SR, LET, FTL & Causality Violation

[Dale]

I agree. But I disagree with the implications. The way I see it, this simply means that "LET uses the Lorentz transform to make its experimental predictions". It doesn't entail exclusion of other transforms to make its experimental predictions.

Such a theory (one that changes its method of making predictions on a whim) is non-falsifiable and therefore non-scientific. If you want to have a scientific theory then you have to make a specific prediction that is subject to experimental falsification. You should read up on falsifiability.

With regards specifically to LET, can you provide any authoritative source claiming that the LET uses any other mathematical framework besides the Lorentz transform?

 

[kmarinas86]

Newtonian structure says there is absolute space and time.

And that information can propagate with infinite velocity, so that Galilean invariance holds. If that isn't part of your definition of "absolute space and time", then you are not talking about "Newtonian structure", you're talking about something else.

[Overlaying additional structure on top of it means that when an object moves, it physical contracts and slow downs which has same effect as length contraction and time dilation... which falls under Lorentz Transformation. Therefore by merely adding physical length contraction and time slowing down in moving objects over Newtonian structure. This LET like mechanism produce the same prediction as SR.] Hence by this mechanism one can change "Galilean invariance to Lorentz invariance just by "overlaying" additional structure on top of Newtonian physics.

Doing this is *not* overlaying additional structure on Newtonian physics; it is *changing* the causal structure of Newtonian physics, i.e., it is *destroying* the old causal structure and replacing it with a new one. SR doesn't just introduce length contraction and time dilation; it introduces a finite speed of light (i.e., finite speed of information propagation). That changes the causal structure of spacetime; events that would have been causally connected under Galilean invariance are no longer causally connected under Lorentz invariance. You can't do that with just an "overlay".

Lorentz invariance is a property of spacetime. LET does not have spacetime. Time and space are not linked in LET. There is no such thing as a spacetime interval in LET. In LET, causal structure is only "real" in the preferred inertial frame of LET. So LET cannot have Lorentz invariance. In the strict sense of the way the term "Lorentz transformation" is now used, LET cannot even have a Lorentz transformation, because this term now refers to the transformation of space and time as described by SR.

LET cannot be accurately described as a theory of "Lorentz transformations". The Lorentz-FitzGerald contraction hypothesis applied to an "immobile aether" is what LET ultimately relies upon to make predictions also made by SR. That contraction was originally conceived in three dimensional Euclidean space, no spacetime.

 

[kmarinas86]

The black swan analogy doesn't make sense to me.

Please answer this clearly: Do you agree or disagree that LET uses the Lorentz transform to make its experimental predictions?

In light of my recent post just above that the Lorentz transform involves spacetime, while LET has no spacetime, I retract my agreement. Now my corrected response is: I disagree.

 

[Dale]

LET cannot be accurately described as a theory of "Lorentz transformations".

In light of my recent post just above that the Lorentz transform involves spacetime, while LET has no spacetime, I retract my agreement. Now my corrected response is: I disagree.

OK, thanks for the clarification. That at least crystallizes the real issue: this is simply a misunderstanding of LET. I would be glad to provide references if you wish, but LET does in fact use the Lorentz transform to make its experimental predictions.

 

[kmarinas86]

The black swan analogy doesn't make sense to me.

Please answer this clearly: Do you agree or disagree that LET uses the Lorentz transform to make its experimental predictions?

In light of my recent post just above that the Lorentz transform involves spacetime, while LET has no spacetime, I retract my agreement. Now my corrected response is: I disagree.

OK, thanks for the clarification. That at least crystallizes the real issue: this is simply a misunderstanding of LET. I would be glad to provide references if you wish, but LET does in fact use the Lorentz transform to make its experimental predictions.

I would like to see one reference that LET involves spacetime. Thanks.

 

[PeterDonis]

In LET, causal structure is only "real" in the preferred inertial frame of LET.

