Wikipedia

Memorandum for the Historical Record


See reference to John Baez below and additional technical comments. Also note the Chris Hillman says he is "not interested" in quantum theory and my formula combines quantum theory with General Relativity in a new way he has never seen before. Chris Hillman is what Colin Bennett calls a "Victorian Station Master", what John Nash called a "hack mind", what Ayn Rand in "The Fountainhead" called a "second hander". Feynman cautioned against "rigor mortis" where mathematicians like John Baez and even Ed Witten, masquerade in theoretical physicist's clothing. Indeed the whole field of theoretical physics has been hijacked by these Math-Goths. None of Feynman's diagrams nor path integrals were mathematically rigorous and probably are not so to this day, nevertheless they are useful and are used.

OK here is why Chris Hillman and his gang of non-credentialled In-Wikitors defame me as a "crackpot" and "kook" spouting "nonsense" (read "what they cannot understand because it's too original and has not been handed down to them as gospel" or, alternatively, they have no education in the subject at all, as the case may be).

What is the basic issue here? It is the generalized Stoke's theorem:

(p+1|dp) = (&(p+1)|p)

I use Dirac notation in which the "ket" |p) is a Cartan p-form i.e. the thing integrated.

The bra (p+1| is a Cartan p+1 co-form or p-dimensional manifold of integration. When it is multiply-connected with "wormholes" (so to speak) it has a non-trivial co-homology quotient group of cosets Hp = {(p+1)-cycles}/{bounding (p+1)-cycles}, where the denominator is a normal subgroup of the numerator under a composition rule. See Baez's text book for more formal details.

The dual operators & and d are like a & a* in second quantization with Fermi-Dirac statistics in which

aa = a*a* = 0 (Pauli exclusion principle)

aa* + a*a = 1

& is the boundary operator on co-cycles.

&(co-cycle) = 0

&^2 = 0 is Wheeler's famous "Boundary of a boundary is zero".

Similarly for d^2 = 0

Note that Maxwell's EM eqs. are

F = dA

dF = 0

from d^2 = 0

&

d*F = *J

* is the Hodge dual. Again see Baez's book cited below for details.

Local conservation of electric current density is

d^2*F = d*J = 0

A the "vector 4-potential" comes from locally gauging the global abelian EM U(1) internal symmetry group.

If you have a non-Abelian "Yang-Mills" internal symmetry group, e.g. G = SU(2) or SU(3)

Then you must replace d with the covariant

D = d + A/
See Baez for definition of /\ the exterior product.

The Yang-Mills equations, where the gauge fields carry the same charges as the sources (not in U(1) EM) are then

F' = DA

DF' = 0 also called loosely a "Bianchi identity"

D*F' = *J'

D*J' = 0

Now we can do Einstein's 1915 GR in exactly the same way!

Notice that everything here is automatically local frame invariant! We never really need to go to a particular local frame of reference and write out indices.

e = 1 + B

is the Einstein-Cartan tetrad.

Einstein's metric tensor field g(curved) is not an ANTISYMMETRIC Cartan form. It is a SYMMETRIC bi-linear form

g(curved) = (1 + B)n(flat)(1 + B)

No "/\" in the above formula.

this is the local Einstein Equivalence Principle (EEP).

When B = 0, we have global special relativity of 1905.

B is the curved part of the tetrad.

1 is the "identity"

B is to the translation group T4 as A is to the U(1) EM group, or as A' is to the weak force SU(2) and the strong force SU(3) SAME IDEA that Chris Hillman says is "nonsense".

According to Chris Hillman, who boasts he has no interest in quantum theory, the battle-tested Principle of Local Gauge Invariance is "nonsense".

OK Einstein's 1915 GR in modern intrinsic notation is simply

T = D"e = 0

T is the torsion 2-form where

D" = d + W/
Where W is the 1-form spin-connection.

B determines W via the equation

T = de + W/\e = 0

i.e.

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

i.e.

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

The curvature 2-form is

R = D"W = dW + W/\W

Einstein's vacuum field equation with cosmological constant /\zpf (do not confuse with /\ for exterior multiplication) is

R/\e + /\zpfe/\e/\e = 0

See Rovelli's "Quantum Gravity" Ch 2 free online for details.

D"R = 0 is the "Bianchi identity"

D"*R = *J

is essentially Einstein's

Guv = (8piG/c^4)Tuv(Matter)

and

D"^2*R = D"*J = 0

is

Tuv^;v(Matter) = 0

Now we can go on to Gennady Shipov's torsion field theory by

e' = e + S

S is from locally gauging the Lorentz group O(1,3) not done in 1915 GR, but done by Utiyama & Kibble in 1960's after Einstein died in 1955.

