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.
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!
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.
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, Schrodinger and Dirac would be labelled as "crackpots"!
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?
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.
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). 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.)
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.
"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''.
"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!
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!
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.
"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.
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.