No time travel paradoxes!

In refutation of Tim's argument below I quote Igor Novikov. Of course one must read Novikov to get all the details properly.

In reference to Tim's "paradoxes" below:

"Does this paradox demonstrate that time travel [to the past] is impossible? Not at all. The reason is that in our discussion of the paradox [same as Tim's below] I committed a serious logical error. I discussed the situation twice, in two different ways. In the first discussion, I discussed my journey to mouth B assuming there was no meeting with the older version of myself from the future. In the second discussion. I discussed the same journey but assumed that the first discussion was correct and that therefore I could travel back in time and that therefore I could travel back in time and that therefore there was a meeting. The error is the assumption in the first discussion that there was no meeting. If the meeting happened, it happened. So we should take into account the consequences of the meeting from the very beginning. Therefore, even if I am not killed, when I travel into mouth B, then I will remember the meeting with my younger self when I come out of mouth A. So what actually happens ... We see now that there are no contradictions or paradoxes ... Events can be influenced by other events in the future, as well as other events in the past ... however there is only one flow of events, so the past cannot be changed once it has occurred ... in the presence of time machines we have very strange and unusual physical processes taking place, but no contradictions. ... This means that our free will must be constrained. If I meet with a younger version of myself and wish to kill that younger version, then the laws of physics will prevent me from doing so."

Star Gates and Time Travel to The Past (from my 4th book "Star Gate")

The words “Star Gate” and “wormhole” mean the same thing in this book. More precisely I mean “traversable wormholes” without any black hole event horizons. These star gates require anti-gravitating “dark energy” to keep them stable and open. Since our universe is about 73% dark energy on the large scale there is plenty around. Any ETs (Extra-Terrestrials) visiting Earth in their flying saucers are able to do so because they know how to manufacture and also use naturally occurring wormholes that may have been created in the early universe and are time travel machines to the past Stephen Hawking’s “chronology protection conjecture” noted but dismissed because of the facts. Are time machines are dangerous weapons of mass destruction in the wrong hands?

“If someone could travel from our time back into the past, then that person could probably change the past. If so, as a result, he would change all of subsequent history. For example, a person who travels back in time to the beginning of the universe could change the physical conditions at that period, and as a result change the whole history of the universe. The explosion of a hydrogen bomb is nothing compared to such a possibility.” Moscow physicist Igor Novikov at Cal Tech Kipfest 2000.[i]

However, we do not have to worry about changing the past. Novikov proves that is based on faulty logic and that in every case a strange but self-consistent global loop in time happens. We do not have absolute free will to violate the laws of nature. It may be our free will to fly if we walk off a cliff, but we will fall. Similarly, you may go back in time and attempt to make a paradox, but you will fail to do so. Simple models of a billiard ball going back in time to collide with its younger self have consistent histories. If there is a collision it will be a very weak glancing collision that will allow the ball to pass through the wormhole time machine. If the ball is a bomb that explodes at least one fragment from the explosion will go through the time machine to make the ball explode in the first place. If it happens it happens. If you go back in time to meet your younger self you will remember meeting your younger self as you enter the time machine and you will not be able to prevent yourself from doing so. Jean Cocteau’s film “The Last Testament of Orphee” dramatizes this idea as does the film “La Jetee” and “Twelve Monkeys” as well as “The Terminator” series with Arnold. Here the science fiction is actually good physics.

[i] “The Future of Spacetime” ed. Richard Price, p. 58, W.W. Norton (2002)



On Nov 29, 2005, at 4:17 PM, Cassidy-Curtis Timothy G GS-13 30 RMS/RMR wrote:

Well, the math is going to send me back to school, of this I have no
doubt! However, please let me suggest a couple of intriguing thoughts.
Time travel, itself, presents well known paradoxes; Dr. Mallet, himself,
acknowledges and has suggested ways to avoid.

No, this is a Red Herring. It's simply not true at all. The refutation of what you just wrote is in "Can we change the past?" by Professor Igor Novikov given at the Cal Tech Kipfest 2000 printed in "The Future of Spacetime" 2002 California Institute of Technology ISBN 0-393-32446-X-pbk pp 57-86.

The notion of such autocidal paradoxes is based of faulty logic and actual physics calculations show that such arguments are not correct.

We are all familiar with
it, but I describe the paradoxes as Time Loop and Grandfather Paradoxes;
I actually express them in terms of logical argument.

You are simply wrong. If you read Novikov's simple article you will see why. :-)

The Grandfather
Paradox is the well known situation in which one eliminates one's own
cause, and the Time Loop Paradox is where one multiplies an existing
cause (thus creating numerous copies of a result). The logical
expression is the Clarity Principal of Logic, where P must imply P and
NotP must imply NotP. In both cases, P implies NotP (thus violating the
principal); the Grandfather Paradox creates an implication of P implies
Zero and the Time Loop Paradox implies P implies MultipleP (which is a
form of NotP). It has been pointed out that identification of paradox
is tantamount to establishing impossibility.

So, that said, what if we were to see if there were any way to
accomplish Time Travel without invoking Paradox? Dr. Mallet makes an
attempt to do so by suggesting that Time Travel cannot happen prior to
when Time Travel becomes possible. (Actually, Dr. Carl Sagan made the
same constraint in a PBS-broadcast NOVA interview, some years earlier).
It's a game suggestion, alright, but when I thought about it what I
concluded was that it just didn't cut it. So, I tried to see if I could
do better.

What I came up with were two constraints:
1. A time traveler cannot travel to any time in which he has actually
existed

False IMHO

2. A time traveler cannot be able to interact with himself while inside
an energized time travel field (but cannot, in any case, violate #1,
above)

False IMHO

I also construe a time travel field as being a sort of event-horizon
that effectively creates a condition of non-existence between the inside
of the field and the rest of the Universe. It essentially decouples
actions inside the field from outside the field, kind of the same way a
worm-hole decouples intervening space from the end-points.

Again read Novikov. Hawking has a paper after his, but not based upon the kind of
argument you make here. :-)

Now, as you look at my constraints, it's quite possible to say that I've
constrained myself out of time travel. How is it possible to exist
during a time when you do not exist (constraint 1)? You can't. Oh,
wait, but that's the static case.

Now, let's consider the Relativistic case. The Lorentz equation tells
us that there is a T-prime that is different for travelers at
relativistic velocities which is different from the T of the
non-traveling reference case. T-prime is always less than T, and this
is very significant at speeds near C. So, what if, while traveling at
relativistic velocities, you are also inside your time travel field
(effectively traveling along the closed time-like curve and effectively
travel backwards in time)? Consider the time of T minus T-Prime. What
if your time field absolutely, always, and consistently, appeared to
deliver you from time T, (which is what an outside observer would say is
the time you took to travel the distance, and cannot be any smaller than
C/distance traveled) to T minus T-prime (which is the time you think you
spent during your travels due to dilation)? In fact, what if, while
traveling inside your time travel field, you actually never reach time
T, but are always deposited at T minus T-prime; it would somehow be a
function of this type of time travel that T minus T-prime would always
be the result, so no matter what you do, after accelerating up to
relativistic velocity, and turning on your time travel field, the only
point you come out at is a point in time that's T minus T-prime, and
nowhere else? If no other time is possible than T minus T-prime, than
both of my constraints (above) would be satisfied, and paradox is
eliminated.

Well, after looking at this train of logic, I began to wonder if any of
the EFE solutions would favor or result in either T-prime, or T minus
T-prime. That is why Mallet's Time Machine Proposal is so intriguing to
me.

You see, guys, if the math works out, than it may not be as much as time
travel that's been discovered it. It's FTL.

I wrote a paper, and submitted it to the Journal of the British
Interplanetary Society. I am attaching both my paper and the JBIS
response. Needless to say, they did not want to publish it as it was,
but I think their response was kind of intriguing. Looks like if the
math can be worked, it may be a winner. If anybody thinks of a way, I
would be ecstatic about it.

- Tim "C-Squared" Cassidy-Curtis, Solar System Ambassador

-----Original Message-----
From: Jack Sarfatti [mailto:sarfatti@well.com]
Sent: Tuesday, November 29, 2005 2:27 PM
To: Dr. Eric Davis
Cc: Cassidy-Curtis Timothy G GS-13 30 RMS/RMR; Creon Levit; Ron
Pandolfi; alan parker; Dan Smith; S-P Sirag; rkiehn2352@aol.com; David M
Mcmahon; Tony Smith; Mark Pesses
Subject: Re: Ronald Mallett's Time Machine Proposal

Thanks Eric. What's the bottom line here in your opinion? I mean in
terms of a practical device with this approach. I will look also when I
can.

On Nov 29, 2005, at 12:45 PM, Dr. Eric Davis wrote:

Gentlemen:

Here are the relevant references that you require per the below post.

I also attached Scully's paper because Mallett references it in his
papers and it is of relevance to the question that Mallett is
addressing in his time machine proposal.

I talked to Mallett three years ago and obtained other material which
is not available for public release.

Regards,

Eric

Eric W. Davis, Ph.D., FBIS
Inst. for Advanced Studies at Austin
4030 W. Braker Lane, Suite 300
Austin, TX 78759


From: "Cassidy-Curtis Timothy G GS-13 30 RMS/RMR" Curtis@vandenberg.af.mil>
To: "Jack Sarfatti"
CC: "Creon Levit" , "Ron Pandolfi"
, "alan parker"
, "Dan Smith"
, "S-P Sirag"
, , "Eric Davis"

Subject: RE: Ronald Mallett's Time Machine Proposal
Date: Tue, 29 Nov 2005 12:02:53 -0800

OK. After sending, I did a bit of digging. You may find the
following of interest.

"The Gravitational Field of a Circulating Light Beam" Ronald
Mallett, PhD, Dept. of Physics, UConn Foundations of Physics [Jnl]
Volume 33, Number 9 September 2003
Pages: 1,307-1,314
(Publisher: Springer Science+Business Media B.V, Formerly Kluwer
Academic Publishers B.V.)

Abstract: Exact solutions of the Einstein field equations are found
for the exterior and interior gravitational field of an infinitely
long circulating cylinder of light. The exterior metric is shown to
contain closed time like lines.

If you can obtain this paper, you may be able to make your own
determinations. The only possible objection I can think of is that
it explicitly refers to an "infinitely long circulating cylinder of
light."
If subsequently constrained to a cylinder of light that is if finite
length the premise may break down...or not. Long ago I learned to be

cautious when applying infinite cases to finite geometries. If it
stands up to a finite geometry, then this could be even more
intriguing.

At any rate, there it is. I have not obtained this paper yet.

________________________________

From: Jack Sarfatti [mailto:sarfatti@well.com]
Sent: Tuesday, November 29, 2005 11:49 AM
To: Cassidy-Curtis Timothy G GS-13 30 RMS/RMR
Cc: Creon Levit; Ron Pandolfi; alan parker; Dan Smith; S-P Sirag;
rkiehn2352@aol.com; Eric Davis
Subject: Re: Ronald Mallett's Time Machine Proposal


I am not familiar with his work. :-)

Nick Herbert on Ray Jensen's FTL signal idea - why it does not work.

