Is there a physical explanation for the relationship between light and space?

[PeterDonis]

If you draw a line between 2 of these spacetime points then would you have a line? If so what if you planted 4 points. Wouldn't you have some kind of spacetime tetrahedron? This is what I'm calling an object with a boundry.

Drawing arbitrary lines doesn't make an object. There has to be something there. If the only thing there is spacetime itself, spacetime doesn't have any kind of boundary like you are describing.

By proper acceleration do you mean proper acceleration through space?

No, I mean proper acceleration that is measured by an accelerometer and felt as weight.

 

[John Morrell]

I think your line of thought with boundaries only really works if you can draw a boundary, the inside of which is space-time and the outside of which is not. That sounds to me like its related to the concept of the edge of the universe, though to be honest I don't have any knowledge about theoretical work done about that.

Space-time is not an object; you can't move it, what would it be moving relative to? You can't touch it, it's just a place-time. Using the word 'physical' makes me think that you are imagining that there is some true-er space that space-time is embedded within, which I don't believe we have any evidence of.

 

[Dale]

Uh-oh, a test! Well it seems spacetime is physical in nature and therefore I suppose you can contain it in a boundary using 4 dimensional points. It also seems you can measure the distance of that boundary using a laser, mirror, and proper time clock. It can expand and carry any object or photon with it as it does so. It can be curved and this is the same thing as tidal gravity, it is flat in the absence of gravity. It can rotate (Lense-Thirring effect or frame dragging) if it is near a rotating body that either surrounds it or is within it.
And most interestingly if it is rotating then any object stationary relative to it and not necessarily at its center, will feel no centrifugal force.

Very good. Now you are thinking about what properties it has. You are not completely correct on those properties but you are closer than most pop sci sources.

Spacetime has geometrical properties. In the language of Riemannian geometry it is a 4 dimensional pseudo-Riemannian manifold with signature (-+++). This means that it has an invariant notion of distance (known as the spacetime interval) and at each point there is one dimension of time (the - signature above) and three dimensions of space (the +++ signature). In local rectilinear coordinates the spacetime interval can be written $ds^2=-dt^2+dx^2+dy^2+dz^2$. From that you can obtain invariant notions of angles and curvature and related concepts. You can also define parallel transport, what it means for a line to be straight (geodesic), and how to take derivatives in the manifold.

Right now, that is just a bunch of terminology to you, but the bottom line is that spacetime has geometrical properties. Those properties are described by the math of Riemannian geometry.

One point that makes me squint is that I don't know why it is not also allowed to move

Because experiments designed to detect that motion have consistently not detected it. It is not that we arbitrarily said "no motion allowed", we did experiments and it seems that it doesn't move. Our model reflects that fact

 

[puzzled fish]

It can expand and carry any object or photon with it as it does so. It can be curved and this is the same thing as tidal gravity, it is flat in the absence of gravity. It can rotate (Lense-Thirring effect or frame dragging) if it is near a rotating body that either surrounds it or is within it.
And most interestingly if it is rotating then any object stationary relative to it and not necessarily at its center, will feel no centrifugal force.

As many have said before in their posts spacetime does not move. You accelerate or rotate relative to the distant galaxies and do not feel any force because your worldline is a geodesic through a given spacetime solution of the EFE equations. This is a manifold with a metric that underlies all its properties.
You do not have to go as far as exotic solutions like the Kerr metric to see this. The familiar Schwartzschild solution in the vacuum is enough. Satellites rotate around with respect to the the distant galaxies ( I do not use Earth here, because where Earth begins we have to use a different spacetime inside it) without any force or acceleration felt because their orbits are geodesics in the Schwartzschild vacuum spacetime solution.

 

[nitsuj]

I meant coordinate acceleration, not proper acceleration, but the point from your previous post that we should be more careful about specifying such things is valid.
With accurate enough measurements, yes, you could, for example, drop two rocks, one slightly above the other, and measure the change in their separation due to tidal gravity. But the point I was making is that this phenomenon is still different from "gravity" as "that which makes the rocks fall at all".

