Sunday, June 17, 2018

Speaking in Tongues (of Quantum Physics)

Danish physicist Niels Bohr (1885-1962)
wikicommons photo ca. 1927
“Local causality is the idea of what we do here in this region of space has no immediate effects in a different region of space. In fact, it has no effects until a lapse of time which is limited by the velocity of light. That was an important principle in Einstein’s relativity. It was one to which he was strongly attached. And it is one which is not presentin quantum mechanics because quantum mechanics doesn’t give you this analysis of the world into different space-time regions. The whole thing is treated as a unified thing.”
                         --Stewart Bell, recorded in a short laudatory documentary uploaded on Vimeo, December 7, 2014.
“We’ve got to take the world as it is given to us and live with it. In fact, as you know, physicists have for 60 years or so worked very successfully with this situation. The formalism of quantum mechanics, using it how we know how to use it, has been fantastically successful, and it shows no sign of running out. I want to make that clear, that the conventional developments that I, most of the time, and most of my colleagues all of the time, are devoted to, are extremely impressive. So it is a very intriguing situation that at the foundation of all that impressive success, there are these great doubts.”
                          --Stewart Bell. Id.

Waves, particles, time travel, multiple universes, action at a distance: the fundaments of reality are mysterious stuff indeed. We read these words and our imagination runs wild. I doubt that our imagination in this regard is a reliable facsimile of the underlying mathematics that is the real language of quantum physics.

But English is the best we can do. It (or whatever your vernacular tongue may be) is all that is available to us. This occult mysteriousness of quantum physics in English fascinates all the more. Can it tell us something about life?

Tim Maudlin puts the question to the test in the Boston Review of Books in his recent article: The Defeat of Reason. At the heart of this article, Maudlin reviews a new book by Adam Becker that attempts to convey the current state of Quantum Physics in English: What is Real? The Unfinished Quest for the Meaning of Quantum Physics. Becker is a writer and astrophysicist, so he knows whereof he speaks. Maudlin, too, is an expert: a professor of philosophy at New York University focusing on the foundations of physics, metaphysics, logic, and philosophy of science. Me, I’m just a reader. Can these experts tell readers like us something meaningful, understandable, and relevant to our lives about quantum physics, in English? Can this kind of writing do more than titillate?

History “Yes,” up to a point; Science “No”

Becker’s book describes a dispute in science between Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Einstein, and others. Maudlin and Becker, based on this review, succeed on the level of story. I don't think Maudlin succeeds at conveying the science in this (not short) review. To me, the discussion soon devolves into occult mysticism when it comes to describing the actual science in English. It can’t be helped, I suspect, because the real language of quantum mechanics is mathematics that is mastered by perhaps a few dozen human beings. And I don’t think any of them can adequately translate their mathematics into English. [Tim Maudlin disagrees. See his comment, which I've appended, and my response][This paragraph revised in light of TM comments]

A Definition

Here is one person’s definition of quantum mechanics: “the branch of mechanics that deals with the mathematical description of the motion and interaction of subatomic particles, incorporating the concepts of quantization of energy, wave-particle duality, the uncertainty principle, and the correspondence principle.”

O.K. then.

The Planetary World of the Atom

We begin on solid ground in terms of story. In 1913 Niels Bohr, a Danish physicist, modeled the atom—a basic building block of matter—proposing that electrons revolve in stable orbits around an atomic nucleus, and that the energy levels of these electrons are discrete. Electrons can jump from one energy level (or orbit) to another, noted physicists.

When electrons jump orbits they emit light. This presented a fundamental problem of quantum mechanics: how do electrons jump orbits, and how do we predict the light (spectra intensity) that will be emitted?

Non-Classical Physics and Problems of Measurement

After more than a decade of attempting and failing to discover how the electrons change orbits Bohr and Heisenberg concluded that they could not visualize the electron changing orbits because the electron changing orbits cannot be visualized in principle. Bohr called the study of that portion of the world that was visualizable “classical physics,” and the study of non-visualizeable objects—like electrons jumping orbits and emitting light—“non classical physics.”

