Difference between timespace expansion/contraction and kinetic motion?

[MiloOfCroton]

How could you tell in an experiment which was happening?

 

[ghwellsjr]

How could you tell in an experiment which was happening?

You can't. Length Contraction and Time Dilation are Coordinate Effects which depend on which Inertial Reference Frame (IRF) you choose to describe an experiment in. Therefore, in one IRF, Length Contraction may explain what is happening and in another IRF, Time Dilation may explain the exact same scenario. The muon example can be analyzed from the Earth's rest IRF in which Time Dilation explains how the muons with a very short half life can survive long enough to reach the surface of the Earth while in the rest IRF of the muons, Length Contraction of the Earth explains the same scenario since they don't have far to go.

 

[MiloOfCroton]

You can't. Length Contraction and Time Dilation are Coordinate Effects which depend on which Inertial Reference Frame (IRF) you choose to describe an experiment in. Therefore, in one IRF, Length Contraction may explain what is happening and in another IRF, Time Dilation may explain the exact same scenario. The muon example can be analyzed from the Earth's rest IRF in which Time Dilation explains how the muons with a very short half life can survive long enough to reach the surface of the Earth while in the rest IRF of the muons, Length Contraction of the Earth explains the same scenario since they don't have far to go.

Has anybody considered eliminating motion all together? It seems to me that non-motion would supercede motion theoretically. Space contraction/expansion can explain all that motion explains PLUS it explains gravity, thanks to General Relativity. Motion just explains all motion, of course.

 

[PeterDonis]

Space contraction/expansion can explain all that motion explains PLUS it explains gravity, thanks to General Relativity.

Why do you think this? Can you give a specific example of space contraction/expansion explaining motion? Are you aware that motion can be present in spacetimes that are static (i.e., not contracting or expanding)? Can you give a specific example of space contraction/expansion explaining gravity? Are you aware that gravity can be present in spacetimes that are static?

 

[MiloOfCroton]

Why do you think this? Can you give a specific example of space contraction/expansion explaining motion? Are you aware that motion can be present in spacetimes that are static (i.e., not contracting or expanding)? Can you give a specific example of space contraction/expansion explaining gravity? Are you aware that gravity can be present in spacetimes that are static?

To your second question: I was lead to believe that spacetime curves in order for gravity to happen. The way that objects gravitate towards each other is along these curved spacetime lines. Furthermore, if the spacetime grid around objects A and B have become curved due to the attraction between them, then the singular spacetime line directly between object A and B will have become shorter. Is that correct? Help out an amateur relativist. :)

To your first and third questions: Is it believed that our universe is static or dynamic? If it is believed to be dynamic, then why should it be relevant if motion or gravity can be present in a static spacetime?

 

[PeterDonis]

I was lead to believe that spacetime curves in order for gravity to happen.

Yes, any spacetime in which gravity is present is curved.

The way that objects gravitate towards each other is along these curved spacetime lines.

Not really. If an object is moving purely under the influence of another object's gravity, its worldline is a geodesic; a geodesic is the closest thing to a straight line in a curved spacetime. I say "the closest thing" because our intuitive concept of a "straight line" doesn't work in a curved spacetime; we have to generalize the concept.

For example, consider a geodesic in an ordinary curved space: a great circle on the surface of the Earth. According to our intuitive concept of a "straight line", a great circle is curved, not straight (hence the name "great circle"). But if we confine ourselves to lines on the surface of the Earth, there are *no* straight lines in our ordinary intuitive sense; *every* line is curved. But we can pick out great circles by focusing on one particular feature of "straight lines" in the ordinary sense that *does* generalize to curved spaces: the shortest distance between any two points on the Earth's surface is along the great circle between them.

In spacetime, there's a further wrinkle, because one of the dimensions is time. In spacetime, a geodesic, like the path that a freely falling object (one moving solely under the influence of gravity) follows, is the path with the *longest* proper time.

