In article ,
Perfectly Innocent wrote:
(Gregory L. Hansen) wrote in message
.com...
(Perfectly Innocent) wrote in message
.com...
I propose that all religious relativists should worship a new axiom of
general relativity.

Instead of the praise and adoration given the non-science of
relative simultaneity in a universe with a presumed (S^3)xR
topology,

That's not an axiom of the theory, it's a conclusion.

Let's see a proof in the simple case of 1 spatial dimension with
topology SxR where the space part of spacetime is just a circle.

Thanks.

Maybe, if you'll tell me what a topology SxR is.


--
"When the fool walks through the street, in his lack of understanding he
calls everything foolish." -- Ecclesiastes 10:3, New American Bible

(Gregory L. Hansen) wrote in message ...
In article ,
Perfectly Innocent wrote:
(Gregory L. Hansen) wrote in message
.com...
Perfectly Innocent wrote in message
. com...
I propose that all religious relativists should worship a new axiom of
general relativity.

Instead of the praise and adoration given the non-science of
relative simultaneity in a universe with a presumed (S^3)xR
topology,

That's not an axiom of the theory, it's a conclusion.

Let's see a proof in the simple case of 1 spatial dimension with
topology SxR where the space part of spacetime is just a circle.

Thanks.

Maybe, if you'll tell me what a topology SxR is.

Gregory,

Please forgive my writing in the elaborate language of mathematicians.
I understand that it's not terribly meaningful to most physicists. I
really do mean to write for the largest audience possible.

S is a circle. S^2 is a sphere and S^3 is a hypersphere. R is the real
line.

In mathematics (point set topology) there is a topological product for
topological spaces. The topological product of S and R is SxR, a
cylinder. As a model of spacetime, I specified that S is the space
part of spacetime. The time part is R so every event of the spacetime
SxR is a point (x,t) where x is a point of S and time t is a point of
R. As you can imagine, all of this formalism is really unessential.
Let me get right to the point.

You wrote:

Time-like separated events do
have a definite order. In particular, if two things happen at the
same place, like a traffic light that turns red and then green, no
reference frame will change the order. More generally, relativity of
simultaneity for spacelike separated events is a prediction of the
Lorentz transformations, which at the very least are math, not
semantics, and required by the postulates of special relativity.

I will prove that your argument is unreliable by repeating your logic
in another coordinate system and arriving at directly opposite
conclusions. The riddle is which coordinate system is physically
meaningful and which is spurious. I claim that the Lorentz
transformation does a poor job of coordinatizing all of SxR. The
synchronization scheme that I propose works globally for SxR and means
precisely the same as the Lorentz transformation equations locally if
you reset all local clocks.

According to my coordinates:

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

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

Now let's repeat your argument in my coordinates. If events E1 (x1,
t1) and E2 (x2, t2) are simultaneous in 1 inertial frame, then t1=t2
and the events are simultaneous in all inertial frames. If event E1
precedes event E2 in 1 inertial frame, then t1t2 and event E1
precedes event E2 in all inertial frames. Consequently, the spacetime
SxR has an absolute time order.

I direct you to http://www.everythingimportant.org/viewtopic.php?t=605
and its links for a more complete exposition of the physics of SxR.

Most importantly, I thank for your courteous reply to my opening
remarks.

Eugene Shubert
http://www.everythingimportant.org/viewtopic.php?t=605

In article ,
Perfectly Innocent wrote:
(Gregory L. Hansen) wrote in message
...
In article ,
Perfectly Innocent wrote:
(Gregory L. Hansen) wrote in message
.com...
Perfectly Innocent wrote in message
. com...
I propose that all religious relativists should worship a new axiom of
general relativity.

Instead of the praise and adoration given the non-science of
relative simultaneity in a universe with a presumed (S^3)xR
topology,

That's not an axiom of the theory, it's a conclusion.

Let's see a proof in the simple case of 1 spatial dimension with
topology SxR where the space part of spacetime is just a circle.

Thanks.

Maybe, if you'll tell me what a topology SxR is.

Gregory,

Please forgive my writing in the elaborate language of mathematicians.
I understand that it's not terribly meaningful to most physicists. I
really do mean to write for the largest audience possible.

S is a circle. S^2 is a sphere and S^3 is a hypersphere. R is the real
line.