Which inertial frame is that? Nobody knows, nor does LET give any way of finding out. So this statement may sound good, but doesn't actually say anything useful.

Also, unless LET claims that whether two events are causally connected is observer-dependent (which would contradict SR), LET and SR must agree on which pairs of events are and are not causally connected. So the above statement is also irrelevant, since SR doesn't care whether the causal structure is "real" in every inertial frame; it only cares that the causal connection, or lack thereof, between any given pair of events is invariant.

LET cannot be accurately described as a theory of "Lorentz transformations". The Lorentz-FitzGerald contraction hypothesis applied to an "immobile aether" is what LET ultimately relies upon to make predictions also made by SR.

How do you make these predictions if you don't know which inertial frame is the "immobile aether" frame?

That contraction was originally conceived in three dimensional Euclidean space, no spacetime.

What about time dilation?

 

[Dale]

I would like to see one reference that LET involves spacetime. Thanks.

You don't need spacetime to have a transform. E.g. the Galilean transform. I never claimed that the LET uses spacetime, only that it uses the Lorentz transform.

Whether you take Minkowski's approach and combine space and time into spacetime or you take Lorentz's approach and keep them separate, the experimental predictions are determined by the Lorentz transform. Spacetime is simply an elegant way of expressing the Lorentz transform, not a necessary part of it.

 

[kmarinas86]

Also, unless LET claims that whether two events are causally connected is observer-dependent (which would contradict SR), LET and SR must agree on which pairs of events are and are not causally connected.

As it was long ago conceived at the prior turn of the century, LET and SR have to agree on the predicted observational measurements.

However, whether those observational measurements actually reflect "causality" or just "order of appearance" is where LET begins to stray from SR (or vice versa). SR invokes relativity of simultaneity. LET rejects relativity of simultaneity.

What about time dilation?

In LET, time dilation was conceived without the spacetime metric.

http://en.wikipedia.org/wiki/Lorentz_ether_theory

A substantially extended work (the so called „Palermo paper“)<ref group=A name=dynam>Poincaré (1906)</ref> was submitted by Poincaré on 23 July 1905, but was published on January 1906, because the journal only appeared two times in a year. He spoke literally of "the postulate of relativity", he showed that the transformations are a consequence of the [[principle of least action]]; he demonstrated in more detail the group characteristics of the transformation, which he called [[Lorentz group]], and he showed that the combination <math>x^2+ y^2+ z^2- c^2t^2</math> is invariant. While elaborating his gravitational theory he noticed that the Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing <math>ct\sqrt{-1}</math> as a fourth imaginary coordinate, and he used an early form of [[four-vector]]s. However, Poincaré later said the translation of physics into the language of four-dimensional metry would entail too much effort for limited profit, and therefore he refused to work out the consequences of this notion. This was later done by Minkowski, see "The shift to relativity".<ref group=B>Walter (2007), Kap. 1</ref>

 

[PeterDonis]

As it was long ago conceived at the prior turn of the century, LET and SR have to agree on the predicted observational measurements.

However, whether those observational measurements actually reflect "causality" or just "order of appearance" is where LET begins to stray from SR (or vice versa). SR invokes relativity of simultaneity. LET rejects relativity of simultaneity.

What does this mean? Does it mean that the "order of appearance" of two spacelike-separated events is not different for different observers in LET? How does that work?

Or does it just mean that LET admits that the "order of appearance" of spacelike separated events can be different for different observers, but still claims those events can be causally connected? This would mean that LET denies that invariant time ordering is a necessary condition for causal connection. This would not necessarily contradict SR, since strictly speaking, SR's definition of "causality" only requires that spacelike-separated experiments must commute (i.e., the results must be independent of which experiment occurs "first"); it does not require that we absolutely rule out causal connection between spacelike-separated events. (For example, the quantum experiments that violate the Bell inequalities are consistent with SR.)

If you don't mean one of the above, but you are saying that LET's definition of "causal connection" is different from SR's, then I don't understand LET's definition of "causal connection".

