Sean Carroll

Author: Sean Carroll

  • Guest Post: David Wallace on the Physicality of the Quantum State

    The question of the day seems to be, “Is the wave function real/physical, or is it merely a way to calculate probabilities?” This issue plays a big role in Tom Banks’s guest post (he’s on the “useful but not real” side), and there is an interesting new paper by Pusey, Barrett, and Rudolph that claims to demonstrate that you can’t simply treat the quantum state as a probability calculator. I haven’t gone through the paper yet, but it’s getting positive reviews. I’m a “realist” myself, as I think the best definition of “real” is “plays a crucial role in a successful model of reality,” and the quantum wave function certainly qualifies.

    To help understand the lay of the land, we’re very happy to host this guest post by David Wallace, a philosopher of science at Oxford. David has been one of the leaders in trying to make sense of the many-worlds interpretation of quantum mechanics, in particular the knotty problem of how to get the Born rule (“the wave function squared is the probability”) out of the this formalism. He was also a participant at our recent time conference, and the co-star of one of the videos I posted. He’s a very clear writer, and I think interested parties will get a lot out of reading this.

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    Why the quantum state isn’t (straightforwardly) probabilistic

    In quantum mechanics, we routinely talk about so-called “superposition states” – both at the microscopic level (“the state of the electron is a superposition of spin-up and spin-down”) and, at least in foundations of physics, at the macroscopic level (“the state of Schrodinger’s cat is a superposition of alive and dead”). Rather a large fraction of the “problem of measurement” is the problem of making sense of these superposition states, and there are basically two views. On the first (“state as physical”), the state of a physical system tells us what that system is actually, physically, like, and from that point of view, Schrodinger’s cat is seriously weird. What does it even mean to say that the cat is both alive and dead? And, if cats can be alive and dead at the same time, how come when we look at them we only see definitely-alive cats or definitely-dead cats? We can try to answer the second question by invoking some mysterious new dynamical process – a “collapse of the wave function” whereby the act of looking at half-alive, half-dead cats magically causes them to jump into alive-cat or dead-cat states – but a physical process which depends for its action on “observations”, “measurements”, even “consciousness”, doesn’t seem scientifically reputable. So people who accept the “state-as-physical” view are generally led either to try to make sense of quantum theory without collapses (that leads you to something like Everett’s many-worlds theory), or to modify or augment quantum theory so as to replace it with something scientifically less problematic.

    On the second view, (“state as probability”), Schrodinger’s cat is totally unmysterious. When we say “the state of the cat is half alive, half dead”, on this view we just mean “it has a 50% probability of being alive and a 50% probability of being dead”. And the so-called collapse of the wavefunction just corresponds to us looking and finding out which it is. From this point of view, to say that the cat is in a superposition of alive and dead is no more mysterious than to say that Sean is 50% likely to be in his office and 50% likely to be at a conference.

    Now, to be sure, probability is a bit philosophically mysterious. (more…)

  • Milestone Watch

    Sometime this Monday afternoon, Cosmic Variance welcomed its 10 millionth visitor. Yay us! (And yay all the visitors!)

  • Guest Post: Tom Banks on Probability and Quantum Mechanics

    The lure of blogging is strong. Having guest-posted about problems with eternal inflation, Tom Banks couldn’t resist coming back for more punishment. Here he tackles a venerable problem: the interpretation of quantum mechanics. Tom argues that the measurement problem in QM becomes a lot easier to understand once we appreciate that even classical mechanics allows for non-commuting observables. In that sense, quantum mechanics is “inevitable”; it’s actually classical physics that is somewhat unusual. If we just take QM seriously as a theory that predicts the probability of different measurement outcomes, all is well.

    Tom’s last post was “technical” in the sense that it dug deeply into speculative ideas at the cutting edge of research. This one is technical in a different sense: the concepts are presented at a level that second-year undergraduate physics majors should have no trouble following, but there are explicit equations that might make it rough going for anyone without at least that much background. The translation from LaTeX to WordPress is a bit kludgy; here is a more elegant-looking pdf version if you’d prefer to read that.

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    Rabbi Eliezer ben Yaakov of Nahariya said in the 6th century, “He who has not said three things to his students, has not conveyed the true essence of quantum mechanics. And these are Probability, Intrinsic Probability, and Peculiar Probability”.

