Tom Roberts' "A Physicist's Derivation of Special Relativity",
http://groups.google.com/groups?q=ph...ent.com&rnum=2

As I understand it, you/he are saying that Einstein's
premise/postulate that the speed of light is constant c in all frames
of reference is not necessary to _derive_ Relativity. Rather, "the
existence of a universal speed (c) is a natural consequence of the
Postulates forming the basis of the derivation". Presumably the
necessary Postulates forming the basis of the derivation are "General
symmetry properties of space-time". And these "are sufficient to
determine the equations of the Lorentz Transformation []". "The bottom
line is that it is IMPOSSIBLE to formulate an alternative to Special
Relativity, while obeying the observed symmetries of space-time and
agreeing with the experimental evidence []".

To quote myself: "Any concept connotes - -implies the entire system of
which it is a feature". That is to say, it really does not matter
where you start in a system; every concept of a system contains the
whole. (It remains beautifully circular, and, I hope I'm using the
term correctly, of invariant rigour).

Pardon me if I say, the challenge is to cop-on to same; to cop-on to,
shall we say, the oneness of derivations, givens and systems.

To weigh a system, I find, is to bring it into relationship with
alternative systems - if any. In the absence of same 'a system' has no
weight as 'a system' - alien though this idea may be to the people
here.


Peter Kinane
http://www.effectuationism.com/forum...tml?1071620499

"Peter Kinane" wrote in message
om...
Tom Roberts' "A Physicist's Derivation of Special Relativity",

http://groups.google.com/groups?q=ph...ent.com&rnum=2

As I understand it, you/he are saying that Einstein's
premise/postulate that the speed of light is constant c in all frames
of reference is not necessary to _derive_ Relativity. Rather, "the
existence of a universal speed (c) is a natural consequence of the
Postulates forming the basis of the derivation". Presumably the
necessary Postulates forming the basis of the derivation are "General
symmetry properties of space-time". And these "are sufficient to
determine the equations of the Lorentz Transformation []". "The bottom
line is that it is IMPOSSIBLE to formulate an alternative to Special
Relativity, while obeying the observed symmetries of space-time and
agreeing with the experimental evidence []".

To quote myself: "Any concept connotes - -implies the entire system of
which it is a feature". That is to say, it really does not matter
where you start in a system; every concept of a system contains the
whole. (It remains beautifully circular, and, I hope I'm using the
term correctly, of invariant rigour).

I have no idea what you are trying to say. In mathematics it is well known
that some derivations are more difficult than others, while other have
greater elegance and simplicity. The later is to be preferred. The ancient
paper of Tom Roberts is the best I know that I can readily link to for
deriving the Lorentz transformations


Pardon me if I say, the challenge is to cop-on to same; to cop-on to,
shall we say, the oneness of derivations, givens and systems.


The challenge is to present them is as clear, logical, straightforward and
preferably as elegant way as possible.


To weigh a system, I find, is to bring it into relationship with
alternative systems - if any. In the absence of same 'a system' has no
weight as 'a system' - alien though this idea may be to the people
here.

You may understand the philosophical mumbo jumbo you wrote above but I do
not. Rather than couch your ideas in cryptic terms how about actually
pointing to specifics expressed clearly and concisely? If you do not agree
with in the paper or their are points you would like further clarification
on then post such.

Bill



Peter Kinane
http://www.effectuationism.com/forum...tml?1071620499

"Peter Kinane" wrote in message
om...

Tom Roberts' "A Physicist's Derivation of Special Relativity",


As I understand it, you/he are saying that Einstein's
premise/postulate that the speed of light is constant c in all
frames of reference is not necessary to _derive_ Relativity.
Rather, "the existence of a universal speed (c) is a natural
consequence of the Postulates forming the basis of the
derivation". Presumably the necessary Postulates forming
the basis of the derivation are "General symmetry properties
of space-time". And these "are sufficient to determine the
equations of the Lorentz Transformation []". "The bottom
line is that it is IMPOSSIBLE to formulate an alternative to
Special Relativity, while obeying the observed symmetries
of space-time and agreeing with the experimental evidence []".

Yes, that is what Tom is saying. And his argument would be
valid if he were to clean it up and remove his mathematical errors.
http://groups.google.com/groups?&sel...g. google.com

To quote myself: "Any concept connotes - -implies the entire system
of which it is a feature". That is to say, it really does not matter
where you start in a system; every concept of a system contains the
whole.