In LET, time dilation was conceived without the spacetime metric.

Yes, so was standard SR. That's not what I was asking. You said LET conceives length contraction in 3-dimensional space, which obviously can't hold for time dilation. So how does LET conceive time dilation?

 

[D H]

Yes, so was standard SR.

Exactly. The concept of spacetime was developed after the fact -- and by Poincare, not Einstein. The two key Lie groups that pertain to special relativity are the Lorentz group and the Poincare group. Lorentz and Poincare: These just happen to be the two key people behind Lorentz Ether Theory. The concept of spacetime as an algebraic structure was developed first for LET, and then carried over to simplify/solidify the description of special relativity. That wasn't that hard to do because mathematically, LET and special relativity are one and the same. The two theories differ only in their postulates. Physically, they are not one and the same because we physicists have this nifty little tool called Occam's razor.

 

[ghwellsjr]

The difference between LET and SR is in the second postulate. Einstein claims that light propagates at c in any rest state whereas LET postulates that light propagates at c only in one rest state. Since we cannot know what that rest state is, LET interprets virtually all rest states as being in inertial motion with respect to that one preferred rest state and therefore experiencing time dilation and length contraction (but of some unknowable amount). SR interchanges these two rest states, any rest state is exactly like the LET preferred absolute rest state of the ether where the speed of light is c and so experiences no time dilation or length contraction--all other frames in relative inertial motion are the ones that experience the time dilation and length contraction.

Aside from that one ever-so-minor point of view, there is no difference between LET and SR.

 

[Dale]

As it was long ago conceived at the prior turn of the century, LET and SR have to agree on the predicted observational measurements.

Exactly. And this is a direct result of the fact that both use the Lorentz transform to predict all experimental measurements.

Are you back in agreement now?

 

[D H]

but of some unknowable amount

Einstein's postulate that the speed of light is the to all observers is simply stated. Seemingly paradoxical, but simple. Compare that to the ad hoc LET postulates of length contraction and time dilation.

But that wasn't what ultimately did LET in. What did it in was that the rest frame of the luminiferous aether, while central to the theory, was inherently unknowable and untestable.

 

[atyy]

Einstein's postulate that the speed of light is the to all observers is simply stated. Seemingly paradoxical, but simple. Compare that to the ad hoc LET postulates of length contraction and time dilation.

But that wasn't what ultimately did LET in. What did it in was that the rest frame of the luminiferous aether, while central to the theory, was inherently unknowable and untestable.

OTOH, couldn't one say LET "did itself in" (the part about there being only one preferred frame) by being successfully predicting:) the existence of the whole class of Lorentz inertial frames?

 

[D H]

OTOH, couldn't one say LET "did itself in" (the part about there being only one preferred frame) by being successfully predicting:) the existence of the whole class of Lorentz inertial frames?

I suppose.

OTOH, telling physicists that the central thesis of LET was inherently unobservable and untestable was probably a bit too much in and of itself.

 

[atyy]

IOTOH, telling physicists that the central thesis of LET was inherently unobservable and untestable was probably a bit too much in and of itself.

Yet many prefer GR formulated as a spin-2 field on unobservable flat spacetime (ok, I'm guilty:)

 

[stglyde]

And that information can propagate with infinite velocity, so that Galilean invariance holds. If that isn't part of your definition of "absolute space and time", then you are not talking about "Newtonian structure", you're talking about something else.



Doing this is *not* overlaying additional structure on Newtonian physics; it is *changing* the causal structure of Newtonian physics, i.e., it is *destroying* the old causal structure and replacing it with a new one. SR doesn't just introduce length contraction and time dilation; it introduces a finite speed of light (i.e., finite speed of information propagation). That changes the causal structure of spacetime; events that would have been causally connected under Galilean invariance are no longer causally connected under Lorentz invariance. You can't do that with just an "overlay".

