Inger,
Let me tell you a little story.
Once upon a time, there was a man named Rene Descartes. Rene had written a wonderful, new essay, which he called "Meditations of First Philosophy." Being an ambitious, but cautious man, Rene sought help from the Powers-that-Be, to promote his essay. He wrote to them thus:
"To those Most Wise and Distinguished Men, the Dean and Doctors of the Faculty of Sacred Theology of Paris, Rene Descartes Sends Greetings."
Rene informed those illustrious men, how his new essay would surely convince all unbelievers to believe. He just needed a little help. So he asked those worthies to "assist me with your patronage", and that "its errors would be corrected by you" and then, having rendered this assistance, "these arguments ought to be regarded as the most precise of demonstrations." Then and only then, "you may be of a mind to make such a declaration and publicly attest to it."
Rene went on to complain that, to date, unbelievers had not found his essay to be sufficiently believable. With great indignation, he described how unbelievers "attack not so much on my arguments regarding these issues, as on my conclusions." In his darker moments, Rene assumed that they did this, from malice. But he understood that unbelievers could not be trusted to understand logic and reason; after all, if they did understand his arguments, they would believe. But why would they attack only his conclusions, and not point out any errors in his logic? Surely, it was because they could find none!
But the unbelievers were gentlemen and scholars. They deeply respected Rene's formidable powers of reasoning. Consequently, it would only be logical for them to assume that there could be no errors in his stated arguments. Surely, neither his stated premises nor his clever deductions could possibly be in error. Nevertheless, they were confident that the weirdness of his conclusion rendered that conclusion an obvious absurdity. So, being scholars, they consulted the method of "Reduction to an absurdity", and came to the realization that Rene must have made an erroneous assumption. But surely, any stated assumptions, from a mind such as Rene's, could not be in error. Hence, the assumption must have been unstated! With impeccable logic, these scholars and gentlemen thus realized that there was little point in even reading Rene's story - they must look elsewhere for his unstated assumptions.
I too am an unbeliever. I do not believe the metaphysical stories told by physicists; the conclusions are absurd. But like Descartes's unbelievers, I concede that the physicist's stated logic, the actual physics, is likely to be impeccable, at least as far as it goes. So the actual experiments and mathematical theories need not be questioned. Rather, the unstated assumptions underlying the metaphysical stories, must be discovered, and their story must be told. That is what my essay attempts to do.
Consequently, my essay is not really about either the math or the physics. Rather, it is about the associated metaphysics, that has been mistaken for physics. By metaphysics, I mean all the stories being told, about the "meaning" and the "significance" and the "interpretation" of the actual physics. I call these stories metaphysics, because they are almost entirely independent of the physics. The actual physics, is what it is, with or without these stories (hence the dictum "Shut up and compute!"). But it is this metaphysics that is the source of all the supposed weirdness. So you can eliminate this weirdness, by simply eliminating the current metaphysical story, and replacing it by a different story. The physics remains unchanged. But in order to get people to prefer any new story, over the old one, it has to be a more compelling story. A story devoid of absurdities, which offers an alternative, common-sense "meaning", may provide this compulsion. I aim to tell such a story.
Now to address some of your specific questions:
Math plays the same role in Physics, that it plays in Digital Photography. It can be used to clean up data, summarize data, and describe data, in a compressed, symbolic form (equations). Physicists, almost as a matter of pride, like to assume that it does much more than that. Regarding this point, here is a copy of a post I made in response to Matt Visser's essay:
"In your summary, you ask "Exactly which particular aspect of mathematics is it that is so unreasonably effective?" in describing empirical reality.
I would argue, that is not an aspect of mathematics at all, but rather, an aspect of physics. Specifically, some physical phenomenon are virtually devoid of information. That is, they can be completely described by a small number of symbols, such as mathematical symbols. Physics has merely "cherry picked" these sparse information-content phenomenon, as its subject matter, and left the job of describing high information-content phenomenon, to the other sciences. That is indeed both "trivial and profound", as noted in your abstract."
Here is my alternative story of the double slit experiment:
Lets begin by making an analogy between a radio signal, beamed towards a receiver, and particles beamed through the double slits, towards a detection screen. Suppose the received radio signal behaves oddly. Perhaps it has been distorted while traveling between the emitter and the receiver. Would the odd behavior vanish if the receiver was moved closer to the emitter? In the double slit experiment, odd behavior is said to occur. It is said that the particles behave like waves, when detected at a great distance from the slits. An "interference" pattern appears, and individual particles seem to have flown through both slits at once! My my! Does this odd behavior persist if the detection screen is moved closer? Does an interference pattern appear, when the screen is placed in contact with the slits? I don't think so. Nor does a particle appear to have flown through both slits. Why the difference? Because the particles are scattered by tiny electromagnetic forces produced by the atoms making up the structure of the slits.
To visualize this, suppose we replaced the electromagnetic forces, with a stronger version of the gravitational force. Now suppose a particle is beamed through a single slit. If the particle travels exactly through the middle of the slit, it will pass straight through, undeflected, since the gravitational forces, due to the massive sides of the slits, will be symmetrical, and cancel each other out. But any particle that travels through the slit, slightly off-center, will be pulled slightly to one side; it will be scattered. When the slit is in contact with the screen, this slight deflection is unnoticeable. But when the screen is far from the slit, the slight angular deflection will cause the particle to strike the screen far to one side of the center. Now imagine that the deflection angles are quantized; particles will now only strike the screen at discrete angles. An "interference-like" pattern has appeared. Now add a second slit. This reduces the mass and hence the gravitation force on one side of the slit through which the particle travels, but not the other. So deflecting forces become less symmetrical and the "interference-like" pattern changes in comparison to that of a single slit.
As I have noticed elsewhere in these posts, the magnitude to the Fourier Transform of the slit geometry looks just like an "interference" pattern. This is a mathematical identity. I conclude from this, that it is the attributes of the slit's geometry that are ultimately responsible for the "interference" pattern, not the attributes of the waves or particles beamed through the slits. If you change the geometry, you change the pattern, even through no change has occurred in any attributes of the particles.
This type of alternative story, does not change either the experimental results, or the theoretical results. It is simply a slapped-on "interpretation." But so is the existing absurd story. I remain an unbeliever in absurd stories.
