Do SR and LET differ in a toy model? Rotating composite rotor

[AlexOsipovich]

TL;DR

I am currently studying the conceptual differences between Special Relativity (SR) and the historical Lorentz Ether Theory (LET) by working through a simple toy model. This is purely a conceptual exercise to understand where the mechanical interpretation of LET breaks down.

(This is not an attempt to promote or resuscitate the ether.)
I am working through a conceptual exercise about the historical Lorentz ether theory (LET), and I would like to check my understanding of its internal logic. I am not proposing a new theory. I am trying to see whether a literal reading of LET — where Lorentz contraction is treated as a real physical deformation of electromagnetic bonds — leads to any inconsistency when applied to a rotating heterogeneous body.

The setup is simple:

A rotor moves with the laboratory at some velocity relative to a hypothetical ether (say, the lab moves along the X-axis, so the ether wind is along X).

In LET, the rotor is contracted along X due to the anisotropy of the physical speed of light.

We then start rotating the rotor.

After a 90-degree rotation, the rotor presents a different orientation to the ether wind: it was compressed along its own X-axis, and now it should be compressed along its own Y-axis.

The "signal" for this re-compression travels at the speed of light, but the atoms are massive and cannot rearrange their positions at that speed.

If the rotor were monolithic, the re-compression would presumably occur without heat generation (the material simply relaxes to a new equilibrium). But in a composite rotor — a stiff frame plus a viscoelastic polymer — the two phases have different elastic moduli and different relaxation times. The polymer would respond differently to the changing equilibrium deformation, leading to a non-uniform stress distribution. The viscoelastic polymer might then dissipate energy as it lags behind the faster-responding stiff frame.

My question: within the mechanistic interpretation of LET (where contraction is a real deformation), should heat be generated in such a composite rotor? Or is there an argument why, even in that picture, no net dissipation should occur?

I am not claiming any such effect. I suspect there is a known reason why this toy exercise fails, and I would like to find the error or the relevant literature.

I can provide simple estimates if useful, but I have intentionally omitted experimental details because this is a conceptual/historical question. Any pointers to the relevant physics of viscoelastic composites or to historical discussions of LET would be appreciated.

 

[Ibix]

As far as I'm aware LET is simply SR plus an undetectable choice of ether rest frame. Thus the answer to your question is that mechanical properties vary depending on speed relative to the ether in the same way the mechanical properties of materials can be seen as varying with velocity relative to your choice of inertial frame in SR. You won't get any differential compression because the compression depends only on velocity relative to the ether frame, not material type.

 

[AlexOsipovich]

As far as I'm aware LET is simply SR plus an undetectable choice of ether rest frame. Thus the answer to your question is that mechanical properties vary depending on speed relative to the ether in the same way the mechanical properties of materials can be seen as varying with velocity relative to your choice of inertial frame in SR. You won't get any differential compression because the compression depends only on velocity relative to the ether frame, not material type.

Thanks for the response. You are absolutely right that from an empirical standpoint, LET is just SR plus an undetectable ether frame. If we only look at the final equilibrium state, the kinematics are identical, and we won't see any differential compression.

However, I want to dig specifically into the dynamical interpretation of LET, which was Lorentz's original idea.

As far as I'm in this mechanical picture it is a real physical process of electromagnetic bonds adjusting to the new equilibrium state.

If we view the system from the ether rest frame (where the lab and the rotor are moving at 370 km/s), the rotor is physically contracted along the axis of motion. When the rotor spins (say, with an edge speed of 600 m/s), its material axes are continuously rotating relative to the ether wind. This means the equilibrium shape of the rotor in the ether frame is continuously changing.

In SR, this is just a kinematic projection. But in a dynamical LET, this is a real physical re-compression of the material. Since the atoms are massive and electromagnetic forces propagate at a finite speed, the material cannot adjust instantaneously. There must be some relaxation time.

So my question is precisely about this relaxation process. If the equilibrium state is changing continuously at ~191 Hz, and the material is a heterogeneous composite with different elastic moduli, shouldn't the lag in the material's response lead to internal stresses and viscoelastic dissipation?

 

[Ibix]

So my question is precisely about this relaxation process. If the equilibrium state is changing continuously at ~191 Hz, and the material is a heterogeneous composite with different elastic moduli, shouldn't the lag in the material's response lead to internal stresses and viscoelastic dissipation?

If it's going to reproduce SR, then no. Whatever the deformation process, it can only depend on velocity relative to the ether frame. If it depends on anything else then you're talking about some mechanical ether theory that's inconsistent with relativity. I have no idea if anyone ever developed one of those well enough to test.