Furthermore, if the spacetime grid around objects A and B have become curved due to the attraction between them, then the singular spacetime line directly between object A and B will have become shorter. Is that correct?

No. First, it's often not a good idea to think of the "grid" as being curved; sometimes it can be helpful, but often it isn't, and this is one of the cases where it isn't. It's better to think of geodesics, including the ones that mark out the "grid", as being the "straightest possible" lines in the curved spacetime.

Second, there's no way to make a comparison between the way things actually are, and the way they would have been if gravity weren't present. I know it seems like there ought to be, intuitively, but there isn't; there's no way to collect any experimental data that would tell you how "curving the grid" changes the lengths of lines. All we have are the actual curves in our actual spacetime.

Third, as above, the geodesic paths that freely falling objects follow are paths of *longest* proper time.

To your first and third questions: Is it believed that our universe is static or dynamic?

Dynamic, in the sense that it is expanding. But you have to be careful about what that means. It doesn't mean that the expansion is what causes gravity.

Also, even if the universe as a whole is dynamic, there can still be subsystems within it that are static. See below.

If it is believed to be dynamic, then why should it be relevant if motion or gravity can be present in a static spacetime?

Two reasons: first, you made a general statement that "space contraction/expansion" can explain *everything* that "motion" can explain, plus gravity. You didn't limit it to any particular case.

Second, consider the local patch of spacetime around an isolated gravitating body. That local patch of spacetime is static, even though it happens to be within a universe that is, as a whole, dynamic, and the gravity of the isolated body has to be explained without appealing to the overall dynamic nature of the universe. So any explanation of gravity (and motion, for that matter) has to be able to cover static situations as well as dynamic ones.

 

[MiloOfCroton]

In spacetime, there's a further wrinkle, because one of the dimensions is time. In spacetime, a geodesic, like the path that a freely falling object (one moving solely under the influence of gravity) follows, is the path with the *longest* proper time.

I read the definition for proper time, so I know what that sentence technically means, but I have no idea what the implications are. Can you explain that in a little more detail?

No. First, it's often not a good idea to think of the "grid" as being curved; sometimes it can be helpful, but often it isn't, and this is one of the cases where it isn't. It's better to think of geodesics, including the ones that mark out the "grid", as being the "straightest possible" lines in the curved spacetime.

Second, there's no way to make a comparison between the way things actually are, and the way they would have been if gravity weren't present. I know it seems like there ought to be, intuitively, but there isn't; there's no way to collect any experimental data that would tell you how "curving the grid" changes the lengths of lines. All we have are the actual curves in our actual spacetime.

So you're saying that we have no way of knowing because we only have the objects, and we know how far away they are now; we can't create new circumstances without totally changing the system.

So my idea was that motion does not exist; only space expansion and contraction exists. You say that it cannot be proven, and I counter that it cannot be proven wrong. Is that correct? See the last quote in this post to continue...

Two reasons: first, you made a general statement that "space contraction/expansion" can explain *everything* that "motion" can explain, plus gravity. You didn't limit it to any particular case.

Do you know of a limited set of cases in which motion can be replaced by a dynamic universe?

Second, consider the local patch of spacetime around an isolated gravitating body. That local patch of spacetime is static, even though it happens to be within a universe that is, as a whole, dynamic, and the gravity of the isolated body has to be explained without appealing to the overall dynamic nature of the universe. So any explanation of gravity (and motion, for that matter) has to be able to cover static situations as well as dynamic ones.

How can you test that system to know that it is static?

I assume you're implying that the isolated body would be at rest; there are no forces acting on it to move it; that's what makes it isolated. However (as with my point about the universe being dynamic and your point about spacetime never not having gravity), has there ever been a discovery of an isolated body? How could there be? I would assume an isolated body would be impossible. Even if it were, simply us observing it would make it non-isolated.

 

[PeterDonis]

I read the definition for proper time, so I know what that sentence technically means, but I have no idea what the implications are. Can you explain that in a little more detail?

