There is a very convincing argument for physical length contraction:All relativistic wave equations exhibit physical Lorentz contraction. These wave equations can be implemented with ordinary mechanical mass/spring
systems which show physical Lorentz contraction. For example: A mass/spring grid
with a characteristic speed of 1 meter/second shows the same Lorentz contraction
at 0.9 meter/second as matter wave packets show at 0.9c.It is actually very easy to proof. To start with the classical wave equation:
<br />
\frac{\partial^2 \Phi}{\partial t^2}\ -\ c^2 \frac{\partial^2 \Phi}{\partial x^2}\ -\ c^2 \frac{\partial^2<br />
\Phi}{\partial y^2}\ -\ c^2 \frac{\partial^2 \Phi}{\partial z^2}\ =\ 0<br />
This equation governs propagation in all kinds of classical situations as well as the
propagation of the electromagnetic (potential) field. c is the characteristic speed.
Mathematically, any arbitrary function which is stable (doesn't change in time) and
which shifts along with a velocity v obeys mathematical relations like:
<br />
\frac{\partial \Phi}{\partial t}\ =\ -v \frac{\partial<br />
\Phi}{\partial x} \qquad \qquad \frac{\partial^2 \Phi}{\partial<br />
t^2}\ =\ v^2 \frac{\partial^2 \Phi}{\partial x^2}<br />
These expressions are always valid independent of the shape of the wave function.
We can use the quadratic one to eliminate the dependence on t from the equation:
<br />
\left(1-\frac{v^2}{c^2}\right) \frac{\partial^2 \Phi}{\partial x^2}\ +\ \frac{\partial^2<br />
\Phi}{\partial y^2}\ +\ \frac{\partial^2 \Phi}{\partial z^2}\ =\ 0<br />
This shows that the solutions are Lorentz contracted in the direction of v by a factor
gamma, The first order derivatives are higher by a factor gamma and the second order
ones are higher by a factor gamma^2. It shows that velocities higher as c are impossible.
The proof can't hardly be any simpler.
It is from this chapter of my book:
http://physics-quest.org/Book_Chapter_EM_LorentzContr.pdfRegard, Hans
Regards, Hans