How does science measure and account for non-visualizeable stuff?

In 1925 Werner Heisenberg invented matrix mechanics, which managed to solve the problem of predicting the light intensity emitted when an electron jumps orbit; but this added nothing to explain how the electrons change orbits.

In 1926 Erwin Schrödingercame up with wave mechanics, a different mathematical model, to account for electrons changing orbits. Waves may not be particles, but they are relatively visualizeable objects from everyday life.

Schrödinger’s theory was more intuitive and thus easier to use than Heisenberg’s matrix mechanics formulations. Schrödinger and Paul Dirac proved that Schrödinger’s wave mechanics and Heisenberg’s matrix mechanics accounted for the same observational effects. They concluded that, therefore, they must be the same theory.

This idea that if two mathematical models account for the same observational effects, then they are the same theory, is called “logical positivism.” This philosophical rule of “logical positivism,” says Maudlin “has been killed many times by philosophers,” but it keeps cropping up in physics because physics is concerned with and based on observable consequences. If two mathematical models (like matrix mechanics and wave mechanics) account for the same observable consequences how can physicists distinguish between the two? If a theory can extend beyond its observable consequences (the distinguishing feature in this case) how can the correctness of a theory ever be settled? Better to call it the same theory.

So this left physics in the peculiar situation where electrons jumping orbits and emitting light were both particles and a wave. It’s troubling because, using Heisenberg’s mathematics to derive a particle matrix, physicists can not know how the situation associated with the matrix will appear. They have a problem of prediction. Alternatively, if physicists use Schrödinger’s mathematics of wave mechanics, they can predict and measure, but physicists encounter the problem that matter presents more as particles, they aren’t observing waves.

Although physicists commonly refer to this as a measurement problem, says Maudlin, “it is not really a measurement problem.” The problem is that physicists don’t know how the world we live in manifests in the mathematical theory. For Bohr and Heisenberg the measurement problem is how the unobservable can influence the observable; for Schrödinger the measurement problem is how waves can constitute solid objects because in wave mechanics the neat planetary electron circling a nucleus gets smeared into a cloud surrounding the nucleus.

The Spookiness of “no particular location” and Superpositions

If quantum mechanics provides a complete description of the electron—as Bohr insisted—this diffuseness of the electron is not a reflection merely of our ignorance of where the electron is, it is a reflection of the electron itself. The electron is in no particular location!

In English we are approaching the occult.

The mathematics of quantum mechanics suggests that an elementary particle, or a collection of such particles, can exist in two or more possible states of being at the same time (a “superposition”). An electron, for example, can be in a superposition of different locations, velocities and orientations of its spin. Yet this mathematical hocus pocus—to us laypersons at any rate—does not seem to comport with observed reality: anytime scientists measure one of these properties with precision, they see a definitive result—just one of the elements of the superposition, not a combination of them. Nor do physicists ever observe electrons and photons in superpositions. “The measurement problem boils down to this question,” says Peter Byrne in a Scientific American article: “how and why does the unique world of our experience emerge from the multiplicities of alternatives available in the superposed quantum world?”

The notion of the electron that is “nowhere in particular” gave rise to Schroedinger’s famous and fun thought experiment in 1935 about a cat that is dead and alive at the same time. Absurd! Said Schroedinger and Einstein. Both of them reasonably took this as a sign that something had gone wrong with the theory: that the theory was incomplete.

For Bohr, the interaction between the classical physical world (observable) and the quantum world (not observable) must itself be not observable. When these two realms interact, the most physicists can point to is a probability of different outcomes (e.g. live cat or dead cat). Physicists cannot point to a definitive prediction. “The deterministic world of classical physics has been lost,” says Maudlin.

