Differences in Predictions between SR and LR?

[alexandrinushka]

TL;DR Summary

I am confused. I see it written that standard SR and Lorentz type theories with a preferred frame are equivalent, but...

SR interpreted as having no absolute frame of reference and an absolute frame type version of SR, where the speed of light is isotropic only in one undetectable frame are considered equivalent, since they use the same math.
But here is a scenario in which I don't see how the physical predictions could be the same. What am I getting wrong? How are the below scenarios equivalent?
1. Standard SR. A sphere is rotating at a very fast angular velocity (hypothetical scenario). An observer in the same frame who is not rotating will see it as shrunk. But it will keep its spherical form.
2. Non-standard SR (call it LR) with light speed being isotropic only in one absolute frame. The sphere rotates at angular velocity w. It is not located in the absolute frame, so some parts will have the speed v + w, others v - w. Thus, the sphere will have an egg shape, because the part moving at speed v + w momentarily will contract more than the one with v - w (iff we take the degree of contraction to be proportional to the speed, as Lorentz did).

Therefore, in a world where an alternative interpretation to that of Einstein is adopted the fast moving spheres will be seen egg-shaped in any frame other than the absolute one.

Couldn't not seeing such eggs be a proof of standard SR, excluding any absolute frame?

If SR and LR are not distinguishable even in principle, how is this possible?

Thanks.

 

[malawi_glenn]

I see it written

where?

 

[alexandrinushka]

where?

Experiments that attempt to directly probe the one-way speed of light independent of synchronization have been proposed, but none have succeeded in doing so.[3] Those experiments directly establish that synchronization with slow clock-transport is equivalent to Einstein synchronization, which is an important feature of special relativity. However, those experiments cannot directly establish the isotropy of the one-way speed of light since it has been shown that slow clock-transport, the laws of motion, and the way inertial reference frames are defined already involve the assumption of isotropic one-way speeds and thus, are equally conventional.[4] In general, it was shown that these experiments are consistent with anisotropic one-way light speed as long as the two-way light speed is isotropic.[1][5]

https://en.m.wikipedia.org/wiki/One...ce 1983 the metre has,in 1⁄299,792,458 second.
Also in the FAQ of Physics Forums:
https://www.physicsforums.com/insights/pfs-policy-on-lorentz-ether-theory-and-block-universe/

 

[Ibix]

In a Lorentz ether model the sphere will indeed be contracted in its direction of motion in the absolute frame. So will any device moving with the sphere with which you might try to measure its diameter, and that affects their function. The result is that the sphere is always measured to be spherical (or at least circularly symmetric about its rotation axis, given that stresses will probably render it oblate) by devices moving at the same speed as it.

 

[alexandrinushka]

In a Lorentz ether model the sphere will indeed be contracted in its direction of motion in the absolute frame. So will any device moving with the sphere with which you might try to measure its diameter, and that affects their function. The result is that the sphere is always measured to be spherical (or at least circularly symmetric about its rotation axis, given that stresses will probably render it oblate) by devices moving at the same speed as it.

Thanks a lot @Ibix
The device will be contracted indeed. It us moving at speed v compared to the "absolute frame". But won't it measure the sphere as contracted in the part moving at v + w and dilated at the part moving at v - w? If not, can you please explain why? Sorry, I don't understand...
Thanks a lot again.

 

[Dale]

A sphere is rotating at a very fast angular velocity (hypothetical scenario). An observer in the same frame who is not rotating will see it as shrunk. But it will keep its spherical form.

Your analysis is already wrong here at the first point. Generally it will get larger and turn into an oblate spheroid shape due to material stresses. Determining the shape of a material body that starts as a non-rotating sphere and then starts rotating is somewhat complicated. You are better off to not make any statements about the non-rotating size or shape and simply assert the rotating geometry that you want.

some parts will have the speed v + w, others v - w.

This math doesn’t work even in non-relativistic physics. You need to actually work through the real math to make a real prediction. Once you do so you will inevitably get the same result since both use the same math.

 

[Ibix]

But won't it measure the sphere as contracted in the part moving at v + w and dilated at the part moving at v - w? If not, can you please explain why?

Lorentz ether theory has the same clock synchronisation complexities vanilla SR has. From the "absolute" frame there is a different time difference between the position measurements of leading and trailing ends of the ##v\pm\omega r## parts of the sphere. This exactly cancels the difference in the length contractions so the frame comoving with the sphere sees the same length contraction of both.

 

[Halc]

Thanks a lot @Ibix
But won't it measure the sphere as contracted in the part moving at v + w and dilated at the part moving at v - w?

It does contract more on one side than the other, but this renders the object eliptical shaped, not egg shaped, same as a non-rotating circle at high velocity. Here's an image that illustrates it

This is essentially a wheel rolling (at v, more than half light speed) on a stationary surface. The bottom isn't moving at all, but top is barely moving faster than v. The shape of the wheel is an ellipse.
Viewed in its own frame, the same wheel is circular and has straight spokes, and its physical circumference (measured by a tape measure rotating with it) is considerably greater than 2πR but is contracted down to 2πR due to its speed. The wheel cannot be stopped without stretching or breaking its spokes.

 

[Ibix]

It does contract more on one side than the other

I think @alexandrinushka is asking about the view from the rest frame of the wheel/sphere, whereas you are talking about the frame where the wheel/sphere is moving.

