I was told that the Galilean relative velocity rule does not apply to the speed of...

I was told that the Galilean relative velocity 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?

Expert Solution

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 . 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

genius_generous answered 1 month ago

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