# Speed of light and relativity

1. Apr 9, 2004

### NanakiXIII

Now I'm not absolutely sure this is the right forum, but here goes.

I've been told that the relative speed of light is supposed to be the same in any reference frame. Is that true, and if so, how is that possible?

2. Apr 9, 2004

### mathman

It is possible simply because it happens to be that way. There are many popular books describing special relativity. You should get one.

3. Apr 9, 2004

### NanakiXIII

I've read articles about it, but I just don't understand how that would work. Doesn't it have an absolute speed?

4. Apr 9, 2004

### chroot

Staff Emeritus
Yes, the speed of light appears the same to all observers who measure it, no matter how they happen to be moving. It always appears to be going a specific speed, c. This is the fundamental postulate of the special theory of relativity.

While this may seem hard to swallow at first, it follows naturally from the relativity of velocities. In other words, there's no way to define a velocity without reference to something else. Take, for example, two spaceships passing each other in the depths of space. Which one is moving?

- Warren

5. Apr 9, 2004

### NanakiXIII

But spaceships don't relatively move at the same speed in any reference frame, do they? So why does light?

6. Apr 9, 2004

### FZ+

Because it travels at the speed of light.

More accurately, the velocity addition formula in SR is:

w = (u + v)/(1 + uv/c^2)

Suppose we have an object receding at u, and it measures the speed of light as c... Set u = u, and v = c:

w = (u+c)/(1+u/c)
w = ((u+c)c)/(u+c)
w = c

If our spaceship travelling at the speed of light, things would be very wierd - but fortunately relativity tells us why spaceships can't travel at the speed of light (if it had rest mass), so the question is invalid.

chroot: I don't think it follows naturally from relativity of velocities. More the other way round...

7. Apr 9, 2004

### Kurdt

Staff Emeritus
It may have something to do with the fact that light is the medium by which we sense the universe. Just as one takes for granted certain parts of physics such as our attraction to the Earth and the rotation of the Earth it may also take for granted that light always travels at the same speed since its velocity is so great with respect to our everyday happenings. Hence the slowing down of ageing and so forth is just the fact that information passing from one place to another takes longer and we sense that more time is passing as our brain believes that light is travelling at the same speed as normal. Thus we measure the volcity of light as constant anywhere because it is the fundamental instrument of information transfer. Of course I could be spectacularly wrong.

8. Apr 9, 2004

### Kurdt

Staff Emeritus
PS: I may not have worded my thoughts particularly well so any questions are welcomed.

9. Apr 9, 2004

### jdavel

NanakiXIII,

The fact that light speed relative to us is always c seems hard to believe because we have so much accumulated experience with things (namely objects with mass) whose speed is not always the same relative to us.

Einstein said that his conviction of constant c began to form when he was about 16 and tried to imagine what a light wave would look like if you could travel along with it. Light waves are kind of complicated, and I don't know how much physics you've learned.

But try thinking about what a water wave would look like if you could travel along with it. Suppose you concentrated your vision on just one crest of the wave that you were moving along right next to. Would a big hill of water that seems to be standing still make sense? Why, or why not?

10. Apr 9, 2004

### Integral

Staff Emeritus
As Chroot said, c is a postulate of Special Relativity, this means that it is ASSUMED without proof. So any result of SR cannot be used to prove the constancy of c. SR is an exploration of the effects of a constant c, not the reasons c is constant. There is a big difference.

The primary theoretical derivation of a constant c was done by Clerk Maxwell in about 1867. This result, that the propagation speed of electro magnetic waves through space depended only on fundamental constants and not the motion of the source, sent shock waves through the world of Physics, for the next 50 yrs Physics had to contend with the existence of theoretic waves which did not obey the closely held laws of Mechanics. You are not the first to be bothered by this! It bothered an entire generation of Physicists. This may have been the hottest topic in Physics for the last half of the 19th century. Many attempted to ignore it feeling that it was an error on the part of Maxwell and it was up to him to fix it. Others attempted to find experimental evidence to the contrary, they failed.
The issue was finally resolved by Einstein, the reason no one was concerned by his postulate when he published is because it was the "hot topic" of the day, all of physics was aware of the fact so it did not need proof. Today this fact that a constant c preceded SR by 40 yrs is often forgotten.

11. Apr 9, 2004

### jdavel

Is that really true? The speed of mechanical waves are independent of the motion of the source. So, why would Maxwell's discovery have been such a shock? He believed in an ether, and that the c in his wave equations was constant relative to that ether, just the way mechanical waves travel at a constant speed relative to their medium.

I'm pretty sure if you had asked Maxwell in 1867 what the velocity for the EM wave would be if you traveled in the direction of a light beam at .1*c, he would have .9*c.