What you're saying is completely false. It's a mathematical fact that
the parallel postulate is unprovable from the other postulates of
Euclidean geometry. So you can assume that the parallel postulate is
true and derive valid conclusions about Euclidean geometry. Or you
can assume that the parallel postulate is false and derive valid
conclusions about non-Euclidean geometry. This kind of reasoning is a
standard exercise in pure mathematics. For example, it has been proven
that if the ZF axioms of set theory are consistent, then so are the ZF
axioms plus the axiom of choice. It has also been proven that if the
ZF axioms of set theory are consistent, then so are the ZF axioms and
the negation of the axiom of choice. In other words, the axiom of
choice is independent of the standard axioms of set theory.

It's a well-known fact that you don't need Einstein's second postulate
to derive special relativity.

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

Eugene Shubert

Peter, you are missing a basic fact about Tom's paper:

he did NOT derive the Lorentz-Einstein transformations.

Rather, he got down to a point where he had devised a criterion which set to
zero (which was logical because of its numerator) reduced his derivation to
the Galilean transforms.

But for the Lorentz 'derivation' - the criterion less than zero - he just
waved his hands and said in effect, why don't we let Lorentz represent this
case.

He did NOT derive the Lorentz-Einsten transformations.

eleaticus

"eleaticus" wrote in message
...
Peter, you are missing a basic fact about Tom's paper:

he did NOT derive the Lorentz-Einstein transformations.

Of course he didn't. Neither did Einstein. Nobody can.

For quotations following, reference:
http://www.fourmilab.ch/etexts/einstein/specrel/www/
("On the Electrodynamics of Moving Bodies" by Albert Einstein)

1) "light is always propagated in empty space with a definite velocity c
which is independent of the state of motion of the emitting body",
a totally unproven assumption without any evidence to support it.

2) "In agreement with experience we further assume the quantity
2AB/(t'A-tA) = c to be a universal constant- the velocity of light in empty
space.",
an admitted assumption that is quite worthless when there is any
relative motion between A and B, yet essential to the derivation of the
remainder of Einstein's nonsense.

3) The equation
½[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v)) ,
the ½ of which is derived from 2) above and is tantamount to saying
(1/3 + 2/3)/2 = 1/3.

4) The missing 0' from that equation, since x' = x-vt, hence 0' = 0-vt,
and the equation should be
½[tau(-vt,0,0,t)+tau(-vt,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v))
at the very least.

5) The further assumption "IF we place x' = x-vt ... " without considering
IF we place x' = x+vt, from which we derive (using Einstein's method)
tau = (t+xv/c^2)/sqrt(1-v^2/c^2)
xi = (x + vt)/sqrt(1-v^2/c^2)" -Paul B. Andersen

6) The statements
"But the ray moves relatively to the initial point of k,
when measured in the stationary system, with the velocity c-v..."
and
"It follows, further, that the velocity of light c cannot be altered by
composition with a velocity less than that of light. For this case we obtain
V = (c+w)/(1+w/c) = c."
which are contradictory, the first being Galilean, the second being
contrary to the vector addition of velocities, an axiom of a vector space.

7) The lack of a check to verify the theory is self-consistent by feeding
the new PoR given in 6) into the equation given in 3) and finding a total
failure.
Check:
(t1-t)/(t2-t)*[tau(-vt,0,0,t)+tau(-vt,0,0,t+x'/V+x'/V)] = tau(x',0,0,t+x'/V)
where V = (c+v)/(1+v/c) as required by the redefined PoR.


Rather, he got down to a point where he had devised a criterion which set
to
zero (which was logical because of its numerator) reduced his derivation
to
the Galilean transforms.

But for the Lorentz 'derivation' - the criterion less than zero - he just
waved his hands and said in effect, why don't we let Lorentz represent
this
case.

He did NOT derive the Lorentz-Einsten transformations.

eleaticus
Yep.
Androcles

"Eugene Shubert" http://www.everythingimportant.org wrote in message ...
"Peter Kinane" wrote in message
om...

To all (respondents),


Tom Roberts' "A Physicist's Derivation of Special Relativity",


As I understand it, you/he are saying that Einstein's
premise/postulate that the speed of light is constant c in all
frames of reference is not necessary to _derive_ Relativity.
Rather, "the existence of a universal speed (c) is a natural
consequence of the Postulates forming the basis of the
derivation". Presumably the necessary Postulates forming
the basis of the derivation are "General symmetry properties
of space-time". And these "are sufficient to determine the
equations of the Lorentz Transformation []". "The bottom
line is that it is IMPOSSIBLE to formulate an alternative to
Special Relativity, while obeying the observed symmetries
of space-time and agreeing with the experimental evidence []".

Yes, that is what Tom is saying. And his argument would be
valid if he were to clean it up and remove his mathematical errors.