I see. So you mean even if the Lorentz preferred frame can be distinguished. The lorentz preferred frame on Earth doesn't have the same time as the lorentz preferred frame at alpha centuari 4 light years away (because of the finite velocity of light). But then quantum entanglement is instantaneous across the universe. How do you discount the possibility quantum entanglement uses our old friend Galilean invariance (nothing what you said in the first sentence above "And that information can propagate with infinite velocity, so that Galilean invariance holds").

 

[Dale]

Quantum entanglement cannot be used to transmit information. Many things which do not transmit information go faster than light, but they cannot produce a causality violation.

 

[stglyde]

Quantum entanglement cannot be used to transmit information. Many things which do not transmit information go faster than light, but they cannot produce a causality violation.

I know. But the randomness simultaneous correlations share a "preferred frame" across the universe. So it's like you have something going back and forth in time in different frames.
(In this argument, let's ignore MWI and Copenhagen which explains the correlations in other ways like how locality doesn't exist.. hence nothing to be non-local about. For the purpose of this thread, let's just deal with old fashioned General Relativity (or gLET) spacetime... ).

 

[Dale]

But the randomness simultaneous correlations share a "preferred frame" across the universe.

No, they don't. In every frame the collapse happens instantaneously. There is nothing in that to prefer one frame over another.

 

[stglyde]

No, they don't. In every frame the collapse happens instantaneously. There is nothing in that to prefer one frame over another.

But since each frame has different time... this is because each frame as compared to another is limited in speed by the speed of light. Then the collapse occurs in different time. This is because if you say collapse happens instantaneously in all frames across the universe. Then you are talking about Galilean or Newtonian spacetime. Remember that my time now can't be compared to the time "now" at Alpha Centauri.. which is the essence of Spacetime. Hence you can't say my time now is instantaneous to the time "now" at alpha centari.

 

[Dale]

But since each frame has different time... this is because each frame as compared to another is limited in speed by the speed of light. Then the collapse occurs in different time. This is because if you say collapse happens instantaneously in all frames across the universe. Then you are talking about Galilean or Newtonian spacetime.

I think that you misunderstand what it means for there to be a preferred frame. A preferred frame means that there is some frame where the laws of physics are different than in other frames. If you have a law of physics that says that something happens instantaneously and if that law of physics is the same in each frame then it does not imply a preferred frame.

Remember that my time now can't be compared to the time "now" at Alpha Centauri.. which is the essence of Spacetime. Hence you can't say my time now is instantaneous to the time "now" at alpha centari.

Sure you can. As long as you specify the reference frame you certainly can make such comparisons and statements. They are not invalid statements, just frame-variant.

 

[stglyde]

I think that you misunderstand what it means for there to be a preferred frame. A preferred frame means that there is some frame where the laws of physics are different than in other frames. If you have a law of physics that says that something happens instantaneously and if that law of physics is the same in each frame then it does not imply a preferred frame.

Sure you can. As long as you specify the reference frame you certainly can make such comparisons and statements. They are not invalid statements, just frame-variant.

Wiki says:

"http://en.wikipedia.org/wiki/Preferred_frame

In general relativity, some cosmological models have a preferred frame that allows motion to be defined."

The context means a preferred frame is large across the universe. So if there is something in the preferred frame... then it is instantaneous within that frame. You mentioned that "A preferred frame means that there is some frame where the laws of physics are different than in other frames.". That's right. Laws of physics are different in that frame because it supports superluminal influence for example. Refute it.

 

[Fredrik]

Wiki says:

"http://en.wikipedia.org/wiki/Preferred_frame

In general relativity, some cosmological models have a preferred frame that allows motion to be defined."

The context means a preferred frame is large across the universe. So if there is something in the preferred frame... then it is instantaneous within that frame. You mentioned that "A preferred frame means that there is some frame where the laws of physics are different than in other frames.". That's right. Laws of physics are different in that frame because it supports superluminal influence for example. Refute it.

