The Quantum Pontiff

John Archibald Wheeler (1911-2008)

I just learned the very sad news that John A. Wheeler has passed away. Wheeler was one of my heroes and inspired me in many ways to be where I am today. I’m buried under a heap of work today, but will write more when I can come up for air. Below I’ve pasted a post from my old blog describing a result I first learned about by reading a Wheeler paper.

Note: This post originally appeared at my old blog site.

When I was an undergraduate at Caltech visiting Harvard for the summer I stumbled upon Volume 21 of the International Journal of Theoretical Physics (1982). What was special about this volume of this journal was that it was dedicated to papers on the subject of physics and computation (I believe it was associated with the PhysComp conference?) Now for as long as I can remember I have been interested in physics and computers. Indeed one of the first programs I ever wrote was a gravitational simulator on my TRS-80 Color Computer (my first attempt failed because I didn’t know trig and ended up doing a small angle approximation for resolving vectors…strange orbits those.) Anyway, back to Volume 21. It contained a huge number of papers that I found totally and amazingly interesting. Among my favorites was the plenary talk by Feynman in which he discusses “Simulating Physics with Computers.” This paper is a classic where Feynman discusses the question of whether quantum systems can be probabilistically simulated by a classcal computer. The talk includes a discussion of Bell’s theorem without a single reference to John Bell, Feynman chastizing a questioner for misusing the word “quantizing”, and finally Feynman stating one of my favorite Feynman quotes

The program that Fredkin is always pushing, about trying to find a computer simulation of physics, seem to me an excellent program to follow out. He and I have had wonderful, intense, and interminable arguments, and my argument is always that the real use of it would be with quantum mechanics, and therefore full attention and acceptance of the quantum mechanical phenomena-the challenge of explaining quantum mechanical phenomena-has to be put into the argument, and therefore these phenomena have to be understood ver well in analyzing the situation. And I’m not happy with all the analyses that go with just the classical theory, because nature isn’t classical dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, becuase it doesn’t look so easy.

(That, by the way, is how he ends the paper. Talk about a way to finish!)

Another paper I found fascinating in the volume was a paper by Marvin Minsky in which he points out how cellular automata can give rise to relativistic and quantum like effects. In retrospect I dont see as much amazing about this paper, but it was refreshing to see things we regard as purely physics emerging from simple computational models.

But the final paper, and which to this day I will go back and read, was “The Computer and the Universe” by John Wheeler. Of course this being a Wheeler paper, the paper was something of a poetic romp…but remember I was a literature major so I just ate that style up! But the most important thing I found in that paper was a description by Wheeler of the doctoral thesis of Wootters. Wootters result, is I think, one of the most interesting result in the foundations of quantum theory that you’ve never heard of (unless you’ve read one of the versions of the computation and physics treatise that Wheeler has published.) Further it is one of those results which is hard to find in the literature.

So what is this result that I speak of? What Wootters considers is the following setup. Suppose a transmitter has a machine with a dial which can point in any direction in a plane. I.e. the transmitter has a dial which is an angle between zero and three hundred and sixty degrees. Now this transmitter flips a switch and off goes something…we don’t know what…but at the other end of the line, a receiver sits with another device. This device does one simple thing: it receives that something from the transmitter and then either does or does not turn on a red light. In other words this other device is a measurment aparatus which has two measurment outcomes. Now of course those of you who know quantum theory will recognize the experiment I just described, but you be quiet, I don’t want to hear from you…I want to think, more generally, about this experimental setup.

So we have transmitter with an angle and a reciever with a yes/no measurement. Now yes/no measurements are interesting. Suppose that you do one hundred yes/no measurements and find that yes occurs thirty times. You will conclude that the probability of the yes outcome is then roughly thirty percent. But probabilities are finicky and with one hundred yes/no measurements you can’t be certain that the probability is thirty percent. It could very well be twenty five percent or thirty two percent. Now take this observation and apply it to the setup we have above. Suppose that the transmitter really really wants to tell you the angle he has his device set up at. But the receiver is only getting yes/no measurements. What probability of yes/no measurements should this setup have, such that the the receiver gains the most information about the angle being sent? Or expressed another way, suppose that a large, but finite, number of different angles are being set on the transmitter. If for each of these angles we get to choose a probability distribution, then this probability distribution will have some ability to distinguish from other probability distributions. Suppose that we want to maximizes the number of distinguishable settings for the transmitter. What probability distribution should occur (i.e. what probability of yes should there be as a function of the angle)?