 

[alexandrinushka]

Lorentz ether theory has the same clock synchronisation complexities vanilla SR has. From the "absolute" frame there is a different time difference between the position measurements of leading and trailing ends of the ##v\pm\omega r## parts of the sphere. This exactly cancels the difference in the length contractions so the frame comoving with the sphere sees the same length contraction of both.

Yes, I think you got the exact scenario, which I am not really managing to explain very well.
Observer A is moving at speed v compared to the supposedly absolute frame. Sphere B is also moving at the same speed and direction as A. I am supposing A and B are contracting at the same degree. Now B starts spinning. I am aware the centrifugal forces are making it larger, but let's ignore this.
Since the part of the sphere moving at the "absolute" speed v + w is contracting more than B before rotation and the part moving at "absolute" speed v - w is contracting less, I am supposing it will get an egg shape.
So... if I get you right, because of synchronization issues, observer A will still see just a diminished sphere and no egg?
Again, I do realize this cannot actually be tested, it's a hypothetical scenario.
I like your use of "vanilla SR", I think I'll adopt it.

 

[alexandrinushka]

@Dale it will be torn apart well before any relativistic effects can be observed, you are right. It was a hypothetical scenario ignoring other forces.

 

[Dale]

@Dale it will be torn apart well before any relativistic effects can be observed, you are right. It was a hypothetical scenario ignoring other forces.

It is more than that. Even if you hypothesize an "unobtainium" that is strong enough to not be torn apart, there is simply no Born rigid angular acceleration. Such motion does not exist, regardless of the material.

My recommendation is to simply describe the final state and shape of rotation, without any attempt to link it to the initial shape. Once you have specified that in one frame, then you can describe it in other frames with a Lorentz transform. That Lorentz transform is identical for LR and SR, so the resulting boosted shape will be identical in both.

 

[Ibix]

Perhaps it's easier to ask, if I see two identical rods moving in opposite directions at the same speed, but I'm moving in the Lorentz ether frame, why don't I see the rods as different lengths since they have different speeds in the ether frame. That gets rid of the complexities of spin and keeps what I think is the gist of the question.

The point is that the rods are moving, so to measure the length I need to measure the positions at the same time. If I don't, I get the length plus or minus the velocity times the time difference. But my clocks are desynchronised as viewed from the ether frame, so from that frame I'm not correctly measuring the length. And my failure will be different for each rod, in a way that exactly cancels the difference in length due to the length contraction.

This is exactly the same explanation vanilla SR gives for why moving instruments give measurements as if they were at rest. The only difference is that vanilla SR takes the principle of relativity as an assumption while in Lorentz Ether Theory it emerges from the Lorentz transforms. Don't ask me what the basic assumptions of LET are, though!

 

[alexandrinushka]

Great explanation @Ibix thanks a lot

 

[Mister T]

The only difference is that vanilla SR takes the principle of relativity as an assumption while in Lorentz Ether Theory it emerges from the Lorentz transforms. Don't ask me what the basic assumptions of LET are, though!

That light is a wave and waves must propagate through a medium in order for them to exist.

 

[Sagittarius A-Star]

My recommendation is to simply describe the final state and shape of rotation, without any attempt to link it to the initial shape. Once you have specified that in one frame, then you can describe it in other frames with a Lorentz transform.

I think it's easiest to define the shape of the rotating object in the inertial frame. If you want the define it in the rotating frame, I don't know how mathematicians would call an object with an equator, that has the distance ##R## from the rotation axis, but has a circumference, that is greater than ##2 \pi R##.

 

[PeterDonis]

I don't know how mathematicians would call an object with an equator, that has the distance ##R## from the rotation axis, but has a circumference, that is greater than ##2 \pi R##.

They would call it non-Euclidean geometry. The geometry of a rotating object in its "rotating frame" (using the quotient space construction) is already known to be non-Euclidean.

 

[Dale]

I think it's easiest to define the shape of the rotating object in the inertial frame. If you want the define it in the rotating frame, I don't know how mathematicians would call an object with an equator, that has the distance ##R## from the rotation axis, but has a circumference, that is greater than ##2 \pi R##.

There may have been some miscommunication. I was not talking about rotating vs non-rotating reference frames. I was talking about rotating vs non-rotating objects. There is no Born rigid transformation from a non-rotating object to a rotating one. Rotating reference frames are just a different way to describe the same physics, but a rotating object is physically different from a non-rotating one. And the difference is quite complicated.

So my recommendation is to start with a spherical rotating object. I don’t care what frame they use.

 

[Ibix]

That light is a wave and waves must propagate through a medium in order for them to exist.

Sure, but how you get from there to the Lorentz transforms I'm a bit hazy on. I think Maxwell built mechanical models and developed his equations based on analogies to fluid dynamics, Heaviside neatened them up into the four equations usually called Maxwell's equations these days (the wave equation falls out of them, suggestive of a medium) and Lorentz eventually deduced the transforms that keep them invariant. But there's a lot in there besides "waves need a medium". I don't know of any pithy statement of assumptions like Einstein's postulates.

 

[vanhees71]

From a modern point of view, I think the closest there is to an "aether" is the vacuum state, but this is by construction invariant under Poincare transformations, i.e., it does not (!) define in any way some "preferred frame of reference".

 

[Sagittarius A-Star]

I don't know of any pithy statement of assumptions like Einstein's postulates.

I think, an assumption of LET besides the ether was, that Maxwell's equations and the Lorentz force law are identical in all frames. Compare equation (2) with equations (9) and (10) in his 1904 paper:
https://en.wikisource.org/wiki/Electromagnetic_phenomena