The Andromeda Paradox
https://en.m.wikipedia.org/wiki/RietdijkPutnam_argument
This gives rise to Penroses Andromeda Paradox:
If true, what does this suggest about free will, the future, and truth?
If special relativity is true, then each observer will have their own plane of simultaneity, which contains a unique set of events that constitutes the observer's present moment. Observers moving at different relative velocities have different planes of simultaneity, and hence different sets of events that are present.
This gives rise to Penroses Andromeda Paradox:
Two people pass each other on the street; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability. In fact neither of the people can yet know of the launching of the space fleet. They can know only later, when telescopic observations from Earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter, and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past. Was there then any uncertainty about that future? Or was the future of both people already "fixed"?
If true, what does this suggest about free will, the future, and truth?
Comments (98)
I'm not sure how "according to one of the people" is supposed to be interpreted. Are these two people supposed to have magical physics defying clairvoyance?
But in that case I'm having trouble making sense of "Then they can hark back to that chance encounter, and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past."
Isn't that saying that they can hark back to something that didn't happen?
I know I'm nitpicking on details somewhat irrelevant to answering the question, but I'll give others time to think about it before suggesting an answer.
No? It's just saying that they conclude that at some point in the past, it was true for one of them that the ships had set off and false for the other.
I don't think it's a paradox at all. It's only a paradox if one assumes the absolute Newtonian serial time must exist. It's consistent with local becoming.
A false dichotomy is often set up by advocates of eternalism in the physics literature between some sort of absolute, serial ordering of time and all moments existing at all times in an eternal "block universe." These arguments rely more (arguably entirely) on philosophy than scientific support, since the conjecture is arguably unfalsifiable.
The "Andromeda Paradox" has been a popular vehicle for this, as has the "Twin Paradox." Neither of these are actually paradoxical given an assumption of local becoming, and no reference to rods or clocks is needed to ground our sense of time, although the mathematics involved being abstruse might be why rejections of the paradoxes, which have been around for a century, are less well known than the paradoxes.
We'd probably see a resurgence of interest in these explanations if the evidence for quantum scale time irreversibility hadn't come out at the same time as the Higgs boson discovery, thus overshadowing it. It's not the end of the debate, but we certainly have a universe that appears to run differently forwards in time as opposed to backwards, at both large scales and quantum ones. This isn't at all surprising IMO, since all empirical evidence suggests time only goes in one direction and decoherence/collapse only occur in one direction.
The Reality of Time Flow: Local Becoming in Modern Physics
Formula (I don't know mathjax sorry):
Time differential: (distance * velocity)/c-squared
Where velocity is the speed at which the observer moves to or away from the observed event while the other stands still or moves in opposite direction.
Let's take a velocity of 5 m/s, gives about 15 days at 2.5 million light years. As the distance is reduced, the time differential nears zero. Since nothing travels faster than light the "pretend" observation of knowing what happens simultaneously lightyears away in a theoretical frame of reference is simply nonsense.
But if it wasn't, at least we would have 2.5 million years to get the Milky Way defense fleet ready.
I don't think it suggests anything. The text from the Wikipedia article you includes more that you didn't include:
Quoting Wikipedia - RietdijkPutnam argument
The bolded text is certainly not true in any meaningful sense. The two observers are in the same frame of reference. Any inconsistencies between their so-called "differing" three-dimensional universes are trivial - light can travel from any point on Earth to any other in much less than a second.
Hi Benk.
To suggest anything about these is to confuse coordinate simultaneity (which is what the Andromeda scenario utilizes) with actual simultaneity (certain events having a metaphysical state of 'has happened' or not). Special relativity really only concerns itself with coordinate simultaneity (merely a convention) and not with any statement of presentism or the lack thereof.
Quoting Count Timothy von Icarus
Indeed, not a paradox, even if absolute time exists. 1) It cannot be Newtonian time. That has been falsified. If there is absolute time, then there is no 'according to person X or frame F', there is just reality and any coordinate system that doesn't correspond to that reality is simply wrong. No paradox whatsoever either way.
Quoting Count Timothy von Icarus
Yes
Quoting BenkeiNothing in the Andromeda scenario suggests anybody 'knows' what's going on. OK, I take that back because the implication is that Andromedans want to attack humans, and there's no way they could yet have detected them since we didn't exist 2.5 MY ago. Similarly, Penrose says that 'the launch is inevitable' which bolsters the suggestion of lack of free will about it. But that's Penrose doing that, not Einstein.
Quoting T Clark
This is wrong. The whole point is that trivial differences in frame change have large swings of simultaneity at large distances. Sure, nothing suggests that a frame change (a mere abstract choice) has any kind of causal effect, but the difference in simultaneity is very much on the order of months in this case. Your statement seems to be in denial of this.
If discrete objects do not exist, and things only exist in how they interact (i.e., relations exist, persistent objects with properties at all times do not), then the idea that all becoming is local doesn't seem strange at all. The conception seems to work well with Wheeler's "many fingered time," and arguably also with his more provocative "it from bit."
The idea that things only exist in their relations works
quite well with the holographic principle as well.
Having not spent too much time diving into RQM, it does seem, at first glance, like it would be quite compatible with Floridi's maximally portable ontology of bare, essential ontic difference or various quantum variants that have been proposed. Certainly, it seems to fit well with ontic structural realism, but does so in a way that avoids having to have a multiverse, which in turn avoids having an theory where it still seems like the vast majority of human observers should be Boltzmann Brains.
Interactions are ontologically primitive, not "stuff." These (mostly) occur locally, although one also needs a way to explain (apparent?) non-locality. Best of all, RQM seems to not only deal with this "paradox" quite well, but also experimental results that suggest it is fundementally possible for two observers to observe different facts about a system, leaving no room for a bedrock "objective" world outside of one that is posited based on philosophical inclinations, but which we have to accept as completely inaccessible to all observers.
So do distant events occur in the past relative to my reference frame? Or the future? Or not at all?
When the Mars rover sends a message back to Earth it takes, what, about five to twenty minutes to reach us. When we receive it about five to twenty minutes has elapsed, in our time, since the message was sent. That's how I see it, but I've been wrong before.
Nunh unh.
Quoting noAxioms
Please explain how "even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content." And how can this purported difference in content cause a difference in simultaneity of months?
I'll second that. Curious. Does chaos theory intersect relativity?
Theres some math here that might explain it: https://medium.com/mathadam/the-andromeda-paradox-b4bb30a0e372
Given the distance to the Andromeda galaxy one person moving towards another nearby person at just 5 m/s changes the frame of reference enough that theres a 15 day difference between which events in Andromeda are simultaneous.
And the further the distance the lower the velocity needed to establish such a significant difference. So given a far enough away location even small head movements can bring about a sufficiently different reference frame.
They don't. You can't perceive something 2.5 million light years away that is simultaneous with what you see looking at this text. Not until 2.5 million light years have passed, and as that light nears the "paradox" resolves itself.
The Andromeda thing is an illustration of spacetime geometry, not relevant to interpretations of quantum mechanics. Sure, the state of affairs at distant location X would constitute a counterfactual statement, meaningless under any interpretation that does not presume counterfactuals, RQM being one of those. But the event over there simultaneous with a given event here is still very much frame dependent regardless of the state (an invasion fleet existing at all say) at that distant location, hence no interpretation of QM really having any relevance at all to this problem.