Mostly because of this forum and regularly accurate and insightful posters like you that I get to sometimes follow what's being discussed; thanks for that! :D

 

[nitsuj]

I don't know why it [space or spacetime?] is not also allowed to move. It seems motion is just one step beyond expansion.

what physical effect is there to see "it" move?

I haven't read much about it but have read somewhere on the forum that the term expansion as in the expansion of "space" is not intuitive.

Here is a link to the wiki on Hubble's law which IS the expansion of the universe. The is no talk of moving space, spacetime or anything of the sort. It also said "expansion of the universe is better called "Hubble Flow". I like that because it highlights that all is being done is making a measurement between points...the results are the results...there is nothing extra brought to the results such as saying the space is moving. One thing is for sure...large distances increase the Doppler effect on "light" over time. Note "light speed" is always invariant.

lol what the heck is a parsec?? Is it possible to get an intuition for that unit?

In other words if you observe space moving, you can say space moves. Given there only seems to be spacetime (not just 3d space alone) and it's geometric in nature the concept space moving doesn't make sense to me. That said when first learning about spacetime, I too imagined "space" as moving. The more learned the less that made sense.

 

[Mister T]

If you draw a line between 2 of these spacetime points then would you have a line?

I suggest you start there. Each point is an event, so think of an example of two events and plot them in spacetime. Then consider whether the interval between them is timelike, spacelike, or lightlike. And what that means for this line that you're using to connect those two points.

Physics is not some exercise in visualization and analogy. Those are just things people use to describe and learn the physics. Physics is about an understanding of Nature, so in this case think of two naturally-occurring events, how the points in spacetime represent those events, and what that line you've drawn represents about the behavior of natural objects. It's the behavior of those objects that's important, the physics is just a tool used to understand that behavior.

 

[Dale]

@Buckethead regarding boundaries, spacetime is modeled as a manifold, which requires that all boundaries be open. So if there is a boundary then it is not the kind of boundary that you can place a point on.

 

[Dale]

why we can't really say whether or not a distant galaxy is actually moving away from us at a given speed?

Sorry it took a while to get back to this, but it is an important point.

In spacetime geometry the velocity between two objects is a kind of angle. If two objects collide then their spacetime "worldlines" intersect at a single event and the angle of that intersection is easy to calculate.

However, if two worldlines don't intersect then in order to compare their velocity you have to move one vector to where the other is without turning it. This is called parallel transport.

It turns out that in flat spacetime parallel transport is independent of the path, but in curved spacetime it is not. Consider a sphere with a vector on the equator pointing north and another vector on the exact opposite side of the sphere also pointing north. If you parallel transport along the equator then you get the angle between them is 0, but if you parallel transport along longitude lines then you get 180 deg.

So in a curved spacetime there simply is no unambiguous way to compare the velocity of two distant objects.

 

[Buckethead]

@Buckethead regarding boundaries, spacetime is modeled as a manifold, which requires that all boundaries be open. So if there is a boundary then it is not the kind of boundary that you can place a point on.

In the same way that a small triangle can be defined on a globe for example (a Euclidean representation of a non-Euclidean manifold) can't we section off 4d spacetime into a 3d space the same way? This is an approximation, but still, doesn't it allow for a boundaried section of spacetime to be defined and to exist physically?

 

[Buckethead]

I suggest you start there. Each point is an event, so think of an example of two events and plot them in spacetime. Then consider whether the interval between them is timelike, spacelike, or lightlike. And what that means for this line that you're using to connect those two points.

This is interesting because I understand the timelike, spacelike, or lightlike relationship between the two dots and it makes me wonder about 4 equally spaced events in spacetime. One could say (tongue in cheek) this is a spacetime tetrahedron, but since the relationship between any two of those four points could be either timelike, spacelike, or lightlight, this "tetrahedron" would be a twisted time/space shape that could not be visualized. But could it still be said to be real and physical?

