# Does this theory merrily assert things about the speed of light?

1. May 19, 2012

### davidlones365

As I've understood it, Einstein developed SR in an attempt to explain why the speed of light would be observed as a constant law from any point of reference, but it seems more like he only asserts this and goes on. How does he actually explain it? Does he ever explain why light speed velocities have to be treated so unusually?

2. May 19, 2012

### Staff: Mentor

He doesn't. He takes it and the principle of relativity as postulates and uses those to explain other things.

3. May 19, 2012

### DaveC426913

You are correct. SR's primary postulate (a sort of "Let's suppose...") is that light always moves at c. It does not make any attempt to explain why that might be.

What makes the theory so successfully is that, with that postulate, the theory explains spectacularly and exquisitely exactly what we do see. It goes without saying that it does so far better than any competing theory.

4. May 19, 2012

### Mentz114

He was more concerned about the problem with the electrodynamics of moving bodies which afflicts Maxwells equations in Gallilean relativity. At some point he realised that the problem could be solved by asserting the constancy of the speed of light. There is a big hint in Maxwells equations that this is so.

Remember that it is the locally measured speed of light that is constant. The speed of light is actually frame dependent in curved spacetime.

He does not. No 'explanation' exists as far as I know.
As I said above, he found it necessary to explain electrodynamics in moving frames.

5. May 19, 2012

### Mark M

Welcome to PF!

There were a few reasons to believe light had a constant speed.

Firstly, James Clark Maxwell's equations for electromagnetism gave a speed for light, but not a frame of reference. Most physicists interpreted this to mean that there must be an absolute frame of reference that light traveled through, called the luminiferous aether. In 1887, the Michelson-Morley experiment was conducted to try to find a difference in the speed of light as the Earth orbited the Sun in different directions (Winter/Summer). Their result was negative, and they measured the same speed.

Also, Einstein's main motivation for special relativity was the Principle of Relativity. The PoR states that the laws of physics are the same for all inertial frames of reference. So, an observer in a locked room has no way of knowing if he is in motion or not. But, if the speed of light varied, he could see that the light emitted by his flashlight was moving at a different speed. Einstein felt that no experiment, even the use of optics, should violate the PoR.

The combination of both led him to propose special relativity. Today, even more precise experiments have shown he invariance of the speed of light.

6. May 19, 2012

### davidlones365

Thats my question. There really have been experiments done at a significant fraction of the speed of light showing this? If so, I apologize for my ignorance, but frankly, in my quest to wrap my head around Einstein's words, no one has ever directly cited any.

Last edited: May 19, 2012
7. May 19, 2012

### Mark M

Yes. M-M was the first experiment that refuted the aether and established the invariant speed of light. Since then, there have been more precise experiments. See here.

Also, the Fermi Satellite has, in the past for years, placed extreme limits on any theory that allows for Lorentz violations. (Certain theories of quantum gravity predicted a change in the speed of light at extremely short distances.)

8. May 19, 2012

### Mark M

Oh, and to add. Special relativity in general has been confirmed by mountains of evidence. Time dilation, length contraction, and mass-energy equivalence have all been observed. See here.

9. May 19, 2012

### davidlones365

...well, thank you. I'll have to investigate this further, my own ignorance astounds me. It seems this sort of misunderstanding is common amongst those first studying this. Perhaps it's just laziness.

10. May 19, 2012

### davidlones365

...wait, I still fail to see the need of imposing time dilation and contraction if the formula used to calculate velocities at near light speeds is different. That's the source of my dilemma. I'm going in circles. The only reason explained for things such as time dilation to occur is to in effect "warp" the perception of the "speed" of the light particles to match the "constant" speed of c.

Last edited: May 19, 2012
11. May 19, 2012

### Staff: Mentor

Your best bet will be to retrace Einstein's logic from the start. Time dilation, length contraction, the velocity addition formula, and even $E=mc^{2}$ all follow from a more fundamental set of equations, the Lorentz transforms which relate measurements of time and space taken by one observer to those taken by another observer moving with respect to the first observer.

Einstein's argument is set out in his 1905 paper "On the electrodynamics of moving bodies" (http://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf and many other places on the web), but here's the Cliffs Notes version:

1) We expect that the laws of physics don't change just because you happen to moving. This is basically common sense: even if you think you are standing still, your speed through space changes from midnight to noon as the speed of the rotation of the Earth's surface is added to or subtracted from its speed around the sun... but you don't expect experiments to give different results because of this. There is also a ton of experimental evidence to support this piece of common sense.

