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

[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.

 

[Herman Trivilino]

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.

 

[PeterDonis]

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?

Either one or both could be; there is no way to tell from the description you give. You would have to attach accelerometers and gyroscopes to each ring to see.

Note that "assume an empty universe" means "assume Minkowski spacetime", which means you are still assuming a spacetime geometry. So the general rule I gave--that the spacetime geometry determines which states of motion will show local acceleration and/or rotation using the acceleometers and gyroscopes, and which will not--is still true. It's just that your specification of the problem does not give enough information to know how each of the rings is situated in that spacetime geometry.

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

Basically the same answer as above: the only difference is that you can't assume "an empty universe" in this case because the galaxies certainly have non-negligible stress-energy (whereas we could assume the rings above were idealized rings with negligible stress-energy). But there is still some spacetime geometry present, so the general rule I gave still applies. Again, the issue is that you haven't given enough information to know exactly how each galaxy relates to the spacetime geometry.

 

[PeterDonis]

I take it that such a state of affairs would not be possible in a flat spacetime?

Do you mean the observed acceleration of galaxies away from ours, but with all the galaxies being in free fall? Yes, that would not be possible in flat spacetime.

 

[PeterDonis]

The 2 rings have mass so there isn't null stress energy anywhere.

This is a quibble. You can assume that the rings have negligible stress-energy. We do this all the time when modeling ordinary objects (i.e., things that aren't galaxies, stars, or planets, or objects with similarly huge masses).

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.

This is not correct. Where are you getting this from?

 

[puzzled fish]

This is a quibble. You can assume that the rings have negligible stress-energy. We do this all the time when modeling ordinary objects (i.e., things that aren't galaxies, stars, or planets, or objects with similarly huge masses).
This is not correct. Where are you getting this from?

Peter, I do not know what the OP means by two spinning disks in an empty universe. Are they the one inside the other? Are they separated and spinning as we view the distant galaxies spinning? Since he mentioned Mach, I assume he means something like two persons tied together with a piece of string, in an empty universe, and one is spinning around the other, taken to be at the center and stationary. Judged by their respective FORs, in both frames, one of them appears to be rotating whereas the other not. Yet only one of them experiences centifugal forces.
I maintain this is a completely untenable situation. Take the two persons to be stars.
1st. In the case of 2 stars rotating around their respective center of mass in an empty universe, where is the string binding them together? Only spacetime curvature and geodesics there, hence no acceleration.
2nd. You can't take the stars to have negligible mass. The two stars in an empty universe are all that there is, and they both create a well-known spacetime solution.

 

[PeterDonis]

Are they separated and spinning as we view the distant galaxies spinning?

That's what I assumed, but you're right that it would be nice to have more details from the OP.

However, that is irrelevant to point I was making when I responded to your post. You made a general claim that "you cannot have 2 isolated objects spinning". That claim is false, regardless of what the OP meant by his description.

I assume he means something like two persons tied together with a piece of string, in an empty universe, and one is spinning around the other, taken to be at the center and stationary. Judged by their respective FORs, in both frames, one of them appears to be rotating whereas the other not. Yet only one of them experiences centifugal forces.
I maintain this is a completely untenable situation.

I don't see why. This is just a version of the standard "rotating disk in flat spacetime" scenario in SR, which is perfectly valid. (And note that in this scenario, the observer that is "spinning around the other" does not have a global FOR in the usual sense.)

In any case, this scenario is not how I was interpreting the OP. And the claim you made that I responded to was much more general than the one just quoted. See above.

Take the two persons to be stars.

This is a completely different scenario, in which, as you note, spacetime is not flat. (The absence of the string in this scenario is actually a red herring. There doesn't have to be a string in the flat spacetime case either: the "spinning" observer could be using a rocket or some other self-contained means of propulsion.) There is no useful analogy between the two scenarios.

 

[PAllen]

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?

No, you can define an SR cosmology that has most of first order features of observed cosmology:

1) A flow of inertial bodies each of which sees isotriopic red shift of the others as a function of distance.
2) Superluminal recession rates as this is defined by cosmologists.

However, all of the quantitative relationships required by such flat spacetime model do not match observation. But if the total energy density of the universe were several orders of magnitude less than our universe, the SR model would be quite accurate as to red shifts and distance.

[edit: from seeing Peter's earlier response, some further technical clarification is needed. The flat spacetime model is maximally hyperbolic for the case zero cosmological constant. This, per cosmological terminology, is sometimes described as accelerated expansion. However, another sense of accelerated expansion is positive cosmological constant. The effects of this cannot be achieved in flat spacetime.]

 

[PeterDonis]

you can define an SR cosmology that has most of first order features of observed cosmology

But it does not have the feature of accelerating expansion (due to a positive cosmological constant), as you say. So we need clarification from Mister T on exactly what he meant by "this state of affairs" (I had assumed he meant accelerating expansion due to a positive cosmological constant).

 

[Buckethead]

With regard to the two rings, my scenario was not the rings orbiting each other (if there is such a thing in this scenario) but rather that their angular velocities were different and also they are (if they can be) just test objects so the stress-energy might be ignored.

