# How is c determined to be the maximum speed?

1. Apr 6, 2004

### whitelighter

How is "c" determined to be the maximum speed?

A person I was discussing light with asked me this question:
Is there evidence to support the contention that the maximum speed is 'c'?

I must admit I couldn't answer the question.

I happen to agree that 'c' is the maximum universal speed but I would like to ask my erudite readers if this has actually been proven. That the maximum is in fact the maximum or is it sort of a default statement based on the validity of the rest of the theory, such as because x and Y are true then Z must be the case?

I don't wish to presuppose the answer so any help will be appreciated.

2. Apr 6, 2004

### Kurdt

Staff Emeritus
A prediction of c comes from Maxwell's famous equations for electromagnetism. It can be shown that,

$$\nabla \times \mathbf{B}=\epsilon_0\mu_0\dot{\mathbf{E}}$$
and
$$\nabla \times \mathbf{E}=-\dot{\mathbf{B}}$$

when B or E is eliminated we obtain:

$$\nabla^2\matbf{E} -\epsilon_0\mu_0\frac{\delta^2\mathbf{E}}{\delta t^2}=0$$

which is the equation of a plane wave for the electric field with velocity given by

$$c^2=\frac{1}{\epsilon_0\mu_0}$$

c can also be determined directly from electrical experiments but I hope this helps.

Last edited: Apr 6, 2004
3. Apr 6, 2004

### Kurdt

Staff Emeritus
Oh sorry on the question of the maximum speed it was basically lots of experiments done such as that by michelson and morley always measured the same speed for light no matter what inertial frame they were in which led Einstein to his first work on relativity and his postulate that all inertial observers measure light at the same speed.

4. Apr 6, 2004

### KingNothing

It's pretty well proven that it's the maximum speed. You don't need a lengthy novel to tell you that if you put every possible speed upgrade in the fastest car possible, it would be the fastest a car could go. It's not a whole lot different when it comes to photons. They have every possible advantage they could have over all other particles. As in 0 rest mass, oscillating fields, etc.

Oh, and to elaborate on what Kurdt said, an inertial frame of reference is where the observer is in a state where he is not accelerating or decelerating or rotating. Then a lawrence (or is it lorentz?) transformation can be done to make him "still".

Last edited: Apr 6, 2004
5. Apr 6, 2004

### Staff: Mentor

whitelighter doesn't seem to want the mathematical proof, but the experimental one. The best way is probably a particle accelerator: give a particle a certain amount of energy and then measure its speed. According to Newton's laws, there should be a specific/finite amount of energy associated with an electron (for example) traveling at C. Go above that and see where it gets you.

6. Apr 6, 2004

### Integral

Staff Emeritus
The constancy of c is predicted by Maxwell's equations, as shown above. In his derivation of the Special Relativity, Einstein predicted that a constant c implied that c is a upper speed limit on all motion.

Since all mass is fundamentally electromagnetic, this limitation make sense.

7. Apr 6, 2004

Say what????

8. Apr 6, 2004

### Kurdt

Staff Emeritus
Well mass can be created or destroyed but the energy is not and that energy manifests as electromagnetic waves. Best example of this is a positron-electron pair production and subsequent annihilaton.

9. Apr 6, 2004

### jdavel

whitelighter asked:"Is there evidence to support the contention that the maximum speed is 'c'?"

Yes, there's lots.

The fact that no one has ever made anything go faster than c (or even seen anything going faster than c) is evidence. And since lots of people have tried very hard, it's actually pretty good evidence.

The fact that as you increase the energy of electrons, a graph of speed vs energy shows the speed approaching c asymptotically is pretty convincing evidence. And the fact that the exact shape of the graph is just what SR predicts, and SR says nothing can go faster than c, is even stronger evidence.

None of this, of course, means that it's been proven c is the ultimate speed. Physics can't do that.

10. Apr 6, 2004

### Kurdt

Staff Emeritus
Another problem of course is that particle interactions are believed to be carried by exchange bosons which travel at c. The question arises can anything exist at a speed greater than these exchange bosons which effectively make the physical world around us. On the flip side, tachyons are also a prediction of special relativity which are particles that only travel faster than the speed of light. These have mainly been dismissed as a mathematical oddity of the theory though.

11. Apr 6, 2004

### outandbeyond2004

Yes, plenty of evidence, as shown in previous posts.

Proven? No. Science does not ever prove anything like with mathematical certainity.

The speed of light in vacuum as measured in an inertial reference of frame is taken as a postulate (principle, to be technical). The experimental successes of SR and also GR can be taken as experimental support.

Which comes first, theory or experimental evidence or observations? That is a chicken-egg question.

12. Apr 6, 2004

### Terry Giblin

Gentlemen, whilst we are the subject of the speed of light.

How far can you walk into a circular forest - half way - then your walking out again.

As integral said earlier,

"Since all mass is fundamentally electromagnetic, this limitation make sense"

13. Apr 6, 2004

### whitelighter

Thanks people,

I happen to agree with you, however the arguement goes like this.