    Probability first entered the teachings of men through the work of that dissolute gambler Pascal, who was willing to make a bet on his salvation. It was a way of quantifying our risk of uncertainty. Implicit in Pascal’s thinking, and all who came after him was the idea that there was a certainty, even a predictability, but that we fallible humans may not always have enough data to make the correct predictions. This implicit assumption is completely unnecessary and the mathematical theory of probability makes use of it only through one crucial assumption, which turns out to be wrong in principle but right in practice for many actual events in the real world.

    For simplicity, assume that there are only a finite number of things that one can measure, in order to avoid too much math. List the possible measurements as a sequence

    A = \left( \begin{array}{ccc} a_1 & \ldots & a_N\end{array} \right).
    The aN are the quantities being measured and each could have a finite number of values. Then a probability distribution assigns a number P(A) between zero and one to each possible outcome. The sum of the numbers has to add up to one. The so called frequentist interpretation of these numbers is that if we did the same measurement a large number of times, then the fraction of times or frequency with which we’d find a particular result would approach the probability of that result in the limit of an infinite number of trials. It is mathematically rigorous, but only a fantasy in the real world, where we have no idea whether we have an infinite amount of time to do the experiments. The other interpretation, often called Bayesian, is that probability gives a best guess at what the answer will be in any given trial. It tells you how to bet. This is how the concept is used by most working scientists. You do a few experiments and see how the finite distribution of results compares to the probabilities, and then assign a confidence level to the conclusion that a particular theory of the data is correct. Even in flipping a completely fair coin, it’s possible to get a million heads in a row. If that happens, you’re pretty sure the coin is weighted but you can’t know for sure.

    Physical theories are often couched in the form of equations for the time evolution of the probability distribution, even in classical physics. One introduces “random forces” into Newton’s equations to “approximate the effect of the deterministic motion of parts of the system we don’t observe”. The classic example is the Brownian motion of particles we see under the microscopic, where we think of the random forces in the equations as coming from collisions with the atoms in the fluid in which the particles are suspended. However, there’s no a priori reason why these equations couldn’t be the fundamental laws of nature. Determinism is a philosophical stance, an hypothesis about the way the world works, which has to be subjected to experiment just like anything else. Anyone who’s listened to a geiger counter will recognize that the microscopic process of decay of radioactive nuclei doesn’t seem very deterministic. (more…)

  • New Physics at LHC? An Anomaly in CP Violation

    Here in the Era of 3-Sigma Results, we tend to get excited about hints of new physics that eventually end up going away. That’s okay — excitement is cheap, and eventually one of these results is going to stick and end up changing physics in a dramatic way. Remember that “3 sigma” is the minimum standard required for physicists to take a new result at all seriously; if you want to get really excited, you should wait for 5 sigma significance. What we have here is a 3.5 sigma result, indicating CP violation in the decay of D mesons. Not quite as exciting as superluminal neutrinos, but if it holds up it’s big stuff. You can read about it at Résonaances or Quantum Diaries, or look at the talk recently given at the Hadronic Collider Physics Symposium 2011 in Paris. Here’s my attempt an an explanation.

    The latest hint of a new result comes from the Large Hadron Collider, in particular the LHCb experiment. Unlike the general-purpose CMS and ATLAS experiments, LHCb is specialized: it looks at the decays of heavy mesons (particles consisting of one quark and one antiquark) to search for CP violation. “C” is for “charge” and “P” is for “parity”; so “CP violation” means you measure something happening with some particles, and then you measure the analogous thing happening when you switch particles with antiparticles and take the mirror image. (Parity reverses directions in space.) We know that CP is a pretty good symmetry in nature, but not a perfect one — Cronin and Fitch won the Nobel Prize in 1980 for discovering CP violation experimentally.

    While the existence of CP violation is long established, it remains a target of experimental particle physicists because it’s a great window onto new physics. What we’re generally looking for in these big accelerators are new particles that are just to heavy and short-lived to be easily noticed in our everyday low-energy world. One way to do that is to just make the new particles directly and see them decaying into something. But another way is more indirect — measure the tiny effect of heavy virtual particles on the interactions of known particles. That’s what’s going on here.

