PD wrote on Fri, 04 Apr 2008 06:54:59 -0700:

http://www.math.columbia.edu/~woit/w...#comment-36092

I copy and paste:

{BLOCKQUOTE
Einstein and his successors have regarded the effects of a
gravitational field as producing a change in the geometry of space and
time. At one time it was even hoped that the rest of physics could be
brought into a geometric formulation, but this hope has met with
disappointment, and the geometric interpretation of the theory of
gravitation has dwindled to a mere analogy, which lingers in our
language in terms like "metric," "affine connection," and "curvature,"
but is not otherwise very useful. The important thing is to be able to
make predictions about images on the astronomers' photographic plates,
frequencies of spectral lines, and so on, and it simply doesn't matter
whether we ascribe these predictions to the physical effect of
gravitational fields on the motion of planets and photons or to a
curvature of space and time. (The reader should be warned that these
views are heterodox and would meet with objections from many general
relativists.)

}

--http://canonicalscience.org/en/miscellaneouszone/guidelines.txt

It is also heterodox among a lot of particle physicists as well.

Some list, statistics confirming your statement?

These people look at Feynman diagrams as more than
just mnemonics for writing down terms in a perturbative expansion of a
scattering matrix. Interestingly, Feynman would have been the first to
disagree. He was fond of pointing out that different approaches to
solving the same problem often have completely different pictures of the
underlying reality -- and it's completely impossible to determine which
one of them is "more right", because you can do the same level of
computation with any of them.

Well we may speculate about Feynman thinking on his own diagrams or we
can just quote Feynman thoughts about the geometrical picture of gravity:

{BLOCKQUOTE
The geometrical interpretation is not really necessary or essential to
physics.
}

There is no good quantized theory of gravity at the moment, and so there
is no way to even probe whether there is a mathematical or conceptual
equivalence (cf the caveat above) between the geometric approach and the
perturbative quantum approach.

My postings on this thread were about the geometric and the *classical*
field approach to gravity. The references cited were also about
formulating classical gravity as a relativistic field theory.


--
http://canonicalscience.org/en/misce...guidelines.txt

On Apr 4, 12:55*pm, "Juan R." González-Álvarez
wrote:
PD wrote on Fri, 04 Apr 2008 06:54:59 -0700:



http://www.math.columbia.edu/~woit/w...#comment-36092

I copy and paste:

{BLOCKQUOTE
Einstein and his successors have regarded the effects of a
gravitational field as producing a change in the geometry of space and
time. At one time it was even hoped that the rest of physics could be
brought into a geometric formulation, but this hope has met with
disappointment, and the geometric interpretation of the theory of
gravitation has dwindled to a mere analogy, which lingers in our
language in terms like "metric," "affine connection," and "curvature,"
but is not otherwise very useful. The important thing is to be able to
make predictions about images on the astronomers' photographic plates,
frequencies of spectral lines, and so on, and it simply doesn't matter
whether we ascribe these predictions to the physical effect of
gravitational fields on the motion of planets and photons or to a
curvature of space and time. (The reader should be warned that these
views are heterodox and would meet with objections from many general
relativists.)

}

--http://canonicalscience.org/en/miscellaneouszone/guidelines.txt

It is also heterodox among a lot of particle physicists as well.

Some list, statistics confirming your statement?

Just my contact with my colleagues in particle physics.


These people look at Feynman diagrams as more than
just mnemonics for writing down terms in a perturbative expansion of a
scattering matrix. Interestingly, Feynman would have been the first to
disagree. He was fond of pointing out that different approaches to
solving the same problem often have completely different pictures of the
underlying reality -- and it's completely impossible to determine which
one of them is "more right", because you can do the same level of
computation with any of them.

Well we may speculate about Feynman thinking on his own diagrams or we
can just quote Feynman thoughts about the geometrical picture of gravity:

{BLOCKQUOTE
The geometrical interpretation is not really necessary or essential to
physics.