Physics is not some exercise in visualization and analogy. Those are just things people use to describe and learn the physics. Physics is about an understanding of Nature, so in this case think of two naturally-occurring events, how the points in spacetime represent those events, and what that line you've drawn represents about the behavior of natural objects. It's the behavior of those objects that's important, the physics is just a tool used to understand that behavior.

I clearly see what you are saying here, and I don't disagree. I suppose I use analogies to try and see if I can understand what possible direction the models are allowed to go since I do not have the talent to do it strictly through math (alas...).

 

[Dale]

In the same way that a small triangle can be defined on a globe for example (a Euclidean representation of a non-Euclidean manifold) can't we section off 4d spacetime into a 3d space the same way? This is an approximation, but still, doesn't it allow for a boundaried section of spacetime to be defined and to exist physically?

You are mixing up two separate things. One is the boundary and the other is a foliation. Sectioning off a 3D sub manifold is called foliation. The sub manifold is a manifold in its own right so it also has open boundaries.

 

[Mister T]

This is interesting because I understand the timelike, spacelike, or lightlike relationship between the two dots and it makes me wonder about 4 equally spaced events in spacetime.

Yes, but did you think about examples of two events? Like a fist hits a desk here, and hammer hits a nail there?

One could say (tongue in cheek) this is a spacetime tetrahedron, but since the relationship between any two of those four points could be either timelike, spacelike, or lightlight, this "tetrahedron" would be a twisted time/space shape that could not be visualized. But could it still be said to be real and physical?

I can easily imagine a square with points (0,0), (0,1), (1,0), and (1,1) where the first number is the one-dimensional space coordinate and the second number is the time coordinate. I plot those four points on a spacetime diagram and I have a square. I can think about actual events represented by each corner, that is where and when they occur. I can think about the set events that occur inside that square and the set of events that occur outside that square.

There's nothing particularly difficult or twisted about it.

I clearly see what you are saying here, and I don't disagree. I suppose I use analogies to try and see if I can understand what possible direction the models are allowed to go since I do not have the talent to do it strictly through math (alas...).

You're expending more effort to avoid the math than it's worth. And it's leading you astray. See above.

 

[Nugatory]

In the same way that a small triangle can be defined on a globe for example (a Euclidean representation of a non-Euclidean manifold)...

Yes, a small enough region of spacetime can always be considered flat with a three-dimensional Euclidean space embedded in it. (This is an approximation, but it gets better and better as the region in question gets smaller and smaller, so we can make the approximation arbitrarily good by considering a sufficiently small region of spacetime). However...
[/quote]can't we section off 4d spacetime into a 3d space the same way?...doesn't it allow for a boundaried section of spacetime to be defined and to exist physically?[/QUOTE]No. There are two concerns here. First, the division of the region into space and time is still frame-dependent (observer-dependent; coordinate-dependent). Different observers moving at different speeds relative to one another will make up their Euclidean subset out of different points in the region. It's easiest to see this if you consider that each observer's notion of space is "all the events that share the the same time coordinate", and this is inherently coordinate-dependent.

And second, all we've done is identified a mathematical relationship between the coordinates of points in that region of spacetime. There's no way of getting from there to "exist physically".

 

[Buckethead]

Yes, a small enough region of spacetime can always be considered flat with a three-dimensional Euclidean space embedded in it. (This is an approximation, but it gets better and better as the region in question gets smaller and smaller, so we can make the approximation arbitrarily good by considering a sufficiently small region of spacetime). However...

can't we section off 4d spacetime into a 3d space the same way?...doesn't it allow for a boundaried section of spacetime to be defined and to exist physically?

No. There are two concerns here. First, the division of the region into space and time is still frame-dependent (observer-dependent; coordinate-dependent). Different observers moving at different speeds relative to one another will make up their Euclidean subset out of different points in the region. It's easiest to see this if you consider that each observer's notion of space is "all the events that share the the same time coordinate", and this is inherently coordinate-dependent.

And second, all we've done is identified a mathematical relationship between the coordinates of points in that region of spacetime. There's no way of getting from there to "exist physically".