Quoting jgill
Andromeda is not sufficiently distant to invalidate Einstein's simultaneity convention, but admittedly something much further away (say 17 BLY) is indeed too distant for the convention since signals cannot be exchanged between the locations. There is no limit under special relativity, but special relativity does not describe spacetime at large scales.
Quoting T Clark
I didn't claim the universe was three dimensional, nor did I claim multiple universes. Even the slightest angle results in an arbitrarily large separation at large distances since X sin(a) for a very small angle a can still be a large value if X is large enough. Likewise even a tiny change in reference frames results in a large (months) change in the 3D plane of simultaneity at a sufficiently large distances.
But a plane of simultaneity being 'a universe' seems to be something you're assuming. You seem to suggests a multiverse of different planes rather than some kind of single preferred plane of simultaneity, so perhaps not a stance of presentism. I would admit that simultaneity has nothing to do with frames and motion under presentism, hence the Andromeda thing being mostly irrelevant under it, but I suspect you're not asserting that.
Quoting NotAristotle
They don't. They both see the same thing. But it's not about what they see, it's about which moment they consider to be simultaneous with moments here, no more radical than somebody facing north to consider London to be exact to his right, but somebody facing a tiny bit clockwise of north to consider London to be many km north of a line directly to his right.
Right, I didn't mean RQM has direct relevance to this particular issue; IMO that is explained quite well by the arguments laid out in the quotes in my first post. I meant that the ontological picture painted by RQM flows very nicely with the conception of local becoming existing without any universal serial ordering.
The Andromeda Paradox and the results of modified Wigner's Friend experiments are similar, despite being different areas of physics, in that they paint a picture of a world where observers do not seem to be able to point to an absolute, observer free context for grounding claims about states of affairs. However, it is able to do this without making claims about the necessity of consciousness for existence or a truly absolute relativism, because it can be consistent with a sort of ontic structural realism where knowledge about the relations that generate observations is possible, at least in theory.
Can the laws of physics about unknowable worlds be real, here meaning absolute, or must they be tentative as well?
Things like slight angles of the head and difference in position aren't particularly relevant to the special relativity scenario under consideration. The key thing to consider is the difference in the velocity of the two 'observers', and particularly the component of velocity in the direction of Andromeda. (If the two observers were moving past each other in a direction perpendicular to the direction to Andromeda, they would be viewing the same point in Andromeda's history.)
As the article asks "Can we meaningfully discuss what is happening right now in a galaxy far, far away?" Answer - of course not.
Isn't this the same thing I wrote? If not, I don't understand what you're saying.
The text about the three-dimensional universe and differing content I took from the Wikipedia article linked in the OP.
Is that just because we don't know what is happening, or is it because there's nothing happening? A realist would presumably say that something is happening right now in a galaxy far, far way, but if special relativity is true then what's happening right now depends on our individual, relative velocities, such that what's happening right now in a galaxy far, far way in your reference frame isn't what's happening right now in a galaxy far, far away in my reference frame.
Totally agree, and the 'angle of head thing' was relevant to the London example. 'Movement of head' came from wiki, as if it's our head velocity that matters for some reason.
The movement of one frame as compared to another (either having a stationary head being irrelevant) causes a different angle in the time axis and at least one spatial axis in spacetime which produces large time discrepancy for worldlines of distant objects. That's the geometry of the situtation.
Quoting T Clark
I think it was confusing for Wiki to introduce the notion of 'movement of the head' which at least suggests a velocity difference, but also 'offset in distance between observers' which seems to be totally irrelevant if they're stationary with respect to each other. Hopefully the actual RietdijkPutnam argument
was worded more carefully than that.
Imagine the plane of simultaneity for a pigeon walking with his head bobbing back and forth. I don't think anybody considers 'the universe' for the pigeon to be tipping wildly as it walks.
This line is also questionable, equivocating a plane of simultaneity with a universe, which makes it sound causal. I cannot think of a single interpretation of time that suggests such a thing. It's flat our wrong to consider any such thing,.
They apparently do quote some actual text from Penrose:
[quote=Penrose]They can know only later, when telescopic observations from Earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter, and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past.[/quote]
The latter bit seems unreasonable. If one is a presentist (there being an ontological division between past and future events), then movement of anything has nothing to do with where this division lies, but the statement suggests otherwise. If one does not posit such a division of events, then there is no 'uncertain future' and 'uncertain past'. The statement is thus wrong from any valid point of view. It seems to be there only to attempt to frame the scenario as paradoxical when in fact there is none.
Quoting T Clark
But despite the discussion of such events (the supposed invasion), it actually isn't what is happening that's important in the illustration, it is the time over there, which is the same for a given event despite the lack of measurement. So assuming two relatively moving observers (by a bicycle pace) on Andromeda looking at Earth, they see a clock over here, and very much know where Earth is at any given time, even if humans don't meaningfully exist to them. Yes, 2.5 million years is a long time to extrapolate the orbit of our planets, but it's a pretty predictable clock nonetheless.
Quoting MichaelAnswer to that is interpretation dependent of course.
But SR just says that simultaneity is a convention, not any kind of ontological fact. So yes, the convention is dependent on definition of a frame, and it gets really tricky with Andromeda since the planet way over there is hardly stationary relative to Earth, so there isn't an obvious frame where both are stationary. Pretty hard to find an object stationary relative to Earth, even momentarily. Statistics say that something has to get close by chance now and then, but less likely for anything not nearby.
In the case where people assume there is an absolute time or some absolute reference frame, then one doesn't really encounter a paradox either. One of the two observers or some other third party has it right while the others are just plain wrong.
The paradox seems to come about from accepting the relativity of simultaneity, and not taking it seriously enough. It assumes that we can simply stitch together different presents in order to get the conclusion that everything is present which is where this idea of the future being "fixed" comes from.
I don't know. When I see a sum "c+v" relating to the speed of light I am suspicious. When that occurs there is an additional factor involved which keeps speeds below c. But my knowledge of SR is very limited.
I'm glad you're not on my appointment list.
No. Sorry. I think the difference you describe is meaningless. It certainly has no practical affect and provides no metaphysical insight.
No. I think your formulation is meaningless. It has no practical affect and no metaphysical importance.
The time varies from 5 to 20 minutes depending upon the relative positions of the two planets.
https://mars.nasa.gov/mars2020/spacecraft/rover/communications/ :roll:
Maybe start out smaller and see if you still have a problem with it. This just extrapolates what we know happens at smaller scales and then it doesn't feel so weird at first. Take the train example. Ann is on the train, Bill is at the station. In the middle of the train is a light, which is switched off. The beam of the light is aimed at the front and the back of the train, where two identical clocks hang that are synchronised. They will stop when a light hits the sensor. The train moves at 120 km/hr. As it enters the station the light is switched on, travels through the trains and hits the clocks. Bill films this.
Ann gets off and she and Bill compare notes. Ann says, the clocks were hit simultaneously by the light and stopped at the exact same time. Bill says, that's weird, I can clearly see on my film that the light hit the back of the train before the front.
Do you feel comfortable saying both are correct because neither has a privileged frame of reference? If yes, what makes the Andromeda example different for you? If not, why not?
You think the distinction between "there is intelligent life in the Andromeda Galaxy" being truth-apt and it not being truth-apt is a meaningless distinction?
