Re: ABSOLUTE TRUTH ABOUT ABSOLUTE SPACETIME

From: Perfectly Innocent (perfectlyInnocent_at_as-if.com)
Date: 06/26/04 

Date: 26 Jun 2004 07:50:56 -0700

Correction:

> Some students might enjoy thinking about these things quite early on. But,
> my feelings are that the average beginning student is not going to profit
> from it and is likely to find it confusing. It would be interesting to see
> an outline of a set of lectures that incorporates SxR that you would present
> to students who are learning SR for the first time.

First I'd begin with my derivation of the Lorentz transformation from
a Galilean synchronization:

x'=x-uT
T'=T

http://www.everythingimportant.org/relativity

Then I'd go through my second derivation of the Lorentz
transformation, which completely bypasses the use of Einstein's
bungled relativity principle and the notion of groups. It needs,
primarily, the SxR topology and the Galilean transformation:
http://www.everythingimportant.org/relativity/simultaneity.htm

At this point I would assign an extraordinary exercise:

Without cheating by resetting clocks to make the computations trivial,
use the transformation equations for SxR:

x'=Y(v)(x-vt)
t'=t/Y(v)

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

Compute the outcome to the following experiment in an arbitrary moving
frame. (This to me is a delightful curiosity). Suppose you have two
synchronized clocks side-by-side and slowly transport one of them to
any convenient distance D and then measure the speed of light, i.e.,
D/(t2-t1). Prove that the measured value will be c. (t1 is the time on
the stationary clock when the light pulse is sent. t2 is the time when
the light arrives as measured by the slowly transported clock. Take
the limit of ultraslow transport for a perfect answer of c).

Try this problem. It's amazingly enjoyable!

Also, let me know if you can do the exercises and construct a full
proof of the claims made on this page:

http://www.everythingimportant.org/relativity/generalized.htm

Two dimensional gravity (everything you need to know about the metric

ds^2 = f(x)dt^2 –dx^2

Extending SR to the superluminal realm:
http://groups.google.com/groups?&selm=c45b45b3.0406101321.249fbe82%40posting.google.com

Eugene Shubert
http://www.everythingimportant.org

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