"When doubting these theories doubters are constantly required to prove what they are theorising. They need mathamatical proof, they need to be able to explain and predict phenomenon and they can't be successful only by default"

Arguements that state ...."we can't find anything that goes faster"
or " the theory works everywhere" else etc
are not normally adequate arguements.

The contention that the maximum speed is "c" from what you have confirmed for me is one that is achieved by default, an outcome of the theory and not proven ( yet ) in a way that is required by other theories.

This doesn't mean that the contention is invalid except to say that it is only a contention ( a very strong one at that ) but only a contention.

As far as I'm concerned it's hardly worth the trouble but as far as the "crackpots" are concerned it is a big issue.

I think russ_watters is closest to providing a source of proof.

But the arguement "just because we can't make something go faster than 'c" doesn't mean it can't be done ...only that we are unable to see how to do it"

Maybe this is one question that can never be answered properly, a bit like trying to make a straight line into a circle and saying thant just becasue you can't doesn't make it impossible ( I know guys...someone is bound to say that we can....ha ha...curved space and all that)

For example it could be argued that anything faster than 'c' would be
instantaneous......why?.....pooh...I dunno!!!

Another could be that 'c' is actually zero km / p / sec and everything else is normally ......relative to 'c' .being Zero.....you know the way logic can be thrown about...a bit like calling 'c' as you would zero degrees celcius or what ever

Last edited by a moderator: Apr 6, 2004
14. Apr 6, 2004

### Janus

Staff Emeritus
You're operating under a misconception here; notheory is ever proven. At best, a theory can gain support through increasing evidence. Relativity is no exception and is held to no lower or higher standards than any other theory.

15. Apr 6, 2004

### Staff: Mentor

Its far stricter than that: we can't accelerate an object with mass past c in a Newtonian sense - unless our existing model of the universe is spectacularly wrong.

16. Apr 6, 2004

### whitelighter

well I don't think the understanding of the universe is "spectacularly" wrong at all.....

And I might add these questions will surely be solved in due course.....

So ....

What should my response to the question about "c" as a maximum be....do you think?

17. Apr 7, 2004

### Chi Meson

"There is no (conclusive and repeatable) evidence of any particle with non-zero rest mass traveling as fast as c. There is also no evidence of any particle at all travelling faster than c."

[Then someone says: "well what about tachyons?"]

"Tachyons have never been detected."

PS: excellent thread BTW

18. Apr 7, 2004

### Kurdt

Staff Emeritus
Many people believed the neutrino was a fictional particle until it was found. Granted it is an impossibilty to detect something that travels faster than any detection device can operate so for all purposes tachyons don't exist for us but thats not to say they don't exist at all.

19. Apr 7, 2004

### Staff: Mentor

SR really is that strong of a theory, whitelighter, and so many other theories are based on it that it would bring down most of physics to find it wrong. An enormous amount of our modern technology depends on the correctness of SR.

Go with the experimental evidence thing: adding more energy to an object has been observed to result in less and less acceleration as it aproaches C.

20. Apr 7, 2004

### ZapperZ

Staff Emeritus
Since I had to battle a lot of quacks very often, I happen to have this collection of experimental verifications on hand. So, anyone can refer or use this list. Take note that these are experiments that make a DIRECT test on SR's postulates. So these do NOT include experimental evidence that make use of SR's principles, such as those done in condensed matter physics.

1. B. Schaefer, PRL v.82, p.4964 (1999); or see http://www.aip.org/enews/physnews/1999/split/pnu432-2.htm

2. http://www.aip.org/enews/physnews/2000/split/pnu484-1.htm

3. http://www.aip.org/enews/physnews/2002/split/590-1.html

4. C. Braxmaier et al., PRL v.88, p.010401 (2002); or see http://www.aip.org/enews/physnews/2002/split/571-1.html

5. P. Wolf et al., PRL v.90, p.060403 (2003).

6. J.A. Lipa et al., v.90, p.060403 (2003); or see http://www.aip.org/enews/physnews/2003/split/623-2.html; http://physicsweb.org/article/news/7/2/12

7. J. Luo et al., PRL v. 90, p.081801 (2003); or see http://www.aip.org/enews/physnews/2003/split/625-2.html

8. M. Buttiker and S. Washburn, Nature v.422, p.271 (2003).

9. Muller et al., PRL v.91, p.020401 (2003).

10. M.D. Stenner et al., Nature v.425, p.695 (2003); or see http://physicsweb.org/article/world/16/12/3

11. G. Saathoff et al., PRL v.91, p.190403 (2003); or see http://www.aip.org/enews/physnews/2003/split/655-2.html

This list goes on and on... but I have only collected the most recent, and the most accurate to date in a particular technique or parameter being tested. Anyone wishing to diss, or argue against the validity of SR, will need to address this wealth of experimental verification FIRST.

Zz.

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