The realist would disagree. They would argue that it's truth-apt and either true or false.
The same with something like "a fleet of spaceships has left the Andromeda Galaxy en route to Earth". It's either true or false even if we can't know which it is.
However, what's interesting about special relativity is that it seems to entail that whether or not such a proposition is true is relative to one's reference frame such that if two people cross paths in opposite directions then it can be true for one of them and false for the other. And if it's true for one of them then the future for the other is "fixed".
I don't really understand your question. I certainly accept that special relativity, and its various implications such as the Andromeda Paradox, are correct, but like much of science I find it very peculiar.
Thanks.
Although I've seen it used before, I wasn't familiar with the term "truth-apt," so I looked it up - "A sentence is truth apt if there is some context in which it could be uttered (with its present meaning) and express a true or false proposition." To start, that doesn't seem like a very interesting characterization for any statement. I also don't see how it applies in this context.
But the relativity of simultaneity isn't just about one person seeing something before another person; it's about that thing actually happening for one person before another person. That's what I find peculiar.
A statement such as "a fleet of spaceships has just left the Andromeda Galaxy en route to Earth" is either true or false, even though we don't, and can't, know which.
The "common sense" realist view is that if it's true then it's true for all of us, otherwise it's false for all of us, but if special relativity is correct then whether or not it's true can be relative to our individual movements.
Sorry. It seems trivial. Philosophers sitting around the campfire making up spooky stories, flashlights under their chins. Not that there's anything wrong with that.
About the RietdijkPutnam argument, to which the above link refers to, we read the following:
"In philosophy, the RietdijkPutnam argument, named after C. Wim Rietdijk [nl] and Hilary Putnam, uses 20th-century findings in physics specifically in special relativity to support the philosophical position known as four-dimensionalism."
This reference is among those that can entrap you in an endless nested chain of references within references, as they contain terms that you are not acquainted with and you need to look them up. Even if you can skip some of them, there some that are important for the understanding of the subject at hand. In this case, we have the term "four-dimensionalism". So, from Wikipedia, I read the following:
"In philosophy, four-dimensionalism (also known as the doctrine of temporal parts) is the ontological position that an object's persistence through time is like its extension through space. Thus, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies, just like an object that exists in a region of space has at least one part in every subregion of that space." (https://en.m.wikipedia.org/wiki/Four-dimensionalism)
Now, I had to look up temporal parts, because it is central to the description of four-dimensionalism. It is also an intriguing term, I think:
"In contemporary metaphysics, temporal parts are the parts of an object that exist in time. A temporal part would be something like 'the first year of a person's life', etc."
But can a person's life be considered an "object"? And if we accept that to be true, should we also consider thoughts as objects too? But both are concepts that cannot exist in space! How can we include them in 4 dimensions when they do not exist even in 3 dimensions? See the impasse one could get in? Well, this might be \a problem of mine only ...
However, getting back to the description of four-dimensionalism, there are things that throw me off or, at best, make me wonder:
1) "An object's persistence through time is like its extension through space". But if something (physical) exists a) it exists in space, where else? and b) if something exists (in space) can it not exist in time too?
(And, what does "extension through space" mean? This is too perplexing,)
2) "An object that exists in time has temporal parts in the various subregions of the total region of time it occupies." We say that an object occupies space. I really cannot see how it can also "occupy time". Can time be occupied? If it could, then we wouldnt be able e.g. to hear two sounds together! It would like in the early computers that could only produce monophonic sounds. So, I am wondering, is occupying time just a ridiculous notion or there's something more to it?
This is as far as the RietdijkPutnam argument is concerned. I will reply to the Andromeda Paradox in a separate comment.
Which statement?
Especially if those spooky stories illuminate special relativity in such challenging ways. :roll:
1 ) Event X has occurred at time u in Alice's reference frame.
2 ) Event X has occurred at time v in Bob's reference frame.
Plus:
ROS ) u isn't necessarily equal to v.
There isn't any ambiguity there. Or a contradiction. There would be a contradiction if you add:
3 ) All events have a unique time of occurrence.
Or a variant like:
4 ) Every event's outcome is fixed at some time t.
Both ( 3 ) and ( 4 ) go against the "relativity of simultaneity" concept. The unique time of occurrence in ( 3 ) fixes a time in all reference frames (thus necessary equality), which contradicts relativity of simultaneity. The fixed time in ( 4 ) does the same, as it is unique (thus necessary equality).
That uniqueness isn't of a numerical value, since 2 is always 2, that uniqueness construes each event as indexed by a unique time in a shared index set. Relativising time, as an index set of events, to a reference frame is a core posit of special relativity. The "paradox" is just premise smuggling through ambiguous phrasing. ( 1 ) and ( 2 ) quantify within a reference frame's set of time points, 3 and 4 quantify over both index sets.
Edit: or alternatively, it provides a neat demolition of our pre-theoretical space and time intuitions. They don't represent how nature really works.
Before and after are relative to the frame of reference. So if the two persons are of the same frame of reference, then the event will not happen for one person before the other person. And, if they are of different frames of reference it makes no sense to talk about it "happening for one person before another person" because before and after are frame dependent. That is why it is sometimes necessary to use a "world line", or "proper time", to make sense of such an idea.
In one persons reference frame the event is in the present (or past), and in the other persons reference frame the event is in the future. I find this peculiar.
And, for the purpose of the Andromeda Paradox, it shows that the second persons future is inevitable.
No. This has nothing to do with what one person sees. There are distant events happening in my present that I cannot see because they are too far away. According to special relativity some of these events happen in your future even though they are happening in my present. This is what I find peculiar.
In Special Relativity, an observer can be identified with an inertial reference frame in which they are at rest, and relative to which they make all their space and time measurements. This can be likened to a set of co-moving rods and clocks, all synchronized by light signals. For instance, Clocks A and B can be synchronized through a light signal sent back and forth between them, with the time at Clock B being set at the mid-point interval between the departure and return times at Clock A. Consequently, two observers can have different simultaneity planes due to the fact that events are timed with reference to distinct sets of clocks that have been synchronized differently. @Benkei's train example above illustrates this concept well.
Actual "observers" (such as human beings) are free to choose whatever reference frames they want, and can translate space-time coordinates of events using the Lorentz transformations. So long as they reside outside of their light cones, the issue of events being located in their "relative past" or "relative future" doesn't have any physical or metaphysical significance. It only has relevance to the degree that it challenges certain presentist or "growing block universe" conceptions of time. This was Putnam's main point in his paper, "Time and Physical Geometry".
In addition to the problematic objects, there is also the question of what to do with the uniqueness of observers.
What the Andromeda Paradox implies is that the observed universe apparently shifts in its entirety towards a moving observer. Which means that in the forward moving direction many more of the most distant galaxies come into possible view and we lose some distant galaxies from possible view behind us. This is all pretty absurd, yet it is demonstrably true.
Then this becomes equivalent to an observer shifting its 'present' physically measurably in space toward the direction of motion. The effect is that we can see from some future present some event that can then be prevented from causing harm in the present present after we quickly got back to where we belong.
