Why is energy-momentum symmetry important in special relativity?

[quantumdude]

Tom - we seem to be on a different page - perhaps I am not expressing things well - but let me try again - if we take the example of the well worn light clock, we get the interval transforms directly because the result depends from two over and back beams as in MMx (in actuality a two light clock experiment). We are not measuring one way velocity, but only round trip velocity.

But one-way experiments have been done, and the speed of light comes out to 'c'. Furthermore, those transformations (the very same ones that contain the postulates) are the only ones that leave Maxwell's electrodynamics unchanged in every frame.

The fact that the round trip velocity is constant does not lead to one way isotrophy. Round trip experiments always involve a (v/c)^2 (second order correction) whereas one way experiments involve (v/c) as in aberration.

Sorry, I'm not following. "Corrections" to what, exactly?

(you of course already know this - but point I am attempting to make is that the extension of the over and back experiment(s) to one way isotrophy does not follow). The interval transforms are second order corrections - when you go in reverse you do not necessarily recover the vx/c^2 term unless you reintroduce Einstien's convention that the over and back time periods are equal.

I don't know what you mean by "corrections", but the prediction of the invariance of the speed of light most definitely does follow from the transforms. You can derive the SR velocity addition law directly from them.

 

[yogi]

The one way experiments - if you are referring to GPS - or any other experiments conducted on the earth, they do not confirm one way isotrophy - G field modification of local space can also explain the results. But that is a different issue.

What experiments have been performed to verify the SR velocity additon formula?

By corrections, I am referring to the factors that are required to relate the passage of time in one frame to the passage of time in another.

 

[yogi]

Self Adjoint - didn't mean to get bogged down so as to ignor your reference to the Voigt paper - a most fascinating revelation. Thanks for calling it to our attention.

 

[quantumdude]

The one way experiments - if you are referring to GPS - or any other experiments conducted on the earth, they do not confirm one way isotrophy - G field modification of local space can also explain the results. But that is a different issue.

What experiments have been performed to verify the SR velocity additon formula?

The specific experiment I have in mind is the Alvager experiment, which measures the speed of light emitted by decaying pions. The pions are sources moving at 99%+ of the speed of light, and the photons they emit were measured to be traveling at c.

How does local G-field modification account for that?

By corrections, I am referring to the factors that are required to relate the passage of time in one frame to the passage of time in another.

So the correction is the relativistic correction to the Galilean result then? That's what I'm asking.

The thing that I still don't think is being addressed is the point that Hurkyl and I have both made: The postulates imply the transforms, and vice versa. You and SelfAdjoint both seem to feel uneasy about the biconditional nature of the logical relationship that the postulates bear to the transforms, but the thing is, either can be derived from the other.

For that reason, I still say that tests of the transforms are tests of the postulates, and that no alternative to SR can simultaneously lead to the same transforms and overthrow the postulates. I think that the most any alternative can do is bolster the postulates with the "physical explanation" that you (Yogi) have referred to.

 

[quartodeciman]

The specific experiment I have in mind is the Alvager experiment

Here! Here! {enthusiastic outburst!}

Oh, If only (it happened that) this splendid to-the-point experiment would get some repetitions with refinements once in a while, so we could get the reports.

 

[yogi]

Tom - Re Alvager ... your quite right about the original statement of the second hypothesis - there is not issue that I can see as to the inapplicability of emission theories. What I was thinking was of the consequences of the second and first postulates taken together - this is what leads to the dictum that the one way velocity of light is isotropic with respect to a moving receiver in free space.

Transforms derived by other postulates lead to different theories of space and time which are empirically equivalent to a large extent. Many of the theories are based upon a preferred frame, yet they nontheless predict the same outcome as the many experiments that are cited to validate the special theory. So my question still remains - if you don't introduce the one way velocity of light as a given in every reference frame - how can you recover it?

If you are not already familiar with his work, you might want to read some of Selleri's papers. He starts with a different premise that is not dependent upon one way isotrophy and derives the interval transforms of Lorentz.

 

[quantumdude]

So my question still remains - if you don't introduce the one way velocity of light as a given in every reference frame - how can you recover it?

As I said: You can recover it if you take the Lorentz transforms as a given.

