On Sep 26, 8:19 am, wrote:
I *thought* I understood relativity but a simple calculation this
morning gave me quite a jolt.

Consider two identical meter sticks, both at rest in the reference
frame of observer O and pointed along the x-axis.

At time t=0, one of the two sticks begins traveling in the x-direction
at velocity (say) c/2. An observer O' rides along on the traveling
meter stick.

Nothing else changes, so that at t=1, the second stick is still moving
with a uniform velocity of c/2 relative to the first.

Until today, I thought that each observer would say "My stick still
has length 1; yours has shrunk to sqrt(3/4)".

But now, having drawn the spacetime diagram, I think that observer
O says "Our sticks both still have length 1", while O' says
"Your stick has shrunk to sqrt(3/4) and mine has grown to sqrt(4/3)".

Yes, SR fails as a complete and self-consistent kinematical theory.
You'll find many "bugs" like this in Physics.

Suppose A,B denote the end points of the O'. At time 0 an
instantaneous acceleration is applied simultaneously (along the
simultaneity line 0) everywhere on the Rod.

|
T |
I | A B
M | A B
E | A B
| A B
0----A-----B--------
| A B
| A B
| A B

SPACE

Here the length of the moving rod with respect to itself has changed
violating the supposed invariance of proper units. In other words,
tidal forces arise where they shouldn't.

The solution to this problem is to not apply the acceleration
simultaneously, but apply the acceleration across the rod in a single
unique way such that O' measures the same rod length after the
acceleration. The Spacetime diagram looks something like this

|
T | A B
I | A B
M | A B
E 2 A B
| A B
0----A-----B--------
| A B
| A B
| A B

That sort of acceleration profile is called a "Born rigid
acceleration". An acceleration which does induce tidal forces.

The problem is that out of all the infinite possibile ways the rod
could be accelerated, the rigid profile is merely one of them.


[See http://groups.google.com/group/sci.p...?dmode=source]

[...]