Dr Roberts,

If my derivation of the Lorentz transformation is too easy for you to
understand, why not accept a more difficult challenge? I suppose that
you don't believe that prejudice and brainwashing dominates what is
considered respectable physics research. Then, if you're not afraid
of the certain backlash from the ignorant and deeply religious rabble,
please try to explain my paper to the mildly educated folks around
here who don't understand it yet are too cowardly to specify the first
sentence or equation in it that they think is unclear or demonstrably
false.

http://www.everythingimportant.org/r...ty/special.pdf

Eugene Shubert

Eugene Shubert wrote:
http://www.everythingimportant.org/r...ty/special.pdf

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.

Your derivation is seriously lacking in both of those aspects:
1. On page 2 your assumptions for \mu and \gamma are completely
unsupported, and are not obvious at all -- these are QUITE
unusual assumptions, to say the least; why should anybody
believe them?
2. Your sliding rulers work in 1 spatial dimension, though you have
left a lot out (e.g. how to mark them uniformly; how to
know they move with uniform velocity); your omissions can be
corrected. But it is not at all clear how to apply this to an
arbitrary relative velocity in 3 spatial dimensions.

And you have completely left out any mention of isotropy and
homogeneity, which are important and necessary aspects of inertial
frames in SR. This is, of course, related to the omissions I mentioned
in #2 above; but it is not obvious how to resolve this with your
assumptions, especially isotropy.


A better approach, IMHO, is to use group theory: given sufficient
postulates to establish isotropy and homogeneity of the coordinates,
group theory constrains the transforms to 3 groups:
The Euclid group in 4 dimensions
The Galileo group in 3 dimensions
The Lorentz group in (3+1) dimensions
The first has grossly unphysical consequences, and the second does not
agree with basic observations about the world, such as the simple fact
that pion beams exist. But the Lorentz group works, and is the basis of SR.

Evaluated on the basis of those above criteria, this approach is VASTLY
simpler and more general than yours. It was already old when I first saw
it ~1972.

[I posted a version of this some 15-20 years ago, but realize
my ancient presentation has some major flaws (which can be
corrected).]


Tom Roberts

Tom Roberts wrote in message .com...

A better approach, IMHO, is to use group theory: given sufficient
postulates to establish isotropy and homogeneity of the coordinates,
group theory constrains the transforms to 3 groups:
The Euclid group in 4 dimensions
The Galileo group in 3 dimensions
The Lorentz group in (3+1) dimensions
The first has grossly unphysical consequences, and the second does not
agree with basic observations about the world, such as the simple fact
that pion beams exist. But the Lorentz group works, and is the basis of SR.

Evaluated on the basis of those above criteria, this approach is VASTLY
simpler and more general than yours. It was already old when I first saw
it ~1972.

[I posted a version of this some 15-20 years ago, but realize
my ancient presentation has some major flaws (which can be
corrected).]

I have admired your ancient presentation for some years now, warts and
all (which you have pointed out over the years in multiple posts).
Perhaps it is time you updated your presentation, so that you do not
have to be apologetic about its "major flaws."

After all, it still gets cited a lot...

Myxococcus xanthus

Tom Roberts wrote in message .com...
Eugene Shubert wrote:
http://www.everythingimportant.org/r...ty/special.pdf

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. That describes my paper perfectly.

Your derivation is seriously lacking in both of those aspects:
1. On page 2 your assumptions for \mu and \gamma are completely
unsupported,

My official derivation begins on page 4. The assumption that you refer
to (page 2), the principle called change of variables, also called
substitution, is one of the clearest and most useful mathematical
ideas in high school algebra and baby calculus. What's your dispute
with intuitively simple fundamentals? What support do I need and why
is it an unwarranted physical assumption if I label the function
1/sqrt(1 -v^2/c^2) with the Greek letter gamma?

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? It's just the writing of one parameter in terms of another.

Why is substitution allowable here but not there? Perhaps the
difference is that every child mathematician can plod through
a difficult mathematical proof, checking each step for logical
correctness, whereas mature physicists need their hands held by
someone they trust and have their irrational prejudices pacified
at every step.

2. Your sliding rulers work in 1 spatial dimension,

Thanks for mentioning that. You'd be surprised by the number of
physicists and seemingly educated folks who have an emotional
difficulty with sliding rulers!

though you have left a lot out (e.g. how to mark them uniformly;

I suspect that just about all students of algebra at the high school
level will assume that the rulers are pre-made and that even middle
school students could figure out how "to mark them uniformly."

how to know they move with uniform velocity);

They're assumed to move with uniform velocity. That translates into
equal distances traveled in equal proper times. That's where the
constant u comes from in the general two-ruler synchronization of
the Shubertian clock:

T = T(x,x') = -x'/u + xi(x)
T' = T'(x,x') = x/u + zeta(x')

your omissions can be corrected. But 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.