Let Event 1 be the emission of a light pulse at (x₁=0,t₁=0), as recorded by observer S. Let Event 2 be the absorption of the pulse at (x₂=ct,t₂=t), again as recorded by S. Letting Δx=x₂-x₁ and Δt=t₂-t₁, the speed of the pulse is Δx/Δt=c.

Now let a second observer S', moving with velocity v with respect to the source and in the same direction as the light pulse, record the spacetime coordinates for the same two events. His coordinates can be found from those of S via the LT:

Δx'=γ(Δx-vΔt)
Δt'=γ(Δt-vΔx/c²)

Divide the two equations, and see for yourself that c'=Δx'/Δt'=c.

edit: The exact same result holds if we let the light pulse and the moving observer travel in arbitrary directions.

 

[reilly]

Be Practical

All (well almost) all of particle physics, E&M, and much of modern physics rests on Special Relativity. Why? Because it works; it has yet to fail us. If and when it does, then it will be time to change. Indeed there are various alternative approaches that claim to be as effective as SR. But as the cliche goes -- if it ain't broke, don't fix it. If one of these alternate approaches/theories can either prove to be easier to use, or successfully predict phenomena that SR can't handle, then it will be time to think about doing some fixing. But until that happens, SR is the best game in town.
Regards,
Reilly Atkinson

(Maybe the suggestions of frequency dependence of the speed of light might point to the breaking point. )

 

[Nereid]

(Maybe the suggestions of frequency dependence of the speed of light might point to the breaking point. )

In which frequency regime is it suggested that this might occur? What is the suggested OOM of the dependence? Are there any observations whatsoever that hint at such a dependence?

 

[Mark]

Just going back to the previous comments yogi was making...

I think that it is important to be always questioning SR, and GR for that matter. If i recall we have yet to unify Relativity, and Quantum mechanics, therefore what we know might just be completely untrue.

Did not Newton have experimental evidence that his theories were correct? He did, but Einstein proved him wrong by not mindlessly agreeing with the evidence, he questioned it. I think it should be the same for relativity if we are to yield any significant progress

my two cents

_____________
Mark

 

[Hurkyl]

Einstein didn't "question the evidence"; on the contrary, Special Relativity is actually required to agree with Newton... when only small velocities are involved.

Just like with Newton, there's an overwhelming amount of evidence for SR, GR, and QFT. The next theory must agree with these theores, except on some new set of exceptional circumstances

 

[Tom McCurdy]

Although it is true that Special Relativity is similar to Newton's laws at small velocities, they still are differnt. As long as motion is involved that is greater than 0 then to some degree there is difference between SR and Newton's laws. Its just that it takes greater speeds closer to c to notice the changes.

 

[yogi]

Tom - You do recover the constancy of c from the Lorentz Transformations if you specify the "event" transformations to be spatial or temporal interval transforms, as you have done:

Δx'=γ(Δx-vΔt)
Δt'=γ(Δt-vΔx/c2)

but in the usual derivation these equations, the primed coordinates are assigned to an "event" in the primed frame, rather than temporal "durations" or spatial "differentials." To get the temporal difference equation for Δt', one subtracts the event transforms for t1' and t2', i.e., so when this is done, the term (vΔx/c2) that appears in both t1' and t2' is eliminated. Once eliminated, it cannot be recovered from the time differentials:

Δt' = t2' - t1' = (t2 - t1)(1-B^2)^-1/2




-

 

[quantumdude]

If i recall we have yet to unify Relativity, and Quantum mechanics,

No, those were unified in the 20s, and subsequently SR and quantum theory were combined to form QFT. The problem now is finding a quantum theory of gravity.

therefore what we know might just be completely untrue.

Not so. The theories we have today agree remarkably well with experiment, and the theories of the future will be required to contain them as special cases.

 

[quantumdude]

To get the temporal difference equation for Δt', one subtracts the event transforms for t1' and t2', i.e., so when this is done, the term (vΔx/c2) that appears in both t1' and t2' is eliminated. Once eliminated, it cannot be recovered from the time differentials:

Δt' = t2' - t1' = (t2 - t1)(1-B^2)^-1/2

So? The fact remains that you can:

1. Start with the coordinate transformations for t' and x' for two different events.
2. Subtract them.
3. Conclude that the speed of light is the same in every frame.

