# Why is the speed of light same in all reference frames?

kindly be descriptive

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tiny-tim
Homework Helper
welcome to pf!

hi akshay.wizard! welcome to pf!

the structure (the metric) of space-time has a preferred speed

anything with that speed in one frame will have the same speed in all frames

light happens to travel at that speed

bcrowell
Staff Emeritus
Gold Member
FAQ: Why is the speed of light the same in all frames of reference?

The first thing to worry about here is that when you ask someone for a satisfying answer to a "why" question, you have to define what you think would be satisfying. If you ask Euclid why the Pythagorean theorem is true, he'll show you a proof based on his five postulates. But it's also possible to form a logically equivalent system by replacing his parallel postulate with one that asserts the Pythagorean theorem to be true; in this case, we would say that the reason the "parallel theorem" is true is that we can prove it based on the "Pythagorean postulate."

Einstein's original 1905 postulates for special relativity went like this:

P1 - "The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion."

P2 - "Any ray of light moves in the 'stationary' system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body."

From the modern point of view, it was a mistake for Einstein to single out light for special treatment, and we imagine that the mistake was made because in 1905 the electromagnetic field was the only known fundamental field. Really, relativity is about space and time, not light. We could therefore replace P2 with:

P2* - "There exists a velocity c such that when something has that velocity, all observers agree on it."

And finally, there are completely different systems of axioms that are logically equivalent to Einstein's, and that do not take the frame-independence of c as a postulate (Rindler 1979).

For someone who likes axioms P1+P2, the frame-independence of the speed of light is a postulate, so it can't be proved. The reason we pick it as a postulate is that it appears to be true based on observations such as the Michelson-Morley experiment.

If we prefer P1+P2* instead, then we actually don't know whether the speed of light is frame-independent. What we do know is that the empirical upper bound on the mass of the photon is extremely small (Lakes 1998), and we can prove that massless particles must move at the universal velocity c.

In a system such as Rindler's, the existence of a universal velocity c is proved rather than assumed, and the behavior of photons is related empirically to c in the same way as for P1+P2*. We then have a satisfying answer to the "why" question, which is that existence of a universal speed c is a property of spacetime that must exist because spacetime has certain other properties (basically, it has some symmetries, and it doesn't have universal simultaneity).

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

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

bcrowell - interesting, but I wonder --and it seems pretty important in this discussion-- what were Rindler's axioms?

ghwellsjr
Gold Member
Every time anyone has ever measured the speed of light, they always get the same answer, even if it seems like they should be getting a different answer, depending on the conditions under which the measurement was made. Prior to the famous Michelson-Morley Experiment (affectionately known as MMX), virtually all scientists believed that light had a constant speed through a medium they called the luminiferous æther which they assumed was fixed in space and since the surface of the earth was traveling through space in different directions and at different speeds throughout the day and throughout the year, they believed there would be an æther wind which would modify the measureable speed of light. That's what MMX was attempting to do but they could not detect any variations attributable to the presummed æther wind. Since then, many other people have attempted to detect a variation in the measured speed of light at different times when the earth should be experiencing a changing æther wind, always with the same null result.

You should be aware that each time the surface of the earth changes its direction and speed in space, it is as though observers carried along on the surface of the earth are constantly being dragged into different reference frames. This is the real reason why we now conclude that the speed of light is the same in all reference frames--it's what we measure and what always comes out the same.

But maybe you are asking a different question--the same question the scientists after MMX were asking--how is it possible to always measure the same speed of light, even when you know that you are changing reference frames, that is, traveling through space in different directions and at different speeds? They concluded that the only way this could happen was if their measuring apparatus was getting compressed in the direction of the presumed æther wind and their clocks were running slow. These two adjustments could explain why they always measured the same value for the speed of light.

But, maybe this isn't really what you are asking either. If so, you need to be more definitive in your question so that we will know how to give you a more satisfying answer.

bcrowell
Staff Emeritus
Gold Member
bcrowell - interesting, but I wonder --and it seems pretty important in this discussion-- what were Rindler's axioms?
Unfortunately he doesn't lay them out as a list. But basically it's homogeneity and isotropy of spacetime, relativity of motion, causality, and observer-dependence of time. Here is my own treatment: http://lightandmatter.com/area1book6.html There is an appendix in the back of the book that lists other treatments in this style.

OK. But why is the speed of light the constant why not any other speed?
"Looking at relativity from the perspective of length contraction and time dilation being the cause, and a constant speed of light the effect, is a long-since rejected notion." And why is this perception rejected?
(And i would try and write properly.Sorry for the inconvenience.)

