And towards the interpretations of expressions.
For instance, there is a complete difference between reduction to set theory and basis upon an axiomatic system. Probability theory is now commonly done in one or the other way. The latter is sometimes called the ‘Jeffreys interpretation’.
And there is the misinterpretation of Dirac notation by physicists, as referring to physical entities that I assure you do not exist. The proper interpretation is as propositions.
Just because a physicist has a PhD in Physics and I have some lesser qualification in a different field does not make it so that the physicist is correct. Actually it is the physicist who is straying outside their field—into random process analysis—but they will bully you into ignoring that. And it is irrelevant.
Because anyone who believes in instantaneous action at a distance is a damn fool—especially if they are a physicist and believe it occurs between fragments of the EM field.
Which brings us back to my inclination towards geometry. For there is no getting away from photons being the building blocks of the electromagnetic field, and EM field being universal, and it being a continuous (to first approximation) construct that obeys contact-action and Newton’s laws of motion.
There is no mathematical reconciliation of that with the lunacy of ‘modern physics’ as misinterpreted. Nor with the fake pseudomathematics of Bell, Clauser, Zeilinger, et al.
(Whether the EM field actually is continuous or not is perhaps not resolvable. Photons cannot possibly be space-less points, as they are treated in ‘modern physics’, but in fact must have extent. Likely the extent is in principle continuous ‘forever’, but for practical purposes limited. As in so many things.
So the EM field is probably, for all practical purposes, ‘continuous but lumpy’. But whether there is actual discreteness I suspect cannot be resolved.)
(I know there are physicists who come up with all sorts of speculations. Usually they are particle physicists. The sort who transport antiprotons in trucks and I yawn at their accomplishment because they spend a lot of money and achieve very little except the making of press releases about dubious things.
Are YOU going to take their word about their inferences? John S. Bell was a CERN physicist, after all, and he was utterly incompetent. I know this for a fact.)
(But I am certain that people like Wolfram are out of touch with realities, who imagine replacing analysis and calculus with some kind of ‘discrete mathematics’.
And I deplore this trend of offering ‘discrete mathematics’ as an alternative to calculus. I noticed it in Computer Science curricula some decades ago. You should have to take calculus. How else are you supposed to understand how a computer comes up with the value of sin(t), which is one of its basic functions?)
(BTW I glanced into Wolfram’s vanity book, when it was on tables at B&N, just fresh off the presses.
Wolfram could not even describe what this new non-calculus would be, or why it was needed.
Abraham Robinson had already done non-standard analysis. Which I also reject, as unintuitive, but at least it can be explained and actually functions.
Yes, I know it is SUPPOSED to be MORE intuitive, but it really is not. Epsilon-delta is a perfectly intuitive mechanical system.)
I think what all the foregoing has me deciding this morning is on a new way of viewing photons and the electromagnetic field.
That photons are lumpy undulations in a continuous and universal electromagnetic field, which is thoroughly action-by-contact and obeys Newton’s laws of motion.
There is, of course, not the slightest hint of the ‘action at a distance’ supposedly shown by Clauser and Aspect, who are easily shown to be wrong both in theory and in experimental analysis.
I am sure ‘lumpy undulations’ is hardly a new picture and that many have had this picture of photons. It might even be a common ‘semi-classical’ picture, although I would not consider my view semi-classical.
That is, in particular, I do not adhere to A. F. Kracklauer’s theory of the Aspect experiment. I certainly agree his model gives the correct statistics. I just do not agree it is what happens. His theory says photodetectors fire randomly according to impinging intensity of the light pulses.
If you do this you get the correct statistics.
But I can show that if you assume particles in classical, Newtonian motion then you ALSO get the correct statistics. So there is no need for the extra assumptions Kracklauer is making.
That is, THE MERE FACT THE LIGHT COMES IN PULSES IS ENOUGH to explain the Aspect experiment. You can assume that the photodetectors are perfect.
Really what Kracklauer was doing was taking the continuous analog of the Aspect experiment and adapting an analysis of it to explain the Aspect experiment.
But all of this was difficult because it was done from the point of view of a physicist.
I viewed the problem instead as one of logic and mathematics. If it applied at the continuous level, it must also apply at the discrete level. So I had to prove that. It took many years for me to do so. I did so finally this year.
I mean, I convinced myself of the last final bits of it, this year.
I am a tough customer for my own product.
I still feel plenty of doubt, actually. But that’s a good thing. You know Einstein was that way. It is obvious Einstein was that way, because he was working on that Unified Field Theory, not sitting on his gravitational theory the way people do now.
Barry Schwartz 🫖