I expect that his argument is valid, or would be if as you said. (My
point is that variations of where one starts with Relativity concepts
add nothing to the weight of "Relativity" - based on (my premise-
-principle) that "any concept connotes- -implies the entire system of
which it is a feature").

http://groups.google.com/groups?&sel...g. google.com

To quote myself: "Any concept connotes - -implies the entire system
of which it is a feature". That is to say, it really does not matter
where you start in a system; every concept of a system contains the
whole.

What you're saying is completely false. It's a mathematical fact that
the parallel postulate is unprovable from the other postulates of
Euclidean geometry.

If what you say is so, perhaps it just means that Euclidean geometry
is - to a degree - in-coherent and in-coherent systems feature
in-coherent concepts.


This is my first introduction to this Euclidean problem, and perhaps
not surprisingly, I don't see why the parallel postulate does not
follow - cannot be derived from - the other Euclidean postulates.

Would this not be a satisfactory, shall we say, derivation of or basis
to the parallel postulate?:
Take a fixed line and a point not on that line. Draw a line from the
point such that it is at right angles to a point on the fixed line.
Draw a line through the off-the-line point at right angles to the
connecting line. Such a line necessarily would be at 180 degrees to
the fixed line and, in effect, the only possible line through that
point which would be parallel to the fixed line ( a 180 degree line).

So you can assume that the parallel postulate is
true and derive valid conclusions about Euclidean geometry. Or you
can assume that the parallel postulate is false and derive valid
conclusions about non-Euclidean geometry. This kind of reasoning is a
standard exercise in pure mathematics. For example, it has been proven
that if the ZF axioms of set theory are consistent, then so are the ZF
axioms plus the axiom of choice. It has also been proven that if the
ZF axioms of set theory are consistent, then so are the ZF axioms and
the negation of the axiom of choice. In other words, the axiom of
choice is independent of the standard axioms of set theory.

It's a well-known fact that you don't need Einstein's second postulate
to derive special relativity.

As above, my point is that this does not add to the validity of
Relativity - contrary to what some seem to imply.


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

Eugene Shubert

--
Peter Kinane
http://www.effectuationism.com/

"Peter Kinane" wrote in message
om...

"Eugene Shubert" http://www.everythingimportant.org wrote in
message ...

What you're saying is completely false. It's a mathematical fact
that the parallel postulate is unprovable from the other postulates
of Euclidean geometry.

This is my first introduction to this Euclidean problem, and perhaps
not surprisingly, I don't see why the parallel postulate does not
follow - cannot be derived from - the other Euclidean postulates.

The reason is easy to understand. There are non-Euclidean geometries
where the parallel postulate is false but where the other postulates
are true. How then could you prove the parallel postulate from the
other postulates when there are specific examples of geometries where
the parallel postulate is false and the other postulates are true?

You may want to read more about this argument. It has a fascinating
history.

http://mathworld.wolfram.com/ParallelPostulate.html
http://en.wikipedia.org/wiki/Parallel_postulate
http://www.fact-index.com/p/pa/paral...stulate_1.html
http://math.nmsu.edu/~history/monthly/node5.html
http://www.dpmms.cam.ac.uk/~wtg10/parallel.html
http://www.southernct.edu/~grant/nicolai/history.html
http://www.math.ucla.edu/undergrad/courses/math123/
http://www.beva.org/math323/asgn6/nov19.htm

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

"Eugene Shubert" http://www.everythingimportant.org wrote in message ...
"Peter Kinane" wrote in message
om...

"Eugene Shubert" http://www.everythingimportant.org wrote in
message ...

What you're saying is completely false. It's a mathematical fact
that the parallel postulate is unprovable from the other postulates
of Euclidean geometry.

This is my first introduction to this Euclidean problem, and perhaps
not surprisingly, I don't see why the parallel postulate does not
follow - cannot be derived from - the other Euclidean postulates.

The reason is easy to understand.

If so, it is probably easy to summarise.

There are non-Euclidean geometries
where the parallel postulate is false but where the other postulates
are true. How then could you prove the parallel postulate from the
other postulates when there are specific examples of geometries where
the parallel postulate is false and the other postulates are true?

This seems to involve system jumping.

Also, I regard your apparent idea of "proof" as a feature of, being
polite, old philosophy. I find that value or rigour is a matter of
relating forces, or, as apparently in this case, systems.


You may want to read more about this argument. It has a fascinating
history.

http://mathworld.wolfram.com/ParallelPostulate.html

Not opening.

http://en.wikipedia.org/wiki/Parallel_postulate

"If a line segment intersects two straight lines forming two interior
angles on the same side sum to less than two right angles then the two
lines segments, if extended indefinitely, meet on that side on which
are the angles less than the two right angles.": Of couse. And, as in
my snipped example, if a line segment intersects two straight lines
forming two 90 degree angles then there would be a parrallel line.

