- #36

JesseM

Science Advisor

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JesseM said:The points in his article would apply to any theory that posits a special reference frame (for example, a theory that says there is only one frame where the speed of light is 'really' c in all directions) and yet does not make any predictions about the results of actual experiments which are different from those of SR (so all observers will measure the speed of light to be c in all directions, even if this is explained as a faulty measurement because their clocks are not ticking the 'correct' time and their rulers are not reading the 'correct' length).

Well, think of it this way. Suppose we live in a universe governed by purely Newtonian laws, where light always moves at speed c with respect to the rest frame of the aether, and in other frames it is actually possible to measure your velocity relative to the aether by seeing how fast light moves in one direction vs. the other using ordinary rulers and clocks, just like in our actual universe we could measure our velocity relative to the atmosphere by measuring how fast sound waves move in one direction vs. the other. In this hypothetical universe we have two observers, A who is at rest with respect to the aether, and B who is moving at velocity v with respect to the aether. We give both of them a set of rulers and clocks which they use to define their own coordinate systems, but as a joke, observer B is given special gag rulers that are shorter than normal by a factor of [tex]\sqrt{1 - v^2/c^2}[/tex], and gag clocks whose ticks are longer than normal by a factor of [tex]1/\sqrt{1 - v^2/c^2}[/tex]. What's more, we tell observer B thatAether said:I'm not sure what you mean by the statement in parenthesis.

*he*is the one at rest with respect to the aether, so that he can synchronize his clocks using the assumption that light travels at the same speed in both directions relative to himself. The result will be that the coordinate systems of observer A and observer B will be related by the Lorentz transformation equation, no? And that both will measure light to move at c in all directions relative to themselves, using their own rulers and clocks? But isn't it true that in this universe, observer A's frame is the only one where light "really" moves at c in both directions, while B's measurement was faulty because his clocks are not ticking the "correct" time and their rulers are not reading the "correct" length?

Along the same lines, a believer in the Aether could believe that the real situation is pretty close to this, except that instead of having to give any observer rulers and clocks which we know to work incorrectly, it's just a property of the laws of nature that rulers moving at v relative to the aether will naturally shrink by [tex]\sqrt{1 - v^2/c^2}[/tex] and clocks moving at v relative to the aether will naturally have their ticks extended by [tex]1/\sqrt{1 - v^2/c^2}[/tex]. If this was true there might be no empirical way to decide who was

*really*at rest with respect to the aether and thus whose rulers and clocks were

*really*measuring correctly, but one might believe there was some objective truth about this nonetheless (just like in some interpretations of QM, there is an objective truth about the simultaneous position and momentum of every particle even if there is no way to measure this empirically).

JesseM said:I don't know exactly what you mean by "LET", does it fit both these criteria?

OK, but as Hurkyl says, the choice of coordinate systems is just a convention, simply choosing a different coordinate system does not give you a different theory of physics. I had assumed that LET involved some hypothesis about there being a particular frame which is actually the rest frame of the aether, and that rulers moving relative to this frame shrink and clocks slow down, even if it cannot be determined experimentally which frame this is. Was I misunderstanding?Aether said:I am using "LET" as a label the ether transformation equations from M&S-I (see my post #92 in the "consistency of the speed of light" thread for details); this may not be exactly what anyone else, particularly H.A. Lorentz, means by LET.

JesseM said:That quote doesn't say that aether theories don't exhibit local Lorentz-invariance, it just says that it is an unexplained "happenstance" if they do. In aether theories you need a multitude of separate coincidences to explain why every new phenomena happens to exhibit lorentz-invariance, and you have no reason to predict that new phenomena will exhibit it, whereas SR makes a clear prediction that all phenomena must exhibit local lorentz-invariance, and gives a single conceptual explanation for why they all do.

Again, simply choosing a different coordinate system does not give you a different theory; without some physical assumption about there being a particular frame that is "objectively" special in some way (because it is the rest frame of the aether, perhaps), this is just the theory of SR described in terms of a different choice of coordinates.Aether said:Is this how you would explain the essential differences between the SR and LET transformation equations (from post #92 referenced above)? It seems like a very simple choice of synchronization convention to me when I compare those two sets of equations.