The galaxies you are moving towards would have come into view regardless of your motion, only at a later time as measured by your clock. Similarly, the galaxies you are moving away from will also come into view, but at a later time. In a flat spacetime, you cannot indefinitely outrun light rays. Interestingly, as you acquire more velocity relative to both sets of galaxies, they "move" closer to you due to the effects of Lorentz contraction.
However, as you gain speed, the reason why the light from the galaxy behind you doesn't catch up to you sooner (despite the contracted distance) is due to the recalibration of your plane of simultaneity. As this occurs, the photons that were a distance D away before you started moving suddenly "jump" back in time and are "now" less advanced on their journey towards you!
I have not tackled the Andromeda Paradox yet. In the articles it is said to be an extension by Penrose of "a form of" the RietdijkPutnam argument. I only talked about the RietdijkPutnam argument itself and how it didn't make much sense to me.
So I expected that the OP would clarify at least one or two of my questions. The OP however couldn't care less. Well, there are different ways OPs view and handle their launching of a discussion ...
Afer that, I couldn't care less myself about the Andromeda Paradox, But since you have brought it up, I just had a look on it, in the same article of the link in question.
My first impression is that the "experiment" is unnecessary complex and includes unnecessary details that add nothing to its essence, e.g. the two persons crossing each other --because it is impossible to pass each other ... except if they were foot racing! :grin: They could be anywhere on the planet. The "paradox" has to do mainly with time, and very little with space. Then the trip to Andromeda is too far-fetched and quite unrealistic. The same "paradox" could be set on something much simpler and realistic, like e.g. tennis final. (One can think of a million of such simple examples.) So, one person knows that the match is about to start and the other doesn't know what time the match will start. One can add more uncertainties --always realistic ones-- e.g. wheher the match will take place at the foreseen day or it will be postponed because of weather conditions, which players are going to compete for the title, etc.
Quoting magritte
I see that you introduce more factors than what is described by Penrose. But this can be done also in my own example as I mentioned above. However, the main factor --as I see it-- involved here, the "protagonist", is "uncertainly". Any additions only increase --they might also decrease-- that uncertainty.
Quoting magritte
You see a factor here the importance or even the meaning of which --in the present context-- most probably escapes me: the direction of motion.
Well, It;s good that at least you enjoy this "paradox"! :smile:
Think of what this means as that "the present", or "now" is defined by the frame of reference. This is a type of subjectivity. The present, and therefore future and past, are defined by the frame of reference. So if we want an "objective" present, or now, or an objective divisor between events of one period of time and those of another another, we have to realize that this is impossible under the precept of special relativity. Such divisions of before and after are arbitrary, as is the frame of reference which defines the divisor.
This becomes problematic when you try to relate the before and after of one frame of reference to that of another. This give the problem you describe. Physics resolve this problem with the creation of a "world line" for the object at question, in this case Andromeda. The world line allows for a "proper time" relative to that object. So once a world line is created for Andromeda we could use that to say which events are before others, for Andromeda itself, despite the differences between different frames of reference. The problem with this is that the world line is somewhat arbitrary.
If we send two signals to the Mars Rover, spaced at exactly 10 seconds apart, does the Rover receive them in that same time spread? Assume the relative positions don't change.
If you want to be very precise with the terminology, the Andromeda Paradox shows that some spacelike separated event in my present is some spacelike separated event in some other person's causal future even though that person is also a spacelike separated event in my present. I find that peculiar.
And let's take it further and consider this:
Some event (A[sub]1[/sub]) in my (A[sub]0[/sub]) future is spacelike separated from some event (B[sub]0[/sub]) in someone else's (B[sub]1[/sub]) past, even though this person is spacelike separated from my present. It might be impossible for me to interact with B[sub]1[/sub] (or for B[sub]1[/sub] to interact with A[sub]1[/sub]), but Special Relativity suggests that A[sub]1[/sub] is inevitable, hence why this is an argument for a four-dimensional block universe, which may have implications for free will and truth.
the edge of the visible universe is receding from us faster than the speed of light. Although individual galaxies are much slower than light their apparent movement adds up radially away from us. Over billions of years we would see fewer galaxies spread further apart in ever darkening space.
The moving observer effect is special because it is in the observer's present, here and now. But that present, that 'origin' is not fixed in space-time. I'll throw another log in the fire.
The Hubble space telescope orbits Earth. Let's suppose that when flying at maximum approach speed in the direction of Andromeda it sees a quickly brightening supernova star. Mission control decides to keep the telescope pointed there to record continuously for 10 days. From Earth we will not discover that supernova for another 3 days, and on the other side of the orbit, now moving away from Andromeda, Hubble will not see it for another 3 days. This is not an illusion. NASA could set this up just to make Penrose's point, showing that the universe is a weird place.
The RietdijkPutnam preceded Penrose and is seen more as a philosophical argument in the literature. Frankly, reading wiki and the SEP articles on Time and Becoming and Temporal Parts very little of it makes sense to me either.
That's probably because I am more hung up on Plato's various suggestions of space, time and change.
The Ship of Theseus makes more sense to me in terms of temporal parts, identity and change. but the notion of same time or gaps in time between events still throws me for a loop..
This is due to the expansion of the universe, which is a general relativistic effect. It is unrelated to the shifting of the simultaneity plane due to the substitution of inertial reference frames is special relativity.
In essence, you're saying that even though a distant event currently lies beyond your ability to influence it (due to the fact that any influence you exert cannot travel faster than light), someone else, presently positioned closer to the event, can influence it.
Quoting Michael
If we let c approach infinity, Galilean spacetime converges with Lorentzian spacetime. In this case, the "absolute elsewhere" of an event (the region outside of the light cone) shrinks into a unique simultaneity hyperplane. In Galilean spacetime, an observer at a given time views any event in its (absolute) past as "inevitable." In Lorentzian spacetime, an observer deems "inevitable" any event that resides either in its (absolute) past light cone or in its (also absolute) elsewhere region. The "inevitability" relation between observers-at-a-time (events) and other observers-at-a-time becomes intransitive.
This intransitivity means that even if
1. A1 is inevitable by B1, and
2. B1 is inevitable by A0,
it does not follow that (3) A1 is inevitable by A0.
This inference is invalid because the inability of A0 to affect A1 indirectly by influencing B1 does not mean that A0 can't influence A1 directly.
The argument on that page accepts that relativity of simultaneity is true but claims that "all observers 3D worlds are real at every event" is false because "Our intuitions dont really know how to deal with elsewhere; its neither fixed and certain, since we cant predict what happens there with certainty based only on the data in our past light cone, nor changeable since we cant causally affect what happens there; we can only causally affect events in our future light cone."
This is a non sequitur. That an event cannot be predicted with certainty isn't that the event isn't certain. Or to phrase it another way, even if we cannot know (with certainty) whether or not "there is intelligent alien life in the Andromeda Galaxy" is true, it doesn't follow that it isn't true (or false).
And nobody is suggesting that it's changeable. In fact if the block universe is true then nothing is changeable; it just is what it is.
So the Andromeda Paradox is the claim that if "aliens are leaving Andromeda en route to Earth" is (unknowably) true in some reference frame then "aliens will leave Andromeda en route to Earth" is (unknowably) true in my reference frame.
And furthermore, that for every proposition "X will happen" either there is some reference frame A in my present elsewhere such that "X is happening" is (unknowably) true, and so "X will happen" is (unknowably) true in my reference frame, or there is no reference frame A in my present elsewhere such that "X is happening" is (unknowably) true, and so "X will happen" is (unknowably) false in my reference frame.
