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On May 13, 2004, at 3:35 PM, Tim Ventura wrote:

Hi Guys --
 
I'm no physicist, but one of the things that I have been wondering about is this:
 
Could the Quantum Foam in PV include the previously unseen-forces and/or particles said to reside within the Planck radius in string theory?
 

Your question is meaningless - not well posed. There is no quantum theory in PV. There is no Planck quantum h in any equation of his PV model Hence no quantum foam. PV as published now is strictly a classical phenomenological model. It lacks GCT local symmetry as agreed by Mike Ibison who works with Hal in Austin and who agrees that PV is not as good as Einstein's GR in terms of agreement with observed facts like the pulsar data.

Hal appears to have no understanding of group theory of symmetries in theoretical physics. He never seems to have heard of the Klein Erlangen Program of 1872 that the group of reference frame transformations determines geometry!

http://www.math.mcgill.ca/~malkoun/Erlangen_Program/Erlangen_Program.html

http://www.fact-index.com/e/er/erlangen_program.html

http://encyclopedia.thefreedictionary.com/Erlangen%20program

Hal's PV dynamical action is that of global special relativity of 1905 with the adhoc insertion of a locally variable speed of light in the gamma factors. This itself is at best a very crude approximation, very dubious.

The space-time continuous symmetry of global special relativity is the 10 parameter Poincare group if you include rest mass m as an adoc parameter. If you set m = 0 you get the larger 15 parameter conformal group keeping the causal light cone invariant.

Look at the 6 parameter subgroup of the Poincare group, the Lorentz group. Look at the 3-parameter set of boosts. They connect GIFs to each other. GIF = Global Inertial Frame, i.e. a special class of "inertial observers" moving in globally flat 4D space-time along straight lines in sense of Euclid's 3D geometry at constant speed with zero acceleration! Therefore, this symmetry group cannot answer the question of how to transform the theory between two observers in arbitrary accelerated motion, i.e. in non-inertial frames of reference, who are comparing their measurements on the same phenomena. That is what the new GCT (General Coordinate Transformations) local symmetry group is all about! In addition there is the equivalence principle that an observer at rest in an accelerating (non-inertial frame) feels an "inertial force" that cannot be locally distinguished from a "gravity force" or "g-force." Note that this "g-force" has nothing to do with tidal curvature which is detected by a different operational procedure entirely. You can have two neighboring weightless geodesic observers who detect a local curvature field. The curvature tensor measurement is operationally distinct from g-force measurements!

When I ask Hal what is the full symmetry group of his PV theory of gravity? He is mute. Hal cannot say because he seems not to understand what I am asking him. He falls back on the lame excuse that I am stupid and simply do not understand his theory and that every one else who has written to him privately understands it. Of course, Hal never produces one example of these alleged private notes. He can do it removing the ID so that we can all see what the idea is. Of course, I may be in error, but Hal does not obey the standard rules of engagement in my peer review of his theory. At this point Hal should list all my actual statements that he thinks is in error and misrepresent his theory, and give explanations that we all can look at. If indeed, he makes a good argument and is correct I would say so. He has never done that not even once to my satisfaction at least. Nor have any of the people he alludes to who are obviously following the debate offered a critical defense of his theories. This is a strange silence indeed.

Special Relativity 1905 works only with GIFs in globally flat 4D space-time with the Poincare group. You need the additional local GCT group to describe the relationships of the measurement data on the same objective events between momentarily approximately coincident non-inertial LNIF observers. This is true even if the space-time region is flat with a zero tensor curvature field! GCT can be used, indeed must be used, even in a 4D globally flat spacetime in order to be able to answer a whole class of physical questions. This is an example of Godel's incompleteness theorem in physics! Questions that have no answer in Special Relativity have an answer even in globally flat spacetime when you add the GCT group! This is why any physical theory of spacetime must include GCT whether or not there is curvature. Hal and Mike do not understand this deep physical idea and it is no wonder that ALL alternative theories of "gravity", like Hal's version of PV, that do not have GCT + local equivalence principle fail experimentally.


Define "metric." My understanding of "metric theory" was simply

ds^2 = guv(x)dx^udx^v (eq. I)

where guv(x) is a GCT tensor.

What is your more general formal definition that allows a distinction?

Be precise and detailed so I can see what you mean.

On May 13, 2004, at 4:49 PM, michael ibison wrote:

Your definition of 'metric theory' disagrees with that in MTW and in the book by Will.

No it does not.

