal processes, we need to examine how velocities are defined in this framework, the role of realism, and the implications of non-locality. This response builds on our prior discussion, particularly the interplay between local causality, realism, and the Kochen-Specker (KS) theorem, and provides a concise answer tailored to your question.
Stochastic Mechanics and Reciprocal Processes: Overview
In stochastic mechanics (e.g., Nelsons formulation), quantum systems are modeled as particles undergoing diffusion processes akin to Brownian motion, described by reciprocal processes. These processes are governed by stochastic differential equations (SDEs) with forward and backward drifts derived from the quantum wave function. The particles position is treated as a real, definite property (realism), and its stochastic trajectory is well-defined. Reciprocal processes are locally causal because the dynamics at each time step depend on local drift and noise terms, with non-Markovian behavior arising from statistical conditioning on initial and final states, not nonlocal interactions.
Velocities in Stochastic Mechanics
In stochastic mechanics, the concept of velocity is more nuanced than in classical mechanics due to the stochastic nature of the trajectories. Lets clarify how velocities are defined and interpreted:
Forward and Backward Velocities:
The particles motion is described by a stochastic differential equation, such as:
dXt=bf(Xt,t)dt+2?dWt,dX_t = b_f(X_t, t) dt + \sqrt{2\nu} dW_t,dX_t = b_f(X_t, t) dt + \sqrt{2\nu} dW_t,
where XtX_tX_t
is the particles position, bf(Xt,t)b_f(X_t, t)b_f(X_t, t)
is the forward drift, ?\nu\nu
is the diffusion coefficient (related to ?/2m\hbar/2m\hbar/2m
), and WtW_tW_t
is a Wiener process (Brownian noise).
Similarly, a backward SDE exists with a backward drift bb(Xt,t)b_b(X_t, t)b_b(X_t, t)
. These drifts are derived from the wave function ? (I snipped Grok's unprintable unicode description)
The osmotic velocity u=(bf?bb)/2u = (b_f - b_b)/2u = (b_f - b_b)/2
and current velocity v=(bf+bb)/2v = (b_f + b_b)/2v = (b_f + b_b)/2
are introduced to describe the particles motion. The current velocity ( v ) is analogous to the Bohmian velocity in pilot-wave theory and is often interpreted as the physical velocity of the particle, while the osmotic velocity accounts for the diffusive component.
Realism of Velocities:
If velocities (e.g., the current velocity ( v )) are considered real properties, they are assumed to have definite values at each point along the particles trajectory, consistent with the realist assumption that the particle has a well-defined position and motion.
In stochastic mechanics, the current velocity v=?mIm(???)v = \frac{\hbar}{m} \text{Im} \left( \frac{\nabla \psi}{\psi} \right)v = \frac{\hbar}{m} \text{Im} \left( \frac{\nabla \psi}{\psi} \right)
depends on the wave function, which encodes global information about the quantum system. This raises the question of whether such a velocity, if real, implies non-locality.
Are Velocities Non-Local?
Non-locality in quantum mechanics typically refers to correlations or influences that violate Bells inequalities or Einstein locality, where the state of one system instantaneously affects another at a distance without a local mediating mechanism. To determine if velocities in stochastic mechanics are non-local when treated as real properties, we consider the following:
Dependence on the Wave Function:
The current velocity ( v ) is determined by the gradient of the phase of the wave function ?\psi\psi
. In quantum mechanics, the wave function is a global object that describes the entire system, including entangled or spatially extended states. For example, in an entangled two-particle system, the wave function ?(x1,x2)\psi(x_1, x_2)\psi(x_1, x_2)
depends on the positions of both particles, and the velocity of particle 1, v1=?m1Im(?1??)v_1 = \frac{\hbar}{m_1} \text{Im} \left( \frac{\nabla_1 \psi}{\psi} \right)v_1 = \frac{\hbar}{m_1} \text{Im} \left( \frac{\nabla_1 \psi}{\psi} \right), may depend on the position of particle 2, even if they are far apart.
