Are Lorentz aether theory and special relativity fully equivalent? Following up on this question on whether it's possible to construct a physical theory with invariant space-time and variable speed of light.
I am looking for a authoritative and more definitive answer to the hopefully more precise question: 

Are Lorentz ether theory and special relativity fully
  compatible/interchangeable? 

Interchangeable in the sense that, at least in principle,there is either no different prediction the other doesn't make or if there is it could be settled experimentally (or has been) in favor of one of the two?
From the wikipedia page I gather that they are indistinguishable, but SR is preferred over LET either for practical reasons (elegance, convenient) or because it's assumption are somewhat less arbitrary or don't require somewhat problematic entities such as ether.
 A: 
Are Lorentz ether theory and special relativity fully compatible/interchangeable? Interchangeable in the sense that, at least in principle,there is either no different prediction the other doesn't make or if there is it could be settled experimentally (or has been) in favor of one of the two?

Special relativity (SR) uses the Lorentz transform to make all of its experimental predictions. Lorentz aether theory (LET) also uses the Lorentz transform to make all of its experimental predictions. Furthermore, the reading of a clock or a ruler would be mapped to the same variable in both and also a given reference frame would either be determined to be inertial or non-inertial for both. 
As a result, there is simply no possible way to distinguish between the two experimentally. Any result that is predicted by one is predicted by the other also. Their disagreements are entirely philosophical or metaphysical. Due to that fact it is sometimes considered that both LET and SR are simply different interpretations of the same theory (usually confusingly called SR). 
Here is a solid reference describing the experimental equivalence and the philosophical distinction between the two: 
http://philsci-archive.pitt.edu/5339/1/leszabo-lorein-preprint.pdf 
A: Lorentz ether theory describes a world in which light moves through a medium called ether, and observers that are not at rest with respect to this ether see everything Lorentz transformed. In some philosophical sense, there is a preferred reference frame: that in which the ether is at rest. 
But the funny thing about Lorentz transformations is precisely that they relate reference frames in which light moves in the same way; the speed of light does not change upon applying your favorite Lorentz transformation. For this reason, it is not possible even in principle to determine experimentally what the ether rest frame is, since even light (the stuff that the ether was invented for) moves in the same way in different inertial reference frames. 
The theory of special relativity explains all of this more naturally by postulating that all inertial reference frames are similar and that there is no ether, at least not one that sets one specific reference frame apart. One could try to argue that the electromagnetic field as found in quantum electrodynamics can be called an 'ether'; however, since the electromagnetic field does not have one specific inertial frame it likes to live in, this is mostly semantics. 
A: Ether – less Special Relativity cannot be sound alternative to Lorentz theory.
Special Relativity assumes isotropy of one – way speed of light in all relatively moving frames.This isotropy follows from Einstein synchrony convention,  that makes the one-way speed equal to the two-way speed.
Michelson - Morley experiment confirms, that in moving laboratory round trip speed of light appears to be isotropic, but this experiment says nothing about one - way speed of light. Measured isotropy of two - way speed of light in moving laboratory is due to distortion of interferometer (Lorentz - contraction). 
It should be noted, that one – way speed of light is anisotropic relatively to a rim of rotating ring (Sagnac Effect). The ring can be of arbitrarily large diameter. It is experimentally confirmed fact. Hence, speed of light is anisotropic relatively to any laboratory on the Earth surface.
The only correct answer to this question is that if we assume that the speed of light is isotropic in one reference frame (and synchronize clocks Einstein – way), it is necessarily anisotropic in the other, relatively moving one and one must employ anisotropic (Reichenbach's) synchrony convention which is also self- consistent.
My answer to this question demonstrates, that time dilation is not reciprocal and only absurd synchronization leads to reciprocal time dilation.
If you consider which theory is more elegant and simple, just keep in mind that resolution of twin paradox in frameworks of Lorentz Theory and the ether – less Special Relativity demonstrates ugliness of the latter. Resolution of the Twin paradox in Lorentz Theory fits into one page, while raving fans of ether – less relativity still put forward hypotheses, each his own one.
The same goes to Bell’s spaceship paradox. Explanation why the thread breaks (or spaceships scatter from each other) is very simple in the framework of Lorentz theory.
Champeney and Moon time dilation test demonstrates absence of reciprocal time dilation for two observers that are placed on opposite sides of rotating ring. It is clear why – because their clocks dilate at the same magnitude and this dilation chancel each other. Neither rotating observers, nor purely inertial ones that coincide with rotating at the moment of measurement would not measure any reciprocal time dilation ( See fig. 4 in this article)  
Minkowski formalism cannot be sound alterative to the Ether; it simply turns simple things into complex ones:  it’s just a matter of time when this annoying concept will just be dumped, I believe that the following comment here  indicates that this moment is getting closer:
‚@Dale If one fills all space time with particle fields on which operators work, and posits that this is the underlying reality, as most theoretically inclined people do, what is it but a reemergence of an aether? It just fulfills the function of an aether, for signals, in this case particles.‘
A: It seems to me that an experimental distinction between SR and LR was discovered and articulated 50 years ago by Hafefe and Keating.
They could NOT use SR to predict their experimental results.  They could only use a theory which, like LR, posited a preferred frame (which is strictly forbidden by SR).
The LR theory pre (post) dicted the actual clock differences which occurred.  Again, SR could not do so.
This is explained in one of the footnotes to their paper, which references Builder, the physicist.  As you may know, Builder is the physicist who did an extensive analysis of SR in 1957 in a paper entitled "Ether and Relativity."  He concluded that "The observable effects of absolute accelerations and of absolute velocities must be ascribed to interaction of bodies and physical systems with some absolute inertial system....There is no alternative to the ether hypothesis."
The preferred frame used by Hafefe and Keating was the ECI, as is also used as a preferred frame of reference by the GPS. As with the H-K experiment, special relativity CANNOT be used by the GPS as a theoretical basis for predictions.  Like it or not, it must employ a neo-lorentzian theory to obtain reliable results.
The ultimate test of one competing theory against another is the predictive ability of each.  Philosophical maxims, like Occam's razor, cannot be determinative.  When one theory gives you correct predictions pertaining to empirical phenomena, and the other doesn't, that's the ballgame, right there.
A: In the context of theories of relative motion, the word "ether" simply refers to a "truly" motionless frame of reference.
For decades, astrophyicists and cosmologists have used the CMB as a preferred frame of reference (i.e., a so-called "ether").
George Smoots (and his team) received a Nobel Prize in Physics for his extensive experimentation (over a course of many years) showing the the CMB is indeed what has been called "the rest frame of the universe."  So, here again, an  experimental differentiation of SR from LR has been established.
Here's an excerpt from Smoots' paper on the topic:
"We attribute the dipole anisotropy to the motion of the Earth and Solar System relative to the universal CMB radiation field and thus the distant matter in the Universe. This would seem to violate the postulates of Galilean and Special Relativity but there is a preferred frame in which the expansion of the Universe looks most simple. That frame is the average rest frame of the matter and CMB and from that frame the expansion is essentially isotropic."   https://aether.lbl.gov/www/projects/u2/
Smoot is effectively referring to absolute, not relative, motion here.  Without at least the tacit assumption of a bona fide rest frame ("ether") physics would be impossible.
A: In my prior answer, referring to the analysis of Hafele and Keating regarding their famous "clocks on jets" experiments, I said:  "They could NOT use SR to predict their experimental results. They could only use a theory which, like LR, posited a preferred frame (which is strictly forbidden by SR)."
This post was met with dismissive, hand-waving denial by some members.  I'm not convinced that those posters read (or remembered) the analysis in question, however.  For that reason I am elaborating on the basis of the statement made in my original answer.
Here is a link to a blog post offered a physicist, identity unknown to me, which discussed this issue in some depth.  http://www.conspiracyoflight.com/Hafele/HafeleKeating.html  Here are a few relevant quotes from that submission:
"Hafele, Keating and Builder make some categorically un-relativistic statements, namely:

*

*Inertial motion can only be referenced to the physically privileged frame of the “universe” which is an absolute inertial system.


*The “absolute velocities” must mean motion with respect to this absolute frame of reference.


*There is no alternative to the ether hypothesis....
The Hafele and Keating experiment implies that the earth’s pole, or more perfectly, the fixed stars,* compose the only frame where Einstein synchronization doesn’t break down...
Only if the clocks are synchronized to the Earth Centered Inertial (ECI) frame of reference (i.e. the pole of the earth) do these inconsistencies become manageable.
However, this is tantamount to establishing the ECI frame as a preferred reference frame for motion above all others. [emphasis added]
Although the Hafele and Keating experiment did confirm the gravitational time dilation effect on clocks predicted by Einstein, the velocity time dilation predictions of special relativity (1905) at low velocities would seem to have been proven wrong...
The Sagnac term [employed by H & K] is at odds with a fundamental tenet of relativity theory by requiring an absolute frame of reference for both rotational and inertial motion, defining the latter as relative to a non-rotating universal
frame...
If an argument is going to be made that a speed of light test is invalid because the frame is rotating, or the observer is rotating, then we have to discard all speed of light tests to date since every place that humans have performed a test on the earth or in near space have always been experiencing some form of rotation, either diurnal or orbital, which in modern times has become readily visible.  As Hafele and Keating say in their paper, inertial motion must be referenced to a universal reference frame.
[Allan, Weiss and Ashby] said that the principle of the constancy of the speed of light leads to a prediction of the Sagnac effect in rotating systems; this is an interesting comment since the constant speed of light in their example is in the non-rotating frame of reference - i.e. the frame of the fixed stars just as in Fig. 4 above.  This underlines the extent to which "relativistic" has become interchangeable with "absolute."
===end of quotes====
As you can see for yourselves, this author claims that the additional equations created by H & K operate to disconfirm 5 specific predictions of SR as presented by Einstein (without a "sagnac factor").
The original question was:  "Are Lorentz ether theory and special relativity fully compatible/interchangeable?"  Again this author comments that "This underlines the extent to which "relativistic" has become interchangeable with "absolute."
So I guess the question cannot really be properly addressed unless people agree on what conceptual differences exist, if any, between Lorentzian Relativiy and Special Relativity.
From my experience, there appears to be a substantial disagreement about that.  Many have assured me that the the H-K experiment "confirms" SR.  On the only hand the experimenters themselves (H & K) seem to undermine that claim.  Some seem to think that if the lorentzian transformations are employed, then the theory being employed is "special relativity," but clearly that does not necessarily follow.
A: No. Such equivalence is inconsistent with Galilean principle:  inertial observers are equivalent, and there's no physical processes lest you difference between beying at rest or moving with constant speed.