}

I believe that's what I just said. If two equivalent formalisms and
conceptual frameworks result in the same calculated agreement with
experimental results, then there is no way to determine which of them
is "necessary or essential" as an interpretation.

There is no good quantized theory of gravity at the moment, and so there
is no way to even probe whether there is a mathematical or conceptual
equivalence (cf the caveat above) between the geometric approach and the
perturbative quantum approach.

My postings on this thread were about the geometric and the *classical*
field approach to gravity. The references cited were also about
formulating classical gravity as a relativistic field theory.

--http://canonicalscience.org/en/miscellaneouszone/guidelines.txt

On Apr 4, 12:20 pm, PD wrote:
On Apr 4, 11:26 am, Shubee wrote:



On Mar 30, 7:24 am, PD wrote:

On Mar 29, 3:28 pm, Shubee wrote:

On Mar 29, 2:10 pm, YBM wrote:

Shubee a écrit :

My point is that specifying a particular clock synchronization before
deriving the LT is completely unnecessary.

This is utterly stupid. Without clock synchronization you cannot
even say anything about the "t" coordinate which appears in the
transformations since you haven't defined it...

It's easy to understand how clock time can be defined at every point
while not knowing anything about the meaning of synchronization.

Stand side-to-side on an infinitely long ruler with other cretins like
yourself. (There are so many of you!) Let another infinitely long
ruler slide under all your noses so that your nose moves equal
distances in equal times on the moving ruler. Permit each cretin to
define time at his location to be whatever number his nose is pointing
to on the ruler as it moves by. Would you call those individual clock
times synchronized? Now tell the cretin that is standing on the ruler
at position x that he will be adding a number f(x) to his clock time
thereby resetting his clock time either forward or backward by a
constant amount. Do that for each cretin. I'm certain that all the
cretins will respond as you have done, saying, "It can't be done."
"It's a violation of the laws of physics." Well, as I have said
before, you are an idiot.

Shubee

That doesn't work so well. Suppose the clock readings at successive
locations on the ruler read 12:18, 12:20, 12:19, 12:23, 12:26, 12:27.
Are those clocks synchronized?

Suppose the clock readings on the ruler are 12:18, 12:21, 12:24,
12:27, 12:30, 12:33, but your own wris****ch reads 12:18, 12:20,
12:22, 12:24, 12:26. Are the clocks on the ruler synchronized?

PD

I didn't say or imply that any of those clocks are synchronized.

I just asked if they were. I gather you agree that they are not.

That is correct.

Now
the question is whether you think the clock time as recorded on any of
them is worth anything -- and how you would tell. I mean, as opposed
to something that is a monotonic counter that increments a random
amount at intervals -- which I would submit is useless as a clock.

I have given you a perfectly good definition of a clock positioned at
each point (x,y,z). You need to understand that to an infinite array
of clocks you can add or subtract a constant amount f(x,y,z) to each
one. I'm assuming that you're a physicist so I had to explain that to
you.

Shubee

How
do any of those clock time definitions invalidate my derivation of the
Lorentz transformation athttp://www.everythingimportant.org/relativity/special.pdf
?

Shubee

On Apr 4, 12:31 pm, "Juan R." González-Álvarez
wrote:
Shubee wrote on Fri, 04 Apr 2008 07:34:41 -0700:

Juan,

Lorentz invariance is an extraordinarily beautiful concept in physical
theory.

Beauty is a relative concept. One may call "beauty" other may name "ugly".

And in the end *experiment* is the judge in science. It has no importance
how 'beauty' anyone believes his theory is but it fails to explain data.

How is it that professional physicists today can't find Lorentz
invariant expressions as easily as Poincaré did in 1905?

Fail to understant that are you asking for.

Poincaré lists 8 distinct but elementary invariants in his paper. See
the equation numbers 5 and 7 in http://www.univ-nancy2.fr/poincare/bhp/pdf/hp2007gg.pdf
How many invariants in special relativity are you aware of? How many
distinct invariants of the Poincaré group exist? This is how
mathematicians measure the understanding of physicists in spacetime.

