Re: Another look at the Lorentz factor.


Golden Boar wrote:
PD wrote:
Golden Boar wrote:
The Lorentz factor is usually given by the equation:

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

or by

beta = v/c
gamma = 1/sqrt(1-beta^2)

The equation can be written in a more intuitive (for me at least) way
as shown below:

gamma = c / sqrt(c^2 - v^2)

I think it would benefit you to see the form of the Lorentz
transformations in terms of hyperbolic transcendental functions, where
gamma = cosh(rapidity),
about as simple as you can get.

I don't know.
The rapidity is given by,

(c + v) / sqrt(c^2 - v^2)

So you are implying that,

cosh((c + v) / sqrt(c^2 - v^2))

is simpler than,

c / (sqrt(c^2 - v^2)

No, I'm implying that using rapidity is simpler than using c and v. Why
would you use two parameters for speed when rescaling will give you
one?

In a sensible system of units, you can either choose the maximal speed
to be 1 or infinity (rapidity).

PD


Moreover, the rapidity variable is exceeding useful as well as being
more physically fundamental.

See, for example, http://www.everything2.com/index.pl?node_id=312518

The important thing to note is that, rather than reading up on things
that have already been done a long long time ago, you are spending your
time futzing with equations to stumble on the work yourself. This in
itself is not a bad thing. Thinking that you've done something original
or of interest to others --- that you'll find people have a lesser
opinion of.

PD

.

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