In mathematics (point set topology) there is a topological product for
topological spaces. The topological product of S and R is SxR, a
cylinder. As a model of spacetime, I specified that S is the space
part of spacetime. The time part is R so every event of the spacetime
SxR is a point (x,t) where x is a point of S and time t is a point of
R. As you can imagine, all of this formalism is really unessential.
Let me get right to the point.

Okay, I still don't get what role it's playing here. Are you deriving
transformations or something from this, or do you mean nothing more
astonishing than, say, a cookie cutter coming down and cutting a circle
out of a sheet of dough?


You wrote:

Time-like separated events do
have a definite order. In particular, if two things happen at the
same place, like a traffic light that turns red and then green, no
reference frame will change the order. More generally, relativity of
simultaneity for spacelike separated events is a prediction of the
Lorentz transformations, which at the very least are math, not
semantics, and required by the postulates of special relativity.

I will prove that your argument is unreliable by repeating your logic
in another coordinate system and arriving at directly opposite
conclusions. The riddle is which coordinate system is physically
meaningful and which is spurious. I claim that the Lorentz
transformation does a poor job of coordinatizing all of SxR. The
synchronization scheme that I propose works globally for SxR and means
precisely the same as the Lorentz transformation equations locally if
you reset all local clocks.

According to my coordinates:

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

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

Now let's repeat your argument in my coordinates. If events E1 (x1,
t1) and E2 (x2, t2) are simultaneous in 1 inertial frame, then t1=t2
and the events are simultaneous in all inertial frames. If event E1
precedes event E2 in 1 inertial frame, then t1t2 and event E1
precedes event E2 in all inertial frames. Consequently, the spacetime
SxR has an absolute time order.

Well sure, if you use a theory other than special relativity, you're going
to get results other than special relativity. That doesn't say anything
about whether a result of special relativity comes from the postulates of
special relativity. In particular, if you look at the left and right
edges of a circle of radius R layed down simultaneously (the cookie
cutter) in some frame at t=0, in another frame you'll have

t'_right = (vR/c^2)/sqrt(1-v^2/c^2)

t'_left = (-vR/c^2)/sqrt(1-v^2/c^2)

t'_right t'_left. Go in the other direction,

t'_right = (-vR/c^2)/sqrt(1-v^2/c^2)

t'_left = (vR/c^2)/sqrt(1-v^2/c^2)

t'_right t'_left. Relativity of simultaneity is a conclusion, not a
postulate.

Your transformations lose the invariance of the speed of light, they lose
the principle of relativity, and I'm not even sure what to say about how
Maxwell's equations transform under them because they take the field
tensor into something that's not a field tensor, something that doesn't
even look like it has a physical interpretation. I think it's worth while
for you to try calculating by them what happens when you stick a magnet in
a coil of wire, and what happens when you move the coil of wire around
the magnet. We know exerimentally that the two cases are equivalent and
give the same result of a certain magnitude, I think your transformations
will say different.
--
"When the fool walks through the street, in his lack of understanding he
calls everything foolish." -- Ecclesiastes 10:3, New American Bible

(Perfectly Innocent) wrote in message . com...
(Gregory L. Hansen) wrote in message . com...

I think you didn't do your homework.

And I suspect that you have not read the thread
http://www.everythingimportant.org/viewtopic.php?t=605

That is correct. I'm starting from nothing.

"Bill Hobba" wrote in message
...

[snip]

Dirk Van de moortel wrote:

Looks to me like a case of
http://www.google.com/search?&q=blown+fuse

Thank heaven the knowledgeable people on this site are taking this
person to
task.

I think this person is more 'knowledgeable' in his subject
than I am, but I recognize the symptoms of his condition
when I see them. Sad.

Dirk Vdm

(Gregory L. Hansen) wrote in message . com...
(Perfectly Innocent) wrote in message . com...
(Gregory L. Hansen) wrote in message . com...

I think you didn't do your homework.

And I suspect that you have not read the thread
http://www.everythingimportant.org/viewtopic.php?t=605

That is correct. I'm starting from nothing.

Gregory,

My suggestion is that you start from substance, given he
http://www.everythingimportant.org/viewtopic.php?t=605

Thanks.

Eugene Shubert
http://www.everythingimportant.org/viewtopic.php?t=605

(Gregory L. Hansen) wrote in message ...
In article ,
Perfectly Innocent wrote:

Gregory,

Please forgive my writing in the elaborate language of mathematicians.
I understand that it's not terribly meaningful to most physicists. I
really do mean to write for the largest audience possible.

