Why is energy-momentum symmetry important in special relativity?

[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[/color]))
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[/color].

 

[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[/color]. 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[/color]. 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 ...

!

 

[yogi]

Hi Tom - yes, and hi to you - I suppose my inveterate skepticism was a give away. When they restructured the forums the yogi bear logo wasn't available - so i adopted the name and dropped the Provo. When we last conversed, you were awaiting a decision on a research department appointment that would enable you to continue a particular intrigue re quantum mechanics. Did that come to fruition?

Yes - as to your question if we are interpreting "propriety" in the same way.





Regards

Yogi (Provo)

 

[quantumdude]

Hi Tom - yes, and hi to you - I suppose my inveterate skepticism was a give away.

LOL, no, the clincher was the "Yogi"!

When they restructured the forums the yogi bear logo wasn't available - so i adopted the name and dropped the Provo.

With the new software, you aren't limited to what we have available. If you can find a picture you want online, get the URL and you can upload it to PF through your User Control Panel. That's what I did with mine.

When we last conversed, you were awaiting a decision on a research department appointment that would enable you to continue a particular intrigue re quantum mechanics. Did that come to fruition?

No, I never heard back from them. Right now I'm teaching math and engineering at a small college, and preparing to return next year to get back to work on my PhD.

Yes - as to your question if we are interpreting "propriety" in the same way.

I interpret it as accurately describing observational evidence. As was fleshed out over the course of this thread, my position is that any theory that results in the LT implies the speed of light postulate (I had been saying *both* postulates, but I am still thinking about pmy_phys' comment). That is, alternatives to SR that result in the LT aren't alternatives at all, but rather they are possible explanations as to why SR is true. That is, the alternatives aren't going to tell you that light speed isn't always measured at 'c', but they can possibly explain why this is so. Either way, the postulate of SR is appropriate.




Regards

Yogi (Provo)[/QUOTE]

 

[yogi]

Back to you Tom,

Sorry the appointment didn't materialize - one is never sure about what goes on behind the scenes - who knows, the path you are on now may lead to greater rewards.

Thanks for the tip re the logo - I will try it soon.

The reason SR is of particular interest to me is in connection with a theory of gravity I developed some years ago - it requires that space behave (at least mathematically) as a dynamic - along the lines proposed by Dirac. For me, the search for a physical explanation as to why SR relativity is consistent with experiment is an ongoing hobby.