Is space 4 dimensional?

I saw this cool video on how 4D objects "passing through" a 3D universe would look like. The presenter first shows how a 3D sphere passing through a 2D universe would look like - a growing circle as the 2D plane captures only a slice, which is circular, of the 3D sphere.

Then this popped into my mind: living things grow and that could mean we're 4D entities traversing 3D space. In short GROWTH = 4D objects crossing 3D space. I haven't worked out the details; despite my deep love for the queen of the sciences, she's spurned me like as if I'm a leper. :sad:

P. S. Shrinking in size, same thing!

Hello? Dr. Pym? Hello?

Reply to TiredThinker IIRC, dimensionality corresponds to degrees of freedom of movement. 3-d space describes the freedom to move backward-forward, up-down and right-left in space. That we are – every 3-d thing is – moving (i.e. "arrow of time") adds a 4th-d. Thus, only (Euclidean) abstract space is 3-d; physical (relativistic) spacetime is 4-d.

Reply to Agent Smith Interesting. But when people grow it isn't necessarily uniformed and might further emphasize the 4th dimension as a time dimension rather than strictly spacial?

Reply to 180 Proof

I think recent research simulated 2D space and projected 4D objects into 3D space?

https://bigthink.com/technology-innovation/hints-of-the-4th-dimension-have-been-detected-by-physicists/

I am just curious since gravity is often considered an illusion perhaps once we can see through it we could see 4 dimensionally?

Quoting TiredThinker

If gravity isn't actually a force and it curves space but . . .

I'm uncertain about space but spacetime is curved in appropriate metrics. The simple Euclidean metric is not one of them. Apokrisis could explain this better.

I found this conception of the extra dimensions proposed in string theory, 'graspable.' Its from the physics stack exchange.

[b]Take an 2D antlike entity on a 2D surface, it is like an ant but it has only two dimensions moving within the (x,y) plane. One can pile up an infinity of (x,y) planes with 2D ants on each 2D surface when a z direction is hypothesized by an Einstein of an ant.

In this example the ant could disappear from its plane, with a perpendicular motion and appear on other planes in this z direction. (3rd dimension)

If we hypothesize a fourth space dimension for our three dimensional universe , we could disappear into the perpendicular direction into another three dimensional volume.

There will be a certain amount to the "left," a certain amount "high," and a certain amount front or backward (etc). It's still length, width and depth.

The example of a two dimensional ant should make you understand that different surfaces should exist when adding the third dimension. For the three to four dimensions it is different volumes. And also funny shapes, part within our volume and part outside, As a 3D entity, it would really be confusing for us.

String theories need extra dimensions so as to be able to embed the standard model of particle physics into the vibrations of the strings. The standard model is an encapsulation of practically all the data we have for the quantum mechanical framework of particle physics.

As people do not in reality disappear into other extra dimensional volumes, theorists needed to make the extra dimensions very tiny, to agree with the experimental fact that only in fairy tales people disappear and reappear. The compactified curled up extra dimensions still fulfill the need for embedding the standard model, and also the fact that no extra dimensions have been observed in all our particle experiments either.

In the example of the ant, if one compactified the third, z, dimension, there would be no danger of it sliding around surfaces not existing in its original world, because it could not fit into the curled dimension.[/b]

Reply to TiredThinker Sounds like String theorists' "holographic principle" (derived from "black hole thermodynamics")
https://en.m.wikipedia.org/wiki/Holographic_principle

I think a PBS spacetime video suggested that gravity creates time. So maybe time isn't just strongly connected to space, but a spacial dimension itself with the attribute of duration and causality added to it?

Space is eight dimensional because planets and stars and other space phenomenon are suspended or trickling down like a stock exchange. Plotting a route in space using a 4D mind is partial, you'll note the planet sphere at one angle - you'll note the path between two stars - but noting is weak in comparison to knowing for knowing the whole of space would be different.

Space is not a puzzle, it is a complete image. Planes, sides, polarity can be registered but so too can level (such as with space phenomenon suspension), rigor (such as with how gravity is manifest) and other dimensions. Don't void what is visible as non dimensional, basically the full image of space is dimensional.

Quoting TiredThinker

Interesting. But when people grow it isn't necessarily uniformed and might further emphasize the 4th dimension as a time dimension rather than strictly spacial?

