## Archive for the ‘**quantum mechanics**’ Category

## Parallel universes

This BBC documentary follows Mark Everett, the rock singer son of Hugh Everett III (the discoverer of many worlds quantum mechanics) as he seeks to understand his father’s legacy. Unfortunately I can only find the snippet linked to above — does anyone have a copy? Apparently Hugh Everett and his son were not close. Mark Everett explains that the first time he held his father was on the day he discovered him dead. Hugh was 51, Mark 19.

Another related (and possibly copyright violating) request: anyone have a copy of this Believer article by novelist Rivka Galchen on many worlds quantum mechanics?

…Mark Oliver Everett’s own career path couldn’t have been more different from that of his father.

Mark Everett is the creative force behind the successful American cult rock band Eels. He is the first to admit that he can barely add up a restaurant tip and knows virtually nothing about quantum physics.

The splitting universe

But the main reason Mark decided to participate in the documentary was that he has always felt estranged from his father, and this would be an opportunity to understand his father better.

Along the way, Mark meets many of his father’s old colleagues and also younger physicists who have been inspired by Hugh Everett’s work. …

## Are you Gork?

Slide from this talk.

Survey questions:

1) Could you be Gork the robot? (Do you split into different branches after observing the outcome of, e.g., a Stern-Gerlach measurement?)

2) If not, why? e.g,

*I have a soul and Gork doesn’t*

*Decoherence solved all that!* See previous post.

*I don’t believe that quantum computers will work as designed,* e.g., sufficiently large algorithms or subsystems will lead to real (truly irreversible) collapse. Macroscopic superpositions larger than whatever was done in the lab last week are impossible.

*QM is only an algorithm for computing probabilities* — there is no reality to the quantum state or wavefunction or description of what is happening inside a quantum computer.

*Stop bothering me* — I only care about *real stuff* like the Higgs mass / SUSY-breaking scale / string Landscape / mechanism for high-Tc / LIBOR spread / how to generate alpha.

## Feynman and Everett

A couple of years ago I gave a talk at the Institute for Quantum Information at Caltech about the origin of probability — i.e., the Born rule — in many worlds (“no collapse”) quantum mechanics. It is often claimed that the Born rule is a *consequence* of many worlds — that it can be derived from, and is a prediction of, the no collapse assumption. However, this is only true in a particular limit of infinite numbers of degrees of freedom — it is problematic when only a finite number of degrees of freedom are considered.

After the talk I had a long conversation with John Preskill about many worlds, and he pointed out to me that both Feynman and Gell-Mann were strong advocates: they would go so far as to browbeat visitors on the topic. In fact, both claimed to have invented the idea independently of Everett.

Today I noticed a fascinating paper on the arXiv posted by H.D. Zeh, one of the developers of the theory of decoherence:

Feynman’s quantum theoryH. D. Zeh

(Submitted on 21 Apr 2008)

A historically important but little known debate regarding the necessity and meaning of macroscopic superpositions, in particular those containing different gravitational fields, is discussed from a modern perspective.

The discussion analyzed by Zeh, concerning whether the gravitational field need be quantized, took place at a relativity meeting at the University of North Carolina in Chapel Hill in 1957. Feynman presents a thought experiment in which a macroscopic mass (source for the gravitational field) is placed in a superposition state. One of the central points is necessarily whether the wavefunction describing the macroscopic system must collapse, and if so exactly when. The discussion sheds some light on Feynman’s (early) thoughts on many worlds and his exposure to Everett’s ideas, which apparently occurred even before their publication (see below).

Nowadays no one doubts that large and complex systems can be placed in superposition states. This capability is at the heart of quantum computing. Nevertheless, few have thought through the implications for the necessity of the “collapse” of the wavefunction describing, e.g., our universe as a whole. I often hear statements like “decoherence solved the problem of wavefunction collapse”. I believe that Zeh would agree with me that decoherence is merely the mechanism by which the different Everett worlds lose contact with each other! (And, clearly, this was already understood by Everett to some degree.) Incidentally, if you read the whole paper you can see how confused people — including Feynman — were about the nature of irreversibility, and the difference between effective (statistical) irreversibility and true (quantum) irreversibility.

Zeh: Quantum gravity, which was the subject of the discussion, appears here only as a secondary consequence of the assumed absence of a collapse, while the first one is that “interference” (superpositions) must always be maintained. …

Because of Feynman’s last sentence it is remarkable that neither John Wheeler nor Bryce DeWitt, who were probably both in the audience, stood up at this point to mention Everett, whose paper was in press at the time of the conference because of their support [14]. Feynman himself must have known it already, as he refers to Everett’s “universal wave function” in Session 9 – see below.

Toward the end of the conference (in the Closing Session 9), Cecile DeWitt mentioned that there exists another proposal that there is one “universal wave function”. This function has already been discussed by Everett, and it might be easier to look for this “universal wave function” than to look for all the propagators.

