Here's a relativity question that's been bugging me for about
a year now. I once posted it on the sci.physics Usnet group, but
got only one response - which I frankly could not understand.
The speed of a transverse wave along a string is given by
v = sqr root (T/u),
where T is the tension and u is the linear mass density. Therefore,
by chosing a large enough tension and a small enough linear mass density
it should be possible to propagate a wave, and hence information,
faster than the speed of light.
By first thought at a resolution was that this is making the mistake
of applying a classical equation to a relativistic situation. But then I
began to wonder if the classical approximation is necessarily invalid.
After all, the speed of the wave propagation is not the speed at which
any segment along the string would be moving. Any point along the string
would have a speed on the order of the wave amplitude divided by the
period, Since amplitude and period can be chosen independently of the wave
speed it would seem that the speed at which any matter would be moving
could be made arbitrarily small and the classical approximation as
applicable as we want it to be.
Can anyone help me with the resolution. Thanks in advance.
Ed Schweber (e-mail: EdSchweb@ix.netcom.com)
Physics Teacher
Solomon Schechter Day School
West Orange, New Jersey