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.

This is, of course, related to the omissions I mentioned
in #2 above; but it is not obvious how to resolve this with your
assumptions, especially isotropy.

I encourage students to try to break the no-nonlinearity postulate
of SR and construct all the Shubertian clocks possible that are
unauthorized and frowned upon in conventional physics. I advise that
students and researchers only do so for purely mathematical reasons
so that no sacred traditions are violated and that sacrilege not be
flaunted.

http://www.everythingimportant.org/viewtopic.php?t=221
http://www.everythingimportant.org/r...eneralized.htm

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. You are perfectly free to break with
standard mathematical convention and define what you mean by
homogeneous and isotropic coordinates but I've never seen you do that.
I've seen you presupposing that space and time together is a geometry
called spacetime and that the homogeneity and isotropy of spacetime
automatically implies that coordinate transformations are linear.

The problem with your approach to SR is that you don't define what a
geometry is so it's impossible to really understand the implications
of homogeneity and isotropy in your vague, meaningless and nebulous
terms. I don't mean to discourage you from pursuing a geometric
derivation. It's just that the fallacy of supposed linearity of
coordinate transformations is easily refuted by simply defining
geometry according to Klein's Erlanger program:

"Every geometry is defined by a group of transformations, and
the goal of every geometry is to study invariants of this group."
-Klein, Erlanger Program.

"Each type of geometry is the study of the invariants of a group of
transformations; that is, the symmetry transformation of some chosen
space." Stewart and Golubitsky 1993, p. 44.

"A geometry is defined by a group of transformations, and investigates
everything that is invariant under the transformations of this given
group." Weyl 1952, p. 133.

The geometry of Minkowski space is defined by the Poincaré group.
http://en.wikipedia.org/wiki/Poincar%E9_group
Here's the critical point. It's easy for any child mathematician like
myself to show that the nonlinear transformation group of exercises 1
and 2 of http://www.everythingimportant.org/r...eneralized.htm
is isomorphic to the Poincaré group. That means that their respective
geometries are isomorphic, i.e., indistinguishable. Thus, it's
impossible to prove linearity of coordinate transformations from
homogeneity and isotropy alone. If Minkowski space is isotropic and
homogeneous, then so is the geometry defined by my wildly nonlinear
transformation group.

group theory constrains the transforms to 3 groups:
The Euclid group in 4 dimensions
The Galileo group in 3 dimensions
The Lorentz group in (3+1) dimensions
The first has grossly unphysical consequences, and the second does not
agree with basic observations about the world, such as the simple fact
that pion beams exist. But the Lorentz group works, and is the basis of SR.

Evaluated on the basis of those above criteria, this approach is VASTLY
simpler and more general than yours.

My approach is obviously more general and informative. The Shubertian
clock is the discovery I used to correctly understand and properly
interpret and the first counterexample to Einstein's misunderstood and
thoroughly misguided no-nonlinearity postulate of special relativity.
That's a new result.

When you remove the nonsense argument about homogeneity and isotropy
implies linearity, your approach will be simple. But I use group
theory also and you should notice that I begin with the greatest
conceivable nonlinearity possible and then I quickly and honestly
simplify the problem to linear mathematics, two unknown functions and
an easily invertible matrix. What I've done is spend a lot of time
explaining an intuitively simple and straightforward definition of
time--the Shubertian clock. That's to my credit.

It was already old when I first saw it ~1972.

What you have is just a slight rewrite of the papers of Ignatowsky,
Frank and Rothe in papers written between 1910 and 1912.
. asp.att.net

[I posted a version of this some 15-20 years ago, but realize
my ancient presentation has some major flaws (which can be
corrected).]

Tom Roberts

Eugene Shubert
http://www.everythingimportant.org/r...ty/special.pdf

On Sun, 24 Oct 2004 05:34:24 GMT, Tom Roberts
wrote:
Eugene Shubert wrote:
http://www.everythingimportant.org/r...ty/special.pdf

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.

Your derivation is seriously lacking in both of those aspects:
1. On page 2 your assumptions for \mu and \gamma are completely
unsupported, and are not obvious at all -- these are QUITE
unusual assumptions, to say the least; why should anybody
believe them?
2. Your sliding rulers work in 1 spatial dimension, though you have
left a lot out (e.g. how to mark them uniformly; how to
know they move with uniform velocity); your omissions can be
corrected. But it is not at all clear how to apply this to an
arbitrary relative velocity in 3 spatial dimensions.

And you have completely left out any mention of isotropy and
homogeneity, which are important and necessary aspects of inertial
frames in SR. This is, of course, related to the omissions I mentioned
in #2 above; but it is not obvious how to resolve this with your
assumptions, especially isotropy.


