Re: What is the expert opinion on deriving SR with a Shubertian clock?

From: Perfectly Innocent (perfectlyInnocent_at_as-if.com)
Date: 08/31/04 

Date: 31 Aug 2004 06:57:52 -0700

Perfectly innocent wrote:
http://groups.google.com/groups?&selm=c45b45b3.0408231719.52b9904f@posting.google.com
dubious (Bilge) wrote:
> Perfectly Insignificant:
> >The theory of relativity really has some mystery in it.
>
> What's the mystery?

The mystery is that the Shubertian clock formulation of special
relativity is true yet is unfathomable to some physicists.

>Find the transformation,
>
> x^u -> x^u' = x^u + \delta x^u
>
> which leaves the scalar product of x^u with itself invariant, assuming
> the only metric which is physically admissible. You get all six proper
> lorentz transforms in one shot, i.e., rotations and boosts.

There are advantages in deriving special relativity at a high school
level. You may have noticed that I updated my relativity page to do
just that:

http://www.everythingimportant.org/relativity

> >Let S(x)=x/u and R(x')=-x'/u. So our new clock time T=-x'/u +x/u
> >=(x-x')/u for L and T'=x/u-x'/u =(x-x')/u for L'. Consequently,
> >x'=x-uT and T'=T and we've proven a delightful little theorem: Any
> >two inertial frames of reference have a Galilean synchronization.
>
> That is obviously not true. Two inertial frames with a spacelike
> separation have _no_ synchronization.

I suppose you failed to notice that there isn't any separation between
my two inertial frames? The distance between them is exactly zero.
They're always touching each other physically. The contact is called
frictionless sliding.

L' --> -8__-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4__5__6__7__8
<-- L -8__-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4__5__6__7__8

Time is defined locally. It's an elementary exercise to begin with an
Einsteinian synchronization and adjust clocks so that the Shubertian
clock ends up with a Galilean synchronization. Hopefully, there may be
a slight chance of Tom Roberts responding to your misunderstanding and
correcting you accordingly; but don't count on it. He may expect you
to be reasonable all by yourself.

Eugene Shubert
http://www.everythingimportant.org/relativity

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