There is an excellent website of tutorials on Special Relativity at
http://www.phys.unsw.edu.au/einsteinlight

From it I learned something I had never thought of, and find astonishing.
Consider the following experiments:

Two slightly separated charges of the same sign experience only a
repulsive force given by the equations of electrostatic
repulsion/attraction if they and I are moving at the same velocity in an
inertial frame of reference. I can measure the charges by some kind of
device that measures the force between the charges.

However if the two charges are moving relative to me, in a different inertial
frame, they would also constitute a "current" and produce a magnetic field.
Since the charges are the same, the two "currents" will attract each other
and reduce the net repulsion. I would therefore observe a reduced force 
between the charges with my measuring device.

The effect of the relative motion is given by the same expression for the 
relativistic time/space contraction of Special Relativity.

Hence electric motors are direct demonstrations of the effects of Special 
Relativity. 

[N.B. in a wire carrying electricity the electrons are moving and the
protons, which balance the charge, are not, so only the relativistic
electron motion creates the observed magnetic field. However if I then
start moving at the same speed as the electrons (join their inertial
reference frame) I do not observe a change in the magnetic forces because
then the protons would be in the inertial frame moving with respect to me
in the reverse direction and thereby creating the same relativistic
magnetic field.]

4 responses total.

This is more GR than SR, but: has it been verified experimentally that the
gravitational escape speed is (2 M G / r)^0.5 even when it works out to
relativistic values for the escape speed?

The gravitational escape speed from earth is tiny compared to c. Relativistic
corrections are not required for nearby orbital mechanics except for precision
location devices like GPS. Now, near the event horizon of a black hole,
you'd have to do further calculations....

This is what I'm wondering about. The idea that there *are* such things as
black holes is based on the escape-speed formula holding even for cases of
massive/dense objects, such that it's possible to have things close enough
to it such that Ve +> c. This would indicate an infinite escape *specific
energy*.

But isn't specific energy acceleration integrated over distance?

I'm wondering it it might not be the case that, rather, Uk = M G / r, since
this would be gravitational acceleration integrated from x == inf. to
x == r. Thus Ve would still be less than c at any nonzero radius, contrary
to the notion of a "black hole".

Again, has it been verified that Ve == (2 M G / r)^0.5 *always* holds? Is
there experimental/observed evidence that requires it (ie, requires escape
speeds greater than c)?

I don't understand all the implications of general relativety, but at least
taking just a Newtonianish energy perspective, if G is great enough,
Uk/M could exceed c^2, in which case no escape is possible. 

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