Unifying Forces: Mendel Sachs' Theory and its Validity

[MathematicalPhysicist]

Has anyone read Sach's textbooks and papers?

What is incosistent in his approach, as far as I can tell there's already a theory of electroweak force, so if he did unified EM and the nuclear forces it's a great success, but has he really succeeded?

 

[bapowell]

Has anyone read Sach's textbooks and papers?

What is incosistent in his approach, as far as I can tell there's already a theory of electroweak force, so if he did unified EM and the nuclear forces it's a great success, but has he really succeeded?

I got my phd from SUNY Buffalo where Dr. Sachs used to teach. I had the opportunity to attend a small set of lectures he gave one summer on his research (it was a small group, so we were able to interact easily). His program of reinterpreting spacetime geometry in terms of spinors is important, and I believe was probably initiated by Penrose. However, Sachs' main weakness is that he's a borderline crackpot -- he's obsessed with the quaternion approach to the point of blindness to reason and physical evidence. He disbelieves that QM is a valid microphysical theory. As a result, he discounts the discoveries and advancements of QFT -- including electroweak theory. This presents a huge hurdle for this theory -- the failure to make contact with most of the 20th century's advances in particle experiment. He also discounts the existence of photons and gravitational radiation, and argues that a flat universe is axiomatically forbidden in GR, among other claims.

 

[SJRubenstein]

The problem with bandying around "crackpot" is, how many physicists *outside* the standard model have you heard from since Einstein died? Which isn't to say there aren't crackpots out there. But it's stifling you have to buy into the party line, though it has umpteen unexplained parameters and requires renormalization!

I have been studying Sachs for some time. He is not "obsessed" with quaternions; it is most of the rest of the physics community that is obsessed with mathematics rather than physics! A quaternion formalism is merely what results by exlcuding discrete reflections, leaving the purely *continuous* transformations, that Einstein (and I believe Dirac) sought.

By Sachs' method, there is no need to unify EW; he shows it, and all fields, are unified to begin!

 

[bapowell]

Right...so is his theory consistent with precision electroweak measurements? I call him a crackpot because once you start ignoring empirical data or continue to push a theory despite it's refutation, you are a crackpot.

 

[mendels]

1. I did not claim to fully predict the data on weak interactions. What I said was that there is a strong hint in the formal expression of GR that the weak interaction is a dynamical manifestation of the electromagnetic interaction at sufficiently small impact parameters.

2. What I have claimed in that the quaternion formalism of GR does fully unify the gravitational and electromagnetic forces, in the way that Einstein was seeking in a unified field theory. This theoretical development, published in books and papers over the past 50 years, has never been technically refuted.

3. I claim further to have shown that the formal expression of quantum mechanics is a linear approximation for a nonlinear field theory of the inertia of matter in GR.

4.Powell did not learn the lesson I tried to teach at the University at Buffalo, that the proposal of a new and different approach to physical problems, carried out rigorously and responsibly, does not label the author a "crackpot"! Indeed, the one who rejects such attempts without any technical refutation, but, only because it is a different view from the ongoing ideas, is the real crackpot. In Powell's view, Einstein, Schrödinger and Dirac would be labelled as "crackpots"!

 

[laserblue]

I am familiar with Dr. Sach's papers, publications and books. He has a good website online. He does seem to recycle his papers a bit too much but then people do keep reinventing the wheel. He uses quaternions/spinors as a mathematical formalism that is applicable in both quantum mechanics and general relativity. Physics does need a unified mathematical language as Dr. David Hestenes points out in a paper on that subject. It's interesting to note comments made by Dr. David Hestenes with respect to the vectors vs. quaternions controversy in physics in New Foundations for Mechanics. Did QED really succeed?

 

[mendels]

You ask "Did QED really succeed?" According to Paul Dirac, one of the primary architects of QED, it did not succeed. It is because it is not a mathematically consistent formalism, because of the infinities generated. He had the following to say about this subject: "It seems clear that the present quantum mechanics is not in its final form. Some further changes will be needed, just as drastic as the changes made in passing from Bohr's orbit theory to quantum mechanics. Some day, a new quantum mechanics, a relativistic one. will be discovered, in which we will not have these infinities occurring at all. It might very well be that the new quantum mechanics will have determinism in a way that Einstein wanted", P.A.M. Dirac, in: Albert Einstein, Historical and Cultural Perspectives (Princeton, 1982), p. 79, edited by G. Holton and Y. Elkana. I might add that agreement with the empirical facts is a necessary condition for the success of a scientific theory. But it is not sufficient. For the theory must also be logically and mathematically consistent to claim to be a scientific truth. Quantum mechanics and QED (as well as their extensions, such as the standard model) has not fulfilled this requiremnent.

