Why relativity is right

1. May 27, 2004

krab

(I couldn't resist the title, because I am fed up with all the crackpot threads about why some aspect of modern physics is "incorrect".)

I work at an accelerator lab, dealing with particles whose velocities are not small compared with the speed of light. To me, saying that SR is incorrect is exactly like saying "the internal combustion engine is a fraud and does not work". It's a statement of such silliness as to leave one breathless. It is not as if I use some tiny piece of SR which is just small enough that I wiould get the same answer from another theory (which for example does not insist that simultaneity is relative). No, SR is fleshed out by me and others in excruciating mathematical detail, and if it is even a tiny bit wrong, our accelerator would not work!

Anyway, I thought I would share with everyone an aspect of the beauty of SR that I have never seen described anywhere else. Before SR, it was known that the pair of variables (t,E) acted very like the pairs (x,p_x), (y,p_y), (z,p_z). (These are called "canonical pairs".) It was known for example that in field-free regions,
$$E={p_x^2\over 2m}+{p_y^2\over 2m}+{p_z^2\over 2m}$$
Hamilton showed that considering E to be a function of x,y,z,p_x,p_y,p_z, all the equations of motion could be derived from it. (It's called the "Hamiltonian".) For example, the equations could be derived from the "principal of least action", which involves the following integral
$$\int p_xdx+p_ydy+p_zdz-Edt$$
Notice the symmetry (except for a sign change) between the afore-mentioned canonical pairs.

This symmetry obtains at a very deep level. For example, one could "pretend" that the independent variable is z instead of time t. Then all the equations would no longer answer the question, "Where is the particle at time t and what are its momentum components?", but rather, "I'm at z, so what are the x and y coordinates, the momenta p_x and p_y, and energy E and by the way, what time is it?" This can be obtained by solving the above E equation for p_z, and using p_z as if it were the new Hamiltonian. Amazingly, all the derived dynamics is exactly the same as if t were the independent variable.

There is truly a cyclic symmetry among x,y,z,t, and among p_x,p_y,p_z,E. All this was well-known before anyone ever dreamed of SR. So the question was: Why doesn't the equation for E display this symmetry explicitly? In fact the known dependence of E on momentum was very unsymmetric; for example, the momenta are squared, and the energy is not.

Then SR came along and everything made sense because:
$$E^2-p_x^2c^2-p_y^2c^2-p_z^2c^2=m^2c^4$$
(or, in words, the norm of the 4-momentum is the rest energy). Notice the restoration of symmetry. Notice as well that this equation converges to the previous one (aside from a constant added to E) in the limit $E<<mc^2$

Beauty, ain't it?

2. May 28, 2004

chroot

Staff Emeritus
krab,

I moved your post here because I think no one will benefit from it in the TD section.

geistkiesel,

I deleted your post because I couldn't detect any substantive argument in it.

- Warren

3. May 28, 2004

Staff: Mentor

I know that feeling.
Indeed it is! Thanks for posting that, krab.

4. May 28, 2004

Staff: Mentor

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

5. May 30, 2004

HallsofIvy

And the logic of those who dispute relativity is always the same: "I don't understand it therefore it is wrong"!

6. May 30, 2004

(Q)

Krab

Excellent post! However, if HallsofIvy statement is correct, then it's not likely the crackpots will understand it anyway.

7. May 30, 2004

turin

krab,
I totally agree with your intent (my thesis was on GR, so I feel somewhat of a pang when someone tries to tell me it's bogus), but, I am not entirely convinced that it would be impossible to come up with:

E2 - p.pc2 = m2c4

without SR. The trivial counter-argument that comes to mind is to make the above equation an axiom. A not quite so trivial counter-argument (but almost as ad hoc) would be the generalization of the Schroedinger Equation (for the sake of symmetry) to the Dirac Equation that involves completing the square and requires the use of the Pauli Matrices. In fact, symmetry has seemed to me a powerful argument in itself, so one could just argue for:

E2 + αp.p = constant

and then:

E2 - p.pc2 = m2c4

would likely flesh out naturally (i.e. α would be found to equal -c2 and the constant would be m2c4).

8. May 30, 2004

kurious

KRAB:

"I'm at z, so what are the x and y coordinates, the momenta p_x and p_y, and energy E and by the way, what time is it?"

But if I bring the uncertainty principle into this argument ( momentum x position = h bar) does the symmetry still apply, given that, in general, the uncertainty in momentum is different from the uncertainty in position.

9. May 30, 2004

Tom Mattson

Staff Emeritus
Yes, the symmetry still applies. Don't forget, the uncertainty principle does not hold betwee the components of the 4-momentum, it holds between conjugate pairs.

&Delta;x&Delta;px>=hbar
&Delta;y&Delta;py>=hbar
&Delta;z&Delta;pz>=hbar
&Delta;t&Delta;E>=hbar

which is symmetrical with respect to p and E, as well as x and t.