Here is Peter Byrne’s description:
“Physicists use mathematical entities called wave functions to represent quantum states. A wave function can be thought of as a list of all the possible configurations of a superposed quantum system, along with numbers that give the probability of each configuration’s being the one, seemingly selected at random, that we will detect if we measure the system. The wave function treats each element of the superposition as equally real, if not necessarily equally probable from our point of view.”
If you are like me, we are now listening to a Shaman chant his incantations.

Bohr was left with another problem, says Maudlin. He could not say with certainty what counted as the interaction point between a quantum system and a classical system. Physicists were left with a mystery: under what conditions does an interaction (a measurement of a quantum state) occur? Is a human observer, or some other conscious device necessary?

That is hip sounding, yes? It sounds like something deep and meaningful is going on…, but I feel very much like a non-initiate.

Collapse of the Wave Function

Schrödinger had a different problem with his wave mechanics: although we can visualize the micro-world as waves, at some point these waves must manage to appear as particles, with a definitive position in space and time. This “collapse of the wave-function” presented its own measurement problem: how and when does the wave function collapse? The tentative—and entirely unsatisfactory answer—is “upon measurement.”

In 1927, at the 5th Solvay International Conference in Brussels (the “Solvay Conference”), Einstein reasonably demanded a clear and comprehensible account of what is going on in the physical world—at every level. “God does not play dice,” he said. Bohr insisted that reality could not provide this certainty. But it was not the indeterminacy of quantum mechanics that bothered Einstein, says Maudlin, what really vexed him was the non-locality in quantum mechanics, and the notion that the mathematics seemed to suggest there could be action at a distance. “Beam me up, Scotty” anyone?

When physicists seek to test the collapse of the wave-function they channel an electron wave through a very narrow hole, setting up a hemispheric screen on the other side in order to catch an electron. What they see is a single bright flash in a very definitive location, like a particle hitting the screen. This transition from extended wave to localized particle (observing that sudden appearance of the flash at one spot) said Einstein, implied that there could not be a flash at any other spot, no matter how far away. Einstein looked at this and saw nothing spooky. All you had to believe, he said, was that the electron—contrary to the mathematical theory—was always in some precise location of which we are ignorant, and that this electron “takes a humdrum path” (Maudlin) from the source to the screen, causing a flash.

Is the Theory Complete or Not?

Accepting Einstein’s common sense view implies that the quantum theory is not complete, says Maudlin. Einstein won this logical argument, but Bohr and the Copenhagen school around him won a propaganda campaign for the notion that quantum mechanics was complete, and indeterminacy was unavoidable.

The myth of indeterminacy at the heart of quantum mechanics spread, suggests Maudlin. This occurred despite a paper by Louis de Broghie, also presented at the Solvay Conference, which showed that quantum particles are bothwave andparticle, with the wave-function guiding the particles along their paths, but in a fully deterministic manner, leaving only the problem of prediction.

Multiple Universes?

In 1956, Hugh Everett, a PhD student at Princeton, wrote a long paper entitled Wave Mechanics without Probability.Everett’s analysis broke apart a theoretical logjam in interpreting the how of quantum mechanics. But it did so with another counter-intuitive leap. Everett looked at the mathematics of quantum physics and saw that it implied many-worlds—existing at the same time.

Everett addressed the measurement problem by merging the microscopic and macroscopic worlds. Breaking with Bohr and Heisenberg, he dispensed with the need for the discontinuity of a wave-function collapse. He introduced a universal wave function that links observers and objects as parts of a single quantum system. He described the macroscopic world quantum mechanically and thought of large objects as existing in quantum superpositions as well. Ergo, parallel universes.

Everett may have solved a mathematical problem in quantum mechanics, even if many parallel, simultaneously existing universes do not meet the Einstein common sense test. The idea of multiple parallel universes, says Byrne, “is by no means universally accepted even today.” But Everett’s contributions have lead to “the concept of quantum decoherence— a modern explanation of why the probabilistic weirdness of quantum mechanics resolves itself into the concrete world of our experience.”

“Weirdness” I can relate to.