 

[A. Neumaier]

You ask "Did QED really succeed?" According to Paul Dirac, one of the primary architects of QED, it did not succeed. It is because it is not a mathematically consistent formalism, because of the infinities generated.

Whether modern QED is mathematically consistent is a famous open problem. Only the old, unrenormalized QED is known to be inconsistent. After renormalization and appropriate handling of soft photons via coherent states, QED has no infinities left (except perhaps a Landau pole at immense, trans-physical energies, which doesn't harm).

He had the following to say about this subject: "It seems clear that the present quantum mechanics is not in its final form. Some further changes will be needed, just as drastic as the changes made in passing from Bohr's orbit theory to quantum mechanics. Some day, a new quantum mechanics, a relativistic one. will be discovered, in which we will not have these infinities occurring at all. It might very well be that the new quantum mechanics will have determinism in a way that Einstein wanted", P.A.M. Dirac, in: Albert Einstein, Historical and Cultural Perspectives (Princeton, 1982), p. 79, edited by G. Holton and Y. Elkana.

I agree with this part of Dirac's statement, though of course there cannot be a proof of this until it happened. Some day, I predict, a nonperturbative version of QED will be discovered, which is logically consistent, and possibly deterministic. (Quantum field theory does not suffer from the usual no-go theorems for hidden variable theories of particles.)

 

[mendels]

Dirac's claim of inconsistency of QED came after the renormalization theories were published.

 

[A. Neumaier]

Dirac's claim of inconsistency of QED came after the renormalization theories were published.

Yes, but
1. this does not invalidate my statement;
2. The statement Dirac's you actually quoted didn't claim that QED is inconsistent.

Should Dirac really have claimed this, he would have severely overrated the logical force of his arguments.

For on the usual level of rigor of theoretical physics, QED is fully predictive and hence consistent, while on the mathematical level, there is no theorem that would tell that no quantum field theory can exist whose formal perturbative expansion agrees with that of QED.

 

[mendels]

"QED is fully predictive and hence consistent". This is a logically false statement. A theory can be fully predictive in its domain, yet not mathematically consistent! For example, a theory may predict all of the known facts correctly, but in addition, other facts that are not true! It would then not be a consistent theory!

 

[A. Neumaier]

"QED is fully predictive and hence consistent". This is a logically false statement. A theory can be fully predictive in its domain, yet not mathematically consistent! For example, a theory may predict all of the known facts correctly, but in addition, other facts that are not true! It would then not be a consistent theory!

You didn't notice that I qualified the statement you quoted with ''on the usual level of rigor of theoretical physics'', and made a separate statement about the logically impeccable situation, introduced by ''on the mathematical level''.

 

[mendels]

"On the mathematical level, there can be no theorem that would tell that no quantum field theory can exist whose formal perturbative expansion agrees with that of QED".
But there can exist a field theory (e.g. a nonlinear field theory in general relativity) that does not rely on perturbative expansions in the first place, that supersedes QED, in addition to being free of divergences at the outset!

 

[A. Neumaier]

"On the mathematical level, there can be no theorem that would tell that no quantum field theory can exist whose formal perturbative expansion agrees with that of QED".
But there can exist a field theory (e.g. a nonlinear field theory in general relativity) that does not rely on perturbative expansions in the first place, that supersedes QED, in addition to being free of divergences at the outset!

True, but the latter does not justify calling QED inconsistent.

 

[mendels]

It is certainly true that the possible existence of another field theory that does not rely on perturbative expansions does not justify calling QED inconsistent. But I do believe that Dirac concluded that (even after renormalization) QED is indeed inconsistent. Further, the existence of QED (even though problematic regarding consistency in your judgement) does not rule out the truth of an altetrnative field theory based on general relativity, as I have developed!

 

[atyy]

It's textbook stuff that QED is inconsistent, because of the Landau pole that A. Neumaier mentioned above.

 

[A. Neumaier]

It's textbook stuff that QED is inconsistent, because of the Landau pole that A. Neumaier mentioned above.

The Landau pole is not a rigorously proven fact, only derived from low order of renormalized perturbation theory. It is easy to think of higher order terms that eliminate the Landau pole. Nobody knows whether it is really there.

 

[mendels]

"whether it is really there" (the Landau pole) is the type of assertion that led Dirac to call QED an "ugly" theory, along with his belief that it is at the outset an inconsistent theory, leading him to seek an alternative!