If ( v ) is a real property, this dependence suggests non-locality, as the velocity of one particle is instantaneously influenced by the state or position of another, without a local physical mechanism. This is analogous to the non-locality in Bohmian mechanics, where the velocity of a particle is guided by the non-local quantum potential or wave function.
Reciprocal Processes and Local Causality:
Reciprocal processes themselves are locally causal in their dynamics: the SDEs governing the particles motion depend only on the local drift bfb_fb_f or bbb_bb_b and noise at the current position XtX_tX_t
. The non-Markovian conditioning (dependence on initial and final states) is a statistical constraint, not a dynamical non-locality.
However, the drifts (and thus the velocities) are derived from the wave function, which can encode non-local correlations. For a single particle in a non-entangled state, the velocity ( v ) depends only on the local gradient of ?\psi\psi , and the dynamics appear local. But in entangled or multi-particle systems, the wave functions global nature introduces non-local dependencies, even though the stochastic evolution of each particles position is locally governed.
Comparison to Bohmian Mechanics:
Stochastic mechanics shares similarities with Bohmian mechanics, where the particles velocity is explicitly non-local due to its dependence on the wave function. In Bohmian mechanics, the velocity v=?mIm(???)v = \frac{\hbar}{m} \text{Im} \left( \frac{\nabla \psi}{\psi} \right)v = \frac{\hbar}{m} \text{Im} \left( \frac{\nabla \psi}{\psi} \right) is a real property, and its non-locality is evident in entangled systems (e.g., EPR pairs), where measuring one particles position affects the others velocity instantaneously.
In stochastic mechanics, the current velocity plays a similar role, and if treated as a real property, it inherits the same non-local character. The stochastic noise adds randomness to the trajectories, but the drift (and thus velocity) is still tied to the non-local wave function.
Kochen-Specker Theorem and Contextuality:
As discussed previously, the KS theorem implies that stochastic mechanics cannot assign definite, non-contextual values to all observables (including velocity or momentum) while reproducing quantum mechanics. If velocity is treated as a real, definite property, it must be contextualits value depends on the measurement context or the state of the system (e.g., the wave function).
This contextuality reinforces the potential non-locality: the velocitys dependence on the global wave function means it cannot be determined solely by local properties of the particle, especially in entangled systems.
Non-Locality in Entangled Systems:
For a single particle or non-entangled system, the velocity ( v ) depends on the local gradient of ?\psi\psi
, and the dynamics may appear local. However, in entangled systems, the wave functions non-separable nature means that the velocity of one particle depends on the state of others, regardless of distance. This is a hallmark of quantum non-locality, as demonstrated by violations of Bell inequalities.
If velocities are real properties in stochastic mechanics, this dependence implies dynamical non-locality, where the motion of one particle is influenced by distant events (e.g., the position or measurement of another particle).
Conclusion
If particle velocities (e.g., the current velocity ( v )) are interpreted as real properties in stochastic mechanics, they are non-local in the sense that they depend on the global quantum wave function, which can encode non-local correlations, particularly in entangled systems. This non-locality arises because the velocity is derived from the wave functions phase gradient, which may involve the states of distant particles, mirroring the non-locality in Bohmian mechanics. While reciprocal processes themselves are locally causal in their stochastic dynamics (local SDEs with noise), the realism of velocities introduces non-locality through their dependence on the non-local wave function.
Thus, treating velocities as real properties in stochastic mechanics sacrifices locality in entangled or multi-particle systems, consistent with quantum mechanics non-local correlations. This does not conflict with the KS theorem, which addresses non-contextual realism, but it highlights that realism for velocities comes at the cost of non-locality, especially in quantum systems exhibiting entanglement.
I linked you the EPR paper and the whole centra idea in stochastic mechanics is that you can derive the Schrodinger equation which means that all predictions can be reproduced. The diffusion process in Levy & Krener has conservation laws identical to the Schrodinger equation.
Quoting sime
I don't really understand where you are Chatgp is getting this which just suggests to me that this based on the aforementioned unreliability of these A.I. explanations.