OK, I understand everything you've said here and it makes sense, It seems that even if spacetime we're physical any observer would simply see a distorted view of it compared to any other observer and because time is also part of the coordinate system, when it (or even each particular coordinate) exists would also be in question. However with regard to your second concern, there (in my mind) may still be indications of physical existence. The strongest example being the Lense-Thirring effect as described by Puzzled Fish above where you have a space surrounded by a thick sphere. It is my understanding that if you place stationary test point particles anywhere inside this sphere and you set this sphere spinning, the particles will begin to orbit the center without any forces being felt by the particles. This to me indicates the space inside the sphere is spinning and the particles are simply stationary relative to this space. This space would also be spinning relative to the space located outside the sphere (and far enough away as not to be influenced by it). Now I'm sure I'm missing something here as I'm paraphrasing what I learned elsewhere about the Lense-Thirring effect, but if what I'm saying is true, then wouldn't this be considered one physical space rotating relative to another physical space? Perhaps I'm suppose to replace my use of the word space with spacetime to make what I'm saying more accurate, and that could throw a wrench in the whole thing.

 

[nitsuj]

It maybe possible to call that Alcubierre drive thing a "moving" space, that's apparently possible with math from gr.

 

[Buckethead]

It maybe possible to call that Alcubierre drive thing a "moving" space, that's apparently possible with math from gr.

Yes! Thank you for that reminder. And in such a moving space where the ship is stationary relative to the spacetime warp, the ship experiences no acceleration.

 

[puzzled fish]

The strongest example being the Lense-Thirring effect as described by Puzzled Fish above where you have a space surrounded by a thick sphere. It is my understanding that if you place stationary test point particles anywhere inside this sphere and you set this sphere spinning, the particles will begin to orbit the center without any forces being felt by the particles. This to me indicates the space inside the sphere is spinning and the particles are simply stationary relative to this space. This space would also be spinning relative to the space located outside the sphere (and far enough away as not to be influenced by it). Now I'm sure I'm missing something here as I'm paraphrasing what I learned elsewhere about the Lense-Thirring effect, but if what I'm saying is true, then wouldn't this be considered one physical space rotating relative to another physical space? Perhaps I'm suppose to replace my use of the word space with spacetime to make what I'm saying more accurate, and that could throw a wrench in the whole thing.

No, no, puzzled fish didn't say that... The sphere, which is a planet or a star does not have to rotate. The planet has radius R and is homogeneous everywhere (density = constant). In Newtonian mechanics, you can put inside a disk of radius R with its center the center of the planet and rotate it with constant angular velocity, without any acceleration or forces noticed anywhere on the disk, because the "centrifugal force" anywhere on its surface matches the acceleration inside the planet which is directly proportional to r = distance from its center. Now the spacetime inside the Earth or Sun isn't like that and you cannot find such a disk, but for two points close enough this is a good analogy.
The same thing happens to a satellite when it rotates outside the Earth, there isn't any force, because its orbit is a geodesic in the Schwartschild solution of the Einstein Field Equations in the vacuum. The solution is called a metric and it has been explained before in this thread.
Acceleration force means only one thing: deviation from geodesic. Because you are not being exerted any forces upon on acceleration with regard to distant objects doesn't mean that space is moving with you: it only means that your worldline is a geodesic in a curved spacetime.

 

[Dale]

even if spacetime we're physical

Spacetime is physical. It has physically measurable geometric properties. It just doesn't have motion.

The strongest example being the Lense-Thirring effect

A spiral staircase also rotates without moving.

You need to understand that these experiments have been done. It isn't scientists saying space doesn't move, it is experiment saying space doesn't move and scientists finding models which match that experimental fact.

 

[Dale]

It maybe possible to call that Alcubierre drive thing a "moving" space, that's apparently possible with math from gr.

A shortcut doesn't have to move to get you to your destination sooner.

 

[nitsuj]

A shortcut doesn't have to move to get you to your destination sooner.