 

[A. Neumaier]

"whether it is really there" (the Landau pole) is the type of assertion that led Dirac to call QED an "ugly" theory, along with his belief that it is at the outset an inconsistent theory, leading him to seek an alternative!

Can you substantiate that? As I understood him, Dirac always referred to the infinities in the renormalization procedure as the defect of QFT, not the speculative Landau pole.

 

[petergreat]

QED has an ultraviolet completion in terms of GUTs which are asymptotically free and therefore consistent, so the existence or not of the Landau pole, lying far beyond GUT energy, won't concern us.

 

[revnaknuma]

I agree Suchs is a crackpot.

 

[mendels]

Yes, you are right about Dirac's assertion, that the infinities in the renormalization procedure is the defect of QFT, that he saw as "ugly". All that I said previously was that the reference to the trouble with the Landau pole, is *a type of assertion* that he could not accept in a complete theory. But I am not aware of his actual reference to this particular trouble.

 

[mendels]

There we go again! Referring to someone as a "crackpot" when there is no agreement or understanding of a technical argument.

 

[negru]

People still refer to renormalization as some sort of undesirable artifact? I guess it depends on what qft textbook you use...if you still think of it as "sweeping infinities under a rug", perhaps you should take a condensed matter class to explain to you the procedure more clearly?

Also it's highly irrelevant what Dirac thinks about these topics. I don't like bringing up the Einstein story, but you know how it went in his later years..
I also believe it was Feynman who complained about the Landau pole.

 

[atyy]

Can you substantiate that? As I understood him, Dirac always referred to the infinities in the renormalization procedure as the defect of QFT, not the speculative Landau pole.

People still refer to renormalization as some sort of undesirable artifact? I guess it depends on what qft textbook you use...if you still think of it as "sweeping infinities under a rug", perhaps you should take a condensed matter class to explain to you the procedure more clearly?

Also it's highly irrelevant what Dirac thinks about these topics. I don't like bringing up the Einstein story, but you know how it went in his later years..
I also believe it was Feynman who complained about the Landau pole.

Well, Landau's pole may not be exactly the reason why we think QED is not consistent, but it's similar in spirit. The reason QED is inconsistent is that the fixed point of the renormalization flow is an IR fixed point, not a UV fixed point. This is what is meant nowadays by the "Landau pole", which is perhaps sloppy terminology, but isn't different in spirit. Eg. "This is known as a Landau pole (this terminology is properly associated with QED which, as we shall see, suffers the same fate). ... So the conclusion is, in the absence of a non-trivial fixed point, scalar QFT is not really a renormalizable theory in d = 4. This conclusion applies more or less to the scalar Higgs sector of the standard model, and so in this sense the standard model is not truly a renormalizable theory and so, in a sense, predicts its own demise." http://arxiv.org/abs/0909.0859

Edit: Unless you are suggesting that QED is asymptotically safe?

 

[mendels]

I respect your belief in the integrity of qft. But you must admit that there are varying opinions and that consensus of opinion is not a criterion for scientific truth. That Dirac called for an alternate for qft and Einstein sought a unified field theory, while rejecting the basis of the quantum theory, were not anti-scientific attitudes! Indeed, it was the rejection of their ideas by the physics community that was anti-scientific.

I have proposed and developed to an extent an alternative theory to qft, based on fully exploiting general relativity theory. It is published in books and papers since the 1960s. This research is my main focus, it is not the criticizing of qft (and its extension to the 'standard model').

On the Dirac and Einstein stories, their opinions for the future of physics, in their later years, were rejected by the physics community. But they were both relying on their scientific experience and intuition, not on consensus of opinion.

 

[A. Neumaier]

Well, Landau's pole may not be exactly the reason why we think QED is not consistent, but it's similar in spirit. The reason QED is inconsistent is that the fixed point of the renormalization flow is an IR fixed point, not a UV fixed point.

An IR fixed point is not a proof of nonexistence, only a heuristic indicator (like the landau pole).

Unless you are suggesting that QED is asymptotically safe.

That is another possibility - see http://arxiv.org/pdf/0810.1928

 

[trango]

A theory to be valid must pass 3 tests:

1. Does the theory agree with accepted experimental results?
2. does the theory have "infinities" that do not exist?
3. Does the theory predict novel results that are capable of being tested or possibly refuted?

I make no judgement as to the validity of Mr. Mendel Sachs' theory. It does not matter if the theory appears to be crazy if it satisfies the 3 conditions. If Mr. Sachs' theory cannot be tested, then it is of little use.