On Nov 28, 2005, at 4:09 PM, nick herbert wrote:

Jack, the coincidence circuit in Dopfer's experiment works like it does in the
Aspect/Grangier (AG; see attach.) experiments with 2 polarizers: it matches
which photon corresponds to which. Nothing more.

So, Dopfer uses the circuit to match photons. In addition to weeding out
noise, the circuit coordinates data collection: some of the photons have
siblings measured in the focal plane, others in the imaging plane. You
need to separate the two types of data out, in particular if you are switching the
quantum eraser (QE) randomly between focal and imaging planes.

Now OTOH, suppose you are on the receiving end, with the double slit, and you
receive 1000 photons from correlated pairs. There is no coincidence circuit.
I am the "sender" with QE. Beforehand, I informed you, "either the 1000
photons will all have their siblings measured in the focal plane, or they will all
have been measured in the imaging plane." Can you determine which plane I measured
their siblings?

The answer is of course, so long as there is not too much noise.

Did you mean here

The answer is of course YES, so long as there is not too much noise. ?



You will either see an interference pattern from the data or you will not, allowing you
to answer the question. So assuming my reasoning is correct here, you can
indeed send new information. Just set up regular intervals for both
sender and receiver, and have sender keep the QE either in the focal plane or in the
imaging plane (but not both) between these intervals.

Nick, above I asserted that the coincidence circuit is only for correlating
photons. For the sake of argument, suppose you needed some other information
in order to construct the interference pattern behind the double slit. Now
look at what happens when the QE is in the focal plane (fig 4 in Z.). You get
an interference pattern from the data collected by the QE, but there is no
double slit! Anyway, how is this interference pattern constructed? Is it
necessary to get information from the other side here also? If so, (and it
should be the case due to symmetry) then both sides are dependent on one
other; then the argument becomes circular. So conclusion: there is no other
information necessary for construction of the interference pattern.

Ray


Hi Ray--

I'm sorry that I don't have time to discuss the details of the Dopfer
experiment. I'll have to content myself with critiquing your original
article where I think you erred by adding amplitudes instead of
intensities.

In any scheme that purports to use EPR to send signals FTL, not only must
you propose a scheme but also show how your scheme evades the various
impossibility proofs (Eberhard's for instance.). It seems to me that any
scheme (such as yours) that uses passive elements cannot in principle evade
these proofs. Ya gotta get weird.

That's why I invoke MACRO-QUANTUM ODLRO with a NEW NONLINEAR NONUNITARY LOCAL Landau-Ginzburg eq to get signal nonlocality in violation of micro-quantum theory's assumptions of linearity & unitarity.

For instance, I imagined (in my FLASH proposal) that I had discovered a 3rd
and novel kind of measurement, adding to von Neumann's classic measurements
of the 1st and 2nd kind which leave the measured system in the measured
state (Type 1) or in some other state (Type 2). I proposed to clone the
measured state--a process which seemed on the surface to evade the general
anti-FTL proofs but it turns out that perfect quantum cloning is forbidden
by linearity. The best quantum cloner (developed by Mandel and others) has
a signal to noise ratio of 5 good copies to 1 bad copy but this is exactly
insufficient to signal FTL.

warm regards
Nick Herbert

Round 2. Who is right Nick Herbert or Ray Jensen?


On Nov 27, 2005, at 7:24 PM, Jack Sarfatti wrote:

Another Go at this:

Round 2. :-)

OK, let's look at this once more. The problem here is how to properly apply Feynman's rules. Let's review those rules.

I. Add amplitudes before squaring if one cannot distinguish the alternatives.

II. Square the amplitudes before adding if one can distinguish the alternatives.

Jensen's eq. 3 is, he claims, the coherent superposition

|2> = (1/2)^1/2[|2+> + |2->] (3)

for the total experimental arrangement in fig 3 p. 3.

Let | ) be the basis for the detectors A&B of photon 2 on the RHS of fig 3.

Jensen's eq. 4 is

|2+> = cos@|2A) - sin@|2B)

|2-> = sin@|2A) + cos@|2B) (4)


Substitute (4) into (3) to get

|2> = (1/2)^1/2[(cos@ + sin@)|2A) + (cos@ - sin@)|2B)] (4) + (3)

The key physical assumption here is that (3) is a single pure state not a mixture.

If that assumption is correct, then

p(A) = (1/2)(cos@ + sin@)^2 = (1/2)(1 + cos2@)

p(B) = (1/2)(cos@ - sin@)^2 = (1/2)(1 - cos2@)

Now this is Jensen's argument. Nick seems to be saying that his physical assumption is wrong, i.e. that (3) is not coherent, but is a random mixture, so that

p(A) = p(B) = 1/2 for fig 3

and the same for fig 5. Hence no signal nonlocality.

On the other hand Jensen claims that these modulated probabilities are locally seen in actual experiments? Is that correct. If so, then really you deny Jensen's eq. 3.

On Nov 27, 2005, at 3:13 PM, nick herbert wrote:
Hi Ray--

Your ingenious FTL scheme was forwarded to me by Jack Sarfatti.

Having constructed dozens of such schemes while writing my FTL book (none
of which ever worked) I am familiar with most of the pitfalls a would-be
EPR FTL signaller will encounter.

In your case the problem occurs with your Eq 4 where you give the
for detection of photons at the two interferometer arms. What
you want is the probabilities (amplitudes squared) for each of the two
types of pure-state photons that impinge on the interferometer.

Nick, what do you mean by "two types of pure state photons"? Are you saying

|2> = (1/2)^1/2[(cos@ + sin@)|2A) + (cos@ - sin@)|2B)]

as a single coherent state is wrong, and that there is a mixture of two states

|2>' = cos@|2A) - sin@|2B)

and

|2>" = sin@|2A) + cos@|2B)

each with classical probability 1/2?

I assume that is what you mean?


Since these distributions are caused by separate photons (a single photon
interferes with itself) one must add probabilities--not amplitudes as you
have done. When you do this, the sin squared plus cos squared identity
wipes out all fringe variation and the two cases (0 and 1 input) give
exactly the same result at the output.

What did you expect? That FTL signalling would be easy?

Mother Nature isn't easy. She wants to be coaxed.

But thanks for trying.

warm regards
Nick Herbert
http://members.cruzio.com/~quanta
http://quantumtantra.com

==================================================

Nick Herbert finds Ray Jensen's error in his FTL Signal Thought Experiment


On Nov 27, 2005, at 3:13 PM, nick herbert wrote:
Hi Ray--

Your ingenious FTL scheme was forwarded to me by Jack Sarfatti.

Having constructed dozens of such schemes while writing my FTL book (none
of which ever worked) I am familiar with most of the pitfalls a would-be
EPR FTL signaller will encounter.
In your case the problem occurs with your Eq 4 where you give the
for detection of photons at the two interferometer arms. What
you want is the probabilities (amplitudes squared) for each of the two
types of pure-state photons that impinge on the interferometer.

Since these distributions are caused by separate photons (a single photon
interfers with itself) one must add probabilities--not amplitudes as you
have done. When you do this, the sin squared plus cos squared identity
wipes out all fringe variation and the two cases (0 and 1 input) give
exactly the same result at the output.

Ah yes! Now I recall. It's been 15 years since I thought about that. Nick, I think, is correct.


What did you expect? That FTL signalling would be easy?

Mother Nature isn't easy. She wants to be coaxed.

But thanks for trying.

warm regards
Nick Herbert
http://members.cruzio.com/~quanta
http://quantumtantra.com

==================================================





On Nov 27, 2005, at 1:52 PM, Jack Sarfatti wrote:

The key is his fig 2 & eq. 3. At the moment, without thinking about it very much, I cannot refute what he claims about eq. 3. Does anyone see the error there? If there is no way to tell which path photon 2 takes then there should be local interference according to Feynman. And it seems there is no way to tell what state photon 1 was in on the left. So why won't it work? Any opinions?


On Nov 27, 2005, at 1:30 PM, Jack Sarfatti wrote:

bcc

Probably this paper is wrong, but I have not yet had time to read it carefully. Any opinions? The author is aware of Stapp's et-al objection.

Begin forwarded message:

From: rjensen2@nd.edu
Date: November 27, 2005 1:14:36 PM PST

Subject: Re: Your STAIF paper

enclosed is a copy per your request. Thank you for your
interest. Sincerely,

Ray Jensen





<20050822FTLC3.pdf>

Faster than light?


Begin forwarded message:

From: Jack Sarfatti
Date: November 27, 2005 2:24:57 PM PST
To: Doc Savage
Subject: Re: Your STAIF paper FTL communication in orthodox QM?


On Nov 27, 2005, at 2:07 PM, Kim Burrafato wrote:
This very much reminds of similar schemes, a number of which employed MZ interferometers, that you came up with back in the late 70s and early 80s! I remember a number of designs very close to this one, with a MZI on one end and various detector arrangements on the other side. Weird!


Yes, but I never had it exactly right in terms of the apparatus, but I did have his eqs. 5 & 6! I was trying to "disentangle" his eq. 1 to get his eq 3. So I had the same formal idea for sure, but did not really know how to implement it in the total experimental design as he seems to have done. However, let's see what Stapp et-al have to say about this.

On Nov 27, 2005, at 1:52 PM, Jack Sarfatti wrote:

The key is his fig 2 & eq. 3. At the moment, without thinking about it very much, I cannot refute what he claims about eq. 3. Does anyone see the error there? If there is no way to tell which path photon 2 takes then there should be local interference according to Feynman. And it seems there is no way to tell what state photon 1 was in on the left. So why won't it work? Any opinions?


On Nov 27, 2005, at 1:30 PM, Jack Sarfatti wrote:

bcc

Probably this paper is wrong, but I have not yet had time to read it carefully. Any opinions? The author is aware of Stapp's et-al objection.

Begin forwarded message:

From: rjensen2@nd.edu
Date: November 27, 2005 1:14:36 PM PST

Subject: Re: Your STAIF paper

enclosed is a copy per your request. Thank you for your
interest. Sincerely,

Ray Jensen





<20050822FTLC3.pdf>

Feynman's Credo
On Nov 27, 2005, at 1:50 AM, Jack Sarfatti wrote:

“I can say I am a scientist. I find excitement in discovery. The excitement is not in the fact that you’ve created something, but that you’ve found something beautiful that’s always been there … I want to know what is true. That is why I look into things. To see and to find out what is going on.” Richard Feynman (“Feynman’s Rainbow” p. 158)

Well I read it cover-to-cover in one sitting. Notice how Feynman speaks like Hemingway writes.