I tried to formulate an argument where it'd highlight the interpretation "space moved", by pointing out that synchronized proper times won't deviate after I take that "short cut" / rid that spacetime wave. But if our clocks don't comparatively deviate then neither do our rulers. To stick to my argument I 'd have to say "spacetime moved"...

For me it's a strange concept that while the "short cut" doesn't move, physically I didn't either...despite having changed locations. Here is a case where I really wish I could read math to see what's going on "mechanically", 'cause I can't reason it with the words I know. in other words over my head! :D

But yea, there is no disputing that A shortcut doesn't have to move to get you to your destination sooner.

 

[nitsuj]

Yes! Thank you for that reminder. And in such a moving space where the ship is stationary relative to the spacetime warp, the ship experiences no acceleration.

Read on, imo Dale is right (that's from past experience, not that I follow this concept completely)... Read about how this distortion is created, the initial states required ect its all rather ideal.

"moving space", specifically an experiment to test if space moves this is not...Yoda.

But my intuition really wants to call that moving space (spacetime).

Dale keeps referring to a fact that this has been tested for and remarkable to you (and me kind of) yield null results...why not check the details out?

 

[Buckethead]

Spacetime is physical. It has physically measurable geometric properties. It just doesn't have motion.

A spiral staircase also rotates without moving.

You need to understand that these experiments have been done. It isn't scientists saying space doesn't move, it is experiment saying space doesn't move and scientists finding models which match that experimental fact.

Beside the Michelson-Morley type experiment which to my understanding measures only the change in the speed of light relative to a moving frame of reference containing the experiment, what experiments are there that measure if space moves? Even if space were moving through us, we could not use a measurement of the speed of light to determine that, or are you saying we definitely can?

I wonder if I'm simply forcing the use of the word "move" when it might either be unnecessary or not applicable (and I'm thinking not applicable is better). What I mean is that we can't really measure if space if moving or not even in principle because motion or lack of motion is not a property that is applicable to spacetime in the same way that color cannot be a property of an electron.

When I conceptualize for example a ship in a Alcubierre warp and that ship is accelerating relative to a local star for example, but the ship does not measure acceleration, then I define this as a local spacetime (the one surrounding the ship) accelerating relative to the rest of spacetime, but perhaps this definition is misplaced. What is acceleration of an object if not an accelerated motion relative to spacetime? Now in Mach's Principle it is acceleration relative to the average of all matter in the universe, but opponents of that principle (I think) take the stand that acceleration of an object is an acceleration to something non-material (perhaps a field?), or to nothing at all? I don't really understand what the opposition's stand on this is.

Einstein, in an 1954 article entitled "Relativity and the Problem of Space" pp 375-376 said "[...] space as opposed to "what fills space," which is dependent on the co-ordinates, has no separate existence [...]. There is no such thing as an empty space, i.e., a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field."

Just as a side note, Einstein uses space and space-time interchangeably when talking about existence here but the distinction may be important.

 

[PeterDonis]

we can't really measure if space if moving or not even in principle because motion or lack of motion is not a property that is applicable to spacetime

Yes.

 

[Dale]

Beside the Michelson-Morley type experiment which to my understanding measures only the change in the speed of light relative to a moving frame of reference containing the experiment, what experiments are there that measure if space moves?

See all of sections 3 and 8 here: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

Particularly the ones in section 8 tend to be more recent and probe the strong and weak nuclear forces as well as the EM force. The breadth of experimental investigation is substantial.

Even if space were moving through us, we could not use a measurement of the speed of light to determine that, ... What I mean is that we can't really measure if space if moving or not even in principle

This is the kind of "conspiracy theory" physics we discussed earlier. Yes, you can do it mathematically as I described but since it is undetectable it is unnecessary and physicists only do it if it is convenient.

Now in Mach's Principle i

As philosophically appealing as Mach's principle is, it is difficult to formulate in an experimentally testable manner. As far as I know there is no generally agreed experimental evidence which supports Mach's principle.