Do you understand why a great circle on the Earth's surface is the shortest distance between two points on that surface? If not, you might want to consider that case first. If you do, the case of spacetime works the same way, except that because time is one of the dimensions, the sign is inverted when you're talking about proper time. The reason the sign is inverted is that the metric of spacetime has opposite signs for the time and space terms: for example, in flat spacetime, ##ds^2 = dt^2 - dx^2 - dy^2 - dz^2##, as opposed to flat Euclidean space, where ##ds^2 = dx^2 + dy^2 + dz^2##.

So you're saying that we have no way of knowing because we only have the objects, and we know how far away they are now; we can't create new circumstances without totally changing the system.

No, I'm saying that we only have our actual spacetime, with whatever masses are present in it; we have no way of comparing it with some hypothetical spacetime where there are no masses present, but with everything somehow "in the same place", to see the difference in the "grid lines".

So my idea was that motion does not exist; only space expansion and contraction exists. You say that it cannot be proven

Not really; I'm saying that I'm not sure it even has a consistent meaning, or is testable. You have to have a consistent theory that's testable before you can even ask whether or not it can be "proven" (and anyway scientific theories aren't proven, they're just more accurate or less accurate and have a narrower or wider domain of validity).

I counter that it cannot be proven wrong. Is that correct?

No. That's not how it works; when you propose a new theory, *you* bear the burden of proof--or at least of it being consistent and testable. I'm not sure your proposed theory even meets that burden.

Do you know of a limited set of cases in which motion can be replaced by a dynamic universe?

I'm not even sure I know what you mean by that. That's why I asked *you* for a specific example. If you can't produce one, where are you getting this theory from?

How can you test that system to know that it is static?

By finding a family of observers who (1) stay at rest with respect to each other, and (2) each see the spacetime geometry (which in this case is basically the "strength of gravity") as unchanging in their local vicinity. Around an isolated gravitating body, a family of observers all "hovering" at a constant altitude above the body (but each at a slightly different altitude) meets these two conditions.

I assume you're implying that the isolated body would be at rest

Only in a relative sense; see below.

there are no forces acting on it to move it

That's not the same as being "at rest" in any absolute sense. It is an important physical condition--the condition of free-fall motion (in GR, gravity is not a "force", so objects moving solely under gravity have no forces acting on them); but it doesn't equate to "rest" in any absolute sense, since there is no such thing in relativity.

However (as with my point about the universe being dynamic and your point about spacetime never not having gravity), has there ever been a discovery of an isolated body?

An "isolated body" is an ideal case, of course; no real body exactly meets the conditions. But the Earth, for example, comes reasonably close for many purposes.

I would assume an isolated body would be impossible. Even if it were, simply us observing it would make it non-isolated.

As a philosophical point, this is true, there are no completely isolated bodies. However, we don't need to have completely ideally isolated bodies for GR to work as a theory.

 

[timmdeeg]

Second, there's no way to make a comparison between the way things actually are, and the way they would have been if gravity weren't present. I know it seems like there ought to be, intuitively, but there isn't; there's no way to collect any experimental data that would tell you how "curving the grid" changes the lengths of lines. All we have are the actual curves in our actual spacetime.

But how about the comparison of the shape of the famous freely falling ball of coffee grounds in flat space-time vs. falling towards a gravitatiing mass? Or perhaps your statement refers to the FRW model only and not to the Schwarzschild case? Could you kindly explain?

 

[PeterDonis]

But how about the comparison of the shape of the famous freely falling ball of coffee grounds in flat space-time vs. falling towards a gravitatiing mass?

That's a comparison of two different mathematical models, not a comparison of reality vs. an unmeasurable "the way reality would have been if there were no gravity".

 

[Dale]

I counter that it cannot be proven wrong.

If it is not falsifiable then it is not science.

This forum is not for discussing or even debunking personal theories.