This procedure accomplishes exactly what I said it does: Starting from the LT for individual events (which you said could be arrived at by not assuming a Lorentz-invariant speed of light), you can derive the constancy of the speed of light in one direction.

 

[quantumdude]

To get the temporal difference equation for Δt', one subtracts the event transforms for t1' and t2', i.e., so when this is done, the term (vΔx/c2) that appears in both t1' and t2' is eliminated.

Actually, you're wrong about this too!

It would only be eliminated if x₁ and x₂ were equal.

t₂'=γ(t₂-vx₂/c²)
t₁'=γ(t₁-vx₁/c²)

Now subtract:

Δt'=t₂'-t₁'
Δt'=γ(t₂-t₁-(v/c²)(x₂-x₁))
Δt'=γ(Δt-vΔx/c²)

The term with vΔx/c² doesn't go anywhere.

 

[yogi]

Tom - the x that is referred to in the temporal equation when you take the difference is always the same spatial location - if it isn't you are mixing apples and oranges - different x values in the other frame will have different temporal coordinates - in formulating the temporal interval transform we are always talking about a single spatial location in the other frame.

The correct expression for the delta time in going from one system to the other is delta t = [delta t' ][(1-(v/c)^2]^1/2, and as you know that is what is published in all text(s)

 

[quantumdude]

Tom - the x that is referred to in the temporal equation when you take the difference is always the same spatial location

No, it isn't. I subtracted the time measurements for t₁' and t₂', which contain x₁ and x₂, respectively. They don't involve the same spatial location.

- if it isn't you are mixing apples and oranges - different x values in the other frame will have different temporal coordinates - in formulating the temporal interval transform we are always talking about a single spatial location in the other frame.

No, it isn't mixing apples and oranges. In SR, "mixing apples and oranges" would be taking measurements from two different reference frames to construct an interval. For instance, if I took t₂'-t₁, I wouldn't get anything meaningful. But as it is, there is nothing wrong with calculating a duration t₂'-t₁', and using the LT to relate it to the the spatiotemporal intervals in another frame, even when Δx is not zero.

The correct expression for the delta time in going from one system to the other is delta t = [delta t' ][(1-(v/c)^2]^1/2, and as you know that is what is published in all text(s)

That is what is published in all the texts under the assumption that x₁=x₂. It isn't valid here, because that condition doesn't hold.

IMO, you need to study relativity in more depth. Take any text that refers to the time dilation formula above. If you turn the page and read it, you will find that they also derive the velocity addition formula by the very same analysis I have presented here.

 

[yogi]

Tom - granted - as I previously acknowledged, if you don't define the same spatial point, the x's don't cancel and you are left with Einstein's convention. But what I stated was, that once you define a particular x then the term that results from Einstein's convention of one way isotrophy disappears, and you are left with the simple interval transformation - and that is what is verified by measurements of time dilation - and since that transform can be arrived at by other hypothesis, the experimental results do not confirm the SR postulate, but rather the transform that results when the clock in the primed frame occupies a fixed position.

The addition formula is derived in different ways in different texts - but this is of no moment unless the addition formula can itself be independently verified.

I understand what you are saying - but the point I am trying to get across is, assuming arguendo, if the SR one way isotropic postulate is flawed - the flaw cannot be detected because the experimental results are in agreement with the interval transform obtained when x is a fixed position in the primed frame (experiments do not distinguish between different theories that lead to the interval transform for a fixed x in the other reference frame). Einstein's use of the 1/2 factor to sync a clock using a tranmitted and reflected light signal is arbitrary - and should be considered suspect until actually verified since any other factor will yield the same interval transform for a fixed x.

 

[quantumdude]

Tom - granted - as I previously acknowledged, if you don't define the same spatial point, the x's don't cancel and you are left with Einstein's convention.

What do you mean by "Einstein's convention"? The result is due to the Lorentz transformations and algebra.

But what I stated was, that once you define a particular x then the term that results from Einstein's convention of one way isotrophy disappears, and you are left with the simple interval transformation

I know what you stated. But what you aren't understanding is that even if you don't "define a particular x", then the Lorentz transformations for an interval are perfectly valid. Your "apples and oranges" comment is simply wrong.