Action at a Distance

John Stewart Bell queried whether Einstein’s dreaded spooky action at a distance could be avoided. Copenhagen and the pilot wave theory had both failed this test. “Bell proved that the non-locality is unavoidable. No local theory—the type Einstein had sought—could recover the predictions of quantum mechanics,” says Maudlin. “The predictions of all possible local theories must satisfy the condition called Bell’s inequality. Quantum theory predicts that Bell’s inequality can be violated. All that was left was to ask nature herself. In a series of sophisticated experiments, the answer has been established, says Maudlin: Bell’s inequality is violated. The world is not local.”

In theory, teleportation (“beam-me-up Scotty” like in Star Trek) is possible, says some authoritative sounding fellow at the World Science Festival. But listen to what he says:
“People have been teleporting particles of light from here to over there (for 20 years): you have a pair of entangled photons, you bring in another photon, you make a measurement of this photon with half of the entangled pair, SEND some classical bits of information over here, MONKEY with this other photon, and voila!—it is the same.”
Now this fellow may think he is saying something in English. But, of course, he is not. He is making hip sounds. He has everyone’s attention, but he says nothing that has any actual meaning in English. He leverages and preys on our imagination.

“Send some classical bits” and “monkey with the photon.” Uh-hu.

Follow me on Twitter @RolandNikles

3 comments:

  1. Tim Maudlin has responded and objected to portions of the opening post. His response is reproduced below with permission [in two parts due to length]. I have made some corrections and I have responded in the comment below.

    Here is Maudlin:

    Dear Mr. Nikles,

    There are several points in your post that should be addressed. [Typo information omitted and paragraph numbers added]

    1. [A]ll of this talk of “superpositions” is highly misleading. It makes it sound as if quantum states or wavefunctions can be divided into the “superpositions” (which are “weird”) and the nonsuperpositions, which are not. But that’s wrong. Every quantum state is a superposition of other quantum states. Indeed, every quantum state can be written as the superposition of other quantum states in infinitely many ways: that’s just because the collection of all quantum states forms a vector space (Hilbert space). So there is nothing weird or strange about a system being in a superposition: all systems are always in superpositions. What is harder to understand are systems that are in superpositions of macroscopically different states, such a cat being alive and the same cat being dead. Everett understood this condition as one in which there are really two non-interacting cats, one alive and one dead. Bohm solves this by saying that the quantum state does not give a complete physical description of a system. In this case, the quantum state omits mention of the particles the cat is made of. The particles are never in any superposition: they are always in some particular place, just as you expect particles to be. Given information about the location and motion of the particles, it is easy to tell if the cat is alive or dead. Omitting that information makes it impossible to tell, of course. Finally, objective collapse theories change the dynamics of the theory so such states effectively never occur.

    2. Your comments about mathematics and English (or other natural languages), which seem to be the focus of your piece are also off-target. It is not that there are any important points about quantum theory that cannot be expressed in plain English. But to completely understand the theory you have to read more than a book review. At the end of you blog, when you say that the description of teleportation just sounds “hip” but means nothing, you are mistaken. The description you quote is actually perfectly accurate. It will not be clear to anyone who does not know what a “classical bit” is, but the solution to that is not to learn math but to read more extensively and find out how a “classical bit” and a “quantum bit” (or qubit) are defined. The mathematics involved is not, in any case, very sophisticated: you don’t need more than algebra.

    ... (continued in next comment)

    ReplyDelete
  2. (continuation)....


    3. Your claim that:

    "Becker’s book describes a dispute in science between Ernst Bohr, Werner Heisenberg, Erwin Schrödinger, Einstein, and others. Maudlin and Becker succeed on the level of story. They utterly and unavoidably fail on the level of science. The discussion soon devolves into occult mysticism when it comes to describing the actual science in English. It can’t be helped because the real language of quantum mechanics is mathematics that is mastered by perhaps a few dozen human beings. And I don’t think any of them can adequately translate their mathematics into English.”