 

[Buckethead]

Thanks for the link. Its a lot to read but I'll try and dive into it as time allows. A lot of it is in regard to the speed of light however and I'm not questioning that c is a constant with my questions.

As philosophically appealing as Mach's principle is, it is difficult to formulate in an experimentally testable manner. As far as I know there is no generally agreed experimental evidence which supports Mach's principle.

I'm thinking it would be difficult as you would be trying to find an overall rotation of the universe (or some other motion) relative to an object that is shown to be not spinning due to lack of forces on it. And even if none were found it would not prove that the matter in the universe was the source of the "absoluteness" of acceleration or rotation.

I'm really getting a feel for the way in which spacetime has to be represented. I understand that it's not whether or not spacetime is real or not, it's only its properties that matter and what can be predicted from the models that describe it such as curvature or how it results in "gravitational attraction".

My main goal is to try and understand how rotation or acceleration of an object can be defined without a relationship between the object in question and something else regardless of what that something else is (whether is be space (wrong), or a mathematical model, or the stars (Mach's principle), or something else). If it's just the mathematical model, what is in that model that is being referred to when something is said to be rotating or not or accelerating or not. Now in the case of (let's say) holding an object stationary a few feet above the earth, we can say that this object is experiencing the forces of acceleration even though it is not physcially accelerating and that's all fine, but it still means it is accelerating relative to something, even just sitting there. Let it go and the acceleration stops because it is falling at 32ft/s^2 relative to the surface of the Earth. So in this case it is the Earth that this rock is moving or not moving relative to.

In a flat spacetime with no matter around an object can still feel the forces of acceleration or rotational forces although those that subscribe to Mach's principle would question that accelerational forces or rotational forces would exist in such a universe. But if we say no to Mach's principle and accept that matter has no affect on acceleration forces or rotational forces, then that still leaves what we are accelerating or rotating relative too, if the universe is void.

In a flat universe where there is no gravity, if an object is experiencing rotational forces, is this strictly a SR problem or do you still need GR and if so, what in GR is used at the relationship point that says whether the object is spinning or not in order for the formula to predict what forces (or even if any forces) are felt.

As you can see, I'm still very much confused and thanks everyone for being so patient.

 

[PeterDonis]

My main goal is to try and understand how rotation or acceleration of an object can be defined without a relationship between the object in question and something else

It's defined in terms of accelerometers and gyroscopes. Basically, you set up three gyroscopes whose axes point in three mutually orthogonal spacelike directions. Then you set up accelerometers to measure acceleration in each of those three directions. Then you carry along this apparatus next to the object, so that you can watch the readings of the accelerometers and the relationship between the spatial orientation of the object and the axes of the gyroscopes. Nonzero accelerometer readings means "acceleration"; change in the orientation of the object relative to the gyroscopes means "rotation".

Note that, in a general curved spacetime, these definitions will not give the same results as the intuitive Newtonian (or Machian) definitions of "acceleration" and "rotation" relative to distant objects. Mismatches between the two go by various names in the literature, like "Thomas precession", "de Sitter precession" (or "geodetic precession"), "Lense-Thirring precession", and so on. But if you want a local definition, the above is how to physically realize it. Mathematically, the readings of the accelerometers correspond to the path curvature of the object's worldline (more precisely, of the worldline of its center of mass), and the change in orientation of the object relative to the gyroscopes corresponds to the vorticity of the congruence of worldlines that describes the object (roughly, how the different parts of the object rotate locally around its center of mass).

 

[Buckethead]

Just an addendum to that is another question that's important to me and that is, if a distant galaxy is accelerating away from us (in the way that we've observed distant galaxies to do), is the galaxy itself experiencing acceleration? I'm going to guess it's not and if you compare that to a galaxy that is accelerating and actually feeling those forces, then there is going to be a difference in the formulas that describe these even though both galaxies are experiencing acceleration and should have the same values for their properties.

 

[Buckethead]

It's defined in terms of accelerometers and gyroscopes.