* Would this not be a satisfactory, shall we say, derivation of or
basis
to the parallel postulate?:
Take a fixed line and a point not on that line. Draw a line from the
point such that it is at right angles to a point on the fixed line.
Draw a line through the off-the-line point at right angles to the
connecting line. Such a line necessarily would be at 180 degrees to
the fixed line and, in effect, the only possible line through that
point which would be parallel to the fixed line ( a 180 degree line).
*
--
Peter Kinane
http://www.effectuationism.com/

Peter Kinane wrote:

"Eugene Shubert" http://www.everythingimportant.org wrote in message ...

"Peter Kinane" wrote in message
.com...


"Eugene Shubert" http://www.everythingimportant.org wrote in
message ...

What you're saying is completely false. It's a mathematical fact
that the parallel postulate is unprovable from the other postulates
of Euclidean geometry.

This is my first introduction to this Euclidean problem, and perhaps
not surprisingly, I don't see why the parallel postulate does not
follow - cannot be derived from - the other Euclidean postulates.

The reason is easy to understand.


If so, it is probably easy to summarise.

Here is the summary. The first four of Euclids postulates are satisfied
in several systems, some of which obey Playfair's version of the
parallel postulate and some of which don't. Which proves that the
parallel postulate does not follow from the first four.

Bob Kolker

"robert j. kolker" wrote in message ...


Peter Kinane wrote:

"Eugene Shubert" http://www.everythingimportant.org wrote in message ...

"Peter Kinane" wrote in message
.com...


"Eugene Shubert" http://www.everythingimportant.org wrote in
message ...

What you're saying is completely false. It's a mathematical fact
that the parallel postulate is unprovable from the other postulates
of Euclidean geometry.

This is my first introduction to this Euclidean problem, and perhaps
not surprisingly, I don't see why the parallel postulate does not
follow - cannot be derived from - the other Euclidean postulates.

The reason is easy to understand.


If so, it is probably easy to summarise.

Here is the summary. The first four of Euclids postulates are satisfied
in several systems, some of which obey Playfair's version of the
parallel postulate and some of which don't. Which proves that the
parallel postulate does not follow from the first four.

Bob Kolker

Perhaps I do not have enough of the details- -connotations to
appreciate the subtlety involved in the parallel postulate 'problem',
and I may not digress into it at this point. However:

First, my initial point - opening post - was that "Any concept
connotes - -implies the entire system of which it is a feature". It
does not say that a concept should feature across systems.


Next, re Playfair's version of the parallel postulate, "If a point P
is not on a line K, then there is on P at most one line M that does
not intersect K." I am not familiar with why some of the first four
postulates do not "obey Playfair's version".

In so far as this is relevant,
http://www.1911encyclopedia.org/G/GE/GEOMETRY.htm :
* We may now state Prop. 16 thus:If two straight lines which meet are
cut by a transversal, their alternate angles are unequal. For the
lines will form a triangle, and one of the alternate angles will be an
exterior angle to the triangle, the other interior and opposite to it.

From this follows at once the theorem contained in Prop. 27. If two
straight lines which are cut by a transversal make alternate angles
equal, the lines cannot meet, however far they be produced, hence they
are parallel. This proves the existence of parallel lines.

Prop. 28 states the same fact in different forms. If a straight line,
falling on two other straight lines, make the exterior angle equal to
the interior and opposite angle on the same side of the line, or make
the interior angles on the same side together equal to two right
angles, the two straight tines ihall be parallel to one another.

Hence we know that, if two straight lines which are cut by a
transversal meet, their alternate angles are not equal and hence that,
if alternate angles are equal, then the lines are parallel. *

Seems ok.

* The question now arises, Are the propositions converse to these true
or not ? That is to say,, If alternate angles are unequal, do the
lines meet ? *
Already given above: "We may now state Prop. 16 thus:If two straight
lines which meet are cut by a transversal, their alternate angles are
unequal. For the lines will form a triangle, and one of the alternate
angles will be an exterior angle to the triangle, the other interior
and opposite to it.".

* And if the lines are parallel, are alternate angles necessarily
equal ? *
Already given above: "From this follows at once the theorem contained
in Prop. 27. If two straight lines which are cut by a transversal make
alternate angles equal, the lines cannot meet, however far they be
produced, hence they are parallel.".


* The answer to either of the~e two questions implies the answer to
the other. But it has been found impossible to prove that the negation
or the affirmation of either is true. *
I have not got around to seeing how the standard of proof of this
axiom compares with that for others.
--
Peter Kinane
http://www.effectuationism.com/