That the event is certain to you in your frame of reference is irrelevant to my frame of reference. For us to exchange that information at (sub-)light speeds, brings your event within my frame of reference. The "elsewhere", e.g. anything outside my frame of reference, is incoherent to be talking about as it doesn't exist for me. When the information is exchanged, it's already in my frame of reference.
EDIT: this is why it's useful to realise that when you actually observe the event happening in your frame of reference, you're 15 lightdays away from me, which will then be your present and I'll still not be aware of it. You notify me it's coming and by the time that information reaches me, the light of the event is there as well. Until that time there's no way for me to know what's coming.
This is where a realist would disagree. We can't know what's happening in the Andromeda Galaxy right now, but something is happening. Either "intelligent alien life exists in the Andromeda Galaxy" is (unknowably) true or "intelligent alien life doesn't exist in the Andromeda Galaxy" is (unknowably) true.
If we consider this in the context of presentism, the presentist would claim that only objects that exist in the present (including the present elsewhere) are real. But if B exists in A's present (elsewhere) and C exists in B's present (elsewhere) then C is real, even if C exists in A's future (elsewhere). And if special relativity is true then something like this is the case. Therefore presentism is false (as is the growing block universe theory). Or, given this fact, presentism and eternalism amount to the same theory.
Or are you an antirealist about events outside your (past?) light cone?
Quoting Alkis PiskasAlso known as the block universe, or eternalism, a view that goes back to at least the 11th century.
[quote=wiki?]"In contemporary metaphysics, temporal parts are the parts of an object that exist in time. A temporal part would be something like 'the first year of a person's life', etc."[/quote]Would be more helpful to name a part that isn't a temporal part. If it doesn't exist in time, then it hasn't a location in spacetime, and it effectively doesn't exist.
Yes, quite easily. It being an object only becomes problematic if its identity is challenged, but must such challenges don't apply to a human, at least not significantly beyond a few days from conception. A human life is bounded by a couple meters of space most of the time and several decades of time. That's what a worldline is.
Why, because you don't consider thoughts to be a physical process, or because you don't consider a physical process to be an object. I would probably agree only with the latter. Given other parts of the post, I think you mean the former, in which case it is your choice or not to work with a model compatible with this 4 dimensionalism or not.
But both are concepts that cannot exist in space! How can we include them in 4 dimensions when they do not exist even in 3 dimensions? See the impasse one could get in? Well, this might be \a problem of mine only ...
That's like saying you're ok with bread having width but you can't see how it can have length.
Quoting Benkei
For one thing, when you reference a statement like that, at least quote the statement. Anyway, I just don't see how the statement indicated seems to assume any privileged FoR.
Many of your posts (I lost count) seem to be about what somebody sees rather than which events one considers to be simultaneous with a given event. The scenario isn't empirical at all. It is meant to illustrate relativity of simultaneity, something new under SR. Even in Newtonian physcs, if somebody happens to be closer to the light coming from some distant event, they'll see it before somebody further away.
The scenario has nothing to do with light cones since none of the events in question are in anybody's light cones.
Quoting BenkeiI agree, SR does not imply a block universe. The wording of it pretty much assumes it, but it is quite trivial to change that wording to more empirical wording. So for instance, instead of light moving at constant c relative to any frame, you say that light is measured to move at constant c relative to any frame. The later papers (and GR in particular) are worded more in this fashion.
I've never seen a good proof of either view, and I've put out a few myself, not all taking the same stance. For instance I found an empirical way to disprove presentism, but it works along the same lines as being able to prove the afterlife: You can only prove it to yourself, not to those you leave behind.
Quoting Benkei
But the topic presumes a different view than the one you presume, so your personal beliefs are inapplicable. Your statement here seems outright solipsistic. What exists is determined by you and you alone.
Quoting Michael
The thing is, the way the story is worded seems to presume everybody uses the inertial frame in which they are stationary to consider what is going on. It simply isn't true. Almost everybody uses the same frame from day to day, which is the frame of the ground under you, which just happens to be an accelerating rotating frame, but pragmatically, it works for almost all uses. So the two people passing in the street don't have an opposing view of what time it is in Andromeda.
OK, all that changed a few centuries ago when they realized that such a frame doesn't work so well when looking at things further away than clouds, and in those cases, they probably use something more practical like the frame of the sun instead of the frame of the individual.
The point of the 'paradox' still stands. A small change in inertial coordinate system can translate to significant temporal differences at large distances, and this is what you find peculiar.
The rational part of me has been an eternalist for some time, and I find this intuitive, not peculiar at all. The pragmatic part of me doesn't care and always uses the rotating frame.
Quoting Michael
Careful. The Andromeda scenario is supposed to assume 4 dimensional spacetime in which you don't have a present. So relative to a given event at which you are present, these different inertial frames with minor velocity differences translate to significant time differences at large distances.
You reference the present a lot in your posts. If there is a present, there is but the one, and what day it currently is in Andromeda has nothing to do with anybody's frame. Mixing the two views is what makes it seem paradoxical. So try not to mix.
Quoting Michael
Under relativity, the point is irrelevant. Under QM, it is very relevant, and given a non-counterfactual interpretation of QM, the statement " there is life on
Quoting magritteThere's no such thing as a moving observer without establishing a frame. I suppose 'shifts' can describe the difference in the motion of things when the frame changes (the observer accelerates?). So in my frame, the tree gains velocity relative to me when I run towards it, but that's very different from the tree itself accelerating.
Your velocity doesn't change what you see. OK, it can blueshift it a bit, but nothing comes into view that wasn't already there regardless of your velocity. Of course given enough time, you'll separate yourself from a observer left behind, and that separation (and not the velocity) will change which galaxies are in view.
Quoting jgillThat's just silly. It's not about the respective rate of time passage at all.
Yes, and if the two observer walking past each other simultaneously send signals to Andromeda, and then another signal a minute later, they'd get to Andromeda at the same time, and the second signal a minute later, separated by the time it takes light to go however far apart the guys got in that minute.
Quoting magritteYes, and yet galaxies become visible over time as our expanding visible universe overtakes them. These newly visible galaxies are also receding faster than c (proper distance, constant cosmic time), but not as fast as the 'edge'.
More galaxies actually, but our capacity to see them diminishes as they indeed redshift into less detectable frequencies and lowed brightness due to increasing distances.
[quote="magritte;818434]The Hubble space telescope orbits Earth. Let's suppose that when flying at maximum approach speed in the direction of Andromeda it sees a quickly brightening supernova star. Mission control decides to keep the telescope pointed there to record continuously for 10 days. From Earth we will not discover that supernova for another 3 days[/quote]What? Hubble is in fairly low orbit, hardly 3 light days away. Light from the supernova reaches Earth in the same second as it reaches Hubble, presuming Hubble's view of it isn't blocked by Earth. It has nothing to do with the motion of Hubble, and nothing to do with this topic, which is about Relativity of Simultaneity, not about when things get measured. Hubble most certainly does not see a whole different view of distant things when it is approaching them vs 45 minutes later when its orbit takes it the other way.
Of course.
Quoting Benkei :roll:
Why do you aplogize? I was not expecting a response from you but from the OP of this discussion, @Michael, who seems not to know what a discussion is and/or he lacks communication basics, esp. when he is the OP of a discussion.