OK, but you are basically just saying what the instruments measure when they measure null is just nothing at all. That the null "just is". What is it that is telling the instrument to be null when it's showing null?

 

[PeterDonis]

you are basically just saying what the instruments measure when they measure null is just nothing at all

Only if you view zero acceleration and zero rotation as "nothing at all". But the object is still there; it doesn't disappear just because the accelerometers and gyroscopes read zero.

What is it that is telling the instrument to be null when it's showing null?

According to GR, it's the local spacetime geometry. And according to GR, the local spacetime geometry is determined, via the Einstein Field Equation, by whatever stress-energy is present in the past light cone.

 

[PeterDonis]

if a distant galaxy is accelerating away from us (in the way that we've observed distant galaxies to do), is the galaxy itself experiencing acceleration?

According to our current models, no. We can't know for sure since we can't attach accelerometers and gyroscopes to the distant galaxy, but all the data we have indicates that distant galaxies, like our own, are in free fall, experiencing zero acceleration.

 

[Buckethead]

Only if you view zero acceleration and zero rotation as "nothing at all". But the object is still there; it doesn't disappear just because the accelerometers and gyroscopes read zero.
According to GR, it's the local spacetime geometry. And according to GR, the local spacetime geometry is determined, via the Einstein Field Equation, by whatever stress-energy is present in the past light cone.

OK, I'm satisfied with all that. Next question: Assume an empty universe (no stress-energy anywhere) and you have two rings with a distance between them and one is spinning relative to the other. Will either feel any forces of rotation? And if so which one and why? A more practical alternative to that question might be, if you have two galaxies spinning relative to each other and they are a great distance apart and no other galaxies exist anywhere, can you say which one is spinning (in other words can you say which one will have its stars drop to the center and which one will continue to have orbiting stars). I'm not being sarcastic here, This is really an important question for me.

 

[Mister T]

According to our current models, no. We can't know for sure since we can't attach accelerometers and gyroscopes to the distant galaxy, but all the data we have indicates that distant galaxies, like our own, are in free fall, experiencing zero acceleration.

I take it that such a state of affairs would not be possible in a flat spacetime? And thus we have evidence that the spacetime is curved, and the great mystery is finding the source of the curvature?

 

[puzzled fish]

OK, I'm satisfied with all that. Next question: Assume an empty universe (no stress-energy anywhere) and you have two rings with a distance between them and one is spinning relative to the other. Will either feel any forces of rotation? And if so which one and why? A more practical alternative to that question might be, if you have two galaxies spinning relative to each other and they are a great distance apart and no other galaxies exist anywhere, can you say which one is spinning (in other words can you say which one will have its stars drop to the center and which one will continue to have orbiting stars). I'm not being sarcastic here, This is really an important question for me.

Ill posed question.
1. The 2 rings have mass so there isn't null stress energy anywhere.
2. You cannot have 2 isolated objects spinning ( I think you mean rotating) relative to each other. Only one of them is rotating relative to the other taken to be stationary. They are rotating both, only around their center of mass.
3. What do you mean by Mach's principle? They are at least 11 versions of it!
4. This example is just a satellite rotating around Earth in an empty universe or two planets rotating around their center of mass. It can be explained according to GR or by invoking Newtonian mechanics. Neither will feel forces of rotation. What Mach has to do with it?

 

[Dale]

A lot of it is in regard to the speed of light however and I'm not questioning that c is a constant with my questions.

Well, that is what physicists (the usual non "conspiracy theory" ones) mean when they talk about space moving.

The laws of physics are written as differential equations, often $\partial/\partial t$ or $\partial/\partial x$. So if space moves then we would expect those laws of physics which depend on dx or dt (including Maxwells equations) to change as you change reference frame. In the more modern literature this is called Lorentz violation or CPT violation. It applies not just for the local laws governing the electromagnetic force, but also the strong and weak nuclear forces, and gravity.

So if you accept the invariance of c then you are basically 1/4 of the way to accepting that space doesn't move. All you have to do is check the strong and weak nuclear forces and gravity too.