Apollo & Dionysius (Nietzsche), Narcissus & Goldmund (Hesse) i.e. Greece and Babylon, Left & Right Brain (Sperry)

"Our culture ... is Greek, logic and proof, rules and order ...people who live their lives like Feynman are considered eccentric, for Feynman was a Babylonian ... physics and life were ruled by inspiration, and a disdain for rules and customs. He ignored the conventional methods of physics and invented his own, his sum over paths and his Feynman diagrams ..." p. 162

Feynman did not like string theory or the idea of extra space dimensions. Is the absence of tachyons worth the price of extra dimensions? Yes, if we can detect them. He died in 1989, not sure if he would like it today either. Gell-Mann protected John Schwarz at Cal Tech keeping string theory alive there.

String theory is an act of religious faith. "Theoretical physicists are still searching for the new physical principle string theory presumably represents." p.98

Gell-Mann's talk about data in 1967 in Erice put the bee in Veneziano's bonnet and he found a mysterious formula that explain Gell-Mann's patterns in the hadron collision data. Then in 1970 Nambu and Susskind explained Veneziano's magic formula in terms of tiny wiggling strings rather than point particles. Murray Gell-Mann really thinks that strings gets gravity because it has a massless spin 2 particle. I am not sure if that really is enough to explain gravity without a clear mathematical derivation of Einstein's classical field equations from string theory. Is there one? It is not clear that gravitons should even exist. Classical gravity waves should they be seen directly do not prove the reality of gravitons. If gravity is macro-quantum emergent there should not be any gravitons nor any quantum foam. When the macro-quantum coherence vanishes all that is left are the zero point fluctuations of virtual massless source fermion-anti-fermion pairs and virtual gauge bosons. No spin 2, no spin 3/2. No supersymmetry. Also no real dark matter particles as a matter of principle. OK let's see what experiments say.

On Nov 26, 2005, at 9:00 PM, Jack Sarfatti wrote:

bcc

re:

B = Lp'd'(Goldstone1xGoldstone2x...) = curved part of Einstein-Cartan tetrad 1-form

e.g. n independent Goldstone phases for

V(order parameter) = G(unordered vacuum)/H(ordered vacuum) ~ S1xS1 ... (n times)

nth Homotopy Group(S1xS1x...) ~ Z (or at least not simply the identity group)

"The Greek approach brings with it the full force of the logical machinery of mathematics ... such as Murray's [Gell-Mann] classification of particles. The Babylonian approach allows a certain freedom of imagination ... without worrying about rigor and justification ... In fact, physicists employing this kind of thinking sometimes violate the formal rules of mathematics, or invent strange new (and unproved) math of their own based on their understanding of experimental data ... Feynman considered himself a Babylonian ... Murray was more a Greek" Feynman's Rainbow p. 25
http://www.fotuva.org/feynman/feynman's_rainbow.html

On Nov 23, 2005, at 8:29 AM, Jack Sarfatti wrote:

bcc
OK thanks. :-)

Remember, I derive GR from the coherent Goldstone phases of the vacuum order parameter. The basic formula is extremely simple

B = Lpd(Goldstone Phase)

B is non-trivial curved part of the tetrad 1-form.

Lp^2 = hG/c^3

This is analogous to

v = (h/m)Grad(Phase of Pilot Wave)

in Bohm theory and in superfluid theory.

That is, replace the quantum of circulation h/m for the "liquid" by the quantum of "length" for the covariant "supersolid" "metric elastic" (Sakharov) vacuum.

Note that when there are multiple Goldstone phases in the Higgs-Goldstone field vacuum degenerate manifold

V = G(incoherent false vacuum without gravity)/H(coherent vacuum with gravity)

The basic zero form is the product of the independent Goldstone phases.

For example: if

V = G/H ~ S2

there are 2 independent Goldstone Phase Fields THETA & PHI for the geometrodynamic "monopole" stable topological defect from second homotopy group PI(S2) ~ Z

Coherent vacuum 0-form is (THETA)(PHI)

dL = B(S2) = Lpd[(THETA)(PHI)] = Lp[(dTHETA)(PHI) + (THETA)(dPHI)] length operator

dA = LpdB(S2) = Lp^2(dTheta)/\(dPHI) =/= 0 area operator

"Volume-without-volume" = World Hologram = Singular Gauss Theorem

Closed surface integral of dA surrounding a point defect in the vacuum order parameter

is quantized in units of Lp^2(integer) = Lp^2(Sphere Wrapping Number)

from non-trivial second homotopy group ~ Z of V(S2) = G/H

Therefore I TRIVIALLY DERIVE the Bekenstein "Black Hole Thermodynamics" conjecture.

Similarly, the singular form of Gauss's theorem is

Closed surface integral of dA surrounding a point defect in the vacuum order parameter

= Interior volume integral of 'd'dA

This is the Bohm-Aharonov effect for geometrodynamics. That is,

'd'V is the "Volume-without-volume" operator. That is, exactly like in the Bohm-Aharonov effect 'd'V is locally zero, but is globally non-zero.

We are literally Edwin Abbott's "FLATLANDERS" in this theory, i.e. Holographic projections of 2D data.

Forget Loop Quantum Gravity - we don't need it.

Forget "Quantum Foam" - we don't need it and experiment will show it's not there - if I am right here.

'd'V is the holographic projection "image" of the data on dA.

On the other hand, if we have THREE GOLDSTONE PHASES

V(S3) = G/H

Then dV =/= 0 even locally!

On Nov 23, 2005, at 1:42 AM, Carlos Castro wrote:

Dear Jack :

Look at the appendix in hep-th/0203221. Tomboulis
derives
a Gravitational Action from an underlying dynamics
involving fermions.
He does not start with GR but instead GR emerges as an
effective action

This is why I thought of your work.

Best wishes

Carlos

Feynman's Rainbow 1

On Nov 26, 2005, at 9:00 PM, Jack Sarfatti wrote:

bcc

re:

B = Lp'd'(Goldstone1xGoldstone2x...) = curved part of Einstein-Cartan tetrad 1-form

e.g. n independent Goldstone phases for

V(order parameter) = G(unordered vacuum)/H(ordered vacuum) ~ S1xS1 ... (n times)

nth Homotopy Group(S1xS1x...) ~ Z (or at least not simply the identity group)

"The Greek approach brings with it the full force of the logical machinery of mathematics ... such as Murray's [Gell-Mann] classification of particles. The Babylonian approach allows a certain freedom of imagination ... without worrying about rigor and justification ... In fact, physicists employing this kind of thinking sometimes violate the formal rules of mathematics, or invent strange new (and unproved) math of their own based on their understanding of experimental data ... Feynman considered himself a Babylonian ... Murray was more a Greek" Feynman's Rainbow p. 25
http://www.fotuva.org/feynman/feynman's_rainbow.html

On Nov 23, 2005, at 8:29 AM, Jack Sarfatti wrote:

bcc
OK thanks. :-)

Remember, I derive GR from the coherent Goldstone phases of the vacuum order parameter. The basic formula is extremely simple

B = Lpd(Goldstone Phase)

B is non-trivial curved part of the tetrad 1-form.

Lp^2 = hG/c^3

This is analogous to

v = (h/m)Grad(Phase of Pilot Wave)

in Bohm theory and in superfluid theory.

That is, replace the quantum of circulation h/m for the "liquid" by the quantum of "length" for the covariant "supersolid" "metric elastic" (Sakharov) vacuum.

Note that when there are multiple Goldstone phases in the Higgs-Goldstone field vacuum degenerate manifold

V = G(incoherent false vacuum without gravity)/H(coherent vacuum with gravity)

The basic zero form is the product of the independent Goldstone phases.

For example: if

V = G/H ~ S2

there are 2 independent Goldstone Phase Fields THETA & PHI for the geometrodynamic "monopole" stable topological defect from second homotopy group PI(S2) ~ Z

Coherent vacuum 0-form is (THETA)(PHI)

dL = B(S2) = Lpd[(THETA)(PHI)] = Lp[(dTHETA)(PHI) + (THETA)(dPHI)] length operator

dA = LpdB(S2) = Lp^2(dTheta)/\(dPHI) =/= 0 area operator

"Volume-without-volume" = World Hologram = Singular Gauss Theorem

Closed surface integral of dA surrounding a point defect in the vacuum order parameter

is quantized in units of Lp^2(integer) = Lp^2(Sphere Wrapping Number)

from non-trivial second homotopy group ~ Z of V(S2) = G/H

Therefore I TRIVIALLY DERIVE the Bekenstein "Black Hole Thermodynamics" conjecture.

Similarly, the singular form of Gauss's theorem is

Closed surface integral of dA surrounding a point defect in the vacuum order parameter

= Interior volume integral of 'd'dA

This is the Bohm-Aharonov effect for geometrodynamics. That is,

'd'V is the "Volume-without-volume" operator. That is, exactly like in the Bohm-Aharonov effect 'd'V is locally zero, but is globally non-zero.

We are literally Edwin Abbott's "FLATLANDERS" in this theory, i.e. Holographic projections of 2D data.

Forget Loop Quantum Gravity - we don't need it.

Forget "Quantum Foam" - we don't need it and experiment will show it's not there - if I am right here.

'd'V is the holographic projection "image" of the data on dA.

On the other hand, if we have THREE GOLDSTONE PHASES

V(S3) = G/H

Then dV =/= 0 even locally!

On Nov 23, 2005, at 1:42 AM, Carlos Castro wrote:

Dear Jack :

Look at the appendix in hep-th/0203221. Tomboulis
derives
a Gravitational Action from an underlying dynamics
involving fermions.
He does not start with GR but instead GR emerges as an
effective action

This is why I thought of your work.

Best wishes

Carlos



--- Jack Sarfatti wrote:

Thanks.

But what I am doing is different. They assume GR. I
am DERIVING GR
from the Higgs-Goldstone vacuum field. No one has
ever even thought
of that before I mean deriving the tetrad field from
the Goldstone
phases directly.

On Nov 22, 2005, at 1:30 AM, Carlos Castro wrote:

Dear Jack and Tony :

For your interest in Cosmological models building,
....I am attaching a paper based on I.Segal and my
work, where the conformal group, Anti de Sitter,
etc
is very important. The relevant part concerning
my
work is how I derived ( from first princples )
that
the vacuum energy density is the geometric mean
between the Planck and Hubble scale ( ref-[10 ]of
attached paper ).

You may want also to look at Tomboulis paper :
Photons and Gravitons as Goldstone Bosons and the
Cosmological Constant.
hep-th/0203221.

Best wishes

Carlos

Reply to Gennady Shipov on Gravity and Torsion as a Local Gauge Theory


On Nov 26, 2005, at 1:58 PM, Jack Sarfatti wrote:




http://amazon.com


Oh, it looks like Eric is not talking about dark energy per se, but about the Casimir force. The Casimir force is really only a weak QED boundary effect of Van der Waals electrostatic according to Ian Peterson of Coventry University, but the dark energy is a strong direct gravity effect of the zero point energy.
http://zpenergy.com/modules.php?name=News&file=article&sid=974

Bizarre - Ian Peterson recently died. I was with him in London a year ago and he was not old and seemed fit as a fiddle.

