Given infinity’s potential for troublemaking, it’s small wonder the ancient Greeks abhorred the very notion of it. ...Reading this, it appears that we have not made much progress since the Greeks. No, Einstein did not knit together time and space. That was done by Lorentz and Poincare, and Einstein did not even understand spacetime until after Minkowski's papers became popular. And Einstein had nothing to do with our understanding of infinity, as far as I know.
On Pythagoras’ Table of Opposites, “the finite” was listed along with masculinity and other good things in life, while “the infinite” topped the column of bad traits like femininity. “They saw it as a cosmic fight,” Dr. Moore said, “with the finite constantly having to subjugate the infinite.”
Aristotle helped put an end to the rampant infiniphobia by drawing a distinction between what he called “actual” infinity, something that would exist all at once, at a given moment — which he declared an impossibility — and “potential” infinity, which would unfold over time and which he deemed perfectly intelligible. As a result, Dr. Moore said, “Aristotle believed in finite space and infinite time,” and his ideas held sway for the next 2,000 years.
Newton and Leibniz began monkeying with notions of infinity when they invented calculus, ...
With his majestic theory of relativity, Einstein knitted together time and space, quashing old Aristotelian distinctions between actual and potential infinity and ushering in the contemporary era of infinity seeking. Another advance came in the 1980s, when Alan Guth introduced the idea of cosmic inflation, a kind of vacuum energy that vastly expanded the size of the universe soon after its fiery birth. ...
Relativity and inflation theory, said Dr. Aguirre, “allow us to conceptualize things that would have seemed impossible before.”
Guth's theory is just an interesting hypothesis with no hard evidence.
Ms. Angier raves about the mystical aspects of infinity, and sounds as if she is trying to match that Pythagorean image of women. She seems to think that relativity allows infinity because time is not absolute.
She gives the impression that believing in the multiverse is just like Cantor discovering infinite numbers. It is not.
Mathematical analysis is all about the study of the infinite. But the infinities are usually just shorthands for finitary arguments with precise meanings. When physicists talk about infinities, they are usually very sloppy about what is meant. There is no math to support the infinities of the multiverse.
String theorist Lumo explains:
People such as Sean Carroll or Brian Greene correctly notice that the microscopic laws of Nature are time-reversal-invariant (more precisely, CPT-invariant if we want to include subtle asymmetries of the weak nuclear force) but they're overinterpreting or misinterpreting this fact. This symmetry doesn't mean that every statement about the future and past may be simply reverted upside down. It only means that the microscopic evolution of particular microstates – pure states – to particular other microstates – pure states – may be reverted.I posted before that Unitarity is not a fundamental tenet of quantum mechanics, while a reader accused me of arguing from authority.
But no probabilistic statements may actually be reverted in this naive way.
Belief in unitarity is rooted in the belief that predicting the future is just like predicting the past. That belief is entirely mistaken, as Lumo explains better than I do. I thought that this stuff was obvious, but prominent physicists keep saying crazy things.
Now you might notice that I sometimes quote authorities favorably, and sometimes unfavorably. There is no contradiction. If I am writing about how quantum mechanics has been understood for 80 years, then I quote authorities, because they are the one who define that understanding. But if an expert says something silly, then I criticize it.
In the case of unitarity, I would not mind so much if a physicist said that it was an interesting hypothesis, and wrote a paper exploring the consequences of the hypothesis. It might be true, but it is contrary to the textbooks and contrary to the most common interpretations of the popular experiments. But when a physicist says that it is an essential part of quantum mechanics, he is just wrong.
(Besides the NY Times words, this post has several other words that are not in my dictionary.)
"Guth's theory is just an interesting hypothesis with no hard evidence."
ReplyDeleteIt depends what you mean by hard evidence. Most people would say that measurements of CMB anisotropy provide very strong evidence for inflation...
"Belief in unitarity is rooted in the belief that predicting the future is just like predicting the past."
No, it's not. Belief in unitarity is rooted in observations. You have completely misunderstood Lubos’s article. He said nothing specifically about unitarity in quantum mechanics, and he explained very carefully why quantum mechanics does not allow us to "predict" the past.
"If I am writing about how quantum mechanics has been understood for 80 years, then I quote authorities, because they are the one who define that understanding."
Okay, we're talking about two different things here. If your argument is that physicists have traditionally postulated wavefunction collapse to make predictions in quantum mechanics, then I agree with you. But this whole discussion started because you seemed to be saying that physicists were wrong in assuming that the paradoxes of black holes contradict quantum mechanics. If that’s what you're saying, then it doesn't matter how physicists have traditionally thought about quantum mechanics. It only matters whether unitarity is indeed a fundamental principle of physics, and quoting authorities doesn't help your argument at all.
If unitarity were really a fundamental principle of physics, then predicting the past would be just like predicting the future. There would also ba a Nobel Prize waiting for whoever discovered this unitarity principle. Surely this principle is more important than the Higgs boson. So whom should I credit for this? It must be someone recent, since you admit that physicists have traditionally used non-unitary quantum mechanics for 80 years. Where is the paper that shows them to be wrong?
ReplyDeleteIf you are going to point to papers claiming that we can do without collapse, and stick to unitary wave function evolution, then I agree that people make that argument. But I want to see the paper that demonstrates, with theory or experiment, that unitarity is correct and collapse is wrong.
"If unitarity were really a fundamental principle of physics, then predicting the past would be just like predicting the future."
ReplyDeleteNo, that's just not true. Please reread the article by Lubos. You cannot "predict" the past in quantum mechanics or in any probabilistic theory of physics. This was all explained very precisely in the article you quoted.
"There would also ba a Nobel Prize waiting for whoever discovered this unitarity principle. Surely this principle is more important than the Higgs boson. So whom should I credit for this?"
The unitary evolution of wavefunctions was originally discovered by Erwin Schrödinger, who won the Nobel Prize for this work in 1933. More recently, Serge Haroche showed that decoherence accounts for the appearance of wavefunction collapse, and he was awarded the 2012 Nobel Prize for this.
"Where is the paper that shows them to be wrong?"
Here:
http://prl.aps.org/abstract/PRL/v77/i24/p4887_1
"But I want to see the paper that demonstrates, with theory or experiment, that unitarity is correct and collapse is wrong."
I've already explained that people typically postulate collapse for philosophical reasons. Some people are uncomfortable with the fact that quantum mechanics only predicts probabilities, and they think that wavefunction collapse somehow improves the situation. The same reasoning is often used to argue for the many worlds interpretation. Since these are not scientific ideas, I cannot disprove that they play a role in physics on some level. But that doesn't mean that these ideas need to be taken seriously. People who study black holes have good reason to be concerned if they predict a violation of unitarity.