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Re: [Phys-l] how to explain relativity

On Jun 17, 2010, at 1:50 AM, John Denker wrote:

I don't think length contraction has any physical reality.
In my experience, all the arguments for its physical reality
are grossly flawed. It's just a question of how many
femtoseconds of thought are required to find the flaw.

Unfortunately, this attitude about the "nonreality of length contraction" can get one into trouble if it is taken too far as illustrated here.

One spaceship accelerates for one day
of its proper time. The other spaceship accelerates for one
day of /its/ proper time. The two motions are congruent,
differing only in a change of position.

This is true as long as one confines one's attention to the original rest frame. It is not, however, true in the instantaneous rest frames of either spaceship.

We can represent this
using a super-simple spacetime diagram:

A' B'
/ /
/ /
| |
| |
A B

Indeed, it is precisely this spacetime diagram that establishes the constancy of the separation in the original rest frame.

The initial length of the rope is the proper distance between
A and B. The final length of the rope is the proper distance
between A' and B'. We can easily evaluate both of these lengths
in the lab frame.

Yup.

But proper length is a Lorentz scalar, so
it is the same in /any/ frame.

D'oh! I was afraid this might be coming. Much mischief results from casual use of the idea of "proper length." Better to stay away from it. It is the spacetime interval that is Lorentz invariant. The proper length of an object is determined by finding the interval between two events that take place at the endpoints of an object *at the same time* in the rest frame of the object. In other frames, of course, those events are not simultaneous.

So the rope does not stretch.
Not even a little bit.

This completes the analysis.

Actually, no. It *is* surprising, not well-known, but also uncontroversial that a body *can* be accelerated without deformation only by causing rearward portions to have progressively larger proper accelerations than forward portions.

Google on Born rigidity and/or see

http://www.csupomona.edu/~ajm/professional/talks/relacc.ppt

It is also worth noting that this requirement that rearward portions must have larger accelerations is in keeping with the relativistic transformation of the electrostatic forces that bind the atomic constituents. At high velocities, the equilibrium separations are smaller meaning that an object must REALLY contract as it "speeds up" (relative, of course, to an unaccelerated observer in the original rest frame) if it is to remain unstressed.

John Mallinckrodt
Cal Poly Pomona