PETERSON, Professor Ian Robert. 1945 2005. Loving husband,father, brother and friend. University Medallist and Ph.D inElectrical Engineering (University of Sydney), Habilitation inMolecular Electronics (University of Mainz). Distinguishedscientist, polymath, stoic; pioneer of nanotechnology, monolayermembranes and molecular electronics. Ian died in the U.K. onSeptember 9, 2005 in his laboratory at the University of Coventry.His funeral was held in Warwick on September 26, 2005. He is mourned by his wife Anne, children Kate, Marianne and Richard,sisters Roslyn and Judy, brother Bruce, extended family, friends and colleagues worldwide. IAN'S family, friends and colleagues are invited to a gathering to commemorate his life and achievements, at 11 a.m. on Saturday (November 5, 2005) at the Old DarlingtonSchool, Maze Crescent, Darlington Campus, University of Sydney;enter from Butlin Avenue. For further information please contact:petersonmemorial@yahoo.com.au
The Sydney Morning Herald Saturday, 22 October 2005


http://www.americanantigravity.com/documents/STAIF/STAIF06_SessionsF_15Nov05.pdf

note Davis is presenting a review in F04 Session 3 as well as "Experimental Concepts for Generating" in F06. . .

This is what originally upset me that you aren't presenting at STAIF.



Eric Davis posts several times in accord with your theories. He's delivering at STAIF on generating dark energy in the lab.

He is?

You posted about dark energy detector on Oct 25.

So, is Eric Davis presenting YOUR stuff at STAIF?

I don't think so.


On Nov 26, 2005, at 10:57 AM, Jack Sarfatti wrote:

Note, in addition if the modified uncertainty principle

&p ~ h/&r + (h/Lp)^2(&r/h)

Lp^2 = hG/c^3

is correct as several authors on electronic archive have published, then the Casimir force


|<-L->|Area of plates = A


will be modified to

F(Casimir) ~ (hc/L^4)A ---> ~ c(h/L + (h/Lp)^2(L/h))A/L^3

i.e. a new quantum gravity term in the QED Casimir force

~ (c^4/G)(A/L^2) ~ (String Tension)(A/L^2)

Now this is much too large if Newton's constant works at the separations of the plates.

Therefore, either the modified uncertainty principle is falsified, or the effective string tension is much softer at the current levels of experiments from large extra space dimensions.


On Nov 26, 2005, at 10:36 AM, Jack Sarfatti wrote:

re: Advanced Space Weapons Technology
http://stardrive.org



http://amazon.com


Begin forwarded message:

From: Jack Sarfatti
Date: November 26, 2005 10:23:50 AM PST
To: ...
Subject: Re: dark energy detector


On Nov 26, 2005, at 10:11 AM, ... wrote:

I hope you can catch me up on something I obviously don't understand. The complete lack of enthusiasm on the Stardrive board over what seemed to be an empirical verification of your theory (w=-1) makes me wonder about a few things.

Most people on it are not educated in physics.


You're saying for ages that w=-1. Hal Puthoff et. al. are saying that it's -1/3.

No, Hal says it's +1/3 in some sense for the QED Casimir force boundary effect. He cites some old paper by DeWitt.


Eric Davis works with Hal. You posted about a month ago that it appeared that Hal was ready to throw in the towel on his theory and left a flurry of posts seemingly meant to bury the dead. Looks like ya'll knew about the supernovae data but didn't post about it.

This data has been around for awhile. It's in my books from 2002. This latest is simply more confirmation.

Eric Davis posts several times in accord with your theories. He's delivering at STAIF on generating dark energy in the lab.

He is?

You posted about dark energy detector on Oct 25.

So, is Eric Davis presenting YOUR stuff at STAIF?

Maybe, but he is obviously not giving me the credit!

What was it a month ago that caused you to pen that it seemed Hal was ready to bury the dead dog?


Don't expect me to remember that. Too much volume of e-mail in and out.

Extra Space Dimensions & Casimir Force Data

Note, in addition if the modified uncertainty principle

&p ~ h/&r + (h/Lp)^2(&r/h)

Lp^2 = hG/c^3

is correct as several authors on electronic archive have published, then the Casimir force


|<-L->|Area of plates = A


will be modified to

F(Casimir) ~ (hc/L^4)A ---> ~ c(h/L + (h/Lp)^2(L/h))A/L^3

i.e. a new quantum gravity term in the QED Casimir force

~ (c^4/G)(A/L^2) ~ (String Tension)(A/L^2)

Now this is much too large if Newton's constant works at the separations of the plates.

Therefore, either the modified uncertainty principle is falsified, or the effective string tension is much softer at the current levels of experiments from large extra space dimensions.


On Nov 26, 2005, at 10:36 AM, Jack Sarfatti wrote:

re: Advanced Space Weapons Technology
http://stardrive.org



http://amazon.com

Begin forwarded message:

From: Jack Sarfatti
Date: November 26, 2005 10:23:50 AM PST
To: ...
Subject: Re: dark energy detector


On Nov 26, 2005, at 10:11 AM, ... wrote:

I hope you can catch me up on something I obviously don't understand. The complete lack of enthusiasm on the Stardrive board over what seemed to be an empirical verification of your theory (w=-1) makes me wonder about a few things.

Most people on it are not educated in physics.


You're saying for ages that w=-1. Hal Puthoff et. al. are saying that it's -1/3.

No, Hal says it's +1/3 in some sense for the QED Casimir force boundary effect. He cites some old paper by DeWitt.


Eric Davis works with Hal. You posted about a month ago that it appeared that Hal was ready to throw in the towel on his theory and left a flurry of posts seemingly meant to bury the dead. Looks like ya'll knew about the supernovae data but didn't post about it.

This data has been around for awhile. It's in my books from 2002. This latest is simply more confirmation.

Eric Davis posts several times in accord with your theories. He's delivering at STAIF on generating dark energy in the lab.

He is?

You posted about dark energy detector on Oct 25.

So, is Eric Davis presenting YOUR stuff at STAIF?

Maybe, but he is obviously not giving me the credit!

What was it a month ago that caused you to pen that it seemed Hal was ready to bury the dead dog?


Don't expect me to remember that. Too much volume of e-mail in and out.

Extra Space Dimensions & Casimir Force Data

Note, in addition if the modified uncertainty principle

&p ~ h/&r + (h/Lp)^2(&r/h)

Lp^2 = hG/c^3

is correct as several authors on electronic archive have published, then the Casimir force


|<-L->|Area of plates = A


will be modified to

F(Casimir) ~ (hc/L^4)A ---> ~ c(h/L + (h/Lp)^2(L/h))A/L^3

i.e. a new quantum gravity term in the QED Casimir force

~ (c^4/G)(A/L^2) ~ (String Tension)(A/L^2)

Now this is much too large if Newton's constant works at the separations of the plates.

Therefore, either the modified uncertainty principle is falsified, or the effective string tension is much softer at the current levels of experiments from large extra space dimensions.


On Nov 26, 2005, at 10:36 AM, Jack Sarfatti wrote:

re: Advanced Space Weapons Technology
http://stardrive.org



http://amazon.com

Begin forwarded message:

From: Jack Sarfatti
Date: November 26, 2005 10:23:50 AM PST
To: ...
Subject: Re: dark energy detector


On Nov 26, 2005, at 10:11 AM, ... wrote:

I hope you can catch me up on something I obviously don't understand. The complete lack of enthusiasm on the Stardrive board over what seemed to be an empirical verification of your theory (w=-1) makes me wonder about a few things.

Most people on it are not educated in physics.


You're saying for ages that w=-1. Hal Puthoff et. al. are saying that it's -1/3.

No, Hal says it's +1/3 in some sense for the QED Casimir force boundary effect. He cites some old paper by DeWitt.


Eric Davis works with Hal. You posted about a month ago that it appeared that Hal was ready to throw in the towel on his theory and left a flurry of posts seemingly meant to bury the dead. Looks like ya'll knew about the supernovae data but didn't post about it.

This data has been around for awhile. It's in my books from 2002. This latest is simply more confirmation.

Eric Davis posts several times in accord with your theories. He's delivering at STAIF on generating dark energy in the lab.

He is?

You posted about dark energy detector on Oct 25.

So, is Eric Davis presenting YOUR stuff at STAIF?

Maybe, but he is obviously not giving me the credit!

What was it a month ago that caused you to pen that it seemed Hal was ready to bury the dead dog?


Don't expect me to remember that. Too much volume of e-mail in and out.

On Nov 23, 2005, at 8:29 AM, Jack Sarfatti wrote:

bcc
OK thanks. :-)

Remember, I derive GR from the coherent Goldstone phases of the vacuum order parameter. The basic formula is extremely simple

B = Lpd(Goldstone Phase)

B is non-trivial curved part of the tetrad 1-form.

Lp^2 = hG/c^3

This is analogous to

v = (h/m)Grad(Phase of Pilot Wave)

in Bohm theory and in superfluid theory.

That is, replace the quantum of circulation h/m for the "liquid" by the quantum of "length" for the covariant "supersolid" "metric elastic" (Sakharov) vacuum.

Note that when there are multiple Goldstone phases in the Higgs-Goldstone field vacuum degenerate manifold

V = G(incoherent false vacuum without gravity)/H(coherent vacuum with gravity)

The basic zero form is the product of the independent Goldstone phases.

For example: if

V = G/H ~ S2

there are 2 independent Goldstone Phase Fields THETA & PHI for the geometrodynamic "monopole" stable topological defect from second homotopy group PI(S2) ~ Z

Coherent vacuum 0-form is (THETA)(PHI)

dL = B(S2) = Lpd[(THETA)(PHI)] = Lp[(dTHETA)(PHI) + (THETA)(dPHI)] length operator

dA = LpdB(S2) = Lp^2(dTheta)/\(dPHI) =/= 0 area operator

"Volume-without-volume" = World Hologram = Singular Gauss Theorem

Closed surface integral of dA surrounding a point defect in the vacuum order parameter

is quantized in units of Lp^2(integer) = Lp^2(Sphere Wrapping Number)

from non-trivial second homotopy group ~ Z of V(S2) = G/H

Therefore I TRIVIALLY DERIVE the Bekenstein "Black Hole Thermodynamics" conjecture.

Similarly, the singular form of Gauss's theorem is

Closed surface integral of dA surrounding a point defect in the vacuum order parameter

= Interior volume integral of 'd'dA

This is the Bohm-Aharonov effect for geometrodynamics. That is,

'd'V is the "Volume-without-volume" operator. That is, exactly like in the Bohm-Aharonov effect 'd'V is locally zero, but is globally non-zero.

We are literally Edwin Abbott's "FLATLANDERS" in this theory, i.e. Holographic projections of 2D data.

Forget Loop Quantum Gravity - we don't need it.

Forget "Quantum Foam" - we don't need it and experiment will show it's not there - if I am right here.

'd'V is the holographic projection "image" of the data on dA.

