Relativity without the aether: pseudoscience?

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  • #1
Aether
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Main Question or Discussion Point

Special relativity (SR) SR and Lorentz ether theory (LET) are empirically equivalent systems for interpreting local Lorentz symmetry. These two theories are equally valid, but it is not possible (so far) to demonstrate the truth or falseness of the postulates of either theory over the other by experimentation. Still, a superstition persists in the minds of many that somehow "SR is true, and LET is false". Why isn't "relativity without the aether" fairly described by the term "pseudoscience"?


pseudoscience - Refers to any body of knowledge or practice which purports to be scientific or supported by science but which is judged by the mainstream scientific community to fail to comply with the scientific method.

scientific method n - The principles and empirical processes of discovery and demonstration considered characteristic of or necessary for scientific investigation, generally involving the observation of phenomena, the formulation of a hypothesis concerning the phenomena, experimentation to demonstrate the truth or falseness of the hypothesis, and a conclusion that validates or modifies the hypothesis.

su·per·sti·tion n An irrational belief that an object, action, or circumstance not logically related to a course of events influences its outcome.

1) A belief, practice, or rite irrationally maintained by ignorance of the laws of nature or by faith in magic or chance.

2) A fearful or abject state of mind resulting from such ignorance or irrationality.

3) Idolatry.
 

Answers and Replies

  • #2
Special relativity is physics according to the definition of physics whereas adherence to the aether is a religious belief that doesn't generate any physics.
 
  • #3
Aether
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Perspicacious said:
Special relativity is physics according to the definition of physics whereas adherence to the aether is a religious belief that doesn't generate any physics.
Lorentz symmetry, [itex]\eta_{\mu \nu}[/itex], is coordinate independent physics. Adherence to either one of SR, [itex]\Lambda_\nu^\mu[/itex], or LET, [itex]T_\nu^\mu[/itex], to the exclusion of the other is, it seems to me, a religious superstition that doesn't generate any physics (so far).
 
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  • #4
Postulating Lorentz symmetry generates a lot of physics. Taking as an axiom the existence of an aether only produces narrow-mindedness and noise on newsgroups and physics forums. If an axiom doesn't generate any quantifiable predictions, it's worthless and needs to be thrown out.
 
  • #5
Aether
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Perspicacious said:
Postulating Lorentz symmetry generates a lot of physics.
I agree, but what I am in doubt about is that one can truly appreciate Lorentz symmetry without the combined perspectives of SR & LET. Can you actually visualize Lorentz symmetry from both of these perspectives yourself?

Perspicacious said:
Taking as an axiom the existence of an aether only produces narrow-mindedness and noise on newsgroups and physics forums. If an axiom doesn't generate any quantifiable predictions, it's worthless and needs to be thrown out.
SR and LET are empirically equivalent. Name one quantifiable prediction that is generated by postulating that the speed of light is a constant in all inertial frames that is not also generated by postulating an aether.

I'm not saying that LET should replace SR (yet). I'm saying that either one without the other is a potentially misleading representation of Lorentz symmetry.
 
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  • #6
Tom Mattson
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Aether said:
Why isn't "relativity without the aether" fairly described by the term "pseudoscience"?
Because relativity is testable, and it passes every test to which it is subjected.

As for the fact that there are other theories that are empirically equivalent to SR: this situation is not unique to SR. There are also the pilot waves of Bohmian mechanics, which is empirically equivalent to QM. Should QM be considered pseudoscience? Of course not, the question is ridiculous. And it's just as ridiculous for SR.

Honestly Aether, how many threads do you need to push your agenda?
 
  • #7
Tom Mattson said:
Honestly Aether, how many threads do you need to push your agenda?
This makes four by my count...please kill this thread.
 
  • #8
The Santa Reindeer Postulate

Aether said:
SR and LET are empirically equivalent.
So what! I can create an infinite number of new theories empirically equivalent to SR.

Permit me to illustrate.

Start with SR and create a new theory SR* by adjoining to SR the postulate of Santa Claus and flying reindeer. Realize that SR and SR* are empirically equivalent if we wisely stipulate that Santa Claus and flying reindeer are undetectable. Show the physics of this and how it integrates so naturally with the Santa Reindeer postulate. Estimate the speed and distances covered by Santa Claus on Christmas night. Post a lot of hoopla about it and declare that the physics is unassailable. Also note that the theory has been peer-reviewed and is published on the Fermi National Accelerator Laboratory website.

http://www.fnal.gov/pub/ferminews/santa/
 
  • #9
Aether
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Tom Mattson said:
Honestly Aether, how many threads do you need to push your agenda?
I'm not trying to push an agenda. You have my blessing to kill this thread if you don't think that the question is a valid one. If there was a sub-forum to discuss "Lorentz symmetry" that might be a better place to raise this question, but I really am looking for answers.
 