    More specifically, we’re looking at the decay of D mesons in two different ways, into kaons and pions. If you like thinking in terms of quarks, here are the dramatis personae:

    • D0 meson: charm quark + anti-up quark
    • anti-D0: anti-charm quark + up quark
    • K-: strange quark + anti-up quark
    • K+: anti-strange quark + up quark
    • π-: down quark + anti-up quark
    • π+: anti-down quark + up quark

    Let’s look at the D0 meson. What happens is the charm quark (much heavier than the anti-up) decays into three lighter quarks: either up + strange + anti-strange, or up + down + anti-down. (more…)

  • A Minute of Time

    For you arrow-of-time freaks who have been looking for a quick and engaging intro to the issues (maybe to show your friends to get them to appreciate your obsession), here’s a guest spot I did for the terrific Minute Physics series illustrated by Henry Reich. If you’re not already familiar with them, check out the entire series.

    The Arrow of Time feat. Sean Carroll

    Previously I did one on dark energy. It came out right after the Nobel Prize announcement, but don’t let that trick you into thinking I won the Prize myself. (Some people were tricked.)

    2011 Nobel Prize: Dark Energy feat. Sean Carroll

    Meanwhile, in a parallel universe, instead of writing Spacetime and Geometry, I wrote a massive tome on Cosmology. This parallel universe was featured on this week’s episode of Fringe. Here’s Walter Bishop retrieving his copy from Peter.

    I helped with some of the equations on the episode. Thanks to Glen Whitman and Rob Chiappetta for the shout-out.

  • All-Male Conferences

    We all know that certain areas of academia exhibit a profound gender imbalance — philosophy, it turns out, is nearly as bad as physics. Interestingly, one often sees major conferences organized in which the ratio of men to women on the invited speakers list is substantially higher than one would expect even on the basis of gender-blind selection. I have nothing profound to say about this interesting phenomenon, except to quote in full this lovely comment by “Modalist” concerning the 2011 Oxford Graduate Conference (in philosophy).

    I think it worth emphasizing that the most important thing for everyone involved in the GCC is to ensure, by all means possible, that they bend over backwards so as to make sure that there is never any possibility that some Anonymous Internet Person might conceivably be offended at the suggestion that conference organizers anywhere—let alone conference organizers at an institution such as Oxford, whose commitment to gender equity and rejection of male privilege in education runs as far back as the High Middle Ages I’m sorry, I mean 1974—should risk feeling any twinge of private or, Heaven forfend, public embarrassment in the face of some no doubt imagined tendency to repeatedly organize conferences that feature only men on the program. We are, it is worth remembering, only in the second decade of the twenty first century. Mary Wollstonecraft is not yet cold in her grave. Surely Philosophy as an enterprise—nay, an endeavor; a vocation; the love of wisdom itself; a noble calling that grabs one by the testicles early in life and refuses to let go; perhaps indeed the last best hope of rationality and clarity of argument on this benighted Earth—can only suffer terribly if small, unfunded websites populated by aggressive viragos and their emasculated enablers insist on making a habit of pointing out the unfortunate yet, I am sure, entirely accidental Male Pattern Allness occasionally visible at conferences within the field. I should also like to remind the organizers of this “campaign” that a policy such as I have recommended—characterized as it is by polite deference, an unwillingness to make any person feel in any way even slightly out-of-sorts or unpleasantly compelled to recognize their so-called “privilege” on an otherwise perfectly pleasant sort of afternoon in the Junior Common Room, combined with a constant willingness to apologetically back down at the slightest suggestion that umbrage has been taken, or the first appearance of a convoluted description of an imaginary yet technically possible state of affairs wherein the observed outcome might not have been sexist in any way, shape, or form—has been shown by repeated historical experience to be without question the most effective means of effectuating change, especially the kind of modest, incremental and above all comfortably distant, blame-free social change that I am sure we all agree would be the best outcome in this case. Now if you’ll excuse me, my cocoa is getting cold and I do not want to have to ask my wife to heat it up again.

    Via the always interesting New APPS.

  • A Cornucopia of Time Talks

    I don’t suppose “cornucopia” is the right collective noun, but what does one call a collection of talks centered on the subject of time? I previously linked to these talks from our time conference, but it’s clear from the viewing numbers that not nearly enough of you have taken advantage of them. There’s a lot of great stuff here! So let me pick out some of my very favorites, although I promise they are all good.

    Here’s neuroscientist David Eagleman, talking about how we perceive time.

    David Eagleman on CHOICE

    Here’s physicist-turned-complexity-theorist Raissa D’Souza, talking about complexity.

