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Lorentz Ether Theory (LET): Basic Ideas
The Lorentz Ether Theory (LET) is the commonly used name for the original interpretation of the theory which was originally named Lorentz-Einstein theory and is known today as Special Relativity (SR).  The spacetime interpretation of relativity, which is now the standard interpretation, was proposed by Minkowski only later.

In the Lorentz ether, there exists an absolute space as well as absolute time - these basic concepts of classical physics have not been changed.  The space is filled with an ether, which is homogeneous. static, and incompressible.  As usual in ether theories, the speed of light is simply the speed of sound waves of the ether.  

The clocks as well as the rulers are distorted if they move relative to the ether.  A clock which moves relative to the ether is time-dilated, goes slower by a factor \(\gamma = \sqrt{1-\frac{v^2}{c^2}}\).  A ruler shrinks by the same factor in the direction of movement.  As a consequence of these distortions of our measurement instruments, it becomes impossible to measure the own velocity relative to the ether. This is the consequence of Lorentz symmetry.  If an observer moves with constant velocity, he has no possibility to detect that he moves.  He can, erroneously, assume  that he is in rest, and that the distorted time measured with his clock is true time.  This error is combined with another error, namely an error identifying those events which happen at the same time.  If one is at rest, it makes sense to synchronize time with far away events using Einstein synchronization:  One sends a light signal to a mirror and back and measures the time.  Then the moment when the light ray arrives at the mirror and starts to go back will be after half of the time the light ray needs for the whole way.  If the observer moves, this idea fails, thus, one obtains a wrong synchronization if one uses this Einstein synchronization.  But above errors compensate each other nicely, so that one cannot even identify by some measurements with rulers and clocks that one has made an error assuming that one is at rest.  This is the equivalence principle.  

The mathematical formulas for all observable effects are those of Special Relativity (SR).  Once one cannot find out by measurement if one is at rest or not, and, as a consequence, it is impossible to measure true time and undistorted distances, true time becomes, together with the correct identification of contemporaneity and true distances in space, a hidden variable. Thus, the Lorentz ether is a Hidden Variable Theory.  

Let's note here the major objections against the Lorentz ether:

  1. The positivistic objection:  What really exists, should be observable.  Once we cannot distingush, by observation, if we are at absolute rest, there is no such thing as absolute rest.  Once we cannot meaure, via Einstein synchronization, the contemporaneity of events, no contemporaneity exists in reality.  All what exists is the spacetime as a whole. 
  2. The conspiracy:  To assume that clocks and rulers are somehow distorted would be unproblematic.  But that these distortions conspire in such a way that we cannot even identify if we are at rest or not seems unnatural.  
  3. Occam's razor:  The Lorentz ether has to postulate the existence of an additional element of reality, namely the preferred subdivision of spacetime into absolute space and absolute time. 
  4. The irrelevance of interpretations: Once different interpretations of SR make the same predictions about all observables, the two interpretations are equivalent empirically, as physical theories.  Therefore interpretations are irrelevant.  So, it makes no sense to discuss them, let's follow the one everybody knows, which is the spacetime interpretation.  
  5. No extension to gravity:  SR is no longer relevant, it has been replaced by GR.  For GR, we have only the spacetime interpretation.  
What are the counterarguments?  

  1. Positivism is wrong, and has to be replaced by the Popperian method. It does not contain a requirement that all objects of theories are observable.
  2. Against the conspiracy, already Lorentz has found an argument.  If the force which holds matter together is the electromagnetic force, or some other force which follows a similar equation, then the equations which describe matter, that means, also our rulers and clocks, have the same symmetry as the Maxwell equations of electromagnetism.  But these equations are Lorentz-symmetric.  Therefore, the equations describing clocks and rulers also would have to be Lorentz-symmetric.  This is already sufficient to prove time dilation and length contraction.  
  3. Occam's razor could be, as well, applied against the spacetime.  In the Lorentz ether, only space exists, filled with the ether, and what is in space changes in time. This is sufficient. There does not have to exists some four-dimensional spacetime.  So it is the Minkowski spacetime which introduces entities - a whole additional dimension - without necessity. 
  4. It appears that the two interpretations are not completely equivalent. In the spacetime interpretation, one can prove Einstein causality, and, as a consequence, Bell's inequality for space-like separated events.  The Lorentz ether allows hidden causal influences faster than light, but from past into future in true, absolute time.  This makes it impossible to proof Bell's inequality.  Given that Bell's inequality is violated, this becomes a strong argument in favor of the Lorentz ether. 
  5. An extension of the Lorentz ether interpretation to gravity exists.  It can be considered and discussed here too.  One can reasonably assume that the fact that this ether interpretation for the GR equations was unknown was a decisive argument against the ether. But this decisive argument appears invalid. 
A paper that's well worth reading is The Other Meaning of Special Relativity by Robert Close:

Einstein’s special theory of relativity postulates that the speed of light is a constant for all inertial observers. This postulate can be used to derive the Lorenz transformations relating length and time measurements by different observers. In this paper it is shown that the Lorentz transformations can be obtained for any type of wave simply by defining distance to be proportional to wave propagation time. The special nature of light is that length and time measured by light propagation correspond exactly with length and time measured by material rulers and clocks. This suggests that material objects consist of waves propagating at the speed of light. Taking this as an alternative postulate for special relativity implies constancy of the measured speed of light without any recourse to non-Euclidean geometry of physical space-time. This alternative postulate is consistent with de Broglie’s wave hypothesis, with the Dirac velocity operator of quantum mechanics, and with experimental observations of transformations between matter and light.

Note this near the end:

What has not been generally recognized is that special relativity is a consequence of the wave nature of matter and is entirely consistent with classical notions of absolute space and time.

I've attached the full version below. Since Einstein described space as the ether of general relativity in 1920 (see the Einstein digital papers), and since the CMB provides a de-facto reference frame for the universe  (see Doug Scott's web page), I'm fairly happy with the idea of Lorentz Ether Theory. particularly since spacetime is an abstract arena in which there is no motion: the block universe is static.

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