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Mathematics is not yet ready for such problems. —Paul Erdös It may take another century, but I believe with absolute certainty that Einstein will be vindicate
by korch 16y ago
Mathematics is not yet ready for such problems.
—Paul Erdös
It may take another century, but I believe with absolute certainty that Einstein will be vindicated for thinking Quantum Mechanics was incomplete, rejecting the non-visualizable, non-intuitive, entirely algorithmic hoisting up of the mathematical machinery which Heisenberg, Schrödinger, Dirac, de Broglie et. al. built into quantum mechanics.
Einstein was on the far-most opposite end of the spectrum than all of them. Einstein was looking towards intuition to explain the physics and the experimental reality, while they were looking for mathematical models which seemed to fit the experimental data, while providing no understanding of what it all meant.
Once Heisenberg & Schrödinger made a big break into QM, it's like all of physics jumped on it and forged ahead, damn whether anyone understands what is really happening.
Even Schrödinger himself, in his own first paper presenting his wave mechanics formulation, said there is no hope of visualizing nor understanding what Psi really represents. It's all just empty mathematical symbols, that when manipulated according to a particular set of rules, within a particular context, will give somewhat accurate predictions about some physical experiment. It really doesn't help at all the the entire QM apparatus is just plain ugly, inelegant and incapable of justifying itself. I'm not condemning it, nor any of the enormous geniuses who tossed their own contribution onto our great, immeasurable & eternal bonfire of accumulated human knowledge which we call science.
But if you read through a few grad-level books about QM, it's blindingly obvious that nobody really knows what's really going on. This is more of a consequence of our current gaps in mathematics, more than a failure of any individuals. Believe me, once someone discovers how to solve The Eigenvalue Problem in quadratic time, all of QM, as it is currently formulated, is going to go away and be replaced by a much simpler model. It'll be just as simplifying as centuries ago when we replaced Ptolemy's epicycles with Kepler's elliptic orbits. I bet even the probability concepts embedded in QM will be entirely thrown out(they were never anything but trouble anyways), and replaced by something even more fantastic & currently unimaginable.
- nazgulnarsil 16y agowhen I say that something is unknown I am making a statement about my own ignorance, not a statement about the physical world.
- korch 16y agoI'm not sure what your point is, but it made me think of something amusing: You exist in the physical world. You body is in meatspace, and your mind is in the ever fluctuating electrodynamic field. Both of these can be modeled by physics equations to a very high precision. Therefore when you say you believe you do not know something, even in reference to your own perception of your self-knowledge, you are nonetheless making a statement about the physical world. Sorry if this sounds pedantic. :P
- prodigal_erik 16y agoA statement like "I don't know the momentum of this particle" is likely encoded somehow in the state of specific neurons in my brain (though some philosophers would disagree), but it's not a claim about physical reality inside my head so long as we don't know how it works nor which neurons we would have to examine to verify it.
- eru 16y agoEigenvalues (and eigenvectors etc) can already be calculated numerically in polynomial time. Why would quadratic time make such a difference?
- korch 16y agoWe can lick gravity, but sometimes the paperwork is overwhelming. — Wernher von Braun Because having a worst case algorithm of n^2 is tractable, while solving for n^1000000 or bigger is not so much. The numbers are as shockingly big as in thermodynamics. And for real problems, it's not just one matrix, but thousands, all interlocked. And for some reason, the most common cases involve extremely sparse matrices. Numerical methods can only scratch the surface. On the bright side, we can't even imagine the true difficultly level. Sure computers can model the easy text book examples, but when it comes to modeling the real world, our current best mathematical capabilities don't even get off the paper.