It was just a pattern I saw. It isn't perfect I know, but I'm neither a mathematician nor a physicist; so all I got is a vague intuition.

RE: Is space 4 dimensional?

(First Approximation) In the study of Euclidian Geometry, and most Sacred Geometry, what we would normally consider the Fourth Dimension (4D) would be approximated by the Three Dimensions (3D) (X-Axis, Y-Axis, Z-Axis) coordinate which uniformly moves in one direction along segments of this 4D axis (t) (for time). At higher approximation levels (particularly those that consider the Fourth-Dimensional Existence and begin to allow the influence of Transformation (Reflections, Angular momentum, Rotational Groups, and Symmetry) the one most concerned in most cases is the impact of time-Dilation.

Reply to Agent Smith

(BOTTOM LINE)

Space is expanding. Theoretically, all the astrological objects, bodies, and groups are moving away from each other. This causes a shift in frequency causing light to change in color. 4d(t) uses that space to maintain momentum.

Most Respectfully,
R

Quoting Rocco Rosano

(BOTTOM LINE)

Space is expanding. Theoretically, all the astrological objects, bodies, and groups are moving away from each other. This causes a shift in frequency causing light to change in color. 4d(t) uses that space to maintain momentum.

Is this your theory of dark energy - the mysterious force that's causing cosmic expansion? You didn't mention the acceleratation that some say is occuring.

Quoting Rocco Rosano

time-Dilation

What do you make of Willaim Lane Craig's ([s]physicist[/s] theologian-philosopher) assertion that time dilation applies only to clocks and not "actual" time which remains unaffected?

Maybe if we experienced 4D space we wouldn't see curved lines created from gravity and in fact wouldn't experience gravity at all?

Quoting TiredThinker

Maybe if we experienced 4D space we wouldn't see curved lines created from gravity and in fact wouldn't experience gravity at all?

Have you ever driven through mountains? The curves that hug the slopes are actually straight then, oui? Gravity & the transgender movement, something worth investigating, si señor/señorita?

For a mathematician four dimensions simply means one more variable to deal with. A three dimensional cylinder [math]F\left( x,z,y \right)=0,\text{ }{{x}^{2}}+{{z}^{2}}-{{r}^{2}}=0[/math] is a circular cylinder extending along the y-axis infinitely in both directions. Its four dimensional counterpart could be written [math]F\left( x,z,y,w \right)=0,\text{ }{{x}^{2}}+{{z}^{2}}+{{y}^{2}}-{{r}^{2}}=0[/math] which extends along the mysterious w-axis. Unfortunately, we are unable to see into this fourth dimension, only work with it mathematically. In this example a 3D slice of the 4D figure is a sphere.

Strange things happen when objects are "compressed" down from ND to (N-1)D. Here one sees a series of corrugated "roofs" being squeezed down from wrinkled 3D to a 2D flat square with a bizarre result.

Quoting TiredThinker

If gravity isn't actually a force and it curves space but we don't notice it perhaps we only see 3 dimensions of space when there are actually 4 or more?

There are three macroscopic dimensions of space. If you include time as a spatial dimension, there are four, but most don't include it as a spatial dimension since it has very different properties (x²+y²+z²-t²) than it would as a spatial dimention (x²+y²+z²+t²).

Quoting TiredThinker

But when people grow it isn't necessarily uniformed and might further emphasize the 4th dimension as a time dimension rather than strictly spacial?

You mean when somebody gets physically larger (from the child size say)? That just means you consume more 3D space at later times. In spacetime terms, it means your worldline is thicker at later times.

Quoting TiredThinker

I think recent research simulated 2D space and projected 4D objects into 3D space?

Your view of somebody (yourself or others) at a particular moment in time is a 2D projection. The thing itself at that time (not the image seen) is a 3D cross section (not a projection) of a 4D object into 3D space. Sure, anybody can project higher-D objects into lower-D space, but that projection alters the object and loses information. Looking at something doesn't destroy it, so I think it's a mistake to call it a projection. It's a cross section. The cross section of a sphere passing through a 2D plane is that of a circle that starts and ends small and reaches full diameter halfway through the process. The projection of the same sphere onto the same 2D plane is full diameter period. It's a picture of a sphere.

Quoting TiredThinker

So maybe time isn't just strongly connected to space, but a spacial dimension itself with the attribute of duration and causality added to it?