- and that is what is verified by measurements of time dilation -

Of course that equation is verified by measurements of time dilation. And you know what else? The relation I stated is verified by measurements of lightspeed in one direction. Hey, it's amazing what equations of physics will be verified if you only test them under the conditions in which they are valid!

and since that transform can be arrived at by other hypothesis, the experimental results do not confirm the SR postulate, but rather the transform that results when the clock in the primed frame occupies a fixed position.

I said it once, and I'll say it again: Any experiment that confirms the LT does confirm SR, because SR is derivable from the LT.

The addition formula is derived in different ways in different texts - but this is of no moment unless the addition formula can itself be independently verified.

It has been verified, by Alvager.

In any case, it does not matter if the addition formula can be derived "in different ways" (I don't doubt that that can be done, in fact). What matters is that the addition formula unambiguously implies the invariance of the speed of light in one direction.

I understand what you are saying - but the point I am trying to get across is, assuming arguendo, if the SR one way isotropic postulate is flawed - the flaw cannot be detected because the experimental results are in agreement with the interval transform obtained when x is a fixed position in the primed frame (experiments do not distinguish between different theories that lead to the interval transform for a fixed x in the other reference frame).

Yogi, please just use the LT to predict the speed of a light pulse emitted in a frame S (stationary relative to the source) as measured in a frame S' moving relative to the source. That would save us both a lot of time.

And no, your idea that spatiotemporal intervals cannot be rightly calculated between frames unless Δx=0 is not valid.

Einstein's use of the 1/2 factor to sync a clock using a tranmitted and reflected light signal is arbitrary - and should be considered suspect until actually verified since any other factor will yield the same interval transform for a fixed x.

Who cares about Einstein's numerical factors in thought experiments? Since Einstien wrote his 1905 paper, SR has been put on much more rigorous footings. All those thought experiments about trains and light pulses are totally irrelevant. What matters is the Lorentz transformation, and what matters even more is that the Postulates imply the LT, and vice versa.


You say otherwise, but I don't think you do understand what I am saying in any detail.

If the idea of one way invariance of the speed of light is wrong, then the Lorentz transformation is wrong. There is no escaping this fact. You have only to do the math to see it. Your entire argument is based upon a fallacy, namely that if we take the LT as a given then we cannot recover the postulates.

If we do take the LT as a given, then it is perfectly clear that:

t₂'=g(t₂-vx₂/c²)...(1)
t₁'=g(t₁-vx₁/c²)...(2)

And if we take the definition of "temporal interval" seriously, then it is perfectly clear that:

t₂'-t₁'=Δt'...(3)

is the "duration" of the time starting from event 1 and terminating at event 2.

And further, if we accept algebra, then taking the difference between t₂ and t₁ does not affect equations (1) and (2). Since there's nothing mathematically wrong with calculating a temporal interval that depends on a spatial interval in another frame and since there's nothing about that particular operation that contradicts the postulates, it follows that such an operation is valid. The only way you can defend your position is to insist that, when we subtract t₂'-t₁', that (1) and (2) mysterioulsy no longer hold.

 

[yogi]

I will agree with your statement that:

Any experiment that confirms the LT does confirm SR, because SR is derivable from the LT.

provided we are talking about the transforms that contain the vx/c^2 term.

Experiments that are in accord with the interval transforms where that term does not exist neither disprove nor confirm SR.

 

[arildno]

As to the relativistic addition formula of velocities:
One of the historically important features of SR is that it was consistent with the Fresnel formula for the velocity of light in a transparent fluid with a given current.

This relationship was well-known prior to 1905 (developed in the 1830's, I believe).

 

[Tom McCurdy]

