The Atom at 3 PM

To the Editors:

On my old friend Steven Weinberg’s fascinating review [“The Universes We Still Don’t Know,” NYR, February 10], let me make two points, although a full account of the second would require an essay as long as the review.

1. On the name “M-theory”—a large-scale theory of space-time—introduced by Edward Witten, about which the review says, “Witten has never explained what the ‘M’ stands for,” here is a communication from Witten:

Some of my colleagues thought the theory was a membrane theory, but I wasn’t sure. So I kept the first letter of membrane and called it M-theory, leaving it for time to tell whether M stood for membrane.

2. Weinberg writes that in the language of quantum mechanics “there is nothing weird about the histories of physical systems.” I challenge Weinberg to formulate in ordinary quantum mechanics the proposition “that atom decayed yesterday at three PM.” Quantum mechanics, as usually formulated, tells us about probable futures but nothing about the certain past. Some of us think that this is a puzzle.

Jeremy Bernstein
New York City

Steven Weinberg replies:

I’m grateful to Jeremy Bernstein for his kind words about my review, but though his attitude toward histories in quantum mechanics is widespread, I can’t agree with it. I said in my review that histories in quantum mechanics seem weird only if one insists on describing nature in the terms of classical physics. The example Bernstein uses in his challenge, “that atom decayed yesterday at three PM,” is just the sort of classical statement that I meant had to be forsworn in quantum mechanics.

What quantum mechanics can tell us instead is, for instance, that “at 3 PM yesterday the state vector of the system had a component, with an amplitude of precisely a certain magnitude, in which there was an undecayed atom, and another component, with precisely some other magnitude, in which there were only the decay products of the atom.” (A “vector” refers to any quantity with a magnitude and a direction, and a “state vector” to a particular type of vector in a space of infinite dimensions. The direction of the state vector at any instant encodes the complete state of the system at that instant.) If measurements were made at 3 PM yesterday the probabilities of finding that the atom had not or had decayed would be given by the square of these amplitudes; if no such measurements were made and the system remained isolated, its state vector would go on evolving in a perfectly smooth and deterministic way.