Unique Lorentz Boost?

18-JUN-2006

In the context of a Lorentz boost in the x,x' dimension, and in
dimensionless terms where the velocity of light is given as c = 1, I've
found for parameter 0 v 1, a solution that uniquely satisfies the
following condition:

(v^-1 - v) = p / (E + m), m = 1, p = mv, E = v^2,

where p is momentum, E is total energy and m is rest mass.

Then, also uniquely satisfied, we have

v = (1 / v) / (1 / v^2)

and

(v^2 + c) = (c / v^2).

I have it on good authority that there is absolutely no physics in this
solution... Why that is, was left as an exercise (the royal road of
knowledge is paved with self-help)...

Naively I've arrived at two interpretations:

A. Special relativity specifies a unique, non-trivial linear velocity
for the observable universe, the latter treated as a unitary mass;

B. I am continually falling victim to a reasonable ineffectiveness of
mathematics, owing to my own ignorance.

I'm leaning towards B, in deference to the authorities, despite the
beauty, simplicity and jaw-dropping symmetry I find in my mathematical
results. I'd like to get unlost.

Any suggestions?

Cheers,

mark jonathan horn

wrote:
18-JUN-2006

In the context of a Lorentz boost in the x,x' dimension, and in
dimensionless terms where the velocity of light is given as c = 1, I've
found for parameter 0 v 1, a solution that uniquely satisfies the
following condition:

(v^-1 - v) = p / (E + m), m = 1, p = mv, E = v^2,

where p is momentum, E is total energy and m is rest mass.

Then, also uniquely satisfied, we have

v = (1 / v) / (1 / v^2)


as written, this is equivalent to the first equation; the correct
derivation of unique v is


v = (1 / v) / gamma,


gamma = (1 - v^2 / c^2)^-1/2.


For the unique solution we find


1 / v^2 = gamma. A little confusing, I guess.


[snip rest of original post]


cheers, m