On the other hand, if we have THREE GOLDSTONE PHASES

V(S3) = G/H

Then dV =/= 0 even locally!

On Nov 23, 2005, at 1:42 AM, Carlos Castro wrote:

Dear Jack :

Look at the appendix in hep-th/0203221. Tomboulis
derives
a Gravitational Action from an underlying dynamics
involving fermions.
He does not start with GR but instead GR emerges as an
effective action

This is why I thought of your work.

Best wishes

Carlos



--- Jack Sarfatti wrote:

Thanks.

But what I am doing is different. They assume GR. I
am DERIVING GR
from the Higgs-Goldstone vacuum field. No one has
ever even thought
of that before I mean deriving the tetrad field from
the Goldstone
phases directly.

On Nov 22, 2005, at 1:30 AM, Carlos Castro wrote:

Dear Jack and Tony :

For your interest in Cosmological models building,
....I am attaching a paper based on I.Segal and my
work, where the conformal group, Anti de Sitter,
etc
is very important. The relevant part concerning
my
work is how I derived ( from first princples )
that
the vacuum energy density is the geometric mean
between the Planck and Hubble scale ( ref-[10 ]of
attached paper ).

You may want also to look at Tomboulis paper :
Photons and Gravitons as Goldstone Bosons and the
Cosmological Constant.
hep-th/0203221.

Best wishes

Carlos

Nonlocality of Gravity Energy


On Nov 22, 2005, at 10:41 AM, Alex Poltorak wrote:

"Dear Prof. Kiehn,

Thank you for taking the time to study my paper “Gravity as Nonmetricity.” Without addressing all of the points in your letter, let me address the one point you chose to summarize in your email broadcasted on this list.

As I understand, you take an issue with my statement in that paper that “…the metric g is the potential and the connection is the strength of the gravitational field.” "

[Sarfatti wrote: Yes, this is quite standard text book seen in the Schwarzschild solution for r > 2GM/c^2 where

g00 = (1 + 2V(Newton)/c^2) = - 1/grr

V(Newton) = - GM/r

g = -GradV(Newton) = - GM/r^2 ~ connection]


"Your source for this objection is a quote from Wolfram encyclopedia, which identifies gravitational force with curvature.

Although, Wolfram encyclopedia is hardly an authoritative sources for this debate, your point is well taken as it has been debated for a long time. Indeed, the tidal gravitational forces, which cause geodesic deviation, are due to the Riemannian curvature. Nevertheless, the question of what to consider as potential and what to consider as the strength of the field is a murky and apparently does not have a unique answer (see a discussion of this subject in MTW.)"

[Sarfatti wrote: Indeed, this is made even more apparent when one looks at gravity as a local gauge theory for space-time symmetries in contrast to internal symmetry gauge force theories without the equivalence principle.

In the latter case e.g. Maxwell U(1) EM theory we have the very simple template

F = dA 2-form

dF = 0 3-form

d*F = *j(source) 3-form

d*j = 0 4-form

Note that the A 1-form potential is also the connection in the exterior gauge covariant derivative

D = d + A/\ on source fields for *j(source)

In contrast in 1915 GR, at first it looks like the T4 ---> Diff(4) curvature 2-form R is like the EM 1-form F, i.e. suppressing the Lorentzian indices I,J for brevity, since we have seen them now many times we all understand that e.g.

W/\W means W^IJ/\W^JK =/= 0

R = DW = dW + W/\W

with

DR = 0

So that W looks like U(1) A

and R looks like U(1) F

However, in U(1) EM the source equation is

D*F = *j 3-form

So if the analogy was true we would have

D*R = *J 3-form

but this is WRONG as pointed out by Gennady Shipov.

Define the Einstein curvature 4-form as

*G = D*W

Then the source 4-form equation is

*G = *J

D*J = 0 (5-form in 4-space)

Because of the EQUIVALENCE PRINCIPLE (EEP) absent completely in U(N) internal gauge theories

g(curved) = e(Flat)e

e = 1 + B tetrad field in "subspace"

There is no "subspace" in internal symmetry gauge theory where it's all on the "surface".

in 1915 GR there is zero torsion

De = 0

therefore

dB + W/\(1 + B) = 0

That I solve as

W = -*[dB/\(1 - B)]

Note that W depends on dB exactly like F depends on dA, but we have additional nonlinearity in (1 - B) factor from EEP.

"Although, I cannot readily cite you chapter and verse, as I recall, the upshot of the MTW’s discussion is that it is unclear what is the potential (metric or connection) and what is the field strength (connection of curvature) as all three geometric objects, metric g, connection Г and curvature R describe gravitational field, as far as geometrodynamics is concerned."

Sarfatti wrote: I think I have clarified this somewhat above using the Cartan "Feynman diagram" heuristic.

EEP is subtle, but not malicious.

3-manifold integral of *W ~ 4-manifold integral of d*W = 4-manifold integral of( D*W - W/\*W) = -4-manifold integralW/\*W

This also sheds light on the nonlocality of gravity energy as a geometrodynamic Bohm-Aharonov effect. In vacuum, *G = D*W = 0. But DeRham global integral of gravity flux *W (Hodge star dual of the zero-torsion SPIN-CONNECTION) over a non-bounding 3-cycle in space-time need not vanish even though the integrand *G 4-form is locally strictly zero if there is an appropriate topological defect in the vacuum order parameter generating emergent gravity in the first place! If we take a spacelike slice of this factoring out the "time", then it seems this explains the non-zero flux of gravity waves through asymptotic flat 2D cycles that do not bound.

Basically, the nonlocality of the gravity energy is from the nonlinear term W/\*W that comes from the EEP.

Therefore, any attempt to localize gravity energy violates EEP exactly as MTW says it does! This seems very clear heurstically now using the Cartan "Feynman diagrams" as it were.]


"Needless to say, various approaches to General Relativity highlight different roles of these geometric objects. For example, in a context of classical field theory, the role of field potential is played by the metric and the role of field strength is played by the connection, as seen from the Lagrangian. On the other hand, a gauge theory approach always uses connection as a potential arising in Lie derivative leaving the role of field strength to be played by the curvature. I agree, this approach is more in line with Maxwell electrodynamics, which is a gauge theory, but ultimately, this is a matter of semantics. Another example that highlights how inconsequential is the choice of field potential would be the tetrad formulation of GR wherein the tetrads play the role of potentials of gravitational field. However, this non-traditional choice of field potential (instead of the traditional metric) does not in any way undermine the equivalence of the tetrad formulation to the Einstein traditional metric formulation of GR, as emphasized by MTW.

I am ambivalent as to the choice of words. My point was merely to emphasize that both potential and field strength must be covariant geometric objects (tensors) in order to have a fully covariant theory of gravitation. Obviously, metric and curvature are true tensors. The problem is with the connection, which is not. Therefore, whether you consider connection as the potential or as the field strength, it is a poor choice, because connection is not covariant under general coordinate transformation. A much better choice would be the tensor of affine deformation (the difference between two affine connections, which is always a tensor). The tensor of nonmetricity is a special case of a tensor of affine deformation and is a true tensor. Whether you are going to call it a potential or a field strength (or, in your terminology, field intensity), I propose to describe gravity by a triplet of geometrical objects , where g and R are good old metric and curvature, but S is the tensor of nonmetricity, which replaces Levi-Civita connection of General Relativity, Г. Similarly, in Teleparallel theories, a torsion (which is also a true tensor and another example of the tensor of affine deformation) is used in place of Levi-Civita connection of GR likewise leading to a fully covariant theory.

As we say in the US, call me what you want, just don’t call me late to lunch J. In this vein, call it what you will, just don’t use non-covariant objects to describe the gravitational field. This is the moral of my paper.

I will be studying your other remarks expressed in your letter to me and your paper on the strong equivalence principle as soon as I get some free time.

Best regards,
Alex Poltorak"

From: RKiehn2352@aol.com [mailto:RKiehn2352@aol.com]
Sent: Sunday, November 20, 2005 2:27 PM
To: Alex Poltorak; shipov@aha.ru; sarfatti@pacbell.net

Subject: Re: Physical torsion

Letter to apoltorak (attachment in pdf format)

**
Bottom Line
Non-metricity seems to imply that the potentials are scalar functions,
and forces are related to to the Connections.
I do not buy it.
**
This is counter to the view that the
connection matrix of 1-forms are the potentials
and the curvature matrix of 2-forms are the forces.
(A fact well subscribed to)
*
First draft of a strong equivalence principle (attachment in pdf format)

regards
RMK

Important discovery on macro-quantum geometrodynamics with multiple Goldstone phases.

It's well known that for constant magnitude of ODLRO VEV in V = G(disordered)/H(ordered) coset space:

Zero homotopy group non-trivial has 2D domain wall defects surrounding space of defect is S0 i.e. points -1, +1.
First homotopy group non-trivial has 1D string (vortices) with S1 loop surrounding space and G/H = S1 also.
Second homotopy group non-trivial has 0D point defect "monopole" (not necessarily magnetic, the geometrodynamic neutral monopole gives S/k = AREA/4Lp^2 + World Hologram + maybe NASA Pioneer Anomaly as dark energy hedgehog with wrapping number -1 defect in center of Sun?) with surrounding space = S2 and also G/H = S2.
Third homotopy group non-trivial has "texture" defect with G/H = S3.

Internal symmetries have no non-trivial tetrad valued in the Lie algebra of the locally gauged symmetry group.
Space-time symmetries DO and that is the DIFFERENCE from the EQUIVALENCE PRINCIPLE AKA EEP.

2 independent ideas here

1. Local gauging

2. Spontaneous vacuum symmetry breaking.

In my theory of emergent gravity i.e. my version of Andrei Sakharov's "metric elasticity"

I. I SPONTANEOUS BREAK INTERNAL SYMMETRY at Planck scale -> GUT vacuum phase transition

II. I locally gauge at least 10-parameter Poincare group - ultimately 16 parameter GL(4,R).

Note HOW TO GET GENNADY SHIPOV's 10 MANIFOLD (same as string theory) is to put the entire Lie algebra of the Poincare group into the TETRAD FIELD directly. This makes it a Kaluza-Klein theory. However, I DO NOT DO THIS - but I can later. I keep the tetrad field 4D from T4 and that's why I need the indirect quantities such as

B^I a 1-index 1-form curved tetrad from locally gauging T4

e^I = 1^I + B^I

W^IJ a 2-index 1-form CURVATURE spin-CONNECTION in

D = d + W^IJ/
And also

S^I a 1-index 1-form in the 4D tetrad from locally gauging O(1,3)

e'^I = e^I + S^I

Z^IJ a 2-index 1-form TORSION CONNECTION in

D' = D + Z^IJ/
Where we have the 2-forms

T^I = De = 0

R^IJ = DR^IJ

T'I = D'e'

R'IJ = D'(W^IJ + Z^IJ)

With Bianchi identities (analog of dF = 0 of Maxwell internal U(1) EM field in flat space-time without gravity & torsion)

DR^IJ = 0

D'R'^IJ = 0

D'T'^I = 0

Source equations

D'*W^IK = *J'(T4)^IK

D'*Z^IK = *J(O(1,3)^IK

D'*T^I = *j(O(1,3)^I

Local covariant current density conservation

D'*J'(T4)^IK = 0

D'*J(O(1,3))^IK = 0

D'*j(O(1,3)^I = 0

OK, vortices have degenerate ODLRO macro-quantum manifold V = G/H of local order parameters with topology of the circle. That is we hold the Higgs amplitude fixed and we only have ONE independent Goldstone phase factor e^iTheta where the order parameter has 2 real scalar components.

