Relativity and the Speed of Sound

Question:

information transmitted faster than light?

Submitted 30 September 1997 by J. Lee of San Francisco, CA.

do i understand correctly that nothing travels faster than light, including information? what about information transmitted through a solid object: imagine a solid rod between earth and mars. if i push or twist the object from earth, wouldn't the motion be transmitted instantaneously to the other end, at mars? therefore, we could, theoretically, transmit data instantaneously, faster than the speed of light?

Answer:

5 October 1997

Yes, your understanding about the speed of information transmission being limited to the speed of light is correct. Your question is a good example of the many paradoxes that rush into a thoughtful person's mind when they first hear about the Special Theory of Relativity. In this case, you must realize that real, physical "rigid rods" are not perfectly rigid. That is, if you apply a force to stretch or squeeze them, they do stretch or squeeze a little. Otherwise they would be infinitely strong, which would be wonderful for engineering purposes, but is, alas, unphysical.

If I push on a real rod stretched out in space, the near end moves right away, but the far end does not move immediately. Instead, a compression wave starts propagating down the rod, at the speed of sound in the material of the rod. The far end does not move until the wave reaches it. The speed of sound depends on the rigidity (technically known as "Young's Modulus") of the rod, and also on its density. It is fastest for rigid materials of low density, like diamond or silicon carbide, for example. Typical speeds are a few km per second, roughly 100,000 times slower than the speed of light.

It is worthwhile to reflect that at a microscopic level, all the forces that matter in practice in chemistry and materials science are actually electromagnetic forces, governed by Maxwell's Equations, the fundamental equations of electromagnetism. Einstein constructed his Special Theory of Relativity in 1905 particularly to take account of Maxwell's Equations' radical implications about space and time, which he was the first to appreciate. Thus it is not surprising that the electromagnetic forces acting between atoms and molecules, which give rise to the macroscopic rigidity of materials, are consistent with Special Relativity. If they weren't, Einstein would have failed in his first purpose! Thus, the speed of sound can never be faster than the speed of light in any ordinary material.

Ten years later, he made the General Theory of Relativity to make gravity consistent with what he had learned about space and time from Special Relativity. That was all the forces that were known at that time. Decades later, theories of the other two forces we know (the "strong interaction" and the "weak interaction", governing certain short-range interactions among elementary particles) were constructed within the framework of relativistic quantum field theory, meaning that consistency with Special Relativity was required from the beginning, built into the roots.

And, by George! -- Those theories are consistent with SR too!