I quote:

"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://www.everythingimportant.org/r...eneralized.htm

Shubee

On Apr 4, 1:05*pm, Shubee wrote:
On Apr 4, 12:20 pm, PD wrote:



On Apr 4, 11:26 am, Shubee wrote:

On Mar 30, 7:24 am, PD wrote:

On Mar 29, 3:28 pm, Shubee wrote:

On Mar 29, 2:10 pm, YBM wrote:

Shubee a écrit :

My point is that specifying a particular clock synchronization before
deriving the LT is completely unnecessary.

This is utterly stupid. Without clock synchronization you cannot
even say anything about the "t" coordinate which appears in the
transformations since you haven't defined it...

It's easy to understand how clock time can be defined at every point
while not knowing anything about the meaning of synchronization.

Stand side-to-side on an infinitely long ruler with other cretins like
yourself. (There are so many of you!) Let another infinitely long
ruler slide under all your noses so that your nose moves equal
distances in equal times on the moving ruler. Permit each cretin to
define time at his location to be whatever number his nose is pointing
to on the ruler as it moves by. Would you call those individual clock
times synchronized? Now tell the cretin that is standing on the ruler
at position x that he will be adding a number f(x) to his clock time
thereby resetting his clock time either forward or backward by a
constant amount. Do that for each cretin. I'm certain that all the
cretins will respond as you have done, saying, "It can't be done."
"It's a violation of the laws of physics." Well, as I have said
before, you are an idiot.

Shubee

That doesn't work so well. Suppose the clock readings at successive
locations on the ruler read 12:18, 12:20, 12:19, 12:23, 12:26, 12:27..
Are those clocks synchronized?

Suppose the clock readings on the ruler are 12:18, 12:21, 12:24,
12:27, 12:30, 12:33, but your own wris****ch reads 12:18, 12:20,
12:22, 12:24, 12:26. Are the clocks on the ruler synchronized?

PD

I didn't say or imply that any of those clocks are synchronized.

I just asked if they were. I gather you agree that they are not.

That is correct.

Now
the question is whether you think the clock time as recorded on any of
them is worth anything -- and how you would tell. I mean, as opposed
to something that is a monotonic counter that increments a random
amount at intervals -- which I would submit is useless as a clock.

I have given you a perfectly good definition of a clock positioned at
each point (x,y,z). You need to understand that to an infinite array
of clocks you can add or subtract a constant amount f(x,y,z) to each
one. I'm assuming that you're a physicist so I had to explain that to
you.

OK, but that doesn't help distinguish a set of clocks from a set of
monotonic random number incrementers. You can always add an offset
f(x,y,z) to all of the clocks to get them to correspond at that
moment, but at the next increment, they are all randomly scattered
again. That means that you have to add an offset that not only varies
by position but by time: f(x,y,z,t). This effectively removes their
value as clocks. Moreover, you have to decide how you are going to
determine what the function f(x,y,z,t) is at every increment.

Put it this way. Suppose you have a set of counters a_i (i=1...n),
which generate a decimal number that looks like this: a_i(j) = j +
ran[0,1]_n.
Thus you might see the following:
a_1(1) = 1.0023 a_1(2) = 2.8374 a_1(3) = 3.3113 ...
a_2(1) = 1.4392 a_2(2) = 2.3048 a_2(3) = 3.0309 ...
a_3(1) = 1.9830 a_3(2) = 2.8471 a_3(3) = 3.7582 ...
...
a_n(1) = 1.2922 a_n(2) = 2.3244 a_n(3) = 3.2485 ...

Now, for any j, you can always find a function f_i(j) that turns all
of the a_i(j) to a'_i(j) = j + 0.5 exactly. That is, a_i(1) = 1.5000
for all i, a_i(2) = 2.5000 for all i, a_i(3) = 3.5000 for all i.

But that doesn't change the fact that your a_i's are still randomly
generated, and you're having to adjust them with an f_i(j) that is
just as complex as the clock readings.

Not useful.

PD


Shubee

How
do any of those clock time definitions invalidate my derivation of the
Lorentz transformation athttp://www.everythingimportant.org/relativity/special.pdf
?

Shubee

PD wrote on Fri, 04 Apr 2008 11:00:17 -0700:

It is also heterodox among a lot of particle physicists as well.

Some list, statistics confirming your statement?

Just my contact with my colleagues in particle physics.

Now understand. We may be contacting different people ;-)

These people look at Feynman diagrams as more than just mnemonics for
writing down terms in a perturbative expansion of a scattering
matrix. Interestingly, Feynman would have been the first to disagree.
He was fond of pointing out that different approaches to solving the
same problem often have completely different pictures of the
underlying reality -- and it's completely impossible to determine
which one of them is "more right", because you can do the same level
of computation with any of them.

Well we may speculate about Feynman thinking on his own diagrams or we
can just quote Feynman thoughts about the geometrical picture of
gravity:

{BLOCKQUOTE
The geometrical interpretation is not really necessary or essential to
physics.

}

I believe that's what I just said. If two equivalent formalisms and
conceptual frameworks result in the same calculated agreement with
experimental results, then there is no way to determine which of them is
"necessary or essential" as an interpretation.

An important difference between relativists (geometers) and no-geometers
is that relativists often forget or avoid to speak about the existence of
a nongeometrical formulation.


--
http://canonicalscience.org/en/misce...guidelines.txt

Shubee wrote:
Lorentz invariance is an extraordinarily beautiful concept in physical
theory. How is it that professional physicists today can't find
Lorentz invariant expressions as easily as Poincaré did in 1905?

I have not fully digested all of Juan's claims and statements, but this
is just silly.

EVERY ONE of our current fundamental theories of physics is Lorentz
invariant. A modern physicist can easily and trivially "find"
Lorentz-invariant expressions by simply using an appropriate
representation of the Lorentz group. This of course includes the usual
tensors of GR.

In Poincare's day knowledge of group theory was limited to a handful of
mathematicians; today it is fundamental in nearly every field of
physics, and is taught to undergraduates.


Tom Roberts

On Apr 4, 1:29 pm, PD wrote:
On Apr 4, 1:05 pm, Shubee wrote:



On Apr 4, 12:20 pm, PD wrote:

On Apr 4, 11:26 am, Shubee wrote:

On Mar 30, 7:24 am, PD wrote:

On Mar 29, 3:28 pm, Shubee wrote:

On Mar 29, 2:10 pm, YBM wrote:

Shubee a écrit :

My point is that specifying a particular clock synchronization before
deriving the LT is completely unnecessary.

This is utterly stupid. Without clock synchronization you cannot
even say anything about the "t" coordinate which appears in the
transformations since you haven't defined it...

It's easy to understand how clock time can be defined at every point
while not knowing anything about the meaning of synchronization.

Stand side-to-side on an infinitely long ruler with other cretins like
yourself. (There are so many of you!) Let another infinitely long
ruler slide under all your noses so that your nose moves equal
distances in equal times on the moving ruler. Permit each cretin to
define time at his location to be whatever number his nose is pointing
to on the ruler as it moves by. Would you call those individual clock
times synchronized? Now tell the cretin that is standing on the ruler
at position x that he will be adding a number f(x) to his clock time
thereby resetting his clock time either forward or backward by a
constant amount. Do that for each cretin. I'm certain that all the
cretins will respond as you have done, saying, "It can't be done.."
"It's a violation of the laws of physics." Well, as I have said
before, you are an idiot.

Shubee

That doesn't work so well. Suppose the clock readings at successive
locations on the ruler read 12:18, 12:20, 12:19, 12:23, 12:26, 12:27.
Are those clocks synchronized?

Suppose the clock readings on the ruler are 12:18, 12:21, 12:24,
12:27, 12:30, 12:33, but your own wris****ch reads 12:18, 12:20,
12:22, 12:24, 12:26. Are the clocks on the ruler synchronized?

PD

I didn't say or imply that any of those clocks are synchronized.

I just asked if they were. I gather you agree that they are not.

That is correct.

Now
the question is whether you think the clock time as recorded on any of
them is worth anything -- and how you would tell. I mean, as opposed
to something that is a monotonic counter that increments a random
amount at intervals -- which I would submit is useless as a clock.

I have given you a perfectly good definition of a clock positioned at
each point (x,y,z). You need to understand that to an infinite array
of clocks you can add or subtract a constant amount f(x,y,z) to each
one. I'm assuming that you're a physicist so I had to explain that to
you.

OK, but that doesn't help distinguish a set of clocks from a set of
monotonic random number incrementers. You can always add an offset
f(x,y,z) to all of the clocks to get them to correspond at that
moment, but at the next increment, they are all randomly scattered
again. That means that you have to add an offset that not only varies
by position but by time: f(x,y,z,t). This effectively removes their
value as clocks. Moreover, you have to decide how you are going to
determine what the function f(x,y,z,t) is at every increment.

Put it this way. Suppose you have a set of counters a_i (i=1...n),
which generate a decimal number that looks like this: a_i(j) = j +
ran[0,1]_n.
Thus you might see the following:
a_1(1) = 1.0023 a_1(2) = 2.8374 a_1(3) = 3.3113 ...
a_2(1) = 1.4392 a_2(2) = 2.3048 a_2(3) = 3.0309 ...
a_3(1) = 1.9830 a_3(2) = 2.8471 a_3(3) = 3.7582 ...
...
a_n(1) = 1.2922 a_n(2) = 2.3244 a_n(3) = 3.2485 ...

Now, for any j, you can always find a function f_i(j) that turns all
of the a_i(j) to a'_i(j) = j + 0.5 exactly. That is, a_i(1) = 1.5000
for all i, a_i(2) = 2.5000 for all i, a_i(3) = 3.5000 for all i.

But that doesn't change the fact that your a_i's are still randomly
generated, and you're having to adjust them with an f_i(j) that is
just as complex as the clock readings.

Not useful.

PD

Little children know intuitively that a tiny arrow that moves steadily
along a continuum of numbers is a clock. If you want to reset the
clock time, then you can only add or subtract a constant amount to
whatever the arrow is pointing to. If you disagree with that, then you
need to repeat kindergarten.

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

On Apr 4, 1:34 pm, Tom Roberts wrote:
Shubee wrote:
Lorentz invariance is an extraordinarily beautiful concept in physical
theory. How is it that professional physicists today can't find
Lorentz invariant expressions as easily as Poincaré did in 1905?

I have not fully digested all of Juan's claims and statements, but this
is just silly.

EVERY ONE of our current fundamental theories of physics is Lorentz
invariant. A modern physicist can easily and trivially "find"
Lorentz-invariant expressions by simply using an appropriate
representation of the Lorentz group. This of course includes the usual
tensors of GR.

In Poincare's day knowledge of group theory was limited to a handful of
mathematicians; today it is fundamental in nearly every field of
physics, and is taught to undergraduates.

Tom Roberts

How many distinct invariants of the Poincaré group can you derive?
http://groups.google.com/group/sci.m...4b9f9a04c035ec

Shubee

On Apr 4, 2:01*pm, Shubee wrote:
On Apr 4, 1:29 pm, PD wrote:



On Apr 4, 1:05 pm, Shubee wrote:

On Apr 4, 12:20 pm, PD wrote:

On Apr 4, 11:26 am, Shubee wrote:

On Mar 30, 7:24 am, PD wrote:

On Mar 29, 3:28 pm, Shubee wrote:

On Mar 29, 2:10 pm, YBM wrote:

Shubee a écrit :

My point is that specifying a particular clock synchronization before
deriving the LT is completely unnecessary.

This is utterly stupid. Without clock synchronization you cannot
even say anything about the "t" coordinate which appears in the
transformations since you haven't defined it...

It's easy to understand how clock time can be defined at every point
while not knowing anything about the meaning of synchronization.