Quoting noAxioms
Thanks for letting me know.
Quoting noAxioms
Then we are not speaking about the basic meaning of the term "object", which is anything that is visible or tangible and is relatively stable in form, but about is secondary and more general meaning, i.e. anything to which thought and action is directed, related or referred. The first is clearly physical. The second one not necessarily physical.
Quoting noAxioms
Most probably you mean a "human body". (A life occupying space is just absurd.)
Quoting noAxioms
I don't consider thoughts to be a physical process. There's nothing to prove this. The brain reactions that neurobiologitsts and other consider as thought are just that: reactions. The brain is a stimulous-response mechanism, And as such it reacts to thoughts, in various ways. That's all it does and can do. It cannot originate, create, imagine a thought from scratch.
Quoting noAxioms
"Width and length refer both to space. They have nothing to do with time.
Indeed, how do you imagine an object "occupying time"? I'm very curious ...
My wait was also in vain.
Quoting Alkis Piskas
OK, we differ here. A body might continue after life, but I see no better way to interpret 'a life' than 'a body, while it is alive'. That makes it an object in any scientific sense. If you have a non-scientific definition of such things (and apparently you do), then yes, perhaps your definition isn't compatible with some of the concepts expressed in relativity theory as well as other theories.
Quoting Alkis PiskasDo you have a reference for the consensus view of neurobiology that a brain cannot 'originate, create, imagine a thought from scratch'. I mean, there are probably some that hold such beliefs for supernatural reasons, but I'm speaking of the scientific consensus.
Quoting Alkis Piskas
Under the spacetime view, they're just different dimensions of the same thing, so every 'object' has a series of 4D points (events) that it occupies and the rest of the events which it does not. This is the same as a 3D table in space occupying some points and not the rest.
So you're saying, like so many others, that you just cannot conceive of 4D spacetime, of a block universe, eternalsm, etc. The whole Andromeda scenario presumes it, so if you don't understand it, you're not particularly qualified to critique it.
Obviously.
Quoting noAxioms
What things? And what do you mean by "non-scientific definition"?
Quoting noAxioms
How can I have such a ref? This is an impossible question for a philosophical discussion. It can be asked only and maybe among scientific communities. For out purposes, one can only know about the prevailing views of neuro(bio)logy on the subject. You can google if you like things like "Thoughts are created", "Thoughts are located", etc. You will see that almost all the results refer to the brain.
Quoting noAxioms
This isn't what I asked. I asked "how do you imagine an object 'occupying time'?" And I added that I'm very curious. Well, I'm not anymore! :smile: In fact, I wasn't curious at all. It was a manner of speaking. Because an object occupying time is a totally absurd idea.
Quoting noAxioms
This is called argumentum ad hominem, i.e. "argument against the person". And it's a bad thing.
The same way it occupies space, since time and space are just different dimensions of the same thing under the spacetime view. Under the 3D view, objects and the entire universe are contained by time. I'm not sure if that would be considered 'occupying time' or not, since the term isn't typically used that way.
It's not against you personally. Anybody sufficiently unfamiliar with a given subject is unqualified to meaningfully critique the subject. You seem to attempt to demonstrate this unfamiliarity with statements like the above one where you consider it absurd. It happens to match empirical observations perfectly, so there's nothing absurd about it at all. That alternate views also match empirically indicates that there's no positive evidence one way or another. Somebody familiar with both views would realize that. Somebody positing the impossibility or absurdity of one view or the other only demonstrates ignorance of the subject. I'm ignorant of plenty of subjects, and it isn't anything against me to point out that I'm unqualified to critique them. But I'm quite familiar with this subject, which isn't very complicated at all. It gets more complicated when general relativity sets in and the 3D presentist view gets some real (but not insurmountable) challenges.
One solution is that there is but the one present (not even a frame really), and time doesn't exist at all, and the present doesn't move. It is the same moment forever. The last-Tuesdayism view illustrates this. If you can't defend or counter last-Tuesdayism, then you don't understand the subject very well. This is especially relevant when discussing Boltzmann brains, where last-Tuesdayism isn't just some reducto-absurdum, but is potentially the most probable thing.
Saying "the same way it occupies space" is wrong because space and time are not "just different dimensions of the same thing"; they are two totally different things and concepts. Look them up! Besides, I already mentioned that we can undestand how an oblect occupies space, but we cannot say the same about time. So, you have avoided the question for the nth time.
After all these exchanges between us, you should have either given an exact and/or plausible answer, preferably with an example, or admitted you don't know or admitted that an object cannot actually occupy time.
So, I give up here.
Within a moving ship,relative to an outside observer, a light clock is introduced having a light signal going up horizontally and then being reflected downwards. The observer outside the spaceship will calculate light signal (up and down) having a greater distance to travel relative to the observer inside the ship, however still having a velocity of c; this will bring about an observed time dilation on the part of the moving ship....of course the same can be said for the observer within the spaceship, if the outside observer had a light clock as well, but we will only focus on the first example.
What would happen if the light clock was positioned horizontally instead?
I personally can't see how the horizontal clock would be synchronized with the vertical one.
Grampa Dee
Grampa Dee wrote:
"Within a moving ship,relative to an outside observer, a light clock is introduced having a light signal going up horizontally" ....sorry, I meant vertically...
From the standpoint of the external observer ("stationary" reference frame) the emitted light has to catch up with the receding mirror. On the return path, the travel time is shorter due to the source rushing towards the light ray. It may therefore seem like the two effects cancel out. However, since the distance traveled forward is longer, more time is accrued for the light ray to catch up with the mirror than is saved on the shorter return path. Because of that, there still is time dilation, and calculation shows that the same gamma factor is in play.
You wrote: "On the return path, the travel time is shorter due to the source rushing towards the light ray. It may therefore seem like the two effects cancel out. However, since the distance traveled forward is longer, more time is accrued for the light ray to catch up with the mirror than is saved on the shorter return path. Because of that, there still is time dilation, and calculation shows that the same gamma factor is in play."
Would it be possible for you to write down how this can be achieved, for I don't understand?
The way I see this is simply the length the path of light will have for the first leg would be increased
(L + vt) and the second leg would be foreshortened (L- vt) which, as you mentioned, seems to cancel the effect.
What happens during the first leg which gives the gamma factor is what I still don't understand.
However, this was only part of the problem as S.R. would identify the path itself as being contracted by a factor of gamma, giving (gamma L+vt) + (gamma L - vt) = 2 gamma L . With c being constant,...this seems to give us a time contraction cancelling the effect of the vertical clock..
I sure that I'm misunderstanding something, but don't know what exactly.
thank you for your time
Grampa Dee
Yes, you're right that the Lorentz contraction of the path must also be taken into account. The Lorentz factor, gamma, is always greater than 1, so the contracted length is L/gamma. The time required for the light ray to reach the receding mirror is therefore t1 = d/v1, where d is the distance between the source and the mirror (d = L/gamma) and v1 is the relative velocity between the source and the mirror (v1 = c - v). Similarly, the time required for the light ray to return to the source is therefore t2 = d/v2 where v2 = c + v.