Feynman said that the concept of a “universal wave function” has serious conceptual difficulties. This is so since this function must contain amplitudes for all possible worlds depending on all quantum-mechanical possibilities in the past and thus one is forced to believe in the equal reality [sic!] of an infinity of possible worlds.Well said! Reality is conceptually difficult, and it seems to go beyond what we are able to observe. But he is not ready to draw this ultimate conclusion from the superposition principle that he always defended during the discussion. Why should a superposition not be maintained when it involves an observer? Why “is” there not an amplitude for me (or you) observing this and an amplitude for me (or you) observing that in a quantum measurement – just as it would be required by the Schrödinger equation for a gravitational field? Quantum amplitudes represent more than just probabilities – recall Feynman’s reply to Bondi’s first remark in the quoted discussion. However, in both cases (a gravitational field or an observer) the two macroscopically different states would be irreversibly correlated to different environmental states (possibly including you or me, respectively), and are thus not able to interfere with one another. They form dynamically separate “worlds” in this entangled quantum state.

Feynman then gave a resume of the conference, adding some “critical comments”, from which I here quote only one sentence addressed to mathematical physicists:

Feynman: “Don’t be so rigorous or you will not succeed.”(He explains in detail how he means it.) It is indeed a big question what mathematically rigorous theories can tell us about reality if the axioms they require are not, or not exactly, empirically founded, and in particular if they do not even contain the most general axiom of quantum theory: the superposition principle. It was the important lesson from decoherence theory that this principle holds even where it does not seem to hold. However, many modern field theorists and cosmologists seem to regard quantization as of secondary or merely technical importance (just providing certain “quantum corrections”) for their endevours, which are essentially performed by using classical terms (such as classical fields). It is then not surprising that the measurement problem never comes up for them.

How can anybody do quantum field theory or cosmology at all nowadays without first stating clearly whether he/she is using Everett’s interpretation or some kind of collapse mechanism (or something even more speculative)?

Previous posts on many worlds quantum mechanics.

## On the Hilbert space of quantum gravity

New paper!

http://arxiv.org/abs/0803.4212

This follows up on our earlier work on “monsters” (see here and here) — semiclassical configurations in general relativity with more entropy than black holes of equal ADM mass (second figure below). In this paper we note that if black hole evaporation is complete (no remnants, no spacetime topology change) and physics is unitary, then monsters cannot be part of the Hilbert space of quantum gravity (see first figure below, which is a Penrose diagram of an evaporating black hole). We also introduce another example of high entropy semiclassical configurations, constructed by gluing together closed FRW universes across Einstein-Rosen bridges (third figure below).

The dimensionality of the Hilbert space describing a monster or glued FRW universes is vastly larger than that of the Hilbert space describing the Hawking radiation from a black hole of equal ADM mass. There cannot be a unitary (one to one) map between the two spaces.

I can’t take any credit for the nice figures — they were created by my PhD student David Reeb 🙂

Unitarity and the Hilbert space of quantum gravityStephen D.H. Hsu, David Reeb

Abstract: Under the premises that physics is unitary and black hole evaporation is complete (no remnants, no topology change), there must exist a one-to-one correspondence between states on future null and timelike infinity and on any earlier spacelike Cauchy surface (e.g., slices preceding the formation of the hole). We show that these requirements exclude a large set of semiclassical spacetime configurations from the Hilbert space of quantum gravity. In particular, the highest entropy configurations, which account for almost all of the volume of semiclassical phase space, would not have quantum counterparts, i.e. would not correspond to allowed states in a quantum theory of gravity.

## Bell and GHZ: spooky action at a distance

*I think it is safe to say that no one understands quantum mechanics.* — Richard Feynman

Recently I’ve been lecturing on quantum weirdness (in Einstein’s terminology, “spooky action at a distance”) in my graduate quantum mechanics class. The main result is Bell’s theorem:

**No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.**

Usually this result is proved using the Bell inequalities, which have been tested experimentally. The problem with the Bell inequalities is that they are statistical in nature. I prefer to discuss the so-called GHZ states:

| GHZ > = | 000 > – | 111 >

(after Greenberger, Horne and Zeilinger), with which one can demonstrate a much sharper disagreement between local reality and quantum mechanics.

It’s interesting that so much time elapsed between Einstein’s 1935 paper with Podolsky and Rosen (EPR) that first discussed spooky action at a distance, and Bell’s theorem in 1964. Bell was a particle theorist working at CERN who only did foundations of quantum mechanics on the side (he’s also the Bell in the Adler-Bell-Jackiw anomaly in quantum field theory). The GHZ paper didn’t appear until 1989. For a long time foundations of quantum mechanics was dismissed by physicists as a fringe activity, suitable only for fuzzy headed philosophers. It’s only recently, with the explosion of interest in quantum information, that there has been renewed interest in the subject.

I find that the hardest thing about teaching this material in class is that, after half a year of training students’ brains to think quantum mechanically, it is extremely difficult to get them to *feel* the weirdness of Bell’s theorem and spooky action. It all seems quite normal to them in the context of the course — they know how to calculate, and that’s just how quantum mechanics works!