Now we have

T = dS + W/\S + S/\(1 + B + S)

the torsion 2-form T =/= 0 when S =/= 0

More on this another time.

My ANSATZ for which Chris Hillman wants to burn me at the stake is to invoke the spontaneous breakdown of vacuum symmetry for the SU(2)hypercharge group of the standard model to say

B = (hG/c^3)^1/2"d"(Goldstone Phase)

"Goldstone Phase" here in sense of "mean phase" associated with SU(2).

Details in text books and I will provide them later.

The above is the intuitive idea.


On Sep 25, 2005, at 11:54 AM, Jack Sarfatti wrote:

Alex, a mathematician Chris Hillman, is lying about what you allegedly said about my formula

B = (hG/c^3)^1/2"d"(Goldstone Phase)

Hillman quotes you as saying that you wrote that the "derivation is generally regarded as nonsense". Hillman, or some one else, may have deliberately changed what you did say. Please clarify for the official record here.

Here is what you are cited by Chris Hillman as saying:


::: If you read the history page, you can see who wrote the sentence you are objecting to: ''This "derivation" is generally regarded as nonsense'', and you can see who added the link to the post by Burinskii (who I believe is either a Ph.D. physicist or mathematician, BTW), stating that he considers the alleged 'derivation' to be nonsense, as I do, and as do other knowledgeable scholars I know who have seen it. Since searching Google allows anyone to verify that responses to your 'derivation' was included 'this is nonsense', stating ''the alleged derivation is considered by at least some commentators to be nonsense'' is verifiable factual information. Arguably, you might be right that the current statement is a tad too strong. OTH, while this is harder to verify, I know I am knowledgeable, and I consider the alleged derivation to be utter bosh, so all in all I propose to change this sentence to ''this alleged derivation is considered by at least some knowledgeable commentators to be rubbish; not suprisingly, Sarfatti strongly disagrees with this judgement'', followed by links to your post giving the alleged derivation and to a post by a knowledgeable reader calling it nonsense. Would that be OK by you? Please note that according to my proposal, readers will easily be able to examine your alleged derivation and an objection and to make up their own minds about the likelihood of your derivation being meaningful or important. Fair enough?---[[User:Hillman|CH ]] [[User_talk:Hillman|(talk)]] 09:56, 25 September 2005 (UTC)
http://en.wikipedia.org/wiki/Talk:Jack_Sarfatti

BTW: If Chris Hillman were honest, which he obviously is not, he would give a detailed refutation of why he considers

B = (hG/c^3)^1/2"d"(Goldstone Phase)

nonsense and not simply smear it without justification.

Note that John Baez's book has an example in which d acting on a zero form has a jump phase singularity.

"Flux without flux", i.e. QUANTUM NONLOCALITY of Bohm-Aharonov effect, that Chris Hillman eschews. Pardon me, but who is really the "crackpot" and "kook" here? However, I will keep the "Victor Von Frankenstein Prize for Weird Physics"! ;-)

Go to p. 130 of John Baez's "Gauge Fields. Knots and Gravity" where Baez writes:

"funny things can happen in regions of space that are not simply connected ...'

Baez uses "theta" where I use "Goldstone Phase"

"d"theta = (xdy - ydx)/(x^2 + y^2)

Baez writes: "the coordinate 'theta', in addition to being ill-defined on the z-axis, is really only defined modulo 2pi. Nonetheless it is customary to define the one form "dtheta".

In effect then one gets from the Stoke's theorem

(p+1|dp) = (&(p+1)|p)

->

(2|d1) = (&2|1> = 2piN

N = 0, +-1, +- 2, ... number of flux quanta

|1) = B = (hG/c^3)^1/2"d"(Goldstone Phase)

The important thing here is to see the intuitive idea, THE BIG PICTURE, and not get lost in Feynman's "rigor mortis".

Note gravity is macro-quantum emergent from SU(2)hypercharge broken vacuum symmetry, i.e. ODLRO.

No gravity when h -> 0.

No gravity when c -> infinity

Even when G =/= 0

The broken SU(2) hypercharge local Vacuum ODLRO order parameter is the INFLATION FIELD for the creation of the universe.

Macro-spacetime physics is local because of the locality of ODLRO and the Arrow of Time is explained because ODLRO lowers the phase space volume of the pre-inflation "false vacuum".

And this is what Chris Hillman calls "nonsense" and for this I am a "crackpot" and a "kook".


See "Dirac string" & Hagen Kleinert's "multi-valued gauge transformation".

Since there are knowledgeable people on the list above, integrity demands that Hillman give his reasons in detail.