The total time elapsed is therefore t1 + t2 = L/(gamma(c - v)) + L/(gamma(c+v)). To simplify, you can multiply the numerator and denominator of the first term by c + v and the numerator and denominator of the second term by c - v. You get
t = L(c + v)/(gamma(c^2-v^2))+L(c - v)/(gamma(c^2-v^2)) = 2Lc/(gamma(c^2-v^2))
Since gamma = 1/sqrt(1-v^2/c^2), 2Lc/(gamma(c^2-v^2)) simplifies to 2L*gamma/c which is the same time registered by the vertical light clock.
(Note that c/(gamma(c^2-v^2) = c*sqrt(1 - v^2/c^2)/c^2-v^2 = sqrt(c^2 - v^2)/(c^2-v^2) = 1/sqrt(c^2-v^2) = 1/(c*sqrt(1-v^2/c^2) = gamma/c.)
Intuitively, as v tends towards c and taking into account the Lorentz contraction of the clock, the duration of the return travel tends towards zero. Meanwhile, the duration of the forward travel tends towards infinity despite the shortened distance, as c - v approaches zero faster than sqrt(1-v^2/c^2) does.
Thank you for your time and patience, Pierre Normand
.Quoting Pierre-Normand
Yes; thank you...I always think of gamma as being the SQRT 1 v^2 / c^2, but its actually the inverse.
Quoting Pierre-Normand
I have a problem understanding this though; I rather see the time light displaces any distances as being d / c; I would instead claim that v would be responsible for the length contraction instead, being d or L/ gamma + or - some other distance being vt .Also, isnt the relative velocity between the source and the mirror 0? Therefore, I, for now, understand the 1st path as being
t1 = d / c or (L/gamma +vt) / c
Quoting Pierre-Normand
Again, I would assume t2 = d / c, d being equal to L/gamma vt.in this case.
Quoting Pierre-Normand
Ive got
(L / gamma + vt) / c + (L/gamma vt) / c = 2L/gamma c
Quoting Pierre-Normand
2L*gamma /c was what I had in my first response to you :); however you correctly pointed to me that gamma was a factor which increased the original value, where I needed one which would reduce the outcome ( length contraction).
Now, what I have is instead 2L/gamma c.
I will try to clarify a bit my point. Since the velocity remains c, I think that all we need is the distance for the light to travel in order to calculate the time.
In the first case, (the vertical light clock) the distances the outside observer calculates are the two hypothenuses SQRT L^2 + (vt)^2, the total being 2 * SQRT L^2 + (vt)^2
In the second case,for the horizontal clock, I have L/gamma. + vt one way, and the return path being L/gamma vt.
If L/gamma +vt = L* [SQRT 1 v^2/c^2] +vt ..and.the second path is even shorter.
Heres my problem...as v tends to c, in the vertical clock the path tends towards L^2 +ct^2 ...a very long path,if not infinite, whereas for the horizontal path , it seems the path tends towards 0.
I seem to have two extreme opposite situations.
Quoting Pierre-Normand
Interesting...its what I see in the two clocks...(vertical and horizontal). What I would disagree, for now, is that the duration of the clock for the forward travel (on the horizontal clock) would still tend to 0 due to the length contraction of the path between the source and the mirror
I thank you again for your time.
Grampa Dee.
Yours is an equally valid way to calculate the time required for the pulse to reach the mirror. Mine is only slightly simpler since we don't first need to calculate the total distance travelled but only the time required for the pulse to overtake the mirror (which is initially at the known distance L/gamma) with the knowledge of their relative velocities in the stationary inertial frame. Since the light pulse travels at velocity c and the mirror at velocity v, their relative velocity, and thus the rate at which the gap between them closes, is c - v (and c + v in the return trajectory). I'll nevertheless calculate it your way below.
Thanks for pointing it out. I hadn't yet done the calculation back then ;-)
In the case of the horizontal clock you indeed have d1 = L/gamma + vt for the first path and d2 = L/gamma - vt_2 for the return path. I use "t_2" since the time for traveling the return path is different (shorter). Since in both cases the distance is travelled at c, we have the two equations:
d1 = L/gamma + vt = ct
d2 = L/gamma + vt_2 = ct_2
Isolating t and t_2 in both equations and summing them up, we get the total time:
T = L/((gamma(c - v)) + L/(gamma(c + v)) with is the same result I had obtained more directly by considering the relative velocities of the light pulse and clock.
I had misspoken in the previous post while mentioning the relative velocity between the source and mirror. Good catch! I meant to refer to the relative velocity between the light pulse and mirror (as measured in the stationary frame).
Also, as previously mentioned, although the forward path travelled indeed approaches zero as v tends towards c, the time for travelling it still approaches infinity as our final equation T = 2L*gamma/c shows.
ok: Would vt_2 be equal to -vt?
Quoting Pierre-Normand
This is where it gets foggy for me; you seem to divide by a relative velocity (c+v) instead of adding another distance vt....Im not saying that youre wrong, only that I cant visualize it . If v causes a foreshortening of L, then why not say T = L / (c v) + L / ( c+v) ? but here, we would be in Newtonian mechanics wouldnt we? :)
Would it be possible to give the calculation without having (c+v) or (c v) in the equation?
I understand a bit why youre doing this but Im not comfortable with it. For example: if we take c = 1
and v = .5 , then L /(c+v) = L / 1.5 and L/(c-v) = L/.5...Now let L = 1
We would then have L / 1.5 + L/.5 = .66666 + 2 = 2.66666
But, for ( L +vt) / c and (L vt) / c, we would have [(1+.5t) + (1 -.5t) / 1] = 2
If we start with what you once wrote:
Quoting Pierre-Normand
Without using (c+v)(c-v), could you derive T = 2L*gamma/c in another way ?
Thank you again for your time and patience.
Grampa Dee.
ps: Your name tells me that you might be a french speaking person? I am as well...my name is Andre
:
No, since vt is the distance travelled by the mirror during the forward path while vt_2 is the distance travelled by the source during the return path, and the return path takes a shorter time. t_2 < t.
I followed the method you recommended and then applied an algebraic simplification to make the gamma factor explicit.
Using your method we get
1) d1 = L/gamma + vt = ct
2) d2 = L/gamma - vt_2 = ct_2
There was a typo in my previous post where I had placed a "+" sign rather than a "-" sign. Apologies for this. The rest of the calculation was correct but here it is again, more explicitly:
From the first equation, t = L/(gamma(c - v))
From the second equation, t_2 = L/(gamma(c + v))
Therefore, the total time
T = t+t_2 = L/(gamma(c - v)) + L/(gamma(c + v))
To simplify this, we can multiply the first term by (c+v)/(c+v) and the second term by (c-v)/(c-v), effectively multiplying each term by 1.
T = L(c + v)/(gamma(c - v)(c + v)) + L(c - v)/(gamma(c - v)(c + v))
= L((c + v) + (c - v))/gamma(c2 - v2) = 2Lc/gamma(c2 - v2)
Next, we can express gamma explicitly as 1/sqrt(1 - v^2/c^2), and divide both the numerator and denominator by c^2 to get
T = (2L/c)sqrt(1 - v^2/c^2)/(1 - v^2/c^2) = 2Lgamma/c
As long as all velocity terms are expressed relative to the same inertial frame of reference, the relative velocities between two material objects (or between a material object and a photon) can be expressed as simple sums or differences (e.g., c + v or c - v). This doesn't involve any Newtonian assumptions. When the light pulse travels at c and the clock at v, their relative velocity is c + v (or c - v). This is because it's the rate at which their separation changes, as measured in the stationary reference frame.