Note that assumptions like "electromagnetic forces propagate at finite speed" may not apply, or at least not simply, in such a model, since that's a consequence of EM being a relativistic field theory. You'd need to think about how to build EM in a mechanical ether theory so that you reproduce Maxwell's equations in the contracted frames.

 

[Dale]

The viscoelastic polymer might then dissipate energy
… is there an argument why, even in that picture, no net dissipation should occur?

The Lorentzian strain is stress-free. So there is no energy to dissipate. Work is force times distance, the force is 0 so the work is 0 regardless of the distance.

 

[AlexOsipovich]

If it's going to reproduce SR, then no. Whatever the deformation process, it can only depend on velocity relative to the ether frame. If it depends on anything else then you're talking about some mechanical ether theory that's inconsistent with relativity. I have no idea if anyone ever developed one of those well enough to test.

Note that assumptions like "electromagnetic forces propagate at finite speed" may not apply, or at least not simply, in such a model, since that's a consequence of EM being a relativistic field theory. You'd need to think about how to build EM in a mechanical ether theory so that you reproduce Maxwell's equations in the contracted frames.

I fully accept your point: if we demand exact empirical equivalence with SR, there is no heating. My goal is not to build a new theory, but to explore the internal consistency of Lorentz's dynamical interpretation (LET).

To be precise about the model I have in mind: I am not referring to a mechanical ether with elastic properties. In Lorentz's mature theory, the ether was explicitly deprived of all mechanical properties—it was a purely electromagnetic medium. The contraction of the rotor is therefore not caused by a "mechanical pressure" from an ether wind. It is a consequence of the anisotropy of the physical speed of light in a system moving relative to this electromagnetic ether. The rotor simply adjusts to the new equilibrium configuration dictated by the field.

As far as I'm aware, Maxwell's equations were originally formulated as valid only in the frame at rest with respect to the ether (which is exactly why Michelson and Morley designed their experiment).

Imagine a rotating body: the orientation of the material axes relative to the ether rest frame is continuously changing at a high frequency (e.g., ~191 Hz for a spinning rotor).

This brings me to my core question: how rapidly can massive atoms physically adjust to these constantly changing anisotropy conditions? If the equilibrium state requires a finite relaxation time to adjust to the new field configuration, and if different materials (like a stiff carbon frame vs. a viscoelastic polymer) have different elastic moduli and relaxation times, wouldn't this mechanical lag inherently lead to viscoelastic dissipation?

 

[AlexOsipovich]

The Lorentzian strain is stress-free. So there is no energy to dissipate. Work is force times distance, the force is 0 so the work is 0 regardless of the distance.

This is a fair point, and it highlights exactly the part I am struggling with. I completely agree that the final equilibrium state is stress-free. If the atoms magically and instantaneously adopt the new configuration, then indeed, no work is done, and there is no dissipation.

But my question is about the dynamics of the transition.

Work is force times distance over time. When the rotor rotates, the equilibrium configuration (the shape of the "stress-free" ellipse) is continuously rotating relative to the material. If the atoms are massive, they cannot adjust instantaneously. For a brief moment, the actual positions of the atoms will not match the new "stress-free" equilibrium positions.

During this transient period, there must be internal forces trying to pull the atoms into the new equilibrium. If the material is viscoelastic, these transient forces will do work and dissipate energy. The fact that the final state is stress-free doesn't mean the path to that state is frictionless.

You mentioned that the force is zero, so the work is zero. Could you elaborate on the mathematics of this? Specifically, how is it mathematically guaranteed that massive atoms instantly conform to a continuously rotating stress-free equilibrium without any transient forces (lag) arising?

If I write the equations of motion (Newton's laws or the Navier-Cauchy equations) for a point inside this rotor in the ether frame, where does the instantaneous adjustment come from? Does Lorentz's model implicitly assume that the speed of sound (or the relaxation rate) in the material is infinite?

 

[Dale]

@AlexOsipovich please don't use AI. If I wanted to have a conversation with an AI then I would log in to ChatGPT directly, not PhysicsForums

There is no stress at any time due to the Lorentzian strains. If you are imagining otherwise then you are not doing LET, you are doing some other theory.

 

[AlexOsipovich]

@AlexOsipovich please don't use AI. If I wanted to have a conversation with an AI then I would log in to ChatGPT directly, not PhysicsForums

I don't use AI; I'm just from Belarus, so apologies for my English.

 

[Dale]

I would rather have a conversation with a real person from Belarus with broken English than to have a conversation with an AI with smooth English. Just be yourself.

There is no delay, no relaxation, and no stress for the Lorentzian part of the strain at any time. As the object moves the real forces bring each piece into the proper location automatically. There is no deviation from the equilibrium configuration at any time.

