In 1962, after I'd made a measurement of the velocity of light I attempted to measure the Lorenz contraction predicted by Einstein's special theory of relativity.
This apparent contraction is seen when a measurement of length of an etalon is moving relative to a fixed observer.
I cannot remember exactly what I did in 1962 but if two mirrors, one mounted on a turntable and one stationary, the path the light takes when the turntable is rotating, at the moment of reflection is different from when not turning. This is due to the length contraction. Therefore the interference pattern of light between the two mirrors will differ as the rate of rotation varies.
Experimental arrangement.
In this experiment careful collimation makes the measurement to be made only when the alignment is correct.
I cannot remember the result but I don't think I got one.
The Lorenz transformation
It is just a simultaneous equation.
The invariance of the velocity of light is an experimental result. It means that when you measure the velocity of light some how the result is independent of the velocity of the source, like a star or a lamp on a moving bench.
If you can work out the time an aeroplane takes for a return journey west to east with a constant east wind then you are well on the way to calculating the Lorenz transform.
Suppose the aircraft does v knots through the air and the wind is u knots over land then going from west to east d nautical miles the velocity is v-u and it takes d/(v-u) hours to get there going back it takes d/(v+u) hours. so the average is (d(1/v+u)+d(1/v-u))/2 =
d((v-u)+(v+u))/v+u)(v-u)/2
= d(v)/v^2-u^2)=d/v(1-(u/v)^2)
With the Lorenz transform c is constant so if the velocity of the source is v then to make the velocity c in both frames the distance the light travels must be contracted to make the time d/v once again. So the rest distance is d, if d* is the contracted distance then d*/c=d/c+v and the same for the source with a velocity -v so d*/c=d/c-v so (d*/c)^2=d^2/(c+v)(c-v) so,
d*=d(sqr((c^2/(c^2-v^2)))=d/(sqr(1-(v/c)^2).
This contraction is not real it is an effect like perspective because we use light to measure the distance, it has no physical meaning.
Quite simple really, it is an example of a geometric mean and is called a metric as in differential geometry where you look at a hill, going over the hill is further than along the ground and if you are unaware of the slope the longer distance would be the only way you could know of the hump. Relativity is like that, we cannot see the real path of the light it is distorted by the space distortion caused by the movement of the source or observer. Except that in relativity the path over the hump is shorter that the path along the flat path. Think of a space time diagram the path is a ^ but the path over the ^ is shorter at high velocities than the path and very slow velocities.
A six inch bar is still a 6 inch bar there is no
contraction whatsoever. It is demonstrated each time you use an electric motor
or switch on an electric lamp. The electrons move the positive charges do not,
this means that the electronic length is shorter than the bar of metal they
are moving in but no positive charge occurs at the end so there is no
contraction at all.
There is no contraction really and no upper limit on velocity. If you work out the momentum it Mv/(sqr(1-(v/c)^2) but when you separate it for integration you go M (v/(sqr(1-(v/c)^2) the mass does not increase only the number v/(sqr(1-(v/c)^2) and this is the real velocity V.
Much more fun you can get velocities higher than light with a rocket or accelerators where the phase velocity of the travelling wave (as in a rhombadron) is higher than light. Remember group velocityXphase velocity is c for light in a waveguide and the same is true of matter waves so a stationary electrons phase wave occupies the whole universe and the energy quanta of a free electron is influenced by the size of the universe and all the matter in it.
The increments of energy that an electron is given as it accelerates is in reality determined by the size of the universe. This is because an electron is a group of waves of infinite velocity that extend around the 4-sphere universe. When the group changes its velocity the change is reflected by an alteration in the diffraction pattern as in a boxed particle and a quanta of radiation is emitted that has a frequency determined by the difference in frequency between the frequency of the initial step and the frequency of the final state.
This energy comes from the electric field that pushes it and since this push is by a virtual photon the emitted photon is the realised virtual photon of the electric field brought into existence by the movement of the electron.
When the universe was very small the steps were very large and so the universe was actually very cold at it conception as the quanta were too large for anything to move.
Fascinating is it not?
Chris.
02/01/2010