  • #10
russ_watters
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Aether said:
SR and LET are empirically equivalent.
The fact that they are equivalent, but that one involves assumptions for which there is no evidence and the other doesn't is precisely what makes one science and the other not.

It's the invisible purple elephant postulate: I can postulate that there is an invisible purple elephant in my garage (caveat: I do not have a garage). But that postulate would not affect how we understand gravity, so it would be useless to include it in our theory of gravity.

Aether theorists do, of course, hope that eventually evidence is found that makes SR and LET not empirically equivalent, but until such evidence is found, the postulate is just a superfluous invisible purple elephant. It's a piggyback theory.

It can also not be denied that the box in which the Aether could possibly be found in has been shrinking as physics advances. It is not unreasonable to operate on the assumption that the box is empty until physicists perform an experiment that does not fit with predictions.

edit: dang, Perspicacious beat me to it with his "Santa and the flying reindeer" postulate. However, that postulate is compatible with my invisible purple elephant theory. So how 'bout we co-author a paper about a combined "Relativity and Santa and the Flying Reindeer and the Invisible Purple Elephant Theory of Gravity"?
 
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  • #11
Aether
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russ_watters said:
The fact that they are equivalent, but that one involves assumptions for which there is no evidence and the other doesn't is precisely what makes one science and the other not.
I think that both theories involve such an assumption: SR assumes that the one-way speed of light is isotropic, but this can not be proven by experiment; LET assumes absolute simultaneity, but this hasn't been proven either (yet). Why would an impartial observer, not from our culture, prefer either one of these theories (today) over the other?

russ_watters said:
It's the invisible purple elephant postulate: I can postulate that there is an invisible purple elephant in my garage (caveat: I do not have a garage). But that postulate would not affect how we understand gravity, so it would be useless to include it in our theory of gravity.

Aether theorists do, of course, hope that eventually evidence is found that makes SR and LET not empirically equivalent, but until such evidence is found, the postulate is just a superfluous invisible purple elephant. It's a piggyback theory.
Some people are under the false impression that the speed of light postulate from SR has been "proven by experiment", but that's not true. How can a preference for SR as opposed to SR+LET be a benign choice when it leads so readily to such a misunderstanding?

russ_watters said:
It can also not be denied that the box in which the Aether could possibly be found in has been shrinking as physics advances. It is not unreasonable to operate on the assumption that the box is empty until physicists perform an experiment that does not fit with predictions.
The box for violations of the rotation and boost invariance components of Lorentz symmetry is shrinking, but that still does not predict which theory (SR or LET) an impartial observer would choose (I would hope that they would either choose SR+LET, or better yet a completely coordinate independent approach). Can you visualize Lorentz symmetry from the LET perspective as well as the SR perspective? It's like starting with both eyes open, and closing your left eye, and that's one perspective; then open your left eye and close your right eye, and that's the other perspective. They are both equally valid. I'm just saying, now open both eyes.

russ_watters said:
edit: dang, Perspicacious beat me to it with his "Santa and the flying reindeer" postulate. However, that postulate is compatible with my invisible purple elephant theory. So how 'bout we co-author a paper about a combined "Relativity and Santa and the Flying Reindeer and the Invisible Purple Elephant Theory of Gravity"?
That's fine, but it would apply equally well to SR alone as it does to LET alone if you were an impartial observer. SR+LET has an advantage over either one alone.
 
  • #12
Aether said:
SR assumes that the one-way speed of light is isotropic
Forget about Einstein's tortured derivation. There's no reason to base relativity on Einstein's original presentation. There's no need to fixate on the clumsiness of anyone's baby steps.

Special relativity is best understood without the clutter of unnecessary assumptions. Having to assume anything about the one-way speed of light is absolutely unnecessary. The best derivation of special relativity available anywhere to date in terms of sheer elegance, physical intuitiveness and mathematical simplicity is given here:

http://www.everythingimportant.org/relativity/
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000043000005000434000001 [Broken]
http://arxiv.org/PS_cache/physics/pdf/0302/0302045.pdf [Broken]

Only the mathematically inept believe that Einstein discovered an admirable derivation of special relativity.
 
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  • #13
russ_watters
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One thing I've never understood is why people say that the 1-way speed of light cannot be verified by experiment. It should be simple: place two clocks a set distance apart and synchronize them (there are lots of ways to do this, but the simplest would probably be to use a 3rd clock halfway between them to set them). Then fire a laser from one to the other and measure how long it takes to get there.