Non-integrable Goldstone phase factors e^iQ^a(Theta)a, for Lie algebra [Q^a,Q^b] = f^a^bcQ^c give both the global and local properties of Yang-Mills internal gauge theories as well as gravity and torsion & non-metricity, dilaton gauge theories both classical and quantum via Feynman path integrals.

Point defects has V = S2 with 2 independent Goldstone phase factors e^iTheta and e^iPhi, i.e. polar and azimuthal angles in V = G/H space where the order parameter has 3 real scalar components.

The geometrodynamical fields.

I will only do T4 for simplicity.

CASE 1 V = G/H = S1 with ONE GOLDSTONE PHASE Theta that sweeps out a unit circle.

B^I(S1) = (LpP^I(Theta)/ih

Tetrad

e^I = 1^I + B^I

Einstein invariant is

ds^2 = B^I(Minkowski)IJB^J

QED!

Here we expect STRING DEFECTS!

In simpler completely invariant notation

B(S1) = Lpd(Theta)


Case 2 V = G/H = S2 with TWO INDEPENDENT GOLDSTONE PHASES Theta & Phi that sweep out a unit 2D spherical surface that is G/H topology.

So what do we do?

Simple! I was a DUMMY not to see this weeks ago! But I woke up this morning hundreds of miles north of SF on the beach with the idea crystal clear!

Define the 0-form (Theta)(Phi) these are local functions of Einstein's local coincidences "P" of course.

Our new geometrodynamic 1-form is obviously via product rule of Newton's "fluxions", i.e. "ghosts of departed quantities" (Bishop Berkeley)

B^I(S2) = (LpP^I(ThetaPhi)/ih

i.e. 2 -terms

B^I(S2) = (Lp(P^I(Theta)/ih)Phi + Theta(LpP^I(Phi)/ih = LENGTH OPERATOR

i.e. in completely invariant notation

B(S2) = Lp{d(Theta)Phi + Thetad(Phi)}

using d^2 = 0

We have the 2-form AREA OPERATOR (forget Loop Quantum Gravity & Spin Foams!)

Area = Lp^2dTheta/\dPhi

We also have

Closed surface integral of Area operator = Volume integral of d(Area) = Wrapping Number

when the closed surface surrounds the point defect since second homotopy group for S2 is Z

This is obviously essentially both Hawking-Bekenstein BITS and 't Hooft-Susskind hologram idea that is simply

VOLUME WITHOUT VOLUME as an example of Bohm-Aharonov's "Flux without flux" in which the gauge potentials have direct non-classical physical effects on phenomena.

We can continue this to case

G/H = S3 (textures) where now we have 3 independent Goldstone phases Theta, Phi & Chi with a VOLUME OPERATOR.

If we continue into higher dimensional hyperspace, I suppose V = G/H are what? Calabi-Yau spaces? I will check.

Here we need to extend the EEP tetrad idea missing in conventional internal symmetry Yang-Mills gauge force theories.

Basically we have S1xS1x... for possible V = G/H broken vacuum symmetries.

Geometrodynamic Monopoles & Hawking-Bekenstein BITS

On the other hand, if the initial Planck scale vacuum phase transition has a degenerate vacuum manifold

V(Planck) = G(False Vacuum)/H(GUT) ~ S2

then the GEOMETRODYNAMIC FIELD does not have 1-D string defects, but, rather has 2D point monopole defects where the quantized 1D winding numbers are replaced by 2D wrapping numbers.

That is, we have 2 alternative models for the initial emergence of Einstein's gravity at 10^-43 sec.

I. V(Planck) ~ S1 circle

Here there is only ONE Goldstone phase THETA with 1D string defects where the Higgs magnitude of the vacuum order parameter vanishes along the string and the Goldstone phase THETA is undefined. This is the usual easy to visualize Mexican Hat Potential for renormalizable quantum field theories that spontaneously break internal symmetries.



Here the local virtual vacuum order parameter is a single complex scalar field like in superfluid helium and the BCS superconductor for real bosons on-mass-shell.

Stable quantized circulation comes from the first homotopy group being non-trivial, i.e.

PI1(S1) = Z (integers)

B(curved) = Lp'd'THETA 1-form curved tetrad of Einstein's GR

The geometrodynamic vorticity flux dB(curved) is quantized through areas including the string (vortex) defect. This is an example of Bohm-Aharonov "Flux without flux" because dB = 0 on the loop L in physical space that surrounds the singularity with the Higgs magnitude vanishes and the Goldstone phase is undefined. Going around the loop one in physical space means going around the S1 circle that is the vacuum manifold N times. N is the number of trapped geometrodynamics flux quanta. This is not to be confounded with magnetic flux.


II. V(Planck) ~ S2 spherical surface

Here we obviously have TWO Goldstone phases THETA and PHI with point defects.

How do we construct B(curved)?

Here the local vacuum order parameter is 3 real scalar fields like the 3x3 adjoint irreducible representation of the SU(2) group corresponding to "spin 1" rather than "spin 1/2".

However, the real non-vanishing vacuum order parameter can be chosen to lie completely along the arbitrarily chosen polar axis of S2 = G(False Vacuum)/H(GUT) so that the complementary Goldstone phase is the azimuthal angle PHI in the equatorial plane in this fiber space of degenerate order parameters beyond space-time.

i.e.

B(curved) = Lp'd'PHI 1-form

Here its the second homotopy group that is non-trivial

PI2(S2) = Z

The curvature 2-form with physical dimension 1/(area) is

R = DW

where W is the spin connection 1-form

W = -*[dB/\(1 - B)]

Therefore, the dimensionless DeRham integral of R over a surrounding S2 surface in physical space enclosing the point defect is quantized even though the Bianchi identity DR = 0 everywhere other than the point defect singularity.

That is closed surface integral of the curvature 2-form R ~ Z

The wrapping number around V = G(False Vacuum)/H(GUT) = S2 is the number of Bekenstein bits equal to the number of curvature quanta through the closed surface.

This argument implies that there are no Bekenstein bits in globally flat spacetime.

Note that the curvature 2-form maps to the 4th rank Riemann-Christoffel curvature tensor i.e.

R^ab = R^abuvdx^udx^v

R^wluv = R^abuvea^we^bl

That is, the Bekenstein BITs require B(curved) =/= 0.

Therefore, quantization of "area" has the same status as quantization of circulation in a superfluid. Both point to an underlying ground state order parameter. Geometrodynamics is an emergent local gauge theory of T4 ---> Diff(4) from the spontaneous breaking of an internal symmetry at the Planck era.

We only need ONE point defect geometrodynamic monopole in the universe to produce the Bekenstein BIT exactly like we only need 1 magnetic monopole in the universe at the end of the Dirac string to produce quantization of electric charge.

On Nov 13, 2005, at 8:18 PM, Jack Sarfatti wrote:

Note two meanings of "inertia".

Gravity as a "force" is locally indistinguishable from an inertial force in a non-inertial local frame that is either rotating or on a time-like nongeodesic path or both with respect to the Levi-Civita connection.

"Inertia" as the rest mass of quarks, leptons and W-mesons.

Our universe is thought to have formed in a sequence of spontaneous symmetry breakings of the physical vacuum. Assuming the old Heisenberg uncertainty principle

Planck scale breaking ~ 10^19 Gev ~ 10^-33 cm

GUT scale breaking ~ 10^15 Gev ~ 10^-29 cm

Electroweak breaking ~ 250 Gev ~ 10^-16 cm

In more detail

Time (s) T (Kelvin) Reference Event
CBR
THE QUANTUM GRAVITY ERA

1x10^-43 1x10^32 KT 72 Quantum limit of classical general
relativity

[My comment 1:

I postulate, as there is no fundamental theory of this as yet, the simplest possibility

G(Planck)---> H(Planck)

V (Planck)= G(Planck)/H(Planck) ~ S1(Planck)

from first homotopy group PI1(S1) = Z (integer winding numbers)

i.e. line defects i.e. 1-dim strings

Vacuum coherent order parameter is a single complex scalar field

PSI(Planck) = |PSI|e^iargPSI

Planck-scale Higgs amplitude is |PSI|, Planck-scale Goldstone phase is argPSI.

argPSI is a 0-form

Curved space-time tetrad 1-form is

B = Lp'd'argPSI

ds^2 = (1^a + B^a)(Minkowski)ab(1^b + B^b) is EEP

B is from local gauging of SPACE-TIME SYMMETRY T4 to Diff(4) AND ALSO from spontaneous breaking of INTERNAL SYMMETRY G(Planck) -> H(Planck) to S1 Post-Planck Vacuum Manifold

PSI is the INFLATION FIELD

Diff(4) covariant exterior derivative is

D = d + W/
W^ac = T4 spin-connection

The vanishing torsion 2-form in 1915 GR model is

T^a = De^a = de^a + W^ac/\(1 + B)^c = dB^a + W^ac/\(1 + B)^c = 0

Invert this equation to get the 1-form spin connection

W^a^c = -*[dB^a/\(1 - B)^c]

* is Hodge dual based on Minkowski metric in tangent fiber space.

The geodesic deviation curvature 2-form is

R^ab = DW^ab = dW^ab + W^acW^cb

The Bianchi identity is the 3-form equation (analog to dF(EM) = 0 3-form)

DR^ab = 0

The Einstein-Hilbert vacuum Lagrangian density is the 0-form

*[R^ab/\e^c/\e^d]

The Einstein curvature 4-form is

G^ab = D*W^ab

The Einstein 4-form source equation (analog to d*F(EM) = *j(electric) 3-form) is

G^ab = *J(T4)^ab

Local conservation of stress-energy source current densities is the vanishing 5-form

DG^ab = D*J(T4)^ab = 0 5-form in 4-space is identically zero.

G^ab = *J(T4)^ab

is 4-form because of equivalence principle where even zero point energy with w = -1 gravitates absolutely and not relatively.]

THE INFLATION AND SYMMETRY BREAKING ERA

1x10^-38 1x10^29 KT 72 Limit of perturbative interaction

thermalization of universe

1x10^-35 1x10^28 KT 72 Grand unification spontaneous

symmetry breaking



[My Comment 2

OK, here H(Planck) ---> H(GUT) = U(1)hyperchargeSU(2)weak

SU(3)quark coupling constant splits off from U(1)hyperchargeSU(2)weak with same coupling constant

We do not know the topology of the new vacuum manifold

H(Planck)/U(1)hyperchargeSU(2)weak = V(GUT) = ?