For my limited thoughts on quantum foundations (mostly about many worlds or “no collapse” formulations), see this talk (PDF) I gave at the Institute for Quantum Information at Caltech, and these blog posts.

Amazingly, I found almost all the reference links above (to GHZ, Bell’s theorem, Bell inequality, EPR) on Wikipedia!

**Note added**: See Dave Bacon on ScienceBlogs for more discussion and some comments. It appears many younger physicists claim to not find QM weird. However, there may be some selection bias towards researchers in quantum information, who generally work in a non-relativistic setting, and may not have thought as much about causality, the light cone, the intricate spacetime structure of quantum field theory, etc. (i.e., unlike Einstein). Or, it could really be a generational change 🙂

## Quantum randomness

I’m in a New Scientist article entitled **Universe explained by quantum randomness**. I can’t access the entire thing, since I don’t have a New Scientist subscription, but I’ve pasted the free-access part of the article below.

The article is based on observations made in this paper, where…

…I discuss a rather strong implication of quantum mechanics. Simple entropic or information theoretic arguments, together with standard big bang cosmology, imply that essentially all the detailed aspects of the world around us (the arrangement of galaxies in clusters, electrons in stars, leaves on trees, or books on bookshelves) are random consequences of quantum outcomes. There is simply not enough information in the initial conditions to specify all of these things. Unless their variability is illusory, it must result from quantum randomness. Very little about the universe today is predictable, even with perfect knowledge of the initial conditions and subsequent dynamical evolution.

Universe explained by quantum randomness

08 October 2007

Marcus Chown

Magazine issue 2624Look around you – at the sun in the sky, a tree swaying in the breeze, a woman walking her dog down your street. You may think all these things have a cause. Einstein did. He hated the idea of quantum randomness underlying everything, which is why he declared, “God does not play dice”.

Tough, says Stephen Hsu of the University of Oregon in Eugene. “Not only does God play dice with the universe but, if he did not, the complex universe we see around us would not exist at all. We owe everything to randomness.”

Hsu came to his startling conclusion by comparing the amount of information in today’s universe with that in the first moments of creation. According to standard cosmology, the universe grew enormously in the first split second of its existence, blowing up from a tiny patch of vacuum. “Because the patch was exponentially smaller …

## Many Worlds: A brief guide for the perplexed

I added this to the earlier post 50 years of Many Worlds and thought I would make it into a stand alone post as well.

**Many Worlds: A brief guide for the perplexed**

In quantum mechanics, states can exist in *superpositions*, such as (for an electron spin)

(state) = (up) + (down)

When a measurement on this state is performed, the Copenhagen interpretation says that the state (wavefunction) “collapses” to one of the two possible outcomes:

(up) *or* (down),

with some probability for each outcome depending on the initial state (e.g., 1/2 and 1/2 of measuring up and down). One fundamental difference between quantum and classical mechanics is that even if we have specified the state above *as precisely as is allowed by nature*, we are still left with a probabilistic prediction for what will happen next. In classical physics knowing the state (e.g., position and velocity of a particle) allows perfect future prediction.

There is no satisfactory understanding of how or exactly when the Copenhagen wavefunction “collapse” proceeds. Indeed, collapse introduces confusing issues like consciousness: what, exactly, constitutes an “observer”, capable of causing the collapse?

Everett suggested we simply remove wavefunction collapse from the theory. Then the state evolves in time always according to the Schrodinger equation. Suppose we follow our electron state through a device which measures its spin. For example: by deflecting the electron using a magnetic field and recording the spin-dendent path of the deflected electron using a detector which *amplifies* the result. The result is recorded in some macroscopic way: e.g., a red or green bulb lights up depending on whether deflection was up or down. The whole process is described by the Schrodinger equation, with the final state being

(state) = (up) (device recorded up) + (down) (device recorded down)

Here “device” could, but does not necessarily, refer to the human or robot brain which saw the detector bulb flash. What matters is that the device is macroscopic and has a large (e.g., Avogadro’s number) number of degrees of freedom. In that case, as noted by Everett, the two sub-states of the world (or device) *after* the measurement are effectively orthogonal (have zero overlap). In other words, the quantum state describing a huge number of emitted red photons and zero emitted green photons is orthogonal to the complementary state.

If a robot or human brain is watching the experiment, it *perceives* a unique outcome just as predicted by Copenhagen. Success! The experimental outcome is predicted by a *simpler* (sans collapse) version of the theory. The tricky part: there are now necessarily parts of the final state (wavefunction) describing *both* the up and down outcomes (I saw red vs I saw green). These are the many worlds of the Everett interpretation.

Personally, I prefer to call it No Collapse instead of Many Worlds — why not emphasize the advantageous rather than the confusing part of the interpretation?

Do the other worlds exist? Can we interact with them? These are the tricky questions remaining…

Some eminent physicists who (as far as I can tell) believe(d) in MW: Feynman, Gell-Mann, Hawking, Steve Weinberg, Bryce DeWitt, David Deutsch, Sidney Coleman … In fact, I was told that Feynman and Gell-Mann each claim(ed) to have independently invented MW, without any knowledge of Everett!