"Bill Owen" wrote in message ...

[snip]

Why is Savard multiplying xi by beta instead of dividing?

Because the expression on the right-hand side uses tau, not t. It's
certainly true that x = xi/beta + vt.

Here's the trivial derivation.

1) Solve tau = beta(t-vx/c^2) for t:
t = (tau/beta) + vx/c^2.

2) Multiply both sides by v:
vt = (v tau)/beta + (v^2c^2) x.

3) Solve xi = beta(x-vt) for (vt):
vt = x - xi/beta.

4) Equate the right-hand sides of (2) and (3):
(v tau)/beta + (v^2/c^2) x = x - xi/beta.

5) Solve for x:
(v tau)/beta + xi/beta = x - (v^2/c^2) x
= (1 - v^2/c^2) x
= x / beta^2

6) Multiply both sides by beta^2:
beta(v tau + xi) = x
which is half of the inverse transformation. Solve for t in terms of xi
and tau similarly, by solving the equations for xi(x,t) and tau(x,t) for
x, equating the two expressions for x, and solving for t. The result is
t = beta (tau + v xi/c^2).
================================================== ==============
v = x/t, so
t = beta (tau + x/t xi/c^2).

Incomplete, you still have 1/t on the RHS, Compo.
"Because the expression on the right-hand side uses tau, not t. " -- Bill
Owen, above.

v = dx/dt (which can be integrated to x plus a constant) and since v is a
constant too we have v = x/t anywhere on the x-axis.
This the velocity of the train/ship/plane/car in the Earth's Euclidean
coordinate system.

Unfortunately for you the velocity of Earth anywhere on the xi-axis of the
vehicle's coordinate system is upsilon = dxi/dtau = xi/tau and upsilon does
not equal v.

To demonstrate, let v = 0.866c so that beta = 1/sqrt(1-0.866^2) = 2
Choosing x = 0.866, we have t = 1 for simplicity.
Hence tau = t * sqrt(1-0.866^2) = 0.5

xi = beta(0.866 - 0.866*1) = 0, the Earth is at the origin of the vehicle's
coordinate system at tau = 0.5, so it must have been at beta(0-vt) at tau =
0 and travelled a distance dxi = 0-upsilon.tau in time dtau = 0.5-0 with
velocity upsilon = xi/tau = 1.732/0.5 = 3.464c

Perhaps you can explain how the Earth exceeds the speed of light in the
frame of the vehicle, but I'm certainly not going to accept your's or
Savard's ASSUMPTION that upsilon = v when length xxi and time t tau,
that way lies insanity.

So why is Savard multiplying xi by beta instead of dividing?
Answer: To deliberately obfuscate and pretend he's slick, the contemptible
arrogant *******.

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Lord Androcles, Zeroth Earl of Medway.
When I get my O.B.E. I'll be an earlobe.

P.S. Kelleher, you're welcome.