Note the sequence:

G(Planck) ---> H(Planck) ---> H(GUT) = U(1)hyperchargeSU(2)weak

G/(Planck)/H(Planck) ---> H(Planck)/H(GUT)

i.e.

V(Planck) ---> V(GUT)

But what does this mean in terms of the vacuum order parameter?

V(Planck) does not disappear. It is robust from Goldstone phase rigidity and it is the Hercules supporting The World Geometrodynamic Field



V(Planck)

Indeed the total vacuum manifold has grown more complex into the TENSOR PRODUCT

V(Planck)xV(GUT)



1x10^-34 1x10^27 KT 274 Approximate start of inflation

1x10^-32 1x10^27 KT 274 Approximate start of reheating and

end of inflation

1x10^-11 3x10^15 KT 72 Electroweak unification spontaneous

symmetry breaking

[My Comment 3

Here H(GUT) = U(1)hyperchargeSU(2)weak --3x3 adjoint irrep--> U(1)em

V(Electroweak) = U(1)hyperchargeSU(2)weak/U(1)em ~ S^2

with point defects. W+,W0, W- massive A(photon) massless, 1 Higgs & masses of leptons & quarks from Yukawa couplings.

Prior to that 250 Gev scale all quantum fields are massless. There is gravity already emergent from Planck era. It does not have to be put in by hand adhoc anymore. You can have curved spacetime without massive particles but not vice-versa, because to do so violates the equivalence principle.

Now the vacuum manifold is V(Planck)xV(GUT)xV(Electroweak)

Although the short-scale vacuum order parameter may be a single complex scalar field with an S1 vacuum manifold, there is reason to believe that the larger-scale vacuum order parameter after the electroweak splitting of the weak SU(2) charge from the U(1) electromagnetic charge is essentially of the character of isovector, i.e. 3x3 adjoint irrep of SU(2) with effective vacuum manifold S2 hence geometrodynamic point defects not to be confused with magnetic monopoles. Having geometrodynamic point defects instantly gives the Hawking-Bekenstein area quantization because of the second homotopy group PI2(S2) = Z giving stable 2D "wrapping numbers" instead of the stable 1D winding numbers. The 3-adjoint irrep of SU(2) is 3 real scalar fields of which in one Higgs model only one scalar field develops a non-vanishing VEV Higgs amplitude. We can imagine its conjugate Goldstone phase as the rotation about it as an axis in V(Electroweak) ~ S2 i.e. the azimuthal angle about the "z" axis chosen so that the order parameter is electrically neutral. We then must assume that this is the same Goldstone phase that survived from the Planck era. These speculations are of course very new.]

THE QUARK-LEPTON ERA

2x10^-7 2x10^13 HA 353 Tauon anti-tauon annihilation

1x10^-5 2x10^12 KT 72 Formation of hadrons from quarks

7x10^-5 1x10^12 HA 353 Muon anti-muon annihilation

5x10^-4 4x10^11 KT 159, 281 By this time the universe has a

baryon-antibaryon asymmetry

which results from post-inflationary

B,C,CP violating processes

1x10^-1 3x10^10 BS Neutral current weak interactions

become too slow and neutrinos

decouple

1x10^0 1x10^10 BS Charged current weak interactions

become too slow and neutron to

proton ratio freezes out

1x10^1 5x10^9 BS Electron positron annihilation



THE RADIATION ERA

1x10^2 1x10^9 BS Typical photon energies drop below

the deuteron binding energy and

nucleosynthesis begins

1x10^3 4x10^8 BS Particle energies drop below coulomb

barrier energies and nucleosynthesis

ends

4x10^10 6x10^4 KT 77 Matter density becomes equal to

radiation density



THE MATTER ERA

4x10^12 3.5x10^3 KT 78 Electrons and protons recombine into

hydrogen atoms

6x10^12 3.0x10^3 KT 80 Photon decoupling

2x10^16 20 HA 349 Formation of galaxies

(X-1.4x10^17) --- KT 12 Formation of the solar system

(X-9.9x10^16) --- HA 390 Emergence of life on Earth

X ~ 4.7x10^17 2.726 KT 12 Today

These values are rough estimates only. I have taken Omega_0=1, Lambda_0=0, and h=1.

http://www.talkorigins.org/origins/cosmo_timeline.html

Planck Era Emergent Gravity, Lepton Quark Rest Masses & Bekenstein Area Quantization
Note two meanings of "inertia".

Gravity as a "force" is locally indistinguishable from an inertial force in a non-inertial local frame that is either rotating or on a time-like nongeodesic path or both with respect to the Levi-Civita connection.

"Inertia" as the rest mass of quarks, leptons and W-mesons.

Our universe is thought to have formed in a sequence of spontaneous symmetry breakings of the physical vacuum. Assuming the old Heisenberg uncertainty principle

Planck scale breaking ~ 10^19 Gev ~ 10^-33 cm

GUT scale breaking ~ 10^15 Gev ~ 10^-29 cm

Electroweak breaking ~ 250 Gev ~ 10^-16 cm

In more detail

Time (s) T (Kelvin) Reference Event
CBR
THE QUANTUM GRAVITY ERA

1x10^-43 1x10^32 KT 72 Quantum limit of classical general
relativity

[My comment 1:

I postulate, as there is no fundamental theory of this as yet, the simplest possibility

G(Planck)---> H(Planck)

V (Planck)= G(Planck)/H(Planck) ~ S1(Planck)

from first homotopy group PI1(S1) = Z (integer winding numbers)

i.e. line defects i.e. 1-dim strings

Vacuum coherent order parameter is a single complex scalar field

PSI(Planck) = |PSI|e^iargPSI

Planck-scale Higgs amplitude is |PSI|, Planck-scale Goldstone phase is argPSI.

argPSI is a 0-form

Curved space-time tetrad 1-form is

B = Lp'd'argPSI

ds^2 = (1^a + B^a)(Minkowski)ab(1^b + B^b) is EEP

B is from local gauging of SPACE-TIME SYMMETRY T4 to Diff(4) AND ALSO from spontaneous breaking of INTERNAL SYMMETRY G(Planck) -> H(Planck) to S1 Post-Planck Vacuum Manifold

PSI is the INFLATION FIELD

Diff(4) covariant exterior derivative is

D = d + W/
W^ac = T4 spin-connection

The vanishing torsion 2-form in 1915 GR model is

T^a = De^a = de^a + W^ac/\(1 + B)^c = dB^a + W^ac/\(1 + B)^c = 0

Invert this equation to get the 1-form spin connection

W^a^c = -*[dB^a/\(1 - B)^c]

* is Hodge dual based on Minkowski metric in tangent fiber space.

The geodesic deviation curvature 2-form is

R^ab = DW^ab = dW^ab + W^acW^cb

The Bianchi identity is the 3-form equation (analog to dF(EM) = 0 3-form)

DR^ab = 0

The Einstein-Hilbert vacuum Lagrangian density is the 0-form

*[R^ab/\e^c/\e^d]

The Einstein curvature 4-form is

G^ab = D*W^ab

The Einstein 4-form source equation (analog to d*F(EM) = *j(electric) 3-form) is

G^ab = *J(T4)^ab

Local conservation of stress-energy source current densities is the vanishing 5-form

DG^ab = D*J(T4)^ab = 0 5-form in 4-space is identically zero.

G^ab = *J(T4)^ab

is 4-form because of equivalence principle where even zero point energy with w = -1 gravitates absolutely and not relatively.]

THE INFLATION AND SYMMETRY BREAKING ERA

1x10^-38 1x10^29 KT 72 Limit of perturbative interaction

thermalization of universe

1x10^-35 1x10^28 KT 72 Grand unification spontaneous

symmetry breaking



[My Comment 2

OK, here H(Planck) ---> H(GUT) = U(1)hyperchargeSU(2)weak

SU(3)quark coupling constant splits off from U(1)hyperchargeSU(2)weak with same coupling constant

We do not know the topology of the new vacuum manifold

H(Planck)/U(1)hyperchargeSU(2)weak = V(GUT) = ?

Note the sequence:

G(Planck) ---> H(Planck) ---> H(GUT) = U(1)hyperchargeSU(2)weak

G/(Planck)/H(Planck) ---> H(Planck)/H(GUT)

i.e.

V(Planck) ---> V(GUT)

But what does this mean in terms of the vacuum order parameter?

V(Planck) does not disappear. It is robust from Goldstone phase rigidity and it is the Hercules supporting The World Geometrodynamic Field



V(Planck)

Indeed the total vacuum manifold has grown more complex into the TENSOR PRODUCT

V(Planck)xV(GUT)



1x10^-34 1x10^27 KT 274 Approximate start of inflation

1x10^-32 1x10^27 KT 274 Approximate start of reheating and

end of inflation

1x10^-11 3x10^15 KT 72 Electroweak unification spontaneous

symmetry breaking

[My Comment 3

Here H(GUT) = U(1)hyperchargeSU(2)weak --3x3 adjoint irrep--> U(1)em

V(Electroweak) = U(1)hyperchargeSU(2)weak/U(1)em ~ S^2

with point defects. W+,W0, W- massive A(photon) massless, 1 Higgs & masses of leptons & quarks from Yukawa couplings.

Prior to that 250 Gev scale all quantum fields are massless. There is gravity already emergent from Planck era. It does not have to be put in by hand adhoc anymore. You can have curved spacetime without massive particles but not vice-versa, because to do so violates the equivalence principle.

Now the vacuum manifold is V(Planck)xV(GUT)xV(Electroweak)

Although the short-scale vacuum order parameter may be a single complex scalar field with an S1 vacuum manifold, there is reason to believe that the larger-scale vacuum order parameter after the electroweak splitting of the weak SU(2) charge from the U(1) electromagnetic charge is essentially of the character of isovector, i.e. 3x3 adjoint irrep of SU(2) with effective vacuum manifold S2 hence geometrodynamic point defects not to be confused with magnetic monopoles. Having geometrodynamic point defects instantly gives the Hawking-Bekenstein area quantization because of the second homotopy group PI2(S2) = Z giving stable 2D "wrapping numbers" instead of the stable 1D winding numbers. The 3-adjoint irrep of SU(2) is 3 real scalar fields of which in one Higgs model only one scalar field develops a non-vanishing VEV Higgs amplitude. We can imagine its conjugate Goldstone phase as the rotation about it as an axis in V(Electroweak) ~ S2 i.e. the azimuthal angle about the "z" axis chosen so that the order parameter is electrically neutral. We then must assume that this is the same Goldstone phase that survived from the Planck era. These speculations are of course very new.]

