Why is energy-momentum symmetry important in special relativity?

[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.