That's reasonably accurate, yes.

Quoting Agent Smith

Is this your theory of dark energy - the mysterious force that's causing cosmic expansion?

Dark energy is only there to explain acceleration of expansion. Expansion itself works just fine without DE, but it would decelerate over time if gravity was the only influence on it. It did decelerate for a long time (6-7 BY?) when mass energy was greater than dark energy, but once the mass density dropped below the density of DE, the acceleration took over.

Quoting Agent Smith

What do you make of Willaim Lane Craig's (physicist theologian-philosopher) assertion that time dilation applies only to clocks and not "actual" time which remains unaffected?

What other kind of time is there? What possible evidence is there of this other time if it isn't measured by a clock? Mind you, I cannot think of any physical process involving change that doesn't qualify as a clock. This includes one's biological sense of time. Paint peeling is a clock. All these are subject to dilation.

Craig has an agenda and speaks to his sponsors more than he speaks to his knowledge of physics, but this statement, if accurately stated, is over the top even for him.

Quoting TiredThinker

Maybe if we experienced 4D space we wouldn't see curved lines created from gravity and in fact wouldn't experience gravity at all?

What 'lines' do you see? We cannot experience 4D space since we're 3D beings. You'd need to be a 4D spatial being to experience that.

If, again, you count time as a spatial dimension (it isn't invalid to talk about a km of time), then we are experiencing 4D space, so there's no 'if' about it.

Reply to noAxioms

[quote=Ms. Marple]Most interesting.[/quote]

Everything is a clock. I'd like you to, if possible, expand and elaborate that point. Muchas gracias in advance.

Reply to TiredThinker, do you mean whether 3-dimensional space needs another spatial dimension to wobble in and out of, if you will?
From memory, that's not needed (for relativity at least).
Might need someone well versed in relativity to respond, in case that's what you meant.

Reply to jgill, neat.
Reminded me a bit of Aristotle's wheel, though it doesn't go all ?.

Reply to noAxioms

What makes us 3D beings? If dimensionality is more complex than math and simply running a 3D sphere through a 2D plane showing only a 2D circle? What if we could be made of and represented by more dimensions and still have trouble experiencing them all?

Reply to jorndoe

What are you asking? I am just wondering about anything that might be hiding potential higher spacial dimensions from us.

Quoting jgill

For a mathematician four dimensions simply means one more variable to deal with. A three dimensional cylinder is a circular cylinder extending along the y-axis infinitely in both directions. Its four dimensional counterpart could be written which extends along the mysterious w-axis. Unfortunately, we are unable to see into this fourth dimension, only work with it mathematically. In this example a 3D slice of the 4D figure is a sphere.

Strange things happen when objects are "compressed" down from ND to (N-1)D. Here one sees a series of corrugated "roofs" being squeezed down from wrinkled 3D to a 2D flat square with a bizarre result.

This is mighty interesting. Algebra can explore other dimensions beyond the 3 we're familiar with and unlike a normal 3D cylinder which we can see in our minds, a n-dimensional (n > 3) is, as of yet, beyond the reach of our imagination. Where it blows my mind is even contradictions (a square circle for example) are inconceivable. Is there something contradictory about dimensions higher than 3?

Reply to jorndoe Interesting puzzle, the Aristotle wheel? What's the solution?

Quoting Agent Smith

Everything is a clock. I'd like you to, if possible, expand and elaborate that point.

I gave a few examles (paint peeling, radioactive substance, etc) in my prior post. I can think of only a few things (objects) that don't change over time, and thus don't act as a clock.

To elaborate more, I need to know what Craig meant. I need the context. What you said seems to imply that there's evidence of some sort that there's something that measures time in a way that is not subject to inertial-frame dependent time dilation. Such a thing could be used to empirically determine a preferred frame, and this violates the last 120 years of physics. I suspect he wouldn't say anything that obviously wrong despite his naive paying audience. So I suspect he said something else.

Quoting TiredThinker

What makes us 3D beings?

At a given time, it takes 3 coordinates to locate any particular piece of any object (a living being is no different than a house in this respect). At different times, that location may or may not change.
Not sure if this is what you're asking. It seems too obvious of an answer, so maybe you're asking something else.

If dimensionality is more complex than math and simply running a 3D sphere through a 2D plane showing only a 2D circle?