10. Jun 3, 2004

yogi

Most of the questions that arise re SR do not involve the correctness of the interval transforms, but the propriety of the postulates - there are alternative ways to arrive at the Lorentz transforms (for example those of Lorentz). Before you condemn the "crackpot threads" you should take the time to read what is being questioned. Here is a quote from one of the doubters:

“There is no idea of which I would be sure that it would stand the
test of time, and I have doubts whether I am on the right way
In general ...feelings of dissatisfaction come from the inside.”

Albert Einstein

11. Jun 3, 2004

kurious

“There is no idea of which I would be sure that it would stand the
test of time, and I have doubts whether I am on the right way
In general ...feelings of dissatisfaction come from the inside.”

Albert Einstein

And Einstein could not at first believe he was right and Newton was not.
I don't think relativity is wrong - I just think that one day there will be a more fundamental explanation of why it is right.

12. Jun 3, 2004

DrChinese

"More fundamental explanation" is in the eye of the beholder. "More fundamental description" is not likely, as the equations are already quite straightforward. The only real possibility is why c has the value it does.

And I want to throw my lot in with moving this thread from TD to SR/GR. 'Bout time...

13. Jun 3, 2004

Tom Mattson

Staff Emeritus
In what way is the propriety of the postulates still questionable? Both have been directly tested experimentally.

We all know that.

Most of the crackpots threads attack the interval transforms, and say that we should go back to Galileo.

This doesn't carry much weight. You can find similar quotes from the founders of quantum mechanics, expressing doubts about their subject. Once the trauma of the paradigm shift wears off and the experimental confirmation starts raining down in buckets, the doubts get quenched pretty fast.

14. Jun 3, 2004

yogi

Kurious - I believe you have the time sequence reversed - the quote from Einstein was near the end of his life - after he had reflected upon these ideas for many years.

Dr Chinese - I would wager that a more fundamental description is on the horizon - SR is not really a physical theory as originally interpreted by Einstein himself - it is a mathematically elegant exemplification of symmetry without physics - but as early as 1915 Einstein begin leaning toward the notion of some sort of medium -- having properties necessary to explain gravity vis a vis G.R. - we will likely not find anything as beautiful and simple as SR - but it is likely that a better understanding of space will lead to a functional relationship between the transforms and the universe.

15. Jun 3, 2004

yogi

Tom - your comment, as with that posted by Kurious - would only be appropriate if the doubts were voiced in his early writings - Einstein reflected upon his theories for the better part of his life - after considerable experimental evidence had been amassed to substantiate time dilation (which can be used to derive all of the other SR relationships that have been experimentally confirmed).

When you say the postulates have been experimentally confirmed - you bypass the essence of the argument - the alternative theories such as Lorentz Ether, local G field modification of space, Inflow theory, etc, are also validated by the experiments - The Selleri tranforms lead to exactly the same results. I am not advocating anything personally - what I am about is to question dogmatic certainty.

16. Jun 3, 2004

krab

You have not defined "crackpot threads". See below. Most of us here, and especially the mentors, "take the time to read what is being questioned".
I don't know why this is a remarkable quote. All the really great physicists had in common the humility to realize that they do not have a lock on the truth. But those I would call "crackpots" are exactly the opposite. Countless times, I've read threads by people who say "Einstein wrong...", or "Michelson-Morley misinterpreted". Here's a typical example:
It is always "a little cogitation" or some such. Yet it always develops that the crackpot knows far far less physics than the people who developed, worked on, work with the theory. In fact it is very striking how often such people say "I'm not much good with math...". The same people are always so certain of their own theories that they then misinterpret the humility of great physicists as being a sign that these theories were/are really shaky.

17. Jun 3, 2004

yogi

Krab - yes - I agree with all that you have said in your last post - there are many unfounded, ridiculous and arbitrary theories based upon nonsense... not worth audience or reply. What is of concern to me is the danger in asserting that SR (or any other theory for that matter) should be closed to further examination. SR is of particular interest because it can be interpreted in different ways, and has been by well reasoning intelligent persons. I wouldn't give a hoot for a theorist that is unable to derive the mathematical relationships that are required to evalute the merits of his musings

18. Jun 4, 2004

DrChinese

The dogmatic certainty is that previous experiments have been done which yield constraints as to theory development. The certainty is not that the existing theory is perfect, final, or somehow exempt from modification when new results are found.

This is freely acknowledged by mainstream science, as is the idea that we are ignorant in many areas and much more work remains. That too is a "dogmatic certainty". But not exactly a dark conspiracy of closed-minded hacks.

19. Jun 5, 2004

yogi

Dr Chinese - that is the way it should be - but history teaches us that authoritarians resist change - I don't have Planck's quote correct - but it was to the effect that we have to wait for the present generation to die off before the new ideas can take root.

20. Jun 5, 2004

Nereid

Staff Emeritus
Excuse my ignorance, but do these alternative theories (or at least some of them) yield the same predictions (etc) as SR/GR, no matter what (in other words, they are, from the point of view of anything that could ever be done, experimentally or observationally, identical to SR/GR)?

If not, what specific predictions do these make that can, in principle, be tested (and which differ significantly from those of SR/GR)?