A better approach, IMHO, is to use group theory: given sufficient
postulates to establish isotropy and homogeneity of the coordinates,
group theory constrains the transforms to 3 groups:
The Euclid group in 4 dimensions
The Galileo group in 3 dimensions
The Lorentz group in (3+1) dimensions
The first has grossly unphysical consequences, and the second does not
agree with basic observations about the world, such as the simple fact
that pion beams exist. But the Lorentz group works, and is the basis of SR.

Evaluated on the basis of those above criteria, this approach is VASTLY
simpler and more general than yours. It was already old when I first saw
it ~1972.

[I posted a version of this some 15-20 years ago, but realize
my ancient presentation has some major flaws (which can be
corrected).]

I really wish that I could say that anyone who could think that a
great deal of the other rubish on that site was true would obviously
not have even HEARD of Group Theory, but I cannot because I know for a
fact that anyone doing nuclear weapons research is pretty much going
to have to have had more than a passing familiarity with Group Theory
in order to be able to do physics at that kind of level, and there ARE
such people who are absolutely certain that the kind of codswallop
blathered on about there is all true.

Eugene Shubert wrote:
Tom Roberts wrote in message
.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

Eugene Shubert wrote
http://www.everythingimportant.org/v...hp?p=3437#3437
Tom Roberts wrote

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.

Perhaps you should learn how to listen. Mathematicians speak of the
generality of a certain idea, axiom or technique and they mean
something capable of being generalized and having the richness to
yield fruitful, far-reaching consequences, i.e., having usefulness in
many situations as opposed to a highly specialized trick that only
works in a single unique instance.

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.

You're ignoring the power of my approach in that it has created a
clearer understanding and new results. It refutes a confused
understanding that many relativists have, even in 1+1 dimensions.
You're also ignoring the sheer entertainment value of being able to
derive the Lorentz transformation from the Galilean transformation.

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.

Does that concept trouble you?

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.

The actual computations that you are whining about on page 2 were
rendered invisible in my official derivation on pages 4-6. I added the
computational details of page 2 and 3 because the furious physicist
Rage Bilge didn't have a clue about how to reset a Shubertian clock.
He calls my derivation (pages 4-6) symbol manipulation.
http://groups.google.com/groups?selm...g.g oogle.com

What's your dispute with intuitively simple fundamentals?

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

Your insistence on misunderstanding is alarming. I said very clearly
on page 2 that what I was doing there was just "a prelude to the still
upcoming derivation of relativity theory."

I was justifying what Bilge thinks is too impossible to believe.
http://physics.nad.ru/engboard/messages/1432.html

Real mathematicians are qualified to pluck equations out of the air.
They do it all the time. And those skilled in mathematics are
absolutely clear about when they can do this to construct a logical
proof. Proof by mathematical induction is a perfect example.

All logical proofs are believable. My postulates are practically
invisible on pages 4-6. Does that give them a lesser or greater
magical appearance?

and are not obvious at all -- these are QUITE unusual assumptions,
to say the least; why should anybody believe them?

Actually, the justification of page 2 and 3 is extraordinarily easy.
Let c be any real number. Try to argue how the substitution
u=v/sqrt(1 –v^2/c^2) could be invalid in a Galilean universe or in any
other universe. Understand that I started my paper by defining u, not
v. I never gave v a physical meaning. So where's the contradiction?
Devise a gedanken experiment in a Galilean universe to prove this
substitution wrong. It's impossible. Inconceivable! It can't even be
imagined to be false. So it's true. Recall my claim of mathematical
trickery. http://www.everythingimportant.org/viewtopic.php?t=451

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.

There are plenty of derivations of the Lorentz Transformation
equations that don't define theta. Take Einstein's tortured derivation
for example (Dover, The Principle of Relativity). And try to find a
mathematician who isn't going to laugh at you. If theta isn't defined
anywhere in a derivation, then you are perfectly free to let theta be
anything that pleases you at any step in a derivation. And even if a
simple substitution/transformation doesn't please some physicists,
it still has every mathematical right to exist.

There is no physical assumption in the mathematical substitution
u=v/sqrt(1 –v^2/c^2).

Eugene Shubert
http://www.everythingimportant.org/r...ty/special.pdf

Tom Roberts wrote

Eugene Shubert wrote http://www.everythingimportant.org/v...hp?p=3437#3437

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

Mathematicians do so.

Correct. And your opinions contradict those definitions.

And the blind faith required to establish uniform motion robs
it of any informative value.

I assumed uniform motion. It's reasonable. You're speaking gibberish.

Eugene Shubert
http://www.everythingimportant.org/r...ty/special.pdf