The formal definition of a metric theory is probably given by Schiff and by Dicke. Roughly, it is a theory in which some quantity guv(x) is sandwiched in between all products of vectors and (other) tensors which go in to making the scalar action. In such a theory, the effective line element is then ds^2 = g_{uv}(x)dx^udx^v as you have given. For example, if in a g-free theory the EM interaction (in the action) is A^u j_u, then in a metric theory it must appear as A^u g_{uv} j^v

That does not contradict what I said.

Satisfaction of the above ('metric theory requirement') is necessary but not sufficient for a theory to be GCTI. In the last email I sent a list of metric theories that are not GCTI.

And all those theories are wrong experimentally!

BTW you left out my two other equations

gu'v'(P) = Xu'^u(P)Xv'^v(P)guv(P) (eq. II)

i.e. the basic "GCT" equation.

+ the local equivalence principle expressed as

guv(P) = Xu^a(P)Xv^b(P)nab (eq. III)

where nab is the FLAT 4D Minkowski metric in the geodesic LIF at P

guv(P) is the CURVED 4D metric in the LNIF at P

I am not sure that your statement that g_{uv}(x) is a GCT tensor means anything. 

It means the two equations I just wrote. I do not see how any of this fancy dancing helps Hal's case for PV? Do you?

A theory as a whole may be GCTI, but each tensor in in the theory guv, Fuv, ... may be changed under a coordinate transformation, whether or not the theory as a whole is GCTI.
 

Huh? In any case, what's your point? How does this help justify Hal's PV as a viable contender for metric engineering?

You seemed to agree with me before that all theories without GCT as I mean in context of the three above LOCAL equations I, II, III disagree with experiment including Hal's PV. Hal's PV without GCT is physically incomplete in a Godelian sense as I explained above.


In a message dated 5/13/04 6:32:39 PM, sarfatti@pacbell.net writes:

Jack: If you were to list my errors of understanding of your PV and ZPE theories I would publish them and subject them to honest open debate. ... Show us.

On May 13, 2004, at 4:45 PM, Puthoff@aol.com wrote:

OK, let's start with this.  It's a global issue in your arguments:

In a message dated 5/13/04 6:19:08 PM, sarfatti@pacbell.net writes:

JS: By "metric theory" I mean a theory with a "metric tensor" therefore GCT is implied.

HP: Your definition is just incorrect.  There is a standard definition in GR theory, and what you say is not it.  Yes, metric theory means a metric tensor is involved, but it does not necessarily imply GCT.

JS: Define the math you mean for "GCT." When I say "GCT" I mean the local equation II above. I mean this:

gu'v'(P) = Xu'^u(P)Xv'^v(P)guv(P) (eq. II)

What do you mean? Show us with the math. Even if my definition were in some way incorrect. How does that help your PV theory, which Ibison says lacks GCT?

HP: For starters, in Clifford Will's article, Ch. 2, p. 48 of Hawking's and Israels's book "General Relativity,"  Will discusses Rosen's bimetric theory.  It is a metric theory, it has a metric tensor, but it also has a background metric and so does not satisfy GCT.  So a metric theory with a metric tensor does not automatically imply GCT; only in special cases (e.g., Einsteinian GR is one) is that the case.

JS: So what's your point here? How does this help establish your PV as a plausible model for metric engineering. Who says Rosen's bimetric theory is any good? Does it explain the observations? Is it a hot topic in the key physics journals on relativity? No. I gave you my meaning for GCT in eq II,

HP: Ibison gave you all the references about this issue.  Check them out.  I now see why you have had so much confusion over this issue, and have said the (incorrect) things you have said in attempting to assess much of my work.

JS: Your logic here is bogus. Show us explicitly how any of the references you just gave above justifies your PV? Since I am sure that every one is now confused let me ask:

Q1. Does your PV have GCT or not?

My understanding is that it does not.

Suppose your PV is a metric theory without GCT.

Q2. How does this help your argument?

Q3. What is the complete symmetry group of your PV theory?

Remember tensors are defined relative to a given symmetry group.

Q4. Remember, I say the physical meaning of GCT is that it shows us how to compare local observations on the same events made by two coincident observers looking at same events in their neighborhood of coincidence. Do you agree with that or not?

Therefore, if you agree, that means PV is physically incomplete in the operational sense of PW Bridgman.

Q5. Suppose for the sake of argument, I was wrong about metric theories and GCT, how does that help your argument for PV?

Q6. Do you agree that a theory that makes wrong predictions should be abandoned?

Q7. If yes on Q6, why do you still cling to PV that gives a wrong prediction on the pulsar data as shown by Ibison?

Q8. How many fudge factors will you add before giving up?

BTW, now that I have coaxed you into a rational substantive discussion with the PRAVDA articles, I will include this in Super Cosmos to give a fair representation of your position on PV. :-)

However, even if I granted you this point. I do not see how it helps your case? Please explain.