The "preferred frames" in GR are just coordinate systems in which it's particularly easy to describe the distribution and other properties of matter in the universe. In a FLRW solution for example, the "preferred" coordinate system is the one in which the distribution of matter in space (defined as a 3-manifold of constant time coordinate) is homogeneous and isotropic everywhere. There are no superluminal influences.

 

[stglyde]

Sure you can. As long as you specify the reference frame you certainly can make such comparisons and statements. They are not invalid statements, just frame-variant.

I thought relativity taught that it is meaningless to compare the now here and the "now" in alpha centauri because of SR. But you said it is possible. So how do you specify the reference frame that can compare the now here and in the alpha centauri?

 

[kmarinas86]

[H]ow does LET conceive time dilation?

In the same way that SR would for an arbitrary observer:

http://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Accelerated_motion

== Accelerated motion ==

For general accelerated motion, or when the motions of the source and receiver are analyzed in an arbitrary inertial frame, the distinction between source and emitter motion must again be taken into account.

The Doppler shift when observed from an arbitrary inertial frame:<ref>{{cite web
| url = http://www.mathpages.com/rr/s2-04/2-04.htm
| source = Mathpages
| title = Doppler Shift for Sound and Light
| author = Kevin S Brown
| pages = 121–129
| accessdate = 1/09/2011 }}</ref>

$\frac{f_o}{f_s} = \frac{ 1 - \frac{ \|\vec{v_o}\|}{\|\vec{c}\|} cos(\theta_{co}) } { 1 - \frac{ \|\vec{v_s}\|}{\|\vec{c}\|} cos(\theta_{cs}) } \sqrt{ \frac{ 1-(v_s/c)^2 }{ 1-(v_o/c)^2 } }$

where:
$$\vec{v_s}$$ is the velocity of the source at the time of emission
$$\vec{v_o}$$ is the velocity of the receiver at the time of reception
$$\vec{c}$$ is the light velocity vector
$$\theta_{cs}$$ is the angle between the source velocity and the light velocity at the time of emission
$$\theta_{co}$$ is the angle between the receiver velocity and the light velocity at the time of reception

If $\vec{c}$ is parallel to $\vec{v_s}$, then $\theta_{cs} = 0^{\circ}$, which causes the frequency measured by the receiver $f_o$ to increase relative to the frequency emitted at the source $f_s$. Similarly, if $\vec{c}$ is anti-parallel to $\vec{v_s}$, $\theta_{cs} = 180^{\circ}$, which causes the frequency measured by the receiver $f_o$ to decrease relative to the frequency emitted at the source $f_s$.

This is the classical Doppler effect multiplied by the ratio of the receiver and source Lorentz factors.

Due to the possibility of refraction, the light's direction at emission is generally not the same as its direction at reception. In refractive media, the light's path generally deviates from the straight distance between the points of emission and reception. The Doppler effect depends on the component of the emitter's velocity parallel to the light's direction at emission, and the component of the receiver's velocity parallel to the light's direction at absorption.<ref>{{cite web
| url = http://tmo.jpl.nasa.gov/progress_report2/III/IIII.PDF
| title = An Additional Effect of Tropospheric Refraction on the Radio Tracking of Near-Earth Spacecraft at Low Elevation Angles
| year = 1971
| author = Chao, Mayer
| accessdate = 1/09/2011 }}</ref> This does not contradict Special Relativity.

The transverse Doppler effect can be analyzed from a reference frame where the source and receiver have equal and opposite velocities. In such a frame the ratio of the Lorentz factors is always 1, and all Doppler shifts appear to be classical in origin. In general, the observed frequency shift is an invariant, but the relative contributions of time dilation and the Doppler effect are frame dependent.

So, in LET, there are "real" and physical time dilation and doppler effects, and then there are apparent time dilation and doppler effects due to the bias of the observer.

