Re: On reference frames in 4D space

In sci.physics.relativity, vps137@xxxxxxxxx
<vps137@xxxxxxxxx>
wrote
on 29 Jan 2007 19:32:40 -0800
<1170127960.724640.71790@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>:


On 29 ???., 18:39, jem <x...@xxxxxxx> wrote:
vps...@xxxxxxxxx wrote:

On 27 ñÎ×., 19:27, jem <x...@xxxxxxx> wrote:

Excepting the trivial case v=0, the Lorentz
transformation and the Galilean transformation are mutually
inconsistent, so one can't be derived from the other.

No. The Lorentz transformation becomes Galilean at low v too.

The LT "becomes" the GT only when v=0 - at "low v" the LT /approximates/
the GT.  At "low v" the expression v+1 approximates 1 too, but try using
that to derive the result v+1 = 1.

You are not quite true.
At low v relation (v/c)^2 becomes very low and can be neglected.
Therefore the demoninator in LT (eq.(11)) = 1 and we get eq.(1) = GT.

One can also calculate the error for arbitrary v; it turns out to be our
old friend gamma or its reciprocal, for many of the expressions.

For example, in Galilean space

fn/f0 = (1 - v/c)

and in Einsteinian

fe/f0 = sqrt(1-v/c) / sqrt(1+v/c)

and therefore

fn/fe = 1/g

Obviously this quantifies the error to some extent; using SR on
a 1 meter rod moving at highway speeds (30 m/s, or 10^-7 c)
yields an error of about 5 parts in 10^15, or a fraction of the
radius of a proton.

[rest snipped for brevity]

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