Posts Tagged ‘Quantum mechanics’

Gribbin: Six Impossible Things

October 25, 2020

Six Impossible Things
The Mystery of the Quantum World
John Gribbin
(MIT, 2019)
101 p.

The shelves of neighbourhood bookstores groan under the weight of popular science books about quantum theory. Six Impossible Things stands out from this crowd because it focuses not on the mechanics or the findings of quantum theory, but on how to interpret the theory. What is it saying the world is like?

Gribbin opens the book by describing two quantum phenomena in which the strangeness of quantum theory is most evident. The first is the famous double-slit experiment, and the second is entanglement. These form the main course in many popular books on quantum mechanics, but are here only the appetizers.

In the remainder of the book, Gribbin describes six different schools of interpretation of quantum theory, and discusses, in particular, what each of them says is happening in these two famous case studies. These six schools are really schools of interpretation; they all rely on exactly the same mathematics and make exactly the same predictions for experiments. They differ only in how they describe the entities and dynamics underlying the observations. They agree on what happens in the end; they differ on how and why it happens.

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So, for example, the most common school of interpretation among working physicists is the so-called Copenhagen interpretation. On this view, there is an entity called the wave function, the time-evolution of which is described by the Schrodinger equation. Quantum states evolve into superpositions of states, and when a measurement is made the wave function collapses into one state with predictable probability. Quantum mechanical systems don’t have definite properties until measured, on this view. The biggest problem for this school is the “measurement problem”: the measurement intervenes in the physics and itself has no physical description. What is a measurement anyway? Does it require a conscious agent to carry it out? Many physicists have thought so, but this has led to thought experiments like the one with Schrodinger’s cat, which strain credulity as a sound description of the world.

A second interpretation is the “pilot wave” theory, pioneered in the early days by de Broglie and developed at length by David Bohm. On this view, particles (like electrons or photons) are always and only particles with definite properties — there is no wave/particle duality or superposition of states — but the particles interact with a “pilot wave” which evolves dynamically, like the wave function, and which guides particles on different paths through space depending on small variations in initial conditions. The theory is deterministic, but specific outcomes are impossible to predict without more information. This view has its attractions: much of the quantum weirdness found in the Copenhagen interpretation is gone, and there is no measurement problem. But the theory has features not obviously attractive too: the pilot wave affects particles but is itself un-measurable, and the theory requires non-locality — the properties of a particle depend on the properties of all other particles with which it has ever interacted, and on their properties now, not just their past properties.

Third comes my own least favourite: the “many worlds” interpretation. On this view there is no collapse of the wave function so that the outcome of a measurement is one of the range of possible states. Instead all of the possible outcomes are realized each time a measurement is made, each outcome in a different universe. The universe we live in is constantly branching into myriad new universes each time a quantum mechanical system is reduced from a superposition of states to a specific state. Every possible universe is realized somewhere, provided it obeys the laws of physics. The contempt I feel for this interpretation would be difficult to overestimate. Practically the sole consolation it provides is the reassurance that somewhere a living, breathing Elizabeth Bennett is living her life just as was so memorably recounted by Miss Austen in her story.

Another possible interpretation is the ‘decoherence’ view, which takes entanglement, sometimes an odd and slightly annoying phenomenon in the mental universe of physicists, and makes it the key to everything. On this view, quantum systems become entangled with their environments, and these macroscopic entangled states behave, on average, like classical (ie. non-quantum) systems. The larger the distance scale, the faster this entanglement causes the quantum system to ‘decohere’. This view has the advantage of explaining why quantum mechanical systems are generally very small and relatively simple: if they become large or complex, they decohere through interactions with their environments. In fact, to the degree that I understand it, this interpretation of the theory is my own favourite: it is metaphysically modest and makes a lot of sense. However, I may not understand its implications adequately; Gribbin devotes a chunk of his chapter to arguing that the decoherence interpretation is equivalent to something called the Many Histories interpretation, which he encapsulates in this way: “Everything that could possibly happen already has happened, and we only noticed part of it.” That sounds bad, but I confess I don’t understand this alleged equivalence.

Next is the ‘ensemble interpretation’, favoured by Einstein, which attempts to do away with quantum weirdness by claiming that the probabilistic predictions of the theory pertain not to any one quantum system, but to an ensemble (or collection) of such systems, if they existed. On this view, each individual quantum system behaves deterministically, but duplicates of the system could behave differently, according to the probabilities predicted by the theory. It makes a kind of sense, but has trouble explaining why this particular quantum system behaves as it does. The idea has been rejuvenated by Lee Smolin in recent years, who has proposed a highly non-local interpretation whereby the degree of “quantumness” exhibited by a system depends on how many instances of that system exist in the universe, with all such instances together forming an ‘ensemble’  in the relevant sense. Hydrogen atoms behave quantum mechanically because there are many of them, but you and I behave classically because we are unique (or, if you prefer, we know we are unique because we behave classically). This is an interesting view, if you can abide the radical non-locality.

Finally, Gribbin describes the “transactional interpretation”, a view inspired by the fact that the equations of quantum theory allow for solutions travelling both forward and backward in time. The backward-travelling solutions are usually regarded as spurious, but in this interpretation they are taken seriously. The proposal is that physics depends not just on where things have been, but also on where they are going. Not just on where and how a quantum system originated, but also on where and how, in the future, it will be measured. When worked out in detail, this view, rather surprisingly, produces exactly the formalism of quantum mechanics. One hardly knows what to do with this fact.

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Gribbin summarizes the six interpretations he has described in this way:

  1