It has been my understanding that physicists who accept Relativity consider such an experiment to be unnecessary, while aether theorists simply choose not to do it - perhaps because they don't want to see the result.
 
  • #14
JesseM
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If a given aether theory makes precisely the same predictions as SR, then it is not really an alternate "theory" at all, it's more akin to one of the various "interpretations" of quantum mechanics. This post from sci.physics.relativity has some good reasons for rejecting such an interpretation on the basis of "elegance" and Occam's razor:

http://groups.google.com/group/sci.physics.relativity/msg/a6f110865893d962

This is the third of three articles posted to sci.physics.relativity:
[1] Subject: Theories Equivalent to SR
[2] Subject: Why the Ether is Unobservable
[3] Subject: Why the Ether is Not Part of Modern Physics
These articles should be read in order, as a set; they do not stand
alone from each other.

In the first two articles of this series I have shown that there is an
infinite class of ether theories each of which is equivalent to SR, in
the sense that they are all experimentally indistinguishable from SR.
Why then, are these theories not given equal weight with SR in the
teaching of modern physics? Why are these ether theories, and indeed
this entire equivalence class of theories, not well known and familiar
to most physicists? What justification is there for the mainstream of
physics to completely ignore these theories which are validated by
experiments to _exactly_ the same extent as is SR?

The answer to all these questions can be summed up in a single word:
Symmetry. This article is devoted to discussing why the symmetry aspects
of SR completely overshadow all of these ether theories in modern physics.

Symmetry in SR is a rich and varied topic. The basic symmetry of SR is
Lorentz invariance, and the essence of SR is encapsulated in the
statement that the laws of physics are locally Lorentz invariant (i.e.
unchanged under the operation of any member of the Lorentz group). This
is an instance of the modern approach to symmetries: a symmetry principle
states that something remains unchanged when a specific type of operation
is performed. Note that Einstein's original two postulates for SR are
both symmetry principles.

Einstein was instrumental in bringing the importance of symmetries to
the forefront of modern physics, and SR is an excellent example of the
power of symmetry groups in determining the possible structure of
physical laws: considerations of group theory alone plus the simple
observation that pion beams exist are sufficient to derive the
equations of SR. In addition, an assumption of Lorentz symmetry and
the guess that electrodynamics is the simplest possible gauge theory
is enough to derive the Maxwell's equations. Symmetry principles are a
very powerful (nay indispensable) tool in modern theoretical physics.

And none of the ether theories contain such a symmetry as a fundamental
part of the theory (LET has an "accidental" Lorentz symmetry, but it is
not a principle of the theory). It is highly doubtful that any of the
modern theories of physics would have been discovered without the
symmetry principles of SR leading the way -- modern gauge theories are
direct descendants of the geometrical description of SR; this includes
both GR and the Standard Model. Such a geometrical description is not
possible in any ether theory (geometry is inherently coordinate
independent, but the ether is not).

There are several auxiliary reasons why the ether is not part of modern
physics. These are essentially confirmations of the basic reason due to
the lack of symmetry in ether theories -- in most cases these are direct
consequences of that lack.

1) In every viable ether theory, the ether itself is unobservable [2].
Quantum theory and the experiments related to it have repeatedly
pounded home the lesson that one must not attempt to describe things
which have not been observed or measured. This is a second powerful
argument against the believability of ether theories.

2) This unobservability of the ether frame borders on a reductio ad
absurdum in math, as the ether is assumed to be unique, but its
unobservability makes it merely one member of the equivalence class
of inertial frames -- _any_ inertial frame can be assumed to be the
ether frame without changing the predictions of any viable ether
theory. And since the ether frame is intrinsically unobservable,
assumptions and guesses are all the ether advocate has.

3) The assumption of a unique ether frame is directly analogous to the
assumption that there is a preferred frame in a Euclidean space. It
is absurd to claim that there _is_ a preferred frame in Euclidean
space but it is unobservable. But that's essentially what the viable
ether theories do.

4) In every viable ether theory one's measurement tools must change in
an unobservable manner if one is moving wrt the ether. This seems
both counterintuitive and strange -- it's as if these effects were
diabolically constructed simply to make the viable ether theories
indistinguishable from SR. As ether theories are a clear attempt to
preserve an older, seemingly "common sense" approach to physics, it
seems unreasonable to have tools change, because there is no
precedent for such behavior in our everyday lives, or in older
physical theories -- this is very much not "common sense".