THE QUARK-LEPTON ERA

2x10^-7 2x10^13 HA 353 Tauon anti-tauon annihilation

1x10^-5 2x10^12 KT 72 Formation of hadrons from quarks

7x10^-5 1x10^12 HA 353 Muon anti-muon annihilation

5x10^-4 4x10^11 KT 159, 281 By this time the universe has a

baryon-antibaryon asymmetry

which results from post-inflationary

B,C,CP violating processes

1x10^-1 3x10^10 BS Neutral current weak interactions

become too slow and neutrinos

decouple

1x10^0 1x10^10 BS Charged current weak interactions

become too slow and neutron to

proton ratio freezes out

1x10^1 5x10^9 BS Electron positron annihilation



THE RADIATION ERA

1x10^2 1x10^9 BS Typical photon energies drop below

the deuteron binding energy and

nucleosynthesis begins

1x10^3 4x10^8 BS Particle energies drop below coulomb

barrier energies and nucleosynthesis

ends

4x10^10 6x10^4 KT 77 Matter density becomes equal to

radiation density



THE MATTER ERA

4x10^12 3.5x10^3 KT 78 Electrons and protons recombine into

hydrogen atoms

6x10^12 3.0x10^3 KT 80 Photon decoupling

2x10^16 20 HA 349 Formation of galaxies

(X-1.4x10^17) --- KT 12 Formation of the solar system

(X-9.9x10^16) --- HA 390 Emergence of life on Earth

X ~ 4.7x10^17 2.726 KT 12 Today

These values are rough estimates only. I have taken Omega_0=1, Lambda_0=0, and h=1.

http://www.talkorigins.org/origins/cosmo_timeline.html

Gennady Shipov, Alex Poltorak, discussion on torsion & non-metricity

On Nov 12, 2005, at 5:24 PM, Alex Poltorak wrote:

Gennady,

Teleparallelism is indeed a metric theory with vanishing covariant derivative of the metric. I never suggested otherwise. I merely said that in my reformulation of GR (which is not Teleparallelism), where gravity is described by nonmetric part of an affine connection induced by the choice of the frame of reference, the Equivalence principle takes form:

[Gravity=nonmetricity] = [Inertia=affine connection]

OK, the way I would say this in my notation is

Alex's theory has Q =/= 0, Gennady's theory has Q = 0.

But what about Gennady's torsion S in Alex's theory?

Also, does Alex have W spin connection = 0?

The most general covariant exterior derivative for the locally-gauged space-time 15 parameter conformal twistor group is the 1-form

D = d + W^ab/\ + S^ab/\ + Q^ab/
Geometrodynamic W^ab ~ {Pa} Lie sub-algebra fragment of 4-parameter T4 is associated with B^a in the "substratum".

Geometrodynamic S^ab ~ {sab} Lie sub-algebra fragment of 6-parameter O(3,1) is associated with T^a in the "substratum".

Geometrodynamic Q^ab ~ {ca, dilation} Lie sub-algebra fragment of 4 + 1-parameter conformal part is associated with C^a, Dilation in the "substratum".

With non-metricity we have a 15-dim parameter configuration space.

What are the possibilities?

Only W =/= 0 i.e. 4-parameter "space-time" of 1915 GR

Only Q =/= 0 i.e. 5-parameter including the dilations.

Only W & S =/= 0 i.e. 10-parameter (Shipov's theory)

Only W & Q =/= 0 i.e. 9-parameter theory

Most general theory has 15-parameters.

The basic physical idea here is to locally gauge ALL continuous space-time symmetry groups, i.e. 15-parameter conformal group.

The above is independent of spontaneous broken vacuum symmetry.

The standard model of leptons and quarks is only formulated for

W = S = Q (2-index 1-forms) = 0 identically globally.

The standard model has U(1)hypercharge SU(2)weakSU(3)strong - but in GUT it has a more general G that breaks to H = U(1)em. There is a general theorem in topological quantum theory that any such G has degenerate macro-quantum coherent vacuum manifold G/H = G/U(1)em ~ S2 with POINT DEFECTS where the Higgs amplitude vanishes and its conjugate Goldstone phase is undetermined. This applies for a 3-vector vacuum order parameter i.e. the 3x3 adjoint irrep of SU(2)weak. The Pioneer anomaly is evidence for the physical reality of this order parameter with a HEDGEHOG point defect of wrapping number -1 at center of Sun. This comes from the fact that the second homotopy group of S2 is Z (the integers). This fact also explains WHY the geometrodynamic flux is quantized in the Hawking-Bekenstein rule Area/Lp^2 ~ Z.

The wrapping number is how many oriented times the S2 in the G/U(1)em vacuum manifold is covered for a single covering of S2 cycle surrounding the point defect in physical space.

One idea here is that the Hawking-Bekenstein geometrodynamical flux quantization has the same kind of explanation as magnetic flux quantization in superconductors, as vorticity quantization in superfluid helium, as resistivity quantization steps in quantum Hall effect in 2D films. Note that fractions would mean that a complete wrapping (or winding depending on dimension of defect) in the physical surrounding circuit only covers a fraction of the G/H ground state manifold.

The point is that Hawking-Bekenstein area quantization means emergent gravity with a local vacuum coherent order parameter that must be the same as in the Higgs mechanism for the origin of the inertia of leptons and quarks in order to obey the equivalence principle.

Therefore, I do not understand the meaning of

[Gravity=nonmetricity] = [Inertia=affine connection]

Because I associate "Inertia" with the "rest mass" m of micro-geon models of leptons & quarks that are only seen in NON-GEODESICS, i.e. in 1915 S = Q = 0 GR

md^2X^u/ds^2 + m(^uvw)(dx^v/ds)(dx^w/ds) = e(dx^v/ds)F^u^v(EM) for example

Eq. for a timelike non-geodesic for a charged test particle of rest mass m.

The rest mass "inertia" m drops out of the geodesic equation. I always mean "W-geodesic" from locally gauging ONLY T4 to Diff(4).


Affine connection in this formulation may have Ricci torsion, but this torsion is not due to the gravity, but due to the rotation of the frame of reference.

The difference between my approach and Teleparallelism is that in my approach gravity is described by nonmetricity while in Teleparallelism it is described by Ricci torsion.

Is "Ricci torsion" equivalent to SPIN-CONNECTION W?

i.e.

W = Wu^a^bdx^u&a&b


The similarity of both approaches lies in the fact that both formulations use a true (1,2) tensor (tensor of nonmetricity in my case and torsion in Teleparallelism) to describe gravity, which avoids the Energy Problem of GR arrizing from using a noncovariant quantity -- Levi Civita connection -- to describes gravitational field. Consequently, in both formulations (nonmetric and Teleparallelism) it is possible to construct a covariant energy-momentum tensor of the gravitaitonal field.

Alex

Alex, how do you get tidal geodesic curvature in your theory?

Presumably you have a curvature 2-form, or, equivalently, a 4th rank curvature tensor somewhere in your theory?

How do you get

Guv(Geometry) + kTuv(Matter) = 0

in your theory?


________________________________

From: Gennady Shipov [mailto:shipov@aha.ru]
Sent: Sat 11/12/2005 7:16 AM
To: Jack Sarfatti; Alex Poltorak

Subject: Re: Physical torsion


Alex

Nonmetricity means, that covariant derivative with respect to the metric tensor is not equal to zero. In a case of Teleparallelism it is equal to zero, therefore Teleparallelism is a metric geometry.

What nonmetricity you are talking about?


Sent: Friday, November 11, 2005 4:44 AM
Subject: Re: Physical torsion


On Nov 10, 2005, at 12:33 PM, Alex Poltorak wrote:


Greetings,

For the most part I agree with Gennady. However, my analysis (published in GR9 and, more recently, GR17) suggests that gravity is not a metric curvature 2-form but rather, it is a tensor of nonmetricity or, in Cartan terminology, the symmetric part of the Ricci 2-form; while the inertia is described as affine connection plus Ricci torsion. the Equivalence Principle, gravity = inertia, is therefore expressed as

[Gravity=nonmetricity] = [Inertia=affine connection+Ricci torsion]

Best regards,

Alex Poltorak


Can you rewrite this in the Cartan notation?

Given the spin connection W

R = DW = (d + W/\)W = Ricci curvature 2-form

i.e.

Rab = DWab = dWab + Wa^c/\Wcb = Ricci 2-form

So what is the formula for the symmetric part of Rab?

What is the "Ricci torsion" formula?

Do you do everything with W from T4, or do you need the S from O(1,3) in the local gauge POV?

How do you define "inertia" physically using the above formal definition?

Curvature-Torsion Substratum

Torsion Math 1

D’ = d + W/\ + S/\ = D + S/
W is the (tangent fiber) 2-index spin connection 1-form from T4, i.e. W^ab

W ~ Lie algebra of T4 on the macro-quantum vacuum coherent Goldstone phase field with point defects from vacuum manifold G/U(1)em ~ S2 and 3-vector local order parameter whose single-valuedness implies Bekenstein-Hawking (Area/Lp^2) is quantized geometrodynamic area flux.

S is the 2-index torsion connection 1-form from O(1,3), i.e. S^ab

S ~ Lie algebra of O(1,3) on Goldstone phase.

E’ = 1 + B + T’

is the Einstein-Cartan tetrad field with a one-index torsion 1-form T', i.e. T'^a

D = d + W/
is the 1915 GR covariant exterior derivative with zero torsion i.e. only T4 is locally gauged.

T = DE = 0

implies

W = -*[dB/\(1 - B)] 1-form with 2 indices.

E = 1 + B

is 1915 GR tetrad in invariant SYMBOLIC short-hand notation.

T’ = D’E’ = (d + W/\ + S/\)(1 + B + T’) = (d + W/\)T’ + S/\(1 + B + T’)

T’^a = dT^a + W^ab/\T^b + S^ab/\(1 + B + T’)^b

Note that this is a nonlinear differential equation for T'^a.

T' is to O(1,3) as B is to T4.

T' & S are both 1-forms, but T' has one index and S has two indices.

We can get 2-forms from each of them.

D'S and D'T' are both 2-forms.

Therefore, the possibilities are larger than I first suspected and are even larger if we throw in non-metricity.

B is what I call a substratum quantity whilst W is the geometrodynamical quantity.

Similarly T' is in substratum and S is geometrodynamical.

Generalized curvature 2-form with 2 indices

R' = D'W = DW + S/\W = R + S/\W

with Bianchi identity

D'R' = 0 3-form

Geometrodynamic curvature source equation is

D'*W = *J(T4) 4-form

Current conservation is

D'*J(T4) = 0 5-form

Generalized torsion 2-form with 2-indices is

TORSION = D'S = DS + S/\S

Bianchi identity is

D'TORSION = 0 3-form

Geometrodynamic torsion source equation is

D'*S = *J(O(1,3)) 4-form

D'**J(O(1,3)) = 0 5-form

In contrast INSIDE THE SUBSTRATUM where the 1-forms B & T' have ONE index

F = dB 2-form

dF = 0 3-form

d*F = *j(T4) 3-form

d*j(T4) = 0 4-form

Just like U(1) EM theory

Same story for T' one-index torsion 1-form.