D H
Staff Emeritus
But why is the speed of light the constant why not any other speed?
The snarky answer is "Because." That is the answer given in Einstein's 1905 paper. He postulated that the speed of light is the same to all observers. Remember back to when you were a kid. Some kids pester their parents by repeatedly asking "why?" The parents inevitably get flustered at some point and answer "Because I said so." Think of a postulate as being a scientist's or mathematician's way of saying "Because I said so."

So what motivated Einstein to make this postulate? The answer lies in Maxwell's equations. Maxwell's equations describe electromagnetism. One consequence is that the speed of light is constant. Newtonian mechanics says otherwise. Solving the conflict between Newtonian mechanics and Maxwell's equations was the big problem in physics in the latter part of the 19th century. Einstein's insight was to take Maxwell's equations at face value: The speed of light is the same to all observers.

A more modern view is that in our universe, space on a local scale appears to be Euclidean. A universe that is locally Euclidean almost everywhere must necessarily have a speed, a single speed, that is the same to all observers. One obvious solution is an infinite speed. This is Newton's universe. A finite speed also works, and this is Einstein's universe. Experimentally, there is a single speed that is the same to all observers, and it is finite (the speed of light). Ergo, we live in Einstein's universe, not Newton's.

Looking at relativity from the perspective of length contraction and time dilation being the cause, and a constant speed of light the effect, is a long-since rejected notion.
And why is this perception rejected?
Occam's razor.

Einstein was far from the only physicist working on this problem. Poincare, Lorentz, Fitzgerald, and others worked on it; it was one of the biggest problems in physics of that time. Those other physicists were perhaps too encumbered by the past. Maxwell's equations dictate that light is a wave phenomenon; every wave phenomenon known at that time propagated through some medium. So light must therefore propagate through a medium called the luminiferous aether. Those physicists developed a scheme in which length contraction and time dilation are axioms. A consequence: Their luminiferous aether could never be observed. The theory had two axioms that were very ad hoc and postulated a medium that was inherently unobservable. Yech (physicists don't like ad hoc laws) and double yech (physicists really don't like a theory in which something basic is inherently unobservable).

The two theories, Lorentz Ether Theory and Special Relativity, are mathematically equivalent (they predict the same outcomes for any experiment). Einstein showed that the two key axioms of Lorentz Ether Theory are not needed, nor is the luminiferous aether. Occam's razor says that in the case of two competing theories that fully explain the same phenomena, the simpler explanation is usually the correct one.

Dale
Mentor
What about possible ether dragging proportionally to gravitational force (or maybe proportionally to gravitation energy density) + Lorentz contraction together?
In this way famous MMX becomes unable to measure anything.
That was a thought that also occured to scientists of the time. They tried many variations at different altitudes, with different amounts of matter nearby, etc. Nothing made any difference.

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

Staff Emeritus
2019 Award
I had to do some thread cleanup - this thread was sidetracked onto two different side tracks by two different individuals. Let's get back to the OP's question.

rbj

hi akshay.wizard! welcome to pf!
the structure (the metric) of space-time has a preferred speed
anything with that speed in one frame will have the same speed in all frames
light happens to travel at that speed
i really think that the fundamental answer to the question is an extrapolation that Einstein made from perceived reality (observation) to reality.

you have two observers, both in inertial frames of reference (neither is accelerated, BTW akshay, it's in all inertial reference frames where the speed of light is the same), but they very well may be moving relative to the other observer. but both observers look at themselves and conclude that they, themselves, are not moving but it's the other guy who is moving. both observers have equal claim to being the stationary observer and that it's the other observer who is moving. if there was an aether defining a reference frame that is truly stationary, that could settle the dispute between the two observers as to which of them is stationary and who is the one that is moving, but there is no such thing as aether and, while it wouldn't have surprized Albert, it did surprize Michaelson and Morley (if i recall correctly) when they tried to measure our motion through this hypothetical aether.

so now think of it, if both observers truly have an equivalent claim to being the stationary observer, then both observers must have identical laws of physics. not just identical in form (say the 4 Maxwell's equations), but also identical regarding constants or parameters in such laws. if Observer A's reference frame is no difference in properties as Observer B's frame (even if they are not the same frame of reference and are moving relative to each other), then where would a difference in any parameter come from. they would both have the same $G$, the same $\hbar$, the same $k_B$, the same $\epsilon_0$, the same $\mu_0$, and from the latter two, , the same $c$.