S is a circle. S^2 is a sphere and S^3 is a hypersphere. R is the real
line.

In mathematics (point set topology) there is a topological product for
topological spaces. The topological product of S and R is SxR, a
cylinder. As a model of spacetime, I specified that S is the space
part of spacetime. The time part is R so every event of the spacetime
SxR is a point (x,t) where x is a point of S and time t is a point of
R. As you can imagine, all of this formalism is really unessential.
Let me get right to the point.

Okay, I still don't get what role it's playing here. Are you deriving
transformations or something from this, or do you mean nothing more
astonishing than, say, a cookie cutter coming down and cutting a circle
out of a sheet of dough?

Gregory,

I derive my transformation equations on the page:
http://www.everythingimportant.org/r...multaneity.htm
which, in fact, borrows one equation from the page:
http://www.everythingimportant.org/relativity/

I view the page http://www.everythingimportant.org/viewtopic.php?t=605
as a simplified approach to the whole theory.

The reason for the fancy language is that I'm attempting a compromise.
I'm trying to show a little professionalism in my writing but I also
want to speak as simply as the subject allows.

I'm certain that writing just to pretend that the subject is beyond
the comprehension of ordinary mortals is a sin and I do realize that
I'm paying a price for wishing to communicate at an elementary level.
I've been advised by a very capable graduate student in physics (in
the thread http://www.everythingimportant.org/r.../Soleimani.htm
) that I'm dumbing down my interesting physics too far.

In the thread that I've just cited, Ali Soleimani wrote:

"BTW, I think perhaps you should repost this under a different
title... toss around 'topologies' or 'global symmetry breaking' or
something. Most people I think will assume you've just got some
juvenile crackpot objection to SR and skip it, and this is one of the
most interesting posts I've seen in a long while...."

So to answer your question, I was only describing the shape of space
so to speak (one axiom). I wasn't trying to imply that there is any
special physical content or unusual claim being made. I was only
saying, consider the most reasonable derivation of special relativity
on a circle universe:
http://www.everythingimportant.org/r...multaneity.htm and
what that says about time order.

You wrote:

Time-like separated events do
have a definite order. In particular, if two things happen at the
same place, like a traffic light that turns red and then green, no
reference frame will change the order. More generally, relativity of
simultaneity for spacelike separated events is a prediction of the
Lorentz transformations, which at the very least are math, not
semantics, and required by the postulates of special relativity.

I will prove that your argument is unreliable by repeating your logic
in another coordinate system and arriving at directly opposite
conclusions. The riddle is which coordinate system is physically
meaningful and which is spurious. I claim that the Lorentz
transformation does a poor job of coordinatizing all of SxR. The
synchronization scheme that I propose works globally for SxR and means
precisely the same as the Lorentz transformation equations locally if
you reset all local clocks.

According to my coordinates:

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

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

Now let's repeat your argument in my coordinates. If events E1 (x1,
t1) and E2 (x2, t2) are simultaneous in 1 inertial frame, then t1=t2
and the events are simultaneous in all inertial frames. If event E1
precedes event E2 in 1 inertial frame, then t1t2 and event E1
precedes event E2 in all inertial frames. Consequently, the spacetime
SxR has an absolute time order.

Well sure, if you use a theory other than special relativity, you're going
to get results other than special relativity.

Ah, but that's just my point. I'm claiming that SxR is virtually
indistinguishable from SR.

http://www.everythingimportant.org/viewtopic.php?t=605

Warning, please understand that I'm using cryptic notation. Here's the
clarification:

By SxR, I sometimes mean the SeXieR and more modern version of SR. The
X stands for Modern as in OSX or Windows XP. Obviously, SxR also
represents a cylinder, which again, represents my theory:

http://www.everythingimportant.org/r...multaneity.htm

Sincerely not X (eXperimental).

That doesn't say anything
about whether a result of special relativity comes from the postulates of
special relativity.

But the second postulate can't possibly work in a circle universe. See

http://www.everythingimportant.org/r...multaneity.htm

Relativity of simultaneity is a conclusion, not a postulate.

Again, the question is, how do you make SR work in a circle universe?

Your transformations lose the invariance of the speed of light, they lose
the principle of relativity,

I'm saying that you have no choice. What other SR type theory and
transformation equations do you think can be made to work in a
circular universe?