Yes, from the Montreal area, in Quebec, Canada. Nice meeting you, André.
Ok...Maybe this is where Im off the rail.I was visualizing the light going to the mirror as traveling a distance vt further away from the length of the apparatus (distance between source and mirror)and a distance vt less than the apparatus when coming back towards the source being the reason why it took a shorter time.Maybe, somehow I will focus on this part.
[b]Quoting Pierre-Normand[/b]
What I will do for now, Pierre-Normand, is try to understand on my own your derivation using (c+v)(c-v)method since it does indeed seem to make sense. Right now, the way Im visualizing this, I am calculating the distances travelled by the moving apparatus vt and then claiming that the light is travelling with the velocity of "c" in between those distances (L+vt). The other thing I will focus on is my visualizing the return path as being vt shorter than the apparatus. If you think of some way to clarify any of this, I will
certainly look at it; if not, its ok; for this is simply a pastime of mine, I dont feel the need to understand any of this.
[b]Quoting Pierre-Normand[/b]
Hello Pierre-Normand, Im your next door neighbor from northern Ontario.
Take care....well probably chat again sometime.
Grampa Dee
Andre
Your thinking was correct, but since both the forward and the return path are travelled by the light pulse at the same speed c (in any referential frame), and since the return path is shorter, the time to travel it is also shorter. This is why you must setup two distinct equations:
d1 = L/gamma + vt_1 = ct_1
d2 = L/gamma - vt_2 = ct_2
The first equation states that the distance the mirror has travelled away from the source (with a L/gamma head start) by the time the light pulse reaches it is the same as the distance travelled by the light pulse at that time; and similarly for the second equation. Each equation allows to solve for t_1 and t_2. The rest only involves algebraic manipulation.
Think of two people walking an unleashed dog at a steady pace v thereby keeping a constant distance L between them. Picture the dog running back and forth between them at constant speed v_2 > v. The forward path for the dog is longer than L since the person ahead keeps moving the 'goalpost' further away until the dog reaches them. Conversely, the person behind moves the 'goalpost' closer during the time when the dog returns.
I hope those further explanations help, Andre. Feel free to reach out if you have any further questions. Happy thinking!
Hello Pierre-Normand, nice to hear form you again
[b]Quoting Pierre-Normand
I don't think I have any problem with upper statement.
[/b]Quoting Pierre-Normand[/b]
I was able to visualize the situation using (c+v) (c-v) instead of the increase/decrease of length to the light path thanks to your example of the two people and the dog.However, I must have something missing here as well because I still arrive at the same conclusion. Maybe you will be able to spot my error.
If we have a moving platform with a velocity of v relative to us (moving from left to right),and lets say that a camera is recording the event and what we see is the platform on a monitor as though it isnt moving.The source is at the left and the mirror is located to the right of the platform.
Now we will observe a ray of light travelling from the source to the mirror as having a velocity of (c-v) towards the mirror. Afterwards, the light ray will travel in the opposite direction, back towards the source with a velocity of (c+v).
Here is where I might be wrong (if Im not wrong already :) ), the average velocity the light ray will have is going to be c. However, we are also observing the platform as having been contracted by gamma^-1. This, in my mind, identifies a time contraction of gamma^1 instead of a time dilation of gamma, it seems.
I hope you dont think that Im merely trolling here. I sincerely have problems understanding s.r.
The example that you gave (people and dog) was very good and easy to understand, however, my problem stems directly in the invariant speed of light.
Thanks again for your time and patience..
Andre
In this case, you're using the camera to register the events as they occur relative to the moving reference frame (i.e., the inertial frame in which the light clock is stationary).
This, along with the Lorentz contractions of the platform, are what you register in the inertial referential frame in which you are at rest, in which the platform is travelling at v, and in which the time registered by the light clock is (consequently) dilated.
The velocity of all light rays always is c as measured from any referential frame. This is a postulate of the Special Theory of Relativity. The Lorentz contraction of the platform only is being registered in the 'stationary' referential frame. There is no Lorentz contraction of the platform observed in the reference frame in which the platform is at rest.
Yes, it's precisely because the speed of light in a vacuum, c, is invariant, that the relative velocity between an object (such as a light clock) and a light ray is frame-dependent. When you measure events in a frame where the object is at rest, its velocity relative to all light rays is c. When you measure events in a frame where the object moves inertially at v, its relative velocity is c - v (or c + v) relative to a light ray moving in the same (or opposite) direction. And that's simply because after some time t has elapsed, the light ray has travelled a distance ct while the object has travelled a lesser distance vt. The distance between the object and the light ray therefore varies at the rate d/t = (ct - vt)/t = c - v (or (ct + vt)/t = c + v). This is what I call their relative velocity in a given referential frame.
I assure you, I never had the impression that you were trolling. Some of these issues are indeed subtle, and it's understandable to have questions. Keep asking - no worries at all!
Hello Pierre Normand; how are you? Thank you again for this interaction.
Pierre Normand wrote ....within our first exchange....I think :)
[b]The time required for the light ray to reach the receding mirror is therefore t1 = d/v1, where d is the distance between the source and the mirror (d = L/gamma) and v1 is the relative velocity between the source and the mirror (v1 = c - v). Similarly, the time required for the light ray to return to the source is therefore t2 = d/v2 where v2 = c + v.
The total time elapsed is therefore t1 + t2 = L/(gamma(c - v)) + L/(gamma(c+v)).[/b]
I agree
Pierre Normand wrote:
To simplify, you can multiply the numerator and denominator of the first term by c + v and the numerator and denominator of the second term by c - v.
As youre multiplying by 1, I fully agree.
Pierre Normand wrote:
[b]You get
t = L(c + v)/(gamma(c^2-v^2))+L(c - v)/(gamma(c^2-v^2)) = 2Lc/(gamma(c^2-v^2))[/b]
ok...good
Pierre Normand wrote:
Since gamma = 1/sqrt(1-v^2/c^2), 2Lc/(gamma(c^2-v^2)) simplifies to 2L*gamma/c which is the same time registered by the vertical light clock.
Shouldnt it be 2Lc*gamma instead?
Grampa Dee (Andre)
That wouldn't work since this has the dimensions of squared meters per seconds and we want something that has the dimensions of seconds.
To arrive at the simplification, note that gamma can be rewritten as [math]\frac{1}{\sqrt{\frac{c^2}{c^2}-\frac{v^2}{c^2}}} = \frac{1}{\sqrt{\frac{(c^2-v^2)}{c^2}}}[/math] and therefore [math]\gamma^2[/math] is [math]\frac{c^2}{c^2-v^2}[/math]
Our expression [math]\frac{2Lc}{\gamma(c^2-v^2)}[/math] can therefore be rewritten as [math]\frac{2L \cdot \gamma^2}{c \cdot \gamma}[/math], which is [math]\frac{2L\gamma}{c}[/math]. As gamma is dimensionless, this expression indeed has the dimensions of seconds.
(Thanks to GPT-4 for help with the formatting of the mathematical expressions.)
Thank you Pierre - Normand; it's now clear as a bell :)
I was impressed with you're mathematical juggling
and I understood everything you did.