This sentence (query?) lacks a verb. Dimensionality seems less complicated to me than what math can be. Yes, any 2D cross section of a sphere is a point or a circle, the former being a circle of zero radius.

What if we could be made of and represented by more dimensions and still have trouble experiencing them all?

Well I think I'm 4D and have little trouble experiencing them all, despite my 2D vision processing system. The two missing dimensions are trivially extrapolated.

Reply to noAxioms Most perceptive of you. Muchas gracias señor, muchas gracias.

P. S. Could we say that things that transform slowly (e.g. words etched in stone, inscriptions you see in archaeology) are in a sense travelling at relativistic speeds (time slows down for them) and a mind-blowing corollary would be the changeless/constant are basically light (timeless)?

Once again, four dimensional Euclidean space is not the same as four dimensional spacetime.

Reply to noAxioms

So we are at least 3D despite our visual system only seeing 2D images? So couldn't we be composed of 4, 5, maybe 6 dimensions even if we can't detect them, or they aren't necessary to be known for our survival?

Quoting TiredThinker

So we are at least 3D despite our visual system only seeing 2D images?

Yes, for the reasons posted above. Two coordinates is not enough to identify a location in space, but is enough to locate something on an image. Three is not enough to locate an event in spacetime.

So couldn't we be composed of 4, 5, maybe 6 dimensions even if we can't detect them, or they aren't necessary to be known for our survival?

4 are quite detectable. You seem to be asking if what we sense is a lower dimension cross section of a higher dimensional (5+) thing, which is like asking if the sphere passing through the plane is only aware of the circular cross section and not the rest of itself.
Sure, I can't in any way falsify something like that.


Quoting Agent Smith

Could we say that things that transform slowly (e.g. words etched in stone, inscriptions you see in archaeology) are in a sense travelling at relativistic speeds (time slows down for them)

No. A slow process is just like the hour hand on a clock as compared to the second hand. The hour hand isn't dilated in the proper frame of the clock, and it moves even slower relative to any other frame in which the clock is moving.
A slowly eroding stone with text on it (Rosetta stone say, which I've actually touched), would degrade all the slower relative to a frame in which it is moving fast.

Quoting Agent Smith

(time slows down for them)

Time does not slow down for a fast moving thing since said thing is always stationary in its own frame by definition. You in the hypothetical spaceship would be stationary in your own frame and thus all processes around you including your sense of the flow of time proceed at the normal pace, and in your frame, it is all the processes of moving things around you (like Earth receding from you) that slow down (exhibit dilation).

Reply to noAxioms

There's this natural rate at which chemical reactions take place e.g. 10 mg of H[sub]2[/sub]O per minute[sub]2[/sub]. Catalysts, the right one, can speed reactions up. Suppose with the aid of a catalyst we now get 30 mg of H[sub]2[/sub]O per minute[sub]2[/sub]. A 3-fold increase in water production and what blows my mind is this: 1 minute[sub]2[/sub] = 3 minute[sub]1[/sub]. Time dilation?

Quoting jgill

four dimensional Euclidean space is not the same as four dimensional spacetime.

Certainly!

Quoting TiredThinker

If gravity isn't actually a force and it curves space but we don't notice it perhaps we only see 3 dimensions of space when there are actually 4 or more? We look straight and see different things from where we'd ultimately end up if there was a strong gravity. If we saw 4 dimensionally would we not see things only as if there were only straight lines and have it be accurate?

I wouldn't worry about how many dimensions there are -- as long as you are not walking near a cliff. All dimensions are inferred, hence imaginary. What you infer depends on what you are looking for. And mathematicians are comfortable with models of abstract (less than real) worlds. For example, some physics theories say the world must have 11 dimensions, and some mystical theories postulate a fifth dimension of mind. Also the currently popular Holographic theory says that our reality exists on the surface of a 2 dimensional bubble. Which implies that we are all Flatlanders, with no cliffs to worry about. :joke:


The Entire Universe as a Two Dimensional Object :
That means that every single bit of information that we see in three dimensions is encoded somewhere on the “surface” of the universe in only two dimensions.
https://www.forbes.com/sites/fernandezelizabeth/2020/01/21/could-our-universe-be-2-dimensional-black-holes-offer-a-clue/?sh=27579d6bfc9a