Eugene Shubert

"Perfectly Innocent" wrote in message
om...

snip

Instead of the praise and adoration given the non-science of relative
simultaneity in a universe with a presumed (S^3)xR topology,

snip

If the unanimous belief of professionally trained relativists like Dr.
Tom Roberts is correct,

It's hardly "unanimous", is it? You contradict yourself with a single post.
Totally aside from your inappropriate use of the religious metaphor, this
alone totally disqualifies you from participating in rational discourse.

What do you all think of my proposal of adopting the new axiom?

I think *plonk*


Tom Davidson
Richmond, VA

"Bill Hobba" wrote in message ...
Perfectly innocent wrote:
'If the unanimous belief of professionally trained relativists like Dr Tom
Roberts is correct, then the assumed non-existence of an absolute time order
on SxR, (S^2)xR and (S^3)xR isn't provable, it isn't math or physics; it's
just semantics. If that is true, then we could just as easily replace
non-order with order. What do you all think of my proposal of adopting the
new axiom?'

Your theory is locally
equivalent to SR but globally it is not. Your transformations break the
symmetry properties of an intertial reference frame by not being linear.

Of course my transformation is linear. You're not even on the right
page: http://www.everythingimportant.org/viewtopic.php?t=605

Your circular or cylindrical universe or whatever is not a reasonable
generalization of the properties of inertial reference frames as found on
earth.

You just finished saying that my theory is locally equivalent to SR
but not globally. Why is that not a reasonable generalization?

The natural generalization for an inertial reference frame is to
propose it is valid;

My definition of an inertial frame of reference is indistinguishable
from what's assumed in the standard cosmological model.

not that space is circular.

The standard cosmological model is circular.

In fact it breaks the definition of an inertial reference frame as given
by Rindler in his book Introduction to Special Relativity.

Arguing against a relativistic theory that's indistinguishable from SR
locally and which has similarities to the standard cosmological model
globally is totally absurd.

Why not hyperbolic or some other construct?

Anything closed and bounded suits my purposes.

As for your thought experiment on light beams in your universe
has anyone ever detected a light beam returning; just what evidence do you
have for it is beyond me.

Again, you're just opposing the standard cosmological model. Don't cry
to me about that. Cry to Tom Roberts and he will console you. Complain
to him about me upsetting the natural order of things and he will
double his pretense that I'm some sort of unreasonable heretic.

Eugene Shubert
http://www.everythingimportant.org/viewtopic.php?t=605

Perfectly Innocent wrote:
My definition of an inertial frame of reference is indistinguishable
from what's assumed in the standard cosmological model.

Cosmology does not deal with inertial reference frames or rather it uses GR
in which inertial reference frames are just one possible geometry.

Perfectly Innocent wrote:
The standard cosmological model is circular.

In cosmology we have an expanding universe. That does not imply a priori
your geometry. But that misses the point which is the universe at large is
not the domain of SR it is the domain of GR.

Perfectly Innocent wrote:
Arguing against a relativistic theory that's indistinguishable from SR
locally and which has similarities to the standard cosmological model
globally is totally absurd.

Read carefully what the experts have said - your theory is locally
indistinguishable - there is a big difference. It is globally
distinguishable.

Bill Hobba wrote:
Why not hyperbolic or some other construct?

Perfectly Innocent wrote:
Anything closed and bounded suits my purposes.

Then why not say that.

Bill Hobba wrote:
As for your thought experiment on light beams in your universe
has anyone ever detected a light beam returning; just what evidence do
you
have for it is beyond me.


Perfectly Innocent wrote:
Again, you're just opposing the standard cosmological model. Don't cry
to me about that. Cry to Tom Roberts and he will console you. Complain
to him about me upsetting the natural order of things and he will
double his pretense that I'm some sort of unreasonable heretic.

I am not opposing it at all - by definition SR applies to inertial reference
frames globally. Tom is correct when he points out that SR as a theory
applies to any situation where it is a good model - and I believe he is
correct when he says your theory is locally indistinguishable. But in an
inertial reference frame light does not return to you no matter how long you
wait and space is presumed Euclidian. What I am saying is you can not claim
your theory is a theory of inertial reference frames under the normal
definition of what an inertial reference frame that I have seen. Caveat:
the explanations in more advanced books than I have read may provide an
out - but I doubt it.

Thanks
Bill