And the answer? The answer is p(t)=cos^2(nx/2) where n is an integer and x is the angle. Look familiar? Yep thats the quantum mechanical expression for a setup where you send a spin n/2 particle with its amplitude in a plane, and then you measure along one of the directions in that plane. In other words quantum theory, in this formulation, is set up so that the yes/no distribution maximizes the amount of information we learn about the angle x! Amazing!

You can find all of this in Wootters’s 1980 thesis. A copy of which I first laid my hands on because Patrick Hayden had a copy, and which I subsequently lost, but now have on loan for the next two weeks! Now, of course, there are caviots about all of this and you should read Wootters’s thesis, which I do highly recommend. But what an interesting result. Why haven’t we all heard of it?

Comments

  1. #1 Tom
    April 14, 2008

    The NYT obit gives his birthday as July 9, 1911 (not 1912)

  2. #2 Dave Bacon
    April 14, 2008

    Doh. Fixed. Thanks Tom.

  3. #3 Jonathan Vos Post
    April 14, 2008

    Dave, I commiserate with you as Caltech Physics, and English graduate. In that spirit, however, I offer this hotlink to my poem on Wheeler, a hardcopy of which I gave today (with my sincere sympathy) to his student Kip Thorne.

    Comment #63 of
    http://cosmicvariance.com/2008/04/13/goodbye/#comments

    ====================================================
    John Archibald Wheeler and the Smoky Dragon
    by
    Jonathan Vos Post
    ====================================================

    “It from bit,” said John Archibald Wheeler,
    giant of Physics, the last superhero
    still standing, of Einstein, Feynman, Bohr;
    S-Matrix master, mutating metaphor;
    all collaborators, all decayed towards zero,
    into the black hole of death, beyond any healer.

    Ninety-six years when wormhole pneumonia
    pulled him away from consensus space-time,
    into the ultimate language of clarity,
    collapsing at last to his own singularity,
    the plutonium peak of the Matterhorn,
    Manhattan Project, the rocket-base crime,
    “a smoky dragon” — spirits of ammonia.

    “We are no longer satisfied with insights
    only into particles, or fields of force,
    or geometry, or even space and time.”
    His way with words, a deep internal rhyme,
    blinding as an ultraviolet source,
    and so he writes, calculates, and re-writes.

    “Today we demand? some understanding
    of existence itself,” he said to all teachers,
    stretching the metrics of Physics to breaking,
    we recall, our hearts aching, star-quaking
    geometrodynamics for creatures
    beyond the horizon, an instrument landing.

    “Black hole… teaches us that space can be crumpled
    like a piece of paper, into an infin-
    itesimal dot, that time can be extinguished,”
    he lectured, in his black coat, distinguished,
    “like a blown-out flame,” our identical twin
    aging faster, falling in, stressed spacesuit rumpled.

    He wrote: “The laws of physics that we regard
    as ‘sacred,’ as immutable, are anything
    but.” Not abstract. He made it astrophysics.
    He dragged the game at last into metaphysics.
    Starlight shining on his golden ring
    Magician slams down the ace, last playing card.

    Into the unified field, this is not tragic.
    Fissioning atom, conceived as liquid drop,
    beyond the cosmos, John Archibald Wheeler,
    Physicist, prophet, poet, teacher, feeler,
    “wave function of the universe” — without stop;
    “mass without mass” — magic without magic.

    1240-1435
    14 Apr 2008
    ====================================================
    Copyright (c) 2008 by Magic Dragon Multimedia.
    All rights reserved Worldwide. May not be reproduced without permission.
    May be posted electronically provided that it is transmitted unaltered, in its entirety, and without charge.
    ====================================================

  4. #4 Ian
    April 15, 2008

    Does this mean he’s passed beyond the event horizon?! RIP JAW

  5. #5 Ian Durham
    April 19, 2008

    OMG!! I can’t believe I didn’t hear about this! That is really too bad, but he was well into his 90s. I actually met him once at an APS April Meeting in New Mexico in 2002. I inadvertently sat next to him during a Symposium honoring what would have been Eugene Wigner’s hundredth year on this planet. He was one of the invited speakers and was recollecting some of his work with Wigner during WWII. At some point well into his talk he began to tell the story of his brother who was killed in the invasion of Italy and began to forget where he was so his son had to come up and retrieve him. It was a bit sad, but more because it was clear his brother’s death had had a profound impact on him.

  6. #6 Ian Durham
    April 19, 2008

    Now that the initial shock has worn off, a more succinct and respectful account of my one and only John Wheeler story is here.