5) In every viable ether theory except LET, the one-way speed of light
differs from c, but is unmeasurable. It seems strange that slow clock
transport does not give any method to measure the one-way speed of
light (such approaches always measure c, not the "true" one-way speed
of light). Indeed, _ALL_ one-way speeds are subject to this, and
rulers and clocks cannot measure the "true" one-way speed of
_anything_ in a natural way; this includes police radar guns and your
automobile on the highway; the redshifts of distant galaxies do not
correspond to their "true" velocities; etc. This is decidedly not
"common sense".

6) Ether theories require a new postulate for every new phenomenon that
is discovered, which basically states that the ether applies to it
in the same ways the ether applies to elecromagnetism. SR's symmetry
principles automatically apply to new phenomena, so SR has more
explanatory power than ether theory in this regard. 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. It seems surprising that the "gravitational ether"
has exactly the same underlying properties as the "lumeniferous
ether" and the "weak interaction ether" and the "strong interaction
ether", when these interactions differ so enormously in strength
(by a factor of more than 10^40), and differ so wildly in their
properties (e.g. gravitation and electrodynamics lack the rich
spectrum of particle and resonances characteristic of the others).
But SR naturally and correctly predicts the local Lorentz invariance
of these vastly different phenomena.

In summary, there are good reasons for the ether to be absent from modern
physics; virtually all modern physicists consider these reasons both
cogent and sufficient (at least those modern physicists who have actively
considered the issue), and no ether theory is part of modern physics.
While the viable ether theories are equivalent to SR in the sense that
they are experimentally indistinguishable, they are most definitely NOT
equivalent to SR in either mathematical elegance, explanatory power, or
suitability as a starting point for further theories. But it is these
latter properties which are most important for the basic theories of
physics.

Tom Roberts tjrobe...@lucent.com
 
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  • #15
Aether
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russ_watters said:
One thing I've never understood is why people say that the 1-way speed of light cannot be verified by experiment. It should be simple: place two clocks a set distance apart and synchronize them (there are lots of ways to do this, but the simplest would probably be to use a 3rd clock halfway between them to set them). Then fire a laser from one to the other and measure how long it takes to get there.
The experiment really is just that simple, and anyone can do it, but exactly how you synchronize the clocks is what will always determine the outcome. If we synchronize our clocks so that the speed of light is the same in both (all) directions, then that is Einstein synchronization, relative simultaneity, and SR. However, we are also perfectly free to synchronize them to maintain absolute simultaneity with an "ether" frame, and we will then measure a generally different speed of light going in every direction, and that is LET. What we can not do by experiment(yet) is to say that one synchronization scheme is better than the other.

russ_watters said:
It has been my understanding that physicists who accept Relativity consider such an experiment to be unnecessary, while aether theorists simply choose not to do it - perhaps because they don't want to see the result.
Such an experiment is unnecessary if you accept relativity on philosophical grounds, but it is not appropriate to then forget exactly how it was that you ever came to accept relativity in the first place and then go on to claim that you have done an experiment and that as a result of that experiment we are all compelled to accept relativity. Aether theorists haven't found a locally preferred frame yet, and that maintains their theory at parity (so far) with special relativity as far as experiments go.
 
  • #16
russ_watters said:
place two clocks a set distance apart and synchronize them ... aether theorists simply choose not to do it - perhaps because they don't want to see the result.
No. Actually, they like that method because of the arbitrariness of it. They will quickly point out an explicit assumption in your approach. You're going to end up assuming that light speed from A to B is equal to light speed from B to A. It's better to do an ultraslow clock transport instead.
 
  • #17
Tom Mattson
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russ_watters said:
It has been my understanding that physicists who accept Relativity consider such an experiment to be unnecessary, while aether theorists simply choose not to do it - perhaps because they don't want to see the result.
It's not considered unecessary at all. In fact it's been done!

I think that the most dramatic example is the following:

Alvaeger F.J.M. Farley, J. Kjellman and I Wallin, Physics Letters 12, 260 (1964).

Alvaeger et al measured the speed of gamma rays from decaying pions moving near light speed. The speed of the gamma rays was found to be 'c', modulo a small experimental error.
 
  • #18
JesseM
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Aether said:
Aether theorists haven't found a locally preferred frame yet, and that maintains their theory at parity (so far) with special relativity as far as experiments go.
When you say "yet", are you suggesting you see no reason why some future phenomenon might not respect local Lorentz-invariance? If so, you are underscoring point #6 from the sci.physics.relativity post by Tom Roberts I quoted in my last post:
6) Ether theories require a new postulate for every new phenomenon that
is discovered, which basically states that the ether applies to it
in the same ways the ether applies to elecromagnetism. SR's symmetry
principles automatically apply to new phenomena, so SR has more
explanatory power than ether theory in this regard. 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. It seems surprising that the "gravitational ether"
has exactly the same underlying properties as the "lumeniferous
ether" and the "weak interaction ether" and the "strong interaction
ether", when these interactions differ so enormously in strength
(by a factor of more than 10^40), and differ so wildly in their
properties (e.g. gravitation and electrodynamics lack the rich
spectrum of particle and resonances characteristic of the others).
But SR naturally and correctly predicts the local Lorentz invariance
of these vastly different phenomena.
 