If all aspects of modern physics are correct can someone please explain to me how to solve the paradox I listed in General physics. here is a copy of the letter I wrote ask my physics teacher...
-------------------
Greetings Mr. Sinclair,
I hope you were able to see the transit of Venus clearly from your vantage point; it truly was quite amazing where I was able to view it from out in the fields in Schoolcraft. The reason I was emailing you is I have a question dealing with General Relativity. I was wondering if you could fill me in on some more details of the “instant” phone that I thought had to do with something about electron pairs being separated great distances and since they are on the same quantum state. My question is wouldn’t this spell a huge problem to an already existing paradox in relativity. Let's you have 2 people moving in completely dark environment moving at a good pace of c at a constant velocity. Therefore by the laws of relativity to each own vantage point they are stationary and the other person is moving, therefore the other’s clock is running slower because it is taking some of the motion out of the time dimension and putting it into the other 3 dimensions (the way Einstein described it). The problem arises when they try to compare clocks at first, meaning there would be one true perspective which relativity doesn’t allow. However in trying to compare talks they would have to meet, or change paths feeling acceleration and/or direction compensating for the clocks difference in time. So meeting doesn’t work. However let's say they tried to call each other on their cell phones. This wouldn’t work because the signal would be limited to c and by the time it reaches the other person it to more than compensate for the time differences. However if they had there “instant” phones they would be able to surpass c in signal time and they would be able to communicate with each other right away. This would be a problem because it would mean someone was wrong, and this can’t be according to relativity they both must be right.
----------------------

Anyway if someone could post in the general physics forum here where i started the question

Oh also I have only taken one year of physics at high school so if you could do it without high level mathematics that would be great. (still in high school)

 

[quantumdude]

I will agree with your statement that:

Any experiment that confirms the LT does confirm SR, because SR is derivable from the LT.

provided we are talking about the transforms that contain the vx/c^2 term.

That's fine, since the prediction of the one-way speed of light leaves that term in tact.


edit to add:

Experiments that are in accord with the interval transforms where that term does not exist neither disprove nor confirm SR.

Why not? The formulas for time dilation and length contraction (which don't contain the term vx/c²) are derivable from the LT. If experimental evidence agrees with them, then that is a confirmation of the prediction.

In the same way, SR is derivable from GR. According to your logic, no experiment could confirm or disprove SR, because after all the same predictions are obtainable from GR. And if we continue along these lines, we'd have to note that GR is derivable from string theory, so that experimental confirmations of GR aren't really confirmations of GR either...

It would seem, according to this logic, that no scientific theory can ever be confirmed.

Is that what you believe?

 

[pmb_phy]

I said it once, and I'll say it again: Any experiment that confirms the LT does confirm SR, because SR is derivable from the LT.

Confirmation of the Lorentz transformation does not gaurentee that all foreseable laws of physics are the same in alll inertial frames of reference and that is a postulate of SR.

Pete

 

[quantumdude]

I just deleted a really dumb post that I made in response to this, so if you saw it before I zapped it, just ignore it.

Confirmation of the Lorentz transformation does not gaurentee that all foreseable laws of physics are the same in alll inertial frames of reference and that is a postulate of SR.

Of course, you're right. But confirmation of the LT does not guarantee that all foreseeable measurements of the speed of light are the same in all intertial frames, either. This is just a consequence of humans not being able to know everything.

 

[jdavel]

I think the argument here is just over the difference in definitions of "confirm" and "prove". No experiment can ever prove that SR is correct. But any experiment that is consistent with an SR prediction, confirms SR.

 

[quantumdude]

I think the argument here is just over the difference in definitions of "confirm" and "prove". No experiment can ever prove that SR is correct. But any experiment that is consistent with an SR prediction, confirms SR.

While that is an argument that pops up a lot, I don't think that's what is going on here. The point that is going back and forth between me and Yogi is that of logical implication. That is, can we recover SR from the LT? See, Yogi and I both agree (I think) that the LT is valid and has been confirmed. But he is saying that, since the LT can be arrived at by other ways, then it is possible to confirm the LT, while at the same time one (or both?) of the postulates of SR can be false. This is what I am arguing against, on the following grounds:

1. The LT preserves the form of all known laws of physics, thus reproducing the relativity postulate (we agree on this).
2. The LT predicts that the one-way speed of light will be c in any inertial frame (we disagree on this).

 

[quantumdude]

I think the argument here is just over the difference in definitions of "confirm" and "prove". No experiment can ever prove that SR is correct. But any experiment that is consistent with an SR prediction, confirms SR.

Now that I think about it some more, there is a disagreement about what it means for a theory to be "confirmed". I don't think that either Yogi or myself thinks that any scientific theory can ever be proven (like a mathematical theorem can be). But the difference is that he seems to think that any observation that agrees with more than one theory doesn't confirm any of them, whereas I say that it confirms all of them.

 

[reilly]

Invariance of Maxwell's Eq.

