Hi Vladimir,
I had to think hard before replying, because I recognize your research as idiosyncratic, and I don't wish to tinker with subtleties that I don't understand. So I'm going to use a broad brush, and try to get across that while quantum mechanical theory indeed resembles a building in progress -- relativity theory is nothing like that. Relativity is a mansion designed and built complete.
The eminent relativist George Ellis has explained or implied the mathematical completeness of relativity ("top down causality") much more elegantly than I am capable of. In this year's round of essays, he casts a wide and fine-meshed net that captures modern information theory on the microscale, to smoothly connect the theories of relativity and the quantum on the large scale. Like Einstein, as you say, if the net were to be torn, George would have to start all over -- and as we know, the finer the mesh, the greater the risk.
I apologize in advance for the length of what follows. I think that a series of exchanges last month, between James Putnam and me in the FQXi blog "Essay Contest 2012: Questioning the Foundations," gets across my point of view.
I start:
"Hi James,
One area on which Richard Gill and I agree is that a mathematical model must be independent of experiment. I'm in a rather difficult position defending Joy's framework, because he started out by alienating -- and this is no exaggeration -- every mathematician on the planet ("disproof"). It's a huge irony, because it's the mathematicians, brought up on theorem proving, who would naturally ally themselves with a creative coherent argument if they have or can acquire the background to understand it. Physicists couldn't care less; physicists as a rule take mathematics "off the shelf" and try to fit it into what they are doing experimentally (whether real or gedanken). The job of a mathematician is to create new mathematics.
That's the rub. We can't create "new physics." We can only explain the physics we have. So a physical theory is tested by measured correspondence of a phenomenon against its mathematical explanation. That's what makes quantum mechanics so successful; it is vulnerable, however, to being the victim of its own success. That is, if the mathematical theory were completed, it would not be coherent -- how do we know this? -- because quantum theory at any scale is not coherent without the assumption of nonlocality. Mathematical completeness cannot be compatible with nonlocality, either mathematically or physically.
Einstein stood by his philosophy, "I am not interested in this or that phenomenon, in the spectrum of this or that element; I want to know His thoughts -- the rest are details." In this respect he thought like a mathematician rather than a physicist. Completeness is what the "Old One" imagines. Relativity is mathematically complete in the classical domain.
Believe me, there are many days when I wished I hadn't signed on to this dispute. I've got my own program. And even with the overlap, the distraction is taxing and wasteful of my time. If we are going to be intellectually honest, though, we cannot dismiss arguments that are inconvenient, or that lie outside the rules we have prescribed for ourselves.
When we create new mathematics, we have to be ready to change or reinterpret some rules. When it's complete, *then* we can speak of how it corresponds to the "real world," a physical experiment. Otherwise, we are merely cobbling up explanations for what the real world *appears* to be telling us -- and that doesn't guarantee that we really got the true message (hence, Joy's "illusion of entanglement")and usually, we are simply validating what we already know to a reasonable certainty. A mathematically complete explanation that predicts an unexpected outcome, OTOH, has much greater explanatory power.
Tom
James replies:
"I am unclear about this statement:
'Mathematical completeness cannot be compatible with nonlocality, either mathematically or physically.'
I understand it to be saying that: Since relativity theory is mathematically complete, and, since quantum theory is not, that it is assumed that quantum theory must evolve into a state where it can be absorbed into a fuller theoretical framework dominated by relativity theory.
James
My reply:
"Well put. It's that, yes, but more:
Mathematical language, despite its reputation among many unfamiliar with it, is not mystical. It's built of definitions and theorems rather than bricks and mortar, yet the abstractions are every bit as solidly joined as the best-built dwelling. Imagine that a builder invites you to view your new house from a hilltop. You look down and see a foundation hole, a rickety frame, a partly finished wall, a crumbling chimney. "We're making progress," he says. "When will it be completed?" you ask. He looks puzzled, "What do you mean?"
"When can I expect to live in it?"
"Oh, you can't ever live in it. Wouldn't be safe."
"Excuse me?"
"We don't know when something might collapse."
You are incredulous. "Don't you have plans, drawings, blueprints, specifications?"
"Sure." He hands you the plan. It's an exact copy of the wreck you see below.
"But this doesn't tell me what the house is supposed to look like!"
"Of course it does," he says. "What do you see in the plan that's different from what you see below?"
He's got you there. You can't argue with success.
"That's pretty ugly," you say.
Again, he's puzzled. "Is there some law that says a house has to be pretty?"
You admit, "I suppose not."
"Well, then can you take care of this bill for the progress we've made so far?"
"It's in the mail," you say.
All best,
Tom
