# Why and how is the speed of light constant?

I was told that the relative speed rule does not apply to the speed of light. No matter how fast two objects are moving, the speed of light will remain same for both of them.

How and why is this possible?

Also, why can't anything travel faster than light?

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@Noldorin: I don't agree it is low-level. But it is a duplicate of this question: physics.stackexchange.com/questions/1345/… – Marek Dec 24 '10 at 14:41
@Marek: How is it not low-level? It's fundamental SR; anyone who has done first year undergraduate should understand this. – Noldorin Dec 24 '10 at 15:33
@Noldorin: you will notice that there are high school questions here that are of much lower level. You will also notice that the link I provided is about the same level. I am not saying it's good to have these questions here (although I am not saying it's bad either), just that you are not consistent if you'll leave those other questions open. But you're the boss, so whatever suits you :-P – Marek Dec 24 '10 at 16:32
Graduates are not same all over the world. Everyone using this website does not live in America – LifeH2O Dec 25 '10 at 17:16
It certainly isn't a duplicate of 1345. Someone looking for the answer to this question would not bother to read a post on the nature of vector addition. Nor is the question "fundamental SR". The speed of light is defined in GR, it depends on the coordinate system (and for many of them, on the direction). – Carl Brannen Feb 6 '11 at 23:06

The view of most physicists is that asking "How can it be that the speed of light is constant?" is similar to asking "How can it be that things don't always go in the direction of the force on them?" or "How can it be that quantum-mechanical predictions involve probability?"

The usual answer is that these things simply are. There is no deeper, more fundamental explanation. There is some similarity here with the viewpoint you may have learned in studying Euclidean geometry; we need to start with some axioms that we assume to be true, and cannot justify. Philosophically, these ideas are not precisely the same (mathematical axioms are not subject to experimental test), but the constant speed of light is frequently described as a "postulate" of relativity. Once we assume it is true, we can work out its logical consequences.

This is not to say that, in physics, postulates stay postulates. For example, many people are especially concerned about probability in quantum mechanics, and are trying to understand it based on more fundamental ideas (see decoherence as one example). As another example, Newton's laws of motion were originally taken as unprovable postulates, but are now explained via quantum mechanics (see Ehrenfest's theorem).

At this time, the constancy of the speed of light, or more generally the principle of Lorentz symmetry, is not justified by anything considered to be more fundamental. In fact, the assumption that it is true has been a guiding light to theoretical physicists; quantum field theory was invented by thinking about how quantum mechanics could be made to respect the ideas of relativity.

Although we do not have a theoretical justification for the constancy of the speed of light, we do have very accurate experimental tests of the idea. The most famous is the Michelson-Morley experiment, which measured the relative speed of light in different directions to see if it was affected by the motion of the Earth. This experiment rejected the hypothesis that the motion of the Earth affects the speed of light. According to the Wikipedia article I linked, a modern version of this experiment by Hils and Hall concluded that the difference in the speed of light along directions parallel and perpendicular to Earth's motion is less than one part in $5*10^{12}$. In addition to direct tests of the speed of light, there have also been many other experimental tests of special relativity. (I haven't read this last page carefully, but, on flipping through, it looks good.)

There are a few caveats worth mentioning. In general relativity, the speed of light is only constant locally. This means that the distance between two objects can increase faster than the speed of light, but it is still impossible for light to zip past you at a speed faster than the normal one. Also, in quantum theory, the speed of light is a statistical property. A photon may travel slightly slower or faster than light, and only travels at light speed on average. However, deviations from the speed of light would be probably be too small to observe directly.

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 I have exactly the same thought, if distance b/w two objects can obviously increase with more speed, what will happen? The relative speed of one object will be more than the speed of light? – LifeH2O Dec 17 '11 at 10:29 Yes, one might say the relative speed exceeded $c$ if the distance increased faster than $c$. The speed of light being a maximum is only a local constraint on the speeds. – Mark Eichenlaub Dec 17 '11 at 15:52 I always assumed it was because (in an nutshell) light travels so fast, that we have nothing to compare it to, so therefore, nothing can be faster. Isnt that simpler? – Ender Jun 2 at 20:55

In actual fact, the relative speed rule does not apply, ever.

The relativistically correct speed addition rule is the following:

$$s=\frac{v+u}{1+\frac{vu}{c^2}}$$

When $\frac{vu}{c^2}$ is close to zero (in other words when the velocities invloved are much less than the speed of light, then the correct formula reduces to the Galilean version $s=u+v$.

Nothing can be faster than light, fundamentally, because as you accelerate you not only gain speed, but also mass. As you approach the speed of light, the energy given to you by the force causing the acceleration basically contributes more and more to the increase of your mass and less and less to the increase of your speed. It does this precisely so you never reach the speed of light. Instead, massless particles like photons always travel at the speed of light.

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As to part 2 of your question "Also why nothing can be more speedy than light?", the answer is that it's not just light. The point is that c is the maximal velocity of any causal, information transmitting interaction in the universe, mediated by anything travelling forwards in time (see footnote). Its just that photons, having 0 rest mass, travelling in a vacuum approach that fundamental limit, c.

Footnote: Except maybe 'tachyons' - never seen and traveling backwards in time because they go faster than c. (Note that Norbert Wiener once pointed out that for a causal influence travelling backwards in time, we would experience it as "random", since it would apparently be an event without an antecedent cause to us).

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John Moffat and Moffat and Albrecht and Magueijo have variable speed of light theories where the speed varied in the early universe and is not a constant. Majueijo has a poplular book Faster Than The Speed of Light outlining his theories. IMO the book is quite outrageous and insults various people. I mention this answer for completeness only as I believe the speed of light in a vacuum is constant.

Space can expand faster than the speed of light, but no information can be transmitted. See the Alcubierre warp drive for some fun.

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That the speed of light is invariant is a property of Minkowski spacetime, and there should be plenty on that in Wiki - or search for 'geometric algebra' or Clifford Algebra.

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