12. Apr 9, 2004

### chroot

Staff Emeritus
No. Maxwell's equations are a wave equation with a velocity = c. Nowhere does the velocity of the source or observer appear in the the equation. Maxwell's equations predict the speed of light = c, period.

- Warren

13. Apr 9, 2004

### turin

Perhaps your confusion is based on Galilean relativity. Galilean relativity is simply not believed to be accurate. For about 300 years, considerations of motion were required to adhere to Galilean transformations. When Maxwell's equations came along in the latter part of the 1800's physicists realized that Galilean transformations had to be replaced by more accurate transformations (that approach Galilean transformations in the slow speed limit). This effort culminated in Einstein's SR in 1905 with his radical conjecture that:

t' /= t

!

14. Apr 9, 2004

### jdavel

The same thing can be said about the equation for a sound wave. The velocity that appears in that equation isn't with respect to the source or observer. It's with respect to the medium in which the wave is a disturbance. And in 1867 Maxwell believed that the wave speed c in his equation was with respect to the EM medium; so did everyone else. The first person who didn't, wasn't born until 12 years later.

15. Apr 9, 2004

### jdavel

I don't think that's true. If the Michelson Morley epxeriement had detected a medium for light waves, why would the Galilean transfomations have needed to be replaced? What would have replaced them? Surely not the Lorentz transformations!

16. Apr 9, 2004

### turin

Fair enough.

Why not?

17. Apr 9, 2004

### Integral

Staff Emeritus
Jdavel,
Surely you have heard of the disruption in the world of Physics that occurred in the last half of the 19th century? This is a simple historical fact, it occurred. The source of the troubles was the constancy of c. The speed of sound depends on properties of sound which vary with density of the material, so it was not a fixed constant. The

expression $$\sqrt { \frac 1 {\epsilon_0 \mu_0}}$$
does not vary with any known material properties, these constants were well known and well understood. The implications of this expression were clear to all trained physicists. It received so much press I believe that even the lay people of the day were made aware of the implications of this fact.

As for the constant c originating with Albert Einstein consider that the Michelson Morley experiment was performed about the same time AE was born. So while little Albert was still considered the village idiot the world of physics was aware of the constancy of c and a key experiment to detect the ether had failed. I have no difficulty believing that Albert grew up thinking about the meaning of a constant c, it was a very popular topic in that day. I also cannot believe, as some have claimed, that he had never heard of the results of Michelson and Morley. Michelson was a well known figure in that era, for Albert to be unaware of his work would be like saying a current student of cosmology has never heard of Stephan Hawking. Albert Einstein was a well educated Physicist (though not able to find a job in the field) at the time of the publication of his first papers. It is simply inconceivable that he was not aware of key historic events in his field of interest.

18. Apr 10, 2004

### jdavel

It would be very surprising if it did, since it refers to properties of empty space. But when light travels through matter it slows down, and you can't use this expression to compute the speed.

So Maxwell's wave equation says that the speed of light is c in emtpy space, but something else through matter. The equation for sound says that the speed of sound is 1100ft/sec through air at STP, but something else through air at a different temp or pressure.

So what's so special about the speed derived by Maxwell? As long as you believe there's an ether (and Maxwell did) the answer is nothing. Light waves like all other waves, would travel at a constant speed with respect to the medium on which they propagate. It wasn't until M&M found (to their disbelief) that there is no ether, that light speed began to seem special, because with no medium there doesn't seem to be anything for c to be referenced to. Without a medium, what does c even mean; 300,000km/s with respect to what? The answer turned out to be "with respect to all observers" but nobody knew that until 1905.

19. Apr 10, 2004

### Eyesaw

Note that this expression used to derive the speed of light in vacuum has the same form as that used to derive the speed of light in different mediums, thus it would be interesting and appropriate at this time to discuss the meanings of magnetic permeability and electric permitivitty and the methods by which they are determined. From my understanding of the terms, it seems obvious that under Maxwell's formulation, permitivitty and permeability are properties of an EM propogating medium which varies according to the "density" of the medium. Thus the so called "vacuum" in Maxwell's equations is not really a vacuum but is descriptive of a light propogating medium with a minimum density achievable by available technology.

20. Apr 10, 2004

### da_willem

Actually the speed of light is the same in any medium. The thing that changes is the phase velocity. this is because of the repetative process of scattering with he atoms making up the material, which introduces a phase shift in the scattered light. When this scattered light recombines with the transmitted light it interferes and shifts the phase of the combined wave. This happens continuously, and because the speed of the wave is the rate of advance of the condition of constant phase, a change in the phase should correspond to a change in the speed.

The proces described above can in some circumstances even yield a phase speed higher than c. This does not contradict special relativity because the speed at which information is transported depends on the speed of the photons, wich is still c.