 

[Fredrik]

I thought relativity taught that it is meaningless to compare the now here and the "now" in alpha centauri because of SR. But you said it is possible. So how do you specify the reference frame that can compare the now here and in the alpha centauri?

Almost any way you want to. You just need to make sure that a few mathematical requirements are satisfied. That's why it would be meaningless to think that this assignment has any real significance.

 

[PeterDonis]

I see. So you mean even if the Lorentz preferred frame can be distinguished. The lorentz preferred frame on Earth doesn't have the same time as the lorentz preferred frame at alpha centuari 4 light years away (because of the finite velocity of light).

What I said about causal structure has nothing to do with frames. Whether or not a given pair of events are timelike separated, null separated, or spacelike separated (which is what "causal structure" refers to) is frame-invariant.

Also, you are using the term "preferred frame" in a non-standard way (and also, as far as I can tell, in a different way than you have used it in previous posts). If the Earth and Alpha Centauri are in different "Lorentz frames", meaning they are at rest in different inertial frames, so that their notions of simultaneity are different (i.e., they do not have "the same time"), that is because they are moving relative to each other, not because of the finite speed of light. (Actually, since spacetime is curved, there are no actual SR-style inertial frames that cover both Earth and Alpha Centauri anyway; but we'll pretend here that spacetime is flat so that we can extend Earth's inertial frame all the way to Alpha Centauri, or vice versa, and compare them to see if they're in relative motion or not.) But that fact, in itself, doesn't pick out either frame, the Earth's or Alpha Centauri's, as "preferred".

But then quantum entanglement is instantaneous across the universe. How do you discount the possibility quantum entanglement uses our old friend Galilean invariance (nothing what you said in the first sentence above "And that information can propagate with infinite velocity, so that Galilean invariance holds").

As others have pointed out, quantum entanglement can't be used to transmit information, so entanglement between spacelike separated particles does not contradict Lorentz invariance, or require Galilean invariance.

 

[PeterDonis]

[H]ow does LET conceive time dilation?

In the same way that SR would for an arbitrary observer

In other words, LET is consistent with Lorentz invariance, *not* Galilean invariance. That's what I thought.

So, in LET, there are "real" and physical time dilation and doppler effects, and then there are apparent time dilation and doppler effects due to the bias of the observer.

But the actual observations are the same. It's just that LET insists on making an arbitrary distinction, which cannot be physically observed, between "real" effects (due to the unobservable "aether" frame) and "apparent" effects (due to the observer's rest frame not being the same as the unobservable "aether" frame).

 

[Dale]

Wiki says:

"http://en.wikipedia.org/wiki/Preferred_frame

In general relativity, some cosmological models have a preferred frame that allows motion to be defined."

Thanks, I have fixed it.

You mentioned that "A preferred frame means that there is some frame where the laws of physics are different than in other frames.". That's right. Laws of physics are different in that frame because it supports superluminal influence for example. Refute it.

Again, the "superluminal influence" of entanglement occurs in every frame. So the laws of physics are not different in one frame. Refuted.

Btw, the purpose of this site is not to refute crackpot claims or ignorant assertions. The prupose of this site is to educate about mainstream physics. If you wish to learn then I am glad to help. The proper way to do so is to ask questions about points that confuse you, not to make non-standard assertions and demand refutation. The burden of proof is always on the person going against mainstream science.

 

[Dale]

I thought relativity taught that it is meaningless to compare the now here and the "now" in alpha centauri because of SR. But you said it is possible. So how do you specify the reference frame that can compare the now here and in the alpha centauri?

Any reference frame is fine. You will get different pairs of simultaneous events with every frame, but each is completely valid.

 

[stglyde]

Any reference frame is fine. You will get different pairs of simultaneous events with every frame, but each is completely valid.