    Raissa D'Souza on COMPLEXITY

    Here’s another physicist-turned-complexity-theorist, Geoffrey West, taking the complexity story even further.

    Geoffrey West on COMPLEXITY

    Here’s former guest-blogger, now Discover blogger, and engineer/roboticist/neuroscientist/philosopher Malcolm Maciver, talking about making choices and the evolution of consciousness.

    Malcolm MacIver on CHOICE

    And to top things off, here’s one of those mock debates (where participants attempt to defend the side they don’t believe in). This time it’s David Albert vs. David Wallace, on the many-worlds interpretation of quantum mechanics.

    A Mock Debate on Quantum Mechanics with DAVID ALBERT and DAVID WALLACE

    Seriously good stuff. There are still more talks not yet up, I’ll let you know.

    Update: I didn’t realize my own talk was up. Here it is.

    Sean Carroll, OPENING PANEL at FQXi Conference on Time

  • Column: Looking for New Forces

    While my first column for Discover was on the multiverse, the second one is more down to Earth (as these things go): searching for new forces. Of course we are searching for new short-range forces at the Large Hadron Collider and in other particle-physics experiments, but here I’m talking about long-range “fifth forces.” While there are plausible motivations for searching for such forces, and the experimentalists have done an heroic job in constraining them, I argue that the most impressive thing is how we can say what forces are not out there — in particular, anything that would have any important effect on everyday life. There probably are more forces than we know about, but they’re only going to be of direct interest to physicists, I’m afraid. No tractor beams.

  • From the Tau to Dark Energy: Martin Perl's Blog

    Physicists have certainly been ahead of the information-technological curve at times. The web was invented at CERN, and of course we mastered open publishing simply by doing it, while other disciplines have struggled to come up with workable models. But senior physicists — not youngsters, who are always eager to try new things, but more established types — have generally looked askance at blogging, for hard-to-discern reasons. In math we have Fields Medalists blogging up a storm, in economics there are multiple blogs by Nobel Laureates, but physicists on the far side of the “young and striving”/”senior and respected” divide have largely stayed away. (My colleagues here at CV are enormously respected, but in my mind they will always be youthful.)

    So we’re extremely happy to note that Martin Perl (at an enthusiastic 84 years young!) has jumped into the blogosphere, with Reflections on Physics: From the Tau to Dark Energy. Perl shared the Nobel Prize in 1995 for the kind of result that every physicist dreams of achieving, but few actually do: the discovery of a new elementary particle. In particular, the tau lepton, the heaviest of the three charged leptons (along with the electron and muon). Not too shabby.

    Martin’s first post is on Faster-Than-Light Neutrinos and the Dynamics of the Internet. He finds the OPERA results intriguing, but thinks that figuring them out is going to require new experiments, not clever outsiders trying to figure out where they went wrong. I would tend to trust his judgment here.

    It’s fantastic to have another great physicist taking the time to reach out to a broader audience. Note that Martin is at SLAC, along with our own JoAnne and Risa. Something about the Palo Alto coffee that nudges one toward blogging?

  • Many Kinds of Smart (A Continuing Series)

    Steve Hsu points us to an NYT op-ed by Walter Isaacson, in which he ponders the crucial question, “Was Steve Jobs smart?” Isaacson has written biographies of both Jobs and Albert Einstein, so he should know from smart.

    One might think that the answer is an obvious “yes,” and Isaacson admits this. But then he tells this anecdote:

    But I remember having dinner with him a few months ago around his kitchen table, as he did almost every evening with his wife and kids. Someone brought up one of those brainteasers involving a monkey’s having to carry a load of bananas across a desert, with a set of restrictions about how far and how many he could carry at one time, and you were supposed to figure out how long it would take. Mr. Jobs tossed out a few intuitive guesses but showed no interest in grappling with the problem rigorously.

    And what are we to conclude from this?

    So was Mr. Jobs smart? Not conventionally.

    Arrrgh. I’m not sure what kind of conventionality is being invoked, but I don’t want any part of it.

    We all know about Steve Jobs’s accomplishments. Built a major multinational corporation, created (or at least nurtured) several different devices that noticeably changed our everyday lives, became an icon for user-friendly and design-savvy technology. And he didn’t do it all just by getting lucky, or even by simple hard work. (more…)