What is interesting about Levy & Krener's theory is that it is based on realistic point particles but does not have the non-locality that Bohmian mechanics has, whilst fulfilling all predictions.
It is still Bell non-local which is different. It is widely believed that a kind of Bohmian non-locality is required to explain Bell non-locality in these kinds of models, but Levy & Krener direcrly refutes this thought while also explaining ehy Bohmian non-locality emerges in Markovian stochastic models.
Quoting sime
A full explanation of QM need to violate Bell inequalities whoch falsify non-contextual hidden variable models. But stochastic mechanics is not a non-contextual hidden variable model. The subtlety is that the fact that the model is contextual doesn't necessarily have to mean non-local causation, but such an explanation is vwry intuitive in a scenario like spin measurements.
I think that what sets apart stochastic mechanics from other interpretations of QM is that in all other interpretations, spin is a property of individual particles. In stochastic mechanics, spin is a property of particle statistics that only describe the behavior of particles counterfactuslly under infinite repetition of an experiment.
You can then imagine an infinite ensemble of particle trajectories between some initial preparation and final spin measurement. The final spin measurement just divides the infinite ensembles into pairs of sub-ensembles with different statistics. It can be shown that the spin statistics of these sub-ensembles would have to remain constant between initial preparation and final spin measurement which means that if you introduce another spin measurement on a different ensemble of particles, you could correlate their respective final measurements by allowing them to share an initial preparation which fixed a correlation between them.
Overall, especially closer to the beginning, this was fairly good albeit I would say it saidsome of its claims very overconfidently imo.
But there is some nuance regarding descriptions like the following:
Quoting sime
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The realism of particle configurations in stochastic mechanics has nothing to do with the realism related to the KS theorem. From the stochastic mechanical perspective, KS theorem and similar are about statistics. Particles can then always be in definite positions but their statistics respect the KS non-realism.
I actually used to refer to realism completely in this statistical sense until someone suggested to me it is more intuitive to talk about realism in QM interpretation in realistic fundamental ontology. So I started changing my use of the word more in line with this intuitive way of thinking about what realism is. Stochastic mechanics has realistic ontology of particles but is statistically non-realistic.
The A.I. is right though in line with what I said in my previous post that in stochastic mechanics, momentum and spin are defined statistically so they are not actual properties of individual particles but statistics that could only be related to lots of particles under repetition. You actually can have definite spin or momentum at points in space or for measurement results, just it doesn't apply to any specific particle and there may be a statistical spread over all results. The inclination to call these exact same statistics in other interpretations as "indefinite" in some scenarios (e.g. measurement results indicate equal superposition of spin up and down) comes from the assumption that all this stuff is talking about the property of a single particle. If you do that you cannot help but say that momentum and spin or momentum in these situations are indefinite. But under a statistical or stochastic interpretation, no claims are being made about a single particle so the idea of "indefiniteness" doesn't necessarily hold up except for in the kind of trivial notion that statistics have a spread, which is incontroversial and mundane. Conversely, particle ontology may always take definite positions, but their statistics can have a spread which is what in conventional interpretations would seemingly look like "indefinite" position. But again, this is not about a specific particle but statistics. When you take this into account, the A.I.'s claim that stochastic mechanical definite position is linked to KS realism is false; particle positions in stochastic mechanics can be indefinite in the statistical KS sense (i.e a statistical spread or uncertainty related to measurement interactions) while being definite ontologically for each particle.
Then there is also the following:
Quoting sime
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Yes, wavefunction and velocity fields are global and carry global information but they are not physical things. They are epistemic descriptions of statistics.
It is right Markovian stochastic mechanics is non-local as described in terms of instantaneous influences. But the non-Markovian reciprocal process version by Levy & Krener does not have this property at all, and explains it away as an artifact of an Markovian idealization. It then reproduces the correct behaviors without explicit Bohmian non-locality also responsible for configuration space descriptions where distant particles depend on each other.