# Why is speed of light constant?

1. May 6, 2010

### Tantalos

I am not a physicist, but recently I started to learn relativity theory. Therefore I have following question.
Is there any logical or physical explanation of the phenomena that speed of light is the same for every reference frame? How can two observers moving at two different velocities see light pulses travel with equal speed? How are Maxwell equations related to this phenomena?

2. May 6, 2010

### mgb_phys

There have been a huge number of popular books published about this in the last 100 years - but a quick intro -
The principle of relativity (much older than Einstein's theory) is that you can't tell you are moving (assuming you aren't accelerating) without looking at some outside point.
If this wasn't true and experiemental results depended on how the laboratory was moving your science lesson would be different everyday as we moved around the sun.
So far no problem - everybody accepts this, you can test it yourself when you are on a train and the train next to you pulls away smoothly - only looking out of your window at the other train who is moving ?

Maxwell's equations basically say that there is a constant that is the same everywhere in order for the equations of electricity and magnetism to work. But this constant includes the speed of light.

So Maxwell's equations say the speed of light is fixed in the universe.
But this means you could measure if you were moving by just measuring the speed of light relative to your laboratory.
So the speed of light must be fixed for all observers - this involves having to totally change our idea of how speeds add together, and how length time and mass aren't fixed. That's what special relativity does

3. May 6, 2010

### bcrowell

Staff Emeritus
If you want to give a theoretical explanation for a certain fact, you need to have in mind some other fact that you consider more fundamental, so that you can start from that as an assumption. In mathematical terms, you need to decide on a set of axioms before you can start proving theorems.

There is more than one way to choose your set of axioms for special relativity. In the axioms originally chosen by Einstein (1905), the frame-independence of c is taken as an axiom, so it can't be proved. On the other hand, you can choose a different set of axioms, as in Rindler (1979), in which frame-independence of c is a theorem, not an axiom. Here is an online presentation (mine) in the same spirit as Rindler's: http://www.lightandmatter.com/html_books/6mr/ch01/ch01.html [Broken]

Einstein, "On the electrodynamics of moving bodies," 1905, http://www.fourmilab.ch/etexts/einstein/specrel/www/
Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

Last edited by a moderator: May 4, 2017
4. May 6, 2010

### bcrowell

Staff Emeritus
I don't find anything specific I can disagree with in this argument, but to my taste it kind of misses the target. What's important is to make the distinction between the c that appears in relativity and the speed of light. In 1905, light was the only fundamental field that had ever been detected, so it was natural to think of the speed of light as having some fundamental importance. A more modern way of looking at it is that the c in SR is really a property of spacetime, and massless fields just happen to propagate at c. We don't know whether the photon has a nonvanishing rest mass (Lakes 1998). If it does, then it will have the same status as the neutrino, and we'll have to stop referring to c as the speed of light, but there will be absolutely no consequences for SR.

R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters 80 (1998) 1826, http://silver.neep.wisc.edu/~lakes/mu.html

5. May 6, 2010

### Tantalos

I have thought about it and I came to the following explanation. EM waves are propagated as Maxwell equations describe. Maxwell equations tell that magnetic field has no source. So one could take the source of electric field with him into his reference frame but it is not possible with the magnetic field. Thus the EM wave is propagating totally independent of any reference frame, only the source emitting the wave can be moved with reference frames.
The propagation of the EM wave involves two phenomena:
1. the moving front of the wave,
2. when the front has passed along the observer, then the observer is "sunk" in a space-stationary oscilating EM field.
In the 2nd case every observer moving as he moves in the field will experience only Doppler efects, The speed will apear to him constant, independent of his own speed, because as he moves through the EM field he will only experience that the wave transitions occur at different time in his reference frame.
If observer A sends a light wave in his own reference frame, he will not see any frequency shift, because the source of the ligth moves with the same speed as the receiver. But observer B in another reference frame moving at different speed will also see the light moving at the same speed as will see observer A, only frequency shifted. The only condition is that no object can move at speeds greater than the speed of light.
The relativity then slows down the clock of reference frame A, so that to observer B the frequency of the light is the same as to observer A.
Is this explanation possible?