There are so many "frames", it can get confusing. There are:

1. Reference frame
2. Inertial frame
3. Preferred frame
4. lorentz frame
5. rest frame
6. aether frame
7. what else

Can you or anyone give a one sentence meaningful definition of them?
Also I wonder why it's generically called a "frame". Window frame is rectangular. so I'm imagining it has to do with a slice of spacetime that you guys called a frame?

 

[PeterDonis]

There are so many "frames", it can get confusing. There are:

1. Reference frame
2. Inertial frame
3. Preferred frame
4. lorentz frame
5. rest frame

Can you or anyone give a one sentence meaningful definition of them?
Also I wonder why it's generically called a "frame". Window frame is rectangular. so I'm imagining it has to do with a slice of spacetime that you guys called a frame?

Well, you used the word "frame" yourself in the OP. What did you mean by it?

#1 is the most general term: I would define it as any way of assigning coordinates to events that meets certain very basic conditions (for example, that events which are "close together" should have coordinates which are close in value). Normally we try to have the assignment of coordinates to events be "sensible", meaning there will be some reasonable relationship between the coordinates and something with physical meaning; but in principle we don't have to do this, it just makes calculations easier.

#2 and #4 are basically the same thing: they refer to special cases of #1 in which the metric in the given coordinates assumes the standard Minkowski form: $d\tau^{2} = dt^{2} - dx^{2} - dy^{2} - dz^{2}$. In flat spacetime (i.e., when gravity is negligible), such a frame can be global (i.e., it can cover the entire spacetime); but in curved spacetime (i.e., when gravity is present), such a frame can only be local; it can only cover a small region of spacetime around a given event (how small depends on how accurate we want our answers to be and how strong gravity is).

#5 is a particular instance of #2 and #4 such that an object we are interested in is at rest at the spatial origin in the given frame. In flat spacetime, again, this can be true globally; but in curved spacetime it will only be true locally.

#3 has at least two meanings that I'm aware of:

#3a: A "preferred frame" can be a particular instance of #1 (i.e., it can be any kind of frame, not necessarily an inertial/Lorentz frame) that matches up in some way with a key property of the spacetime we are interested in. For example, in the FRW spacetimes that are used in cosmology, the "comoving" frame, the frame in which the universe looks homogeneous and isotropic, is a preferred frame, because it matches up with the symmetries (homogeneity and isotropy) of the spacetime. The reason such a frame is "preferred" is that calculations are easier in a frame that matches up with the symmetries of the spacetime.

#3b: A "preferred frame" can also be a particular frame that is picked out by someone's physical theory as being "special", regardless of whether there is any actual physical observable that matches up with it. For example, the "aether frame" in LET is a preferred frame in this sense.

 

[Dale]

There are so many "frames", it can get confusing. There are:

1. Reference frame
2. Inertial frame
3. Preferred frame
4. lorentz frame
5. rest frame
6. aether frame
7. what else

Can you or anyone give a one sentence meaningful definition of them?
Also I wonder why it's generically called a "frame". Window frame is rectangular. so I'm imagining it has to do with a slice of spacetime that you guys called a frame?

OK, a reference frame techincally refers to a frame field:
http://en.wikipedia.org/wiki/Frame_fields_in_general_relativity

This is a set of 4 orthonormal vector fields defined across the spacetime. However, loosely speaking most people use "reference frame" as a synonym for "coordinate system". It is slightly sloppy usage, but doesn't usually cause problems except in very detailed discussions.

So using the common (sloppy) usage that a reference frame is a coordinate system then an inertial frame is a coordinate system in which the laws of physics takes the standard textbook form. Specifically, any particle at rest anywhere in an inertial frame experiences 0 proper acceleration.

A preferred frame is a coordinate system in which the laws of physics are uniquely different from any other coordinate systems.

A Lorentz frame is one of a set of coordinate systems that are related to each other via the Lorentz transform.

A rest frame is a coordinate system where the velocity of a given object is 0.

The aether frame is the rest frame of the aether.

 

[PeterDonis]

DaleSpam, no fair electioneering in your sig!