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Relativity without the aether: pseudoscience? 
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#19
Sep2405, 06:10 PM

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PF Gold
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To even begin to say something like "the oneway speed of light is isotropic", it requires one to specify a coordinate chart. Coordinare charts are nonphysical choices. You're thinking about the fact that, among all possible rectilinear coordinate charts we could use, SR chooses to define the orthogonal ones as the inertial reference frames. This choice is exactly analogous to the fact that we generally like, when studying 3space, for our x, y, and z axes to be perpendicular. Special Relativity is generally done in these orthogonal, linear coordinate charts for exactly the same reason that coordinate geometry is generally done with perpendicular axes. Another good reason to use the orthogonal, linear coordinate charts is that such things can be defined experimentally. (Of course, so can other types of coordinate charts) Contrast to the choice of charts used by aether theories which invoke some principle of absolute simultaneity which cannot be experimentally determined. (Since I'm talking about "orthogonal" in the above, that means I'm using some sort of "metric". Of course, I'm using the "metric" of Minowski 4space, because that's the one that appears in all the physical laws) 


#20
Sep2405, 06:17 PM

PF Gold
P: 717

He (and you by quoting it) seems to think that local Lorentz invariance is synonymous with SR to the exclusion of LET: "Note that all phenomena discovered since 1905 do indeed exhibit the local Lorentz invariance of SR  what is happenstance in ether theory was directly predicted by SR." 


#21
Sep2405, 06:26 PM

PF Gold
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#22
Sep2405, 06:38 PM

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#23
Sep2405, 06:42 PM

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You agree that the Lorentz metric is empirically verifiable, correct? Then so must the oneway speed of light in a coordinate chart that is one of Special Relativity's inertial reference frames. (I erred slightly in my previous post  I should have said orthonormal, rather than orthogonal) Maybe this is a clue to the psychology of those who cling to aether theories? Do they believe that coordinate charts are physical things, rather than simply a choice we make when modelling a problem? 


#24
Sep2405, 07:15 PM

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Basically, using for simplicity units where c=1, the coordinate transformation t1 = [itex]t + \beta x[/itex] x1 = x y1 = y z1 = z transforms the Minkowski metric ds^2 = dt^2 dx^2  dy^2  dz^2 into a different metric ds^2 = dt1^2  2 [itex]\beta[/itex] dx1 dt1  (1  [itex]\beta^2[/itex]) dx1^2  dy1^2  dz1^2 [itex] \beta [/itex] plays the role of a velocity here and is equal to v/c, a number between zero and 1. So the isotropy of the speed of light comes from using the Minkowski coordinate chart, by using a different coordinate chart one can work in the LET coordinates where the "coordinate speed" of light is not constant. Both coordinate charts are flat in that they have a zero curvature tensor. The convention that velocities are reported in a Minkowskian metric is very common and useful, for reasons regarding momentum that have been and are being discussed in another thread (no need to repeat them here). The main "feature" of LET that I see is that people who are philosophically comitted to the Gallilean transform have a method that should theoretically enable them to work problems in relativity, in spite of their philosophical blinders. 


#25
Sep2405, 07:38 PM

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I've got a question for Aether.



#26
Sep2405, 08:37 PM

P: 76

In an arbitrary frame of reference, start with two synchronized clocks sidebyside and slowly transport one of them to any convenient distance D. When the ultraslow clock transport is finished, send a light pulse from the stationary clock at local clock time t1. Let t2 be the time when the light arrives as measured by the slowly transported clock. Take the limit of ultraslow transport in the expression D/(t2t1) for a perfect answer of c. Are you asking to be tutored in relativity or do you disbelieve the mathematics? 


#27
Sep2405, 08:58 PM

PF Gold
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#28
Sep2405, 09:03 PM

PF Gold
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#29
Sep2405, 09:24 PM

PF Gold
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#30
Sep2405, 09:29 PM

P: 76

The freedom to reset clocks in the universe with arbitrary synchronizations is widely regarded as legitimate physics. http://arxiv.org/abs/grqc/0409105 http://www.everythingimportant.org/relativity/ 


#31
Sep2405, 09:41 PM

PF Gold
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#32
Sep2405, 09:52 PM

PF Gold
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#33
Sep2405, 10:14 PM

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PF Gold
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I repeat that a coordinate chart is not a physical object. One does not need to make postulates, one can write down a precise definition and say "in my theory, the words 'inertial reference frame' absolutely, positively, unequivocally means this:". Now, one might ask the question if there is any such thing satisfying the definition, but let me remind you that even in a LET, you can take this definition to produce a coordinate chart in which the oneway speed of light is isotropic. Let me say that again: In a Lorenz Ether theory, the Special Relativistic definition of "inertial reference frame" yields a coordinate chart in which the oneway speed of light is constant. Of course, since this chart was chosen to satisfy the SR definition of "inertial reference frame" and not the LET definition of "inertial reference frame", there is no reason to expect this coordinate chart to be an LET inertial reference frame (and generally it will not be). The point stands  even in a LET, you can prove that SRinertial reference frames have a constant oneway speed of light. You focus too much on coordinates, as if they're a fundamental thing  it's the geometry that matters. Both theories let you work in whatever coordinates you like. The difference between SR and LET is that SR postulates nothing more than the geometry. Things like "inertial reference frame" are simply defined from the geometry. Whereas a LET has to make an additional postulate about absolute simultaneity: it cannot be defined from the Minowski geometry alone. Let me repeat this: Both theories postulate Minowski geometry. However, SR makes no additional postulates, defining everything else from the geometry. However, a LET requires at least one additional postulate about absolute simultaneity, since that cannot be defined from the geometry. Actually, as I understand it, LETs do not postulate Minowski geometry  they postulate some other background geometry, postulate some properties of an aether, and then derive the Minowski geometry, or alternatively, let the experimental verification of Minowski geometry constrain the properties of their aether. 


#34
Sep2405, 10:42 PM

PF Gold
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#35
Sep2405, 10:57 PM

P: 76




#36
Sep2405, 10:57 PM

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P: 8,470

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). 


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