 

[Dale]

What you seem to be missing is that in the motion you describe there are real forces. Those real forces are sufficient to explain the motion entirely. There is no additional deviation or relaxation.

In LET Newton's 2nd law is not $\vec F = m \vec a$ but $$\gamma \vec F = m \left( \gamma^2 \vec a + \gamma^4 \frac{\vec a \cdot \vec v}{c^2} \vec v \right)$$
This law brings each piece into place at the right time with no delay and no additional Lorentzian stress. This is how the equilibrium you mention above is always maintained. Following this law there is never any relaxation needed because there is never any deviation from the equilibrium state.

 

[AlexOsipovich]

I would rather have a conversation with a real person from Belarus with broken English than to have a conversation with an AI with smooth English. Just be yourself.

There is no delay, no relaxation, and no stress for the Lorentzian part of the strain at any time. As the object moves the real forces bring each piece into the proper location automatically. There is no deviation from the equilibrium configuration at any time.

Could you please explain the physical mechanism behind this?

If the equilibrium trajectory of the atoms becomes an ellipse rather than a circle, how do the massive atoms physically adjust to this new path? How fast can they do this "automatically"?

 

[Dale]

Could you please explain the physical mechanism behind this?

In LET Newton's 2nd law is not $\vec F = m \vec a$ but $$\gamma \vec F = m \left( \gamma^2 \vec a + \gamma^4 \frac{\vec a \cdot \vec v}{c^2} \vec v \right)$$

If the equilibrium trajectory of the atoms becomes an ellipse rather than a circle, how do the massive atoms physically adjust to this new path?

There is no new path to adjust to. There is only the path that they take under the above force law. They are always on that path and never physically adjust to it because they never go away from it.

 

[AlexOsipovich]

What you seem to be missing is that in the motion you describe there are real forces. Those real forces are sufficient to explain the motion entirely. There is no additional deviation or relaxation.

In LET Newton's 2nd law is not $\vec F = m \vec a$ but $$\gamma \vec F = m \left( \gamma^2 \vec a + \gamma^4 \frac{\vec a \cdot \vec v}{c^2} \vec v \right)$$
This law brings each piece into place at the right time with no delay and no additional Lorentzian stress. This is how the equilibrium you mention above is always maintained. Following this law there is never any relaxation needed because there is never any deviation from the equilibrium state.

Thanks for the clarifications. The equation you wrote is the equation of motion for a single particle under an external force. But in our toy model, the rotor is spinning by inertia.

The shape is maintained solely by the internal electromagnetic forces between the atoms. Since these internal forces propagate at finite speed c (as you noted earlier), they cannot instantaneously enforce the "proper location" for massive atoms.

 

[Dale]

The equation you wrote is the equation of motion for a single particle under an external force. But in our toy model, the rotor is spinning by inertia.

Every particle in the rotor is subject to an external force from the rest of the rotor.

The shape is maintained solely by the internal electromagnetic forces between the atoms.

Yes. Those are the $\vec F$ in the equation above.

Since these internal forces propagate at finite speed c (as you noted earlier), they cannot instantaneously enforce the "proper location" for massive atoms.

Nothing instantaneous is needed. They simply follow the above equation of motion over time to arrive in the location where they should be. The "proper location" is the only location where they are ever located.

 

[PeterDonis]

The shape is maintained solely by the internal electromagnetic forces between the atoms.

Yes.

these internal forces propagate at finite speed c

If the system is stationary (in the final state, rotating with constant angular velocity), nothing has to propagate.

If the system is not stationary, i.e., during the transition from non-rotating to the final rotating state, the force felt by each individual atom--the $\vec{F}$ that appears in @Dale's equation of motion--will indeed not be the same as the "equilibrium" force, because the system is not (yet) in equilibrium. And as a result of that, the shape of the object will change during the transition. It will not be the same as either the original non-rotating shape, or the final equilibrium shape when the rotation is constant.

Note also that, assuming the object had zero internal stress at the start, when it was not rotating, then it will not have zero internal stress when it is in its final rotating state. Even the rotating equilibrium state is not stress-free. It is simply a state in which the internal stresses are just right to produce the equilibrium trajectories of the atoms, so that when each atom follows @Dale's equation of motion, they remain in their equilibrium relative positions.

During this transient period, there must be internal forces trying to pull the atoms into the new equilibrium. If the material is viscoelastic, these transient forces will do work and dissipate energy.

You have it backwards. Work has to be done on the object to spin it up: energy has to be added to it from the outside. Dissipation means that some of that applied energy goes into heat instead of mechanical work, so once the object reaches its final rotating state, it will be at a higher temperature than it was before. But that is a minor effect can be ignored in an idealized thought experiment.