(edit) It also just occurred to me that this scenario might be considered identical a scenario where one ring is orbiting the other with the orbiting ring in lock sync. The ring at the center of this orbit would be the one that is rotating relative to the line that connects the two objects. Or if you chose the ring that is rotating relative to the connecting line and have that orbit instead, then there would be no lock sync and that ring would just be spinning faster (or slower if spinning in the same direction as the orbit). In both cases however it seems neither gravity or a connecting string is necessary to maintain the orbit. In all 3 cases, if there are no forces on the objects then there must be no spacetime either.

 

[puzzled fish]

I don't see why. This is just a version of the standard "rotating disk in flat spacetime" scenario in SR, which is perfectly valid. (And note that in this scenario, the observer that is "spinning around the other" does not have a global FOR in the usual sense.)

No. Rotating disk affects space-time geometry and I do not think is good for such a simple example.
I still maintain that the example I've given above is valid, even for two very small massive objects rotating around their center of mass. Ok, you can fix one of them if you like and rotate the other like one mass on a disk rotates around another one at its center. Then I can find an angular velocity (no matter how small) for which there is no force measured for both. The one because is not rotating (if you like) and the other because it matches the gravitational force between them (no matter how small.) Of course this is attributed to ever so small spacetime curvature there. So, where's Mach's principle there? Still, I see no forces.

 

[PeterDonis]

Rotating disk affects space-time geometry

Not if we idealize it as having negligible stress-energy. That is the standard procedure in the SR model I referred to.

I still maintain that the example I've given above is valid

Can you give a reference for the specific solution of the Einstein Field Equation you are using for that example?

 

[Herman Trivilino]

But it does not have the feature of accelerating expansion (due to a positive cosmological constant), as you say. So we need clarification from Mister T on exactly what he meant by "this state of affairs" (I had assumed he meant accelerating expansion due to a positive cosmological constant).

I did mean accelerating expansion. Can we have an accelerating expansion, but have each galaxy experience a zero proper acceleration, in a flat spacetime.

 

[PeterDonis]

a scenario where one ring is orbiting the other with the orbiting ring in lock sync

Do you mean that the ring at the center has sufficient gravity to keep the other ring in orbit?

In both cases however it seems neither gravity or a connecting string is necessary to maintain the orbit.

I have no idea how this could be the case. Where are you getting this from?

In all 3 cases, if there are no forces on the objects then there must be no spacetime either.

I don't think your scenarios here are physically valid. Again, where are you getting this from?

 

[PAllen]

I did mean accelerating expansion. Can we have an accelerating expansion, but have each galaxy experience a zero proper acceleration, in a flat spacetime.

I think the most common meaning of accelerated expansion is that the function a(t) in the FLRW metric grows faster than a linear function. With that definition, it is not possible for this to occur in a flat spacetime cosmology (in such a cosmology, a(t) must be exactly linear). And by 'cosmology' I mean an isotropically expanding inertial congruence.

[edit: Let me make a few more points here. A flat spacetime cosmology requires linear a(t) and hyperbolic spatial slices of constant cosmological time. Our universe is pretty close to linear expansion (over periods not too long) with flat spatial slices of constant cosmological time. The observable difference is that our universe has much slower growth of red shift per distance defined by standard candles than would be the case for flat spacetime. This by itself establishes spacetime curvature, and this is a MUCH bigger effect than from the tiny cosmological constant. ]

 

[puzzled fish]

Not if we idealize it as having negligible stress-energy. That is the standard procedure in the SR model I referred to.
Can you give a reference for the specific solution of the Einstein Field Equation you are using for that example?

No, I am afraid I can't. I am not aware of any specific solutions to the two-body problem in GR, I am referring to, only numerical ones. The Schwarzschild solution when one of the bodies is substantially less massive than the other is a good approximation.

 

[PeterDonis]

I am not aware of any specific solutions to the two-body problem in GR, I am referring to, only numerical ones.

Ok. Then yes, you are correct that there are numerical solutions in which two bodies mutually orbit each other, and both are in free fall, feeling zero acceleration, and spacetime is curved in the region occupied by the orbits of the two bodies. (The question of vorticity is not so simple, but I don't think we need to go into it at this point.) However, those solutions are also asymptotically flat, which means there is a boundary condition at infinity that is required in order to derive the solution. That boundary condition at infinity, conceptually, represents the effect of all the other matter in the universe, on the idealized assumption that all of that matter is distributed in a spherically symmetric fashion about the isolated two-body system.

In other words, Mach's principle can be viewed as entering into this two-body solution as a boundary condition. Basically, the idea is that, if we have a region of spacetime outside of which everything is spherically symmetric, then the matter in that spherically symmetric outside region causes zero spacetime curvature in the inside region. (This is the GR version of the Newtonian shell theorem.) So we can put any isolated system we like in the inside region, and the spacetime curvature in that inside region will be solely due to that isolated system. But it also means that the spacetime geometry at the boundary of the inside region is determined by all the rest of the matter in the universe.

Of course this case is highly idealized--the matter in the actual universe is not exactly spherically symmetric about any isolated system, such as the solar system. But it turns out to be a very good approximation, which is why asymptotically flat solutions of the EFE are used so much--they are both mathematically tractable and physically reasonable for an isolated system.