2) The laws of electricity and magnetism say that the speed of light in vacuum is equal to c; it's a value that we can calculate from these laws. So if the laws of physics don't change with motion, and the speed of light can be calculated from these laws, we might start to suspect that the speed of light shouldn't change with motion. Furthermore, there is another ton of experimental evidence, starting with the Michelson-Morley experiment, that tells us that the world really does work this way, the speed of light in vacuum really is equal to c for all observers regardless of their relative motion.

3) So Einstein had good reasons for assuming that the speed of light would be constant for all observers, and seeing where this assumption took him. First, he derived the Lorentz transformations from this assumption; you can find the derivation in Appendix A of his book "Relativity: The Special and General Theory" (google it). These formulas relate measurements of time and space taken by one observer to those taken by another observer moving with respect to the first observer.

4) From the formulas, you can derive all the bizarre-sounding bits of special relativity: Time dilation, length contraction, the velocity addition formula, and even $E=mc^{2}$ and all that good stuff. Of course this doesn't mean that it's right, just that it's logical. However....

5) We have piled up an amazingly huge amount of experimental data showing that the world really does work this way, that the bizarre-sounding predictions are correct, atom bombs go boom, moving clocks run slow, velocity addition works as advertised. So now we believe we have a good theory, that Einstein's chain of logic really is valid.

One final note: Because speed is defined as distance traveled divided by time, you shouldn't be surprised to find that any formula that calculates speeds can be recast as a formula involving distance and time, and vice versa. Thus, you shouldn't be thinking of time dilation and length contraction as stuff that was made up just to make the velocity addition formula come out right; instead all three are consequences of the way that time and space behave for observers moving relative to each other.

Final final note: I'll let someone else explain why they're "Lorentz transforms" instead of "Einstein transforms". This post is already too long.

Last edited: May 19, 2012
12. May 19, 2012

### davidlones365

Again, my dilemma is that the velocity addition formula alone accounts for the speed of light remaining constant. I just don't see a need for the other aspects of the theory.

I've been trying to read along with that book, that when my questions arose.

13. May 19, 2012

### ZikZak

The two postulates (relativity and invariance of c) directly imply time dilation, length contraction, and simultaneity failure. That is to say: the Lorentz Transformation. From these principles, one can further derive the velocity addition rule. Velocity addition is a special case of the Lorentz Transformation.

14. May 19, 2012

### Staff: Mentor

It's not so much that the other aspects are needed or not needed - it is that they are inseparable from the velocity addition formula. The argument that leads to the velocity addition formula also leads to the other aspects, so in the process of deriving one (starting with the constant speed of light and moving through the Lorentz transform) you've also derived the others; they come as a package deal.

Another way of thinking about it: If you try playing with the algebra for a while, you'll find that you can derive time dilation and length contraction from the velocity addition formula. So you can't accept the velocity addition formula without accepting the other two, any more than I could accept that 2+2=4 but not that 4-2=2.

15. May 19, 2012

### Staff: Mentor

Grab a copy of the 1905 paper - It's much harder to follow because it assumes much more knowledge on the part of the reader (it was written for professional physicists), but it moves through the steps with more precision than the book.

16. May 19, 2012

### robphy

May I suggest another book:
http://archive.org/details/RelativityCommonSense by Bondi

start at p. 76 to understand the "k-factor" (the doppler factor)
see the diagram on p. 95
p. 102 has the formula for k in terms of v (and soon, the velocity composition formula)
p. 117 derives the Lorentz Transformation, followed by applications

... all implied by (i.e., not chosen but forced upon us by) the Relativity and Speed-of-Light postulates.
Thus, these applications all are consistent with (but don't explain) the Speed-of-Light postulate.

I like radar methods because they give operational meanings of t,x,v, etc... in terms of radar measurements.

17. May 19, 2012

### Staff: Mentor

Absurd of me to respond to the same post three times in a row... But it occurs to me as I reread the above that your confusion may be because you have it backwards....

The velocity addition formula does not account for the constant speed of light. It's the other way around - the constant speed of light accounts for the velocity addition formula and the other stuff.

18. May 19, 2012

### Mark M

The velocity addition formula directly takes into account time dilation and length contraction. If you used the TD and LC formulas, you can calculate velocity addition without the special relativity velocity addition formula. It just makes things easier.

19. May 19, 2012

### davidlones365

Ok, I think I've got it. The thought experiment I had in my head involved two beams of light pointing in opposing directions, with an observer moving parallel to them at a given fraction of c. What I failed to realize was that according to SR its not the speed of the beams themselves in question, it's the speed at which the light reaches the observer.

My conclusion would likely make more sense to you guys if my original thread hadn't been taken down because, according to the mentor, "my speculations were based in faulty understanding" ...anyhow, I'm satisfied at this point.

Last edited: May 19, 2012
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