  • #19
Hurkyl
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Special relativity (SR) SR and Lorentz ether theory (LET) are empirically equivalent systems for interpreting local Lorentz symmetry.
...
Still, a superstition persists in the minds of many that somehow "SR is true, and LET is false".
"True" and "false" aren't really (internally) applicable to science. What is true is that each of the postulates of SR are empirically verifiable, whereas the same cannot be said of LET.


I think that both theories involve such an assumption: SR assumes that the one-way speed of light is isotropic,
No it doesn't. :smile:

To even begin to say something like "the one-way 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 3-space, 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 4-space, because that's the one that appears in all the physical laws)
 
  • #20
Aether
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JesseM said:
When you say "yet", are you suggesting you see no reason why some future phenomenon might not respect local Lorentz-invariance?
Here's the first two lines from a paper from Kostelecky & Mewes for example: http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:hep-ph/0111026 [Broken] "Lorentz violation is a promising candidate signal for Planck-scale physics. For instance, it could arise in string theory and is a basic feature of noncommutative field theories...". So, when I say "yet" I simply mean that I am aware of many physicists who expect to find violations eventually.

JesseM said:
If so, you are underscoring point #6 from the sci.physics.relativity post by Tom Roberts I quoted in my last post:
I know that there are some good points in Tom Robert's articles, and I have read them in the past, but he's talking about a whole infinity of ether theories and I'm just talking about one; LET. So, kindly extract the point from the article that you think applies here.

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."
 
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  • #21
Aether
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Hurkyl said:
What is true is that each of the postulates of SR are empirically verifiable, whereas the same cannot be said of LET.
Let's get empirical then. Show me how the constancy of the one-way speed of light is empirically verifiable; the round-trip speed of light is constant in both theories.

Hurkyl said:
(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 4-space, because that's the one that appears in all the physical laws)
Precisely the same metric that is used by SR is also used by LET. The difference is that the speed of light is invariant while simultaneity is relative in the Lorentz transformation, but absolute simultaneity is maintained with a variable speed of light in LET transformation. Both are equally valid.
 
  • #22
JesseM
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Aether said:
Here's the first two lines from a paper from Kostelecky & Mewes for example: http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:hep-ph/0111026 [Broken] "Lorentz violation is a promising candidate signal for Planck-scale physics. For instance, it could arise in string theory and is a basic feature of noncommutative field theories...". So, when I say "yet" I simply mean that I am aware of many physicists who expect to find violations eventually.
Since I'm not well-versed in quantum gravity I can't say much about this, but I wonder if by "Lorentz violation" they actually mean a preferred reference frame as in aether theories, and if so I wonder how mainstream this point of view is. A quick google search turned up http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:hep-th/0206035 [Broken] which seems to say that noncommutative theories can be compatible with Lorentz symmetry.
Aether said:
I know that there are some good points in Tom Robert's articles, and I have read them in the past, but he's talking about a whole infinity of ether theories and I'm just talking about one; LET. So, kindly extract the point from the article that you think applies here.
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). I don't know exactly what you mean by "LET", does it fit both these criteria?
Aether said:
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."
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.
 
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  • #23
Hurkyl
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Aether said:
Let's get empirical then. Show me how the constancy of the one-way speed of light is empirically verifiable; the round-trip speed of light is constant in both theories.
Given the Lorentz metric, the one-way speed of light is a mathematical consequence of the Special Relativistic definition of an inertial reference frame.

You agree that the Lorentz metric is empirically verifiable, correct? Then so must the one-way 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
pervect
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Hurkyl said:
Given the Lorentz metric, the one-way speed of light is a mathematical consequence of the Special Relativistic definition of an inertial reference frame
I think this is a good observation.

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
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I've got a question for Aether.

Aether said:
LET assumes absolute simultaneity, but this hasn't been proven either (yet). Why would an impartial observer, not from our culture, prefer either one of these theories (today) over the other?
By "absolute simultaneity", do you mean that in LET two events which happen simultaneously in one reference frame happen simultaneously in all, or just that there is a prefered reference frame (the ether) and this reference frame is the one in which simultaneous events are called absolutely simultaneous?
 

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