Maxwell's Eq. are invariant under Lorentz transformations, and rotational transformations (Static roatations, not dynamical ones). This guarantees that the speed of light in vacuum is the same in all directions, that is in all inertial frames. A spherical radiation wavefront in one inertial frame will be a spherical wavefront in any other inertial frame(In the general case of sources, the charge and current must transform like a four-vector, which seems to be the case.) So, there is no need to derive the constancy of the speed of light by coordinate transformations if you start with Maxwell's Eqs.

Certainly it is a mathematical necessity that constancy of c results from Lorentz transforming two appropriate events: emission of light at (x1,t1) and absorbtion at (x2,t2) with

x2-x1=c(t2-t1) and for transformed event coordinates (xN1,tN1) and (xN2,tN2) xN2-xN1=c(tN2-tN1) in any arbitrary inertial frame. Fortunately, different methods of demonstrating the constancy of c under Lorentz and rotation transformations all agree.

If I am stating nothing new, I apologize.
Regards,
Reilly Atkinson

(Re and earlier comment about dispersion: I've heard or read recently of some evidence for frequency dependence of "c" for very high energy photons. Unfortunately, I don't recall when or where.)

 

[Tom McCurdy]

Haha that thought experiment I posted ealier that I wrote to my physics teacher about I just realized is way to come to the conflict between QM and GR and the need for The theory of everythign WITHOUT any math :)

 

[yogi]

Tom - yes - as betwen us, there has been a semantic misunderstanding re the word confirm:

"Now that I think about it some more, there is a disagreement about what it means for a theory to be "confirmed". I don't think that either Yogi or myself thinks that any scientific theory can ever be proven (like a mathematical theorem can be). But the difference is that he seems to think that any observation that agrees with more than one theory doesn't confirm any of them, whereas I say that it confirms all of them."

When so used, I would concur that an experiment that agrees with the transform is confirmation of any theory from which the transform is derived. I usually use the word validate rather than confirm - so that clears up one point - thanks to djavel's observation.
__________________

 

[yogi]

Tom - your quote:

"2. The LT predicts that the one-way speed of light will be c in any inertial frame (we disagree on this)."

I don't disagree with that statement. The LT follow from Lorentz's hypothesis and from Einstein's. Lorentz, FitzGerld, Poincaire, and others were trying to save the ether and explain MMx. Einstein explained MMx (in his view, incidentally) to a more sweeping theoretic overhaul. So, using our updated definition, the experiments to date confirm both theories while proving neither. This leaves one question still pending - as to those theories that do not result in the LT that contain the vx/c^2 term, but only the (1-B^2)^1/2 - are they confirmed by time dilation experiments? How say you?

 

[quantumdude]

Tom - your quote:

"2. The LT predicts that the one-way speed of light will be c in any inertial frame (we disagree on this)."

I don't disagree with that statement.

Well, now I'm thoroughly confused, because you clearly disputed it when I derived the prediction. Did you change your mind as to the validity of that derivation?

The LT follow from Lorentz's hypothesis and from Einstein's. Lorentz, FitzGerld, Poincaire, and others were trying to save the ether and explain MMx. Einstein explained MMx (in his view, incidentally) to a more sweeping theoretic overhaul.

I am somewhat familiar with the history, but the point I am making is that a theory that reaches the LT as its conclusion is equvialent to SR even if it does not make the same postulates as SR. If we can agree on the logical entailment of SR from the postulates, then we will have agreed on the "propriety" of the postulates, thereby completing the discussion. Can we agree on that?

So, using our updated definition, the experiments to date confirm both theories while proving neither.

Of course. Theories are never "proven" anyway. Proofs belong to math, confirmation belongs to science.

This leaves one question still pending - as to those theories that do not result in the LT that contain the vx/c^2 term, but only the (1-B^2)^1/2 - are they confirmed by time dilation experiments? How say you?

If fhe formula is the same, and if it is validly derived from the postulates of the theory, then yes, they are confirmed by time dilation experiments.

By the way, were you formerly known as Provo? If so, then Hi, long time, no see.

 

[StonedPanda]

Its frustrating for me and I'm an engineer - I never work with it. I can't imagine how much it must annoy you.

I'm a high school student who is a geek on the inside, and I can't imagine how much it must annoy ...

!