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.)