    is simply false. Literally millions of people understand the mathematics used in quantum theory perfectly well. It is you who are pushing some sort of math-mysticism here. Anyone who got through high school math without flunking understands enough math. So you are doing your readers a very serious disservice by suggesting that they cannot understand quantum theory (or rather, various different exact interpretations of the quantum formalism) perfectly well without a deep mathematical training. That is just false. And when you say that Becker “utterly and unavoidable fails” at conveying the science when, by your own admission, you have not even read his book is nothing short of irresponsible. I’m sure that I could not convey quantum theory adequately in the space of a book review, which is hardly surprising. But you are explicitly telling your readers that Becker fails when you don’t have a shred of evidence of that. The overall sense I have is that without understanding quantum theory yourself you have just decided that it involves some complicated math, when it doesn’t, so anyone trying to describe the theory in English is just trying to sound “hip”. This is both false and insulting.

    4. There are many poor and misleading account of quantum theory. Peter Byrne is not a trained physicist, and got involved in writing about Hugh Everett completely by accident. But Becker does a splendid job, and whoever was talking about teleportation was doing a fine job, and Bell of course did a perfect job without so much as an equation. So the overall sense I get is that you have some ax to grind, and it is getting in the way of your understanding things. In any case, on no account is it at all fair to write about Becker that way without having read his book. You absolutely must remove that sentence from your blog is you want to be intellectually honest.

    Regards,

    Tim Maudlin

    ReplyDelete
  3. And here is my response:

    Dear Mr. Maudlin:

    Thank you very much for the response. I have corrected all the name issues you have raised. When you say that I don’t understand Quantum theory, you are right. I take it that is not meant as a slight or an appeal to authority. Your article, after all, is written for people like me who do not understand quantum theory. The question I have posed, skeptically, is whether quantum theory can meaningfully be grasped in English without a grasp of the mathematics or science?

    I do intent to read the Becker book. I encourage readers of the blog to do the same.

    Regarding your paragraph I have numbered “1”, I read your sentences. I don’t understand what they mean. You suggest in point “2” that this is because I lack relevant definitions. I have no doubt this is true. It would certainly help if I had a common understanding of what “systems” we are talking about when we are contemplating superpositions of “systems” (a photon? an electron? a bunch of electrons? an atom? everything that makes up a cat?) But will relevant definitions in English really bring enlightenment? Isn’t the problem also that we lack any experience of cat’s being alive and dead at the same time. It’s hard to give a paradox like cats being alive and dead at the same time meaning in ordinary language. Isn’t the notion of time travel a little like that too: it’s easy enough to write a TV series about traveling forward or backwards in time—we know what that means in plain language, but in reality we haven’t a clue; our disbelief is suspended; but our resulting acceptance of time travel is not different than “drink this dandelion extract and your cancer will be cured!”

    In your third point, you claim that anyone who knows enough high school math knows enough. But enough for what? To understand in ordinary English how it can be that a cat is dead and alive at the same time? I don’t recall that being covered in my algebra class. I am not being flip. My goal is to understand.

    I fixed the phrasing about Becker succeeding, or not, which you point out was not logically correct. Thank you. I do think it was pretty clear in the original that my comments were based on your review of Becker, and not on reading Becker himself; I gave you credit for accurately rendering Becker and I do assume that the description by Becker about a cat being alive and dead at the same time, or particles being in different positions at the same time, or electrons being a wave and a particle at the same time, or the specifics of teleportation are not easier for Becker to express meaningfully in plain language than for you in your review.

    As to your fourth point, I have no ax to grind. But I am skeptical about the meaningfulness of a cat being alive and dead at the same time in ordinary language. I am also skeptical that you could reference a simple algebraic equation that would make that idea plain. I am also skeptical of plain language being able to explain some of the other counter-intuitive aspects of quantum theory in plain language. I am not doubting the quantum science; I am doubting the ability of laymen and women to understand it meaningfully and accurately, without wild misconceptions, in ordinary language.

    I respect your view that reading Becker will make everything plain, and I will read him.

    Many thanks again,

    Roland Nikles

    ReplyDelete