On Fri, 8 Aug 2003, wchogg wrote:

On Fri, 8 Aug 2003, Bilge wrote:

Mike Helland:
You are incorrect. My bias is Quantum, not classical.

In that case, curvature should not be a problem. Quantum field
theory makes use of curvature tensors for quantum fields. The
electromagnetic field strength tensor F^uv is the curvature tensor
for the electromagnetic field. Maxwell's equations a

d_{u}F^{uv} = j^{u}

along with the bianchi identity:

d^w F^uv + d^v F^wu + d^v F^uw = 0

The electromagnetic field strength tensor is obtained in exactly the
same way as the gravitational field strength tensor - from the commutator
of covariant derivatives. The equivalent quantity in gravity is the
riemann tensor.

Sorry to keep hasseling you, but are you saying that in a Yang-Mills
theory, that the "curvature" that comes from using the gauge covariant
derivative is the field strength tensor?

Derr..don't mind me, I'm not feeling well today and when I reread your
post I realized you explictely said this.

There was actually another part to my question: So what is the space this
is the curvature of? The field strength is a function of points on
space-time, and it spits out what? The Riemmanian curvature I'm used to
is used to describe geodesic deviation, what does this gauge field
curvature do?

I really need to recheck out Gauge Fields Knots & Gravity from our
library...

I should also post more carefully...

--
William C. Hogg

wchogg:
On Fri, 8 Aug 2003, Bilge wrote:

Mike Helland:
You are incorrect. My bias is Quantum, not classical.

In that case, curvature should not be a problem. Quantum field
theory makes use of curvature tensors for quantum fields. The
electromagnetic field strength tensor F^uv is the curvature tensor
for the electromagnetic field. Maxwell's equations a

d_{u}F^{uv} = j^{u}

along with the bianchi identity:

d^w F^uv + d^v F^wu + d^v F^uw = 0

The electromagnetic field strength tensor is obtained in exactly the
same way as the gravitational field strength tensor - from the commutator
of covariant derivatives. The equivalent quantity in gravity is the
riemann tensor.

Sorry to keep hasseling you,

That's ok. Intelligent discussions sure beat the same old topics
on the twin's paradox and naive ether arguments, not to mention
the potteresque bolshevik science threads.

but are you saying that in a Yang-Mills theory, that the "curvature"
that comes from using the gauge covariant derivative is the field
strength tensor?

Si.

If you just write the gauge covariant derivative for E&M, SU(2) and
SU(3), you get the field strength tensor from:

F_uv = (1/ig)[D_u, D_v]

Compare with general relativity:

R^a_buv V^b = [D_u, D_v] V^a

It's really remarkable how things which appear so different all begin
to look the same. One might even get the idea that there is some truth
to all of it...

In the notation of fibre bundles F_uv goes to:

F = ig F_uv dx^u /\ dx^v

= [D_u, D_v] dx^u /\ dx^v


I really need to recheck out Gauge Fields Knots & Gravity from our
library...

Quite possibly, if you want that sort approach. I'm not very well
versed where fibre bundles are concerned. However, david mcanally
seems to be knowledgeable in that area.

Mike Helland wrote:

John Anderson

Physical theories that are logically inconsistent get eliminated
before they get published.

You are suggesting that we have obtained perfection in our ability to reason.

You are living in a dream world, Mr. Anderson.

Name a few theories that turned out to be logically inconsistentas opposed to
being in disagreement with experiments.

John Anderson

wchogg wrote:
There was actually another part to my question: So what is the space this
is the curvature of?

The underlying fiber bundle.


The field strength is a function of points on
space-time, and it spits out what?

Rather than a function on spacetime, think of it as a fiber "sitting
above" spacetime. The advantage is that geometry becomes possible, and
one can apply notions such as "curvature" to it (in terms of functions,
the curvature tensor is just a complicated functional of the field
function(s), without much discernable use or justification)....


The Riemmanian curvature I'm used to
is used to describe geodesic deviation, what does this gauge field
curvature do?

Describes the behavior of sections of the bundle.


I really need to recheck out Gauge Fields Knots & Gravity from our
library...

An excellent book. All that I know about this stuff came from it.... And
all too much of it have I forgotten (:-().


Tom Roberts

Bilge,

I am admitting that spacetime is curved. You claim that matter is what
curves. I'm wondering if you have an experiment to prove this claim on
cause and effect.

Light follows geodesics. Light follows a curved trajectory as it passes
by the sun. This is measured during an eclipse. The positions of stars
are shifted when compared with the same positions seen in the night sky.

This experiment proves that light follows geodesics. Thats not what I
asked.

Lets say we have two statements:

1. Gravity is light following curved geodesics
2. Gravity curves geodesics

Can you think of an experiment that supports one statement over the
other? That was what I requested. See, right the

"I'm wondering if you have an experiment to prove this claim on cause
and effect."

Your experiment merely proves something about the effects, and not the
cause.

Bilge, it is clear that you are a very knowledgable student of
physics. However, I am trying to discuss this topic at a level of
abstraction that you have not been able to rise to. You have not
addressed my questions of GR at the same level they have been
presented.

In that case, curvature should not be a problem. Quantum field
theory makes use of curvature tensors for quantum fields.

First, you are right, its not a problem. Which is why I said in my
last umpteen messages that "I agree that spacetime is curved."

Second, "making use of" and "causing" are completely different topics.
Once again, I applaud your knowledge, but you have not looked past the
knowledge obtained through your studies to answer questions that are
obviouslly very new to you.

Mike Helland

Mike Helland:
Bilge,

I am admitting that spacetime is curved. You claim that matter is what
curves. I'm wondering if you have an experiment to prove this claim on
cause and effect.

Light follows geodesics. Light follows a curved trajectory as it passes
by the sun. This is measured during an eclipse. The positions of stars
are shifted when compared with the same positions seen in the night sky.

This experiment proves that light follows geodesics. Thats not what I
asked.

Lets say we have two statements:

1. Gravity is light following curved geodesics
2. Gravity curves geodesics

Can you think of an experiment that supports one statement over the
other? That was what I requested. See, right the

"I'm wondering if you have an experiment to prove this claim on cause
and effect."

Your experiment merely proves something about the effects, and not the
cause.

What "causes" the pythagorean theorem? What "causes" F = ma? What
"causes" L = r x p? What "causes" a "straight" line to be straight?
What "causes" the circumference of a circle to be 2\pi x the radius?
What causes the volume of a rectangular parallelepiped to be L X W x H?


Bilge, it is clear that you are a very knowledgable student of
physics. However, I am trying to discuss this topic at a level of
abstraction that you have not been able to rise to.

On the contrary. You are unable to let go of the concrete classical
intuition that biases your thinking. If you could see the bigger picture,
you would realize that what you are asking doesn't make sense any more
sense than asking for a physical reason that there are 2\pi radians in
a circle.

You have not addressed my questions of GR at
the same level they have been presented.

I've tried and it's very frustrating because you won't address the
the questions I've posed to get you to see the problem with your
question.

In that case, curvature should not be a problem. Quantum field
theory makes use of curvature tensors for quantum fields.

First, you are right, its not a problem. Which is why I said in my
last umpteen messages that "I agree that spacetime is curved."

Then, what's the problem?

Second, "making use of" and "causing" are completely different topics.

You have the same problem that others who want a "cause" have. You
fail to see that you don't ask the exact same questions about the
geometry you take for granted. Why are two different paths to the
store, different distances? What causes that?

Once again, I applaud your knowledge, but you have not looked past the
knowledge obtained through your studies to answer questions that are
obviouslly very new to you.

You haven't studied enough physics to realize that your question
is meaningless. You are wanting an answer that would not make sense.
You are not asking anything abstract. You fail to understand the
abstraction. Again, I ask you, why should spacetime need a "cause"
to be curved? Why should in not need a cause to be flat?

Ken S. Tucker

And as Bilge pointed out a few posts ago, this same effect
is consistent with free-fall (non-accelerated systems) systems
moving along geodesics that were first described by Newton's
1st Law of motion. This point is essentially *the principle of
equivalence*. These geodesics corelate with the mass sucking
radial length

You might have answered the question I'm about to ask with the "mass
sucking" comment, but I was flying on a plane yesterday and couldn't
help noticing how beatuiful the clouds were.

Then I could help noticing that they were moving, but not along a
curved geodesic towards earth. They were just floating in the sky
moving around at the same altitude. Why do the clouds not come to the
ground if they are supposed to be moving along curved geodesics?

(and the smart ass answer "they do when it rains" is not acceptable
;-))

Well should the *Laws of Physics* vary from one observer
to another because of funny motion?, of course not.

How about the following question:

Should the laws of physics vary from one observer to another because
of a fundamental difference in the mechanics of observation?

What I mean by this, is we observe something through light
(electromagnetism) and two atoms observe each other through the force
of electromagenetism as well. So because we are observing
fundamentally the same way, our laws of physics will be the same. But
how about the particle carrying electromagenetism?

Two particles don't interact or observe each other through light, and
this is tautologously true because when the particles interact they
are creating light (or electromagenetism) so it would be impossible
from them to observe mechanically identically to the way we observe.

In this case, I assert that the laws of physics are indeed different
because the observers are mechanically different.

Any problems with that? That is the whole premise of my theory of
Multiple Natures:
http://www.techmocracy.net/science/time.htm

Mike Helland

Bilge,

Again, I ask you, why should spacetime need a "cause" to be curved?

Ok, I'll lay out my thought process point by point

A. I personally do not need a cause
B. GR states that matter causes spacetime to curve
C. Because there is a theory that states that cause, I personally need
that statement to be accurate
D. You agree with me that looking for a cause is irrational and
unscientific (right?)
E. Because you agree with me, by questioning the cause I'm trying to
demonstrate that GR irrationally and unscientifically states a cause

Is there a failure in my thought process? If so, please point it out.

If not, I assume that we agree that the statement "matter causes
spacetime to curve" is misleading? And if I assume correctly, I must
also assume that we agree that GR states nothing about what gravity is
even though it accurately states how we observe and therefore how we
can predict the effects of gravity?

Mike Helland

On Wed, 13 Aug 2003 09:58:50 -0700, Mike Helland wrote:

[...]

B. GR states that matter causes spacetime to curve

[...]

GR "states" no such thing. You're describing a heuristic tool used to
explain the mathematics of general relativity to those not familiar with
the theory. The word "cause" is an anthropomorphic mishandling of the
underlying mathematics, but it seems somewhat appropriate to use when
explaining to those new to the subject.

Jeff

Mike Helland:
Bilge,

Again, I ask you, why should spacetime need a "cause" to be curved?

Ok, I'll lay out my thought process point by point

A. I personally do not need a cause
B. GR states that matter causes spacetime to curve
C. Because there is a theory that states that cause, I personally need
that statement to be accurate
D. You agree with me that looking for a cause is irrational and
unscientific (right?)

No, I said the question was meaningless. I ask you again the
following question (In your own format). This time _ANSWER_IT_.

A. The pythagorean theorem says that a right triangle causes the sqaures
of the length of the two sides to equal the square of the hypotenuse.

B. Because there is a theory that states that cause, I personally
need that statement to be accurate.

E. Because you agree with me, by questioning the cause I'm trying to
demonstrate that GR irrationally and unscientifically states a cause

I don't agree with you. You do not understand why the question you're
asking is meaningless. You use the terms "irrational" and "unscientific"
as derogatory terms that mean you shouldn't ask the question because
you think it can't be answered. It was answered. The question itself
is meaningless and you don't really care to pay attention to that
answer.



Is there a failure in my thought process? If so, please point it out.

I have. Apparently your thought processes have failed to the extent
that you can't read the text where I've pointed out what's wrong
with your thought processes.


If not, I assume that we agree that the statement "matter causes
spacetime to curve" is misleading?

It's a slogan that gets the point across to people who aren't
liable to mistake it for the content of general relativity.
It would appear that others become fixated on the slogan because
contrary to their assertions, they are not really interested
enough in the subject to study it, even a little.

And if I assume correctly, I must
also assume that we agree that GR states nothing about what gravity is
even though it accurately states how we observe and therefore how we
can predict the effects of gravity?

You don't assume correctly. You should spend less effort trying
to win a debate by misconstruing my statements and more effort into
trying to find some resources to study general relativity, if you
really are interested in understanding what you claim. Do you think
people spend years studying this stuff because they didn't realize
that someone on usenet could condense it all into a single post
for them?