Re: Too Trivial for Tom Roberts, Impossible for Most

From: Tom Roberts (tjroberts_at_lucent.com)
Date: 10/26/04 

Date: Tue, 26 Oct 2004 16:48:33 -0500

Eugene Shubert wrote:
> Tom Roberts <tjroberts@lucent.com> wrote in message
> news:<A9Hed.15741$5b1.13208@newssvr17.news.prodigy.com>...
>> The quality of a derivation of the equations of SR is usually
>> judged by: 1. the simplicity and physical believability of its
>> assumptions, or lack thereof.
>> and: 2. the generality of those assumptions.
>
> I wholeheartedly agree. And by the generality of those assumptions, I
> assume you mean the value and added clarity that it brings to the
> subject and to the opening of new questions, vistas and future
> research.

No. Perhaps you too should learn how to read. By "the generality of
those assumptions" I means precisely that: how generally valid the
assumptions are. Yours, of course, aren't generally valid at all, as
they only apply to 1+1 dimensions.

> That describes my paper perfectly.

You over-flatter yourself.

>> Your derivation is seriously lacking in both of those aspects: 1.
>> On page 2 your assumptions for \mu and \gamma are completely
>> unsupported,
> The assumption that you
> refer to (page 2), the principle called change of variables, [...]

So change variables using any other functions, and get equally well
supported results.

For the result of a derivation to be believable, it must rest on
believable postulates. You gave no reason whatsoever why your postulates
should be believed.

> What's
> your dispute with intuitively simple fundamentals? What support do I
> need [...] ?

If you want anybody to believe you, you need a physical justification
for the equations you plucked from the air.

>> and are not obvious at all -- these are QUITE unusual assumptions,
>> to say the least; why should anybody believe them?
>
> Why should anyone believe in the substitution v/c = tanh(theta),
> which transforms the usual Lorentz transformation to its hyperbolic
> form?

Because that is not an ASSUMPTION, it is a CONCLUSION.

>> it is not at all clear how to
>> apply this to an arbitrary relative velocity in 3 spatial
>> dimensions.
> My intended audience is second year algebra students in high schools
> and all backward uneducated folks on the newsgroups. Relativity in 3
> spatial dimensions plus 1 time dimension is a college level topic.

3 spatial dimensions are essential to modeling the world.

>> And you have completely left out any mention of isotropy and
>> homogeneity, which are important and necessary aspects of inertial
>> frames in SR.
> Homogeneity and isotropy are geometric ideas of zero or virtually
> zero importance in 1 spatial dimension.

3 spatial dimensions are essential to modeling the world.

>> A better approach, IMHO, is to use group theory: given sufficient
>> postulates to establish isotropy and homogeneity of the
>> coordinates,
>
> Homogeneity and isotropy are mathematical terms that describe a
> geometry, not coordinates.

Yes, there is a pun in my words, but it is a common and appropriate one.
A homogeneous manifold is one in which all translations are Killing
vectors, and homogeneous coordinates are those in which the components
of those Killing vectors are constant. Similarly for isotropy.

> The problem with your approach to SR is that you don't define what a
> geometry is

Mathematicians do so. And there is a clear and obvious mapping from
abstract geometry to the world we inhabit.

> so it's impossible to really understand the implications
> of homogeneity and isotropy in your vague, meaningless and nebulous
> terms.

They are neither vague, meaningless, nor nebulous; my usage is common.
See above.

>> Evaluated on the basis of those above criteria, this [group
>> theoretic] approach is
>> VASTLY simpler and more general than yours.
>
> My approach is obviously more general and informative.

You over-flatter yourself. Your 1+1-d approach is not at all "more
general". And the blind faith required to establish uniform motion robs
it of any informative value.

Tom Roberts tjroberts@lucent.com

Relevant Pages

  • Dr. Tom Roberts Examines the Shubertian Clock
    ... Homogeneity and isotropy are geometric ideas of zero or virtually ... I've seen you presupposing that space and time together is a geometry ... automatically implies that coordinate transformations are linear. ...
    (sci.physics)
  • Dr. Tom Roberts Examines the Shubertian Clock
    ... Homogeneity and isotropy are geometric ideas of zero or virtually ... I've seen you presupposing that space and time together is a geometry ... automatically implies that coordinate transformations are linear. ...
    (sci.physics.relativity)
  • Re: Too Trivial for Tom Roberts, Impossible for Most
    ... Homogeneity and isotropy are geometric ideas of zero or virtually ... I've seen you presupposing that space and time together is a geometry ... automatically implies that coordinate transformations are linear. ...
    (sci.physics.relativity)
  • Inertial Frames
    ... Could someone please provide me with a clear formal definition of what ... properties of homogeneity of time and space and isotropy of space. ... Isotropy means invariance under rotation; ...
    (sci.physics)
  • Re: Gravitational field of a homogeneous universe
    ... Bjoern Feuerbacher wrote: ... >> Because we require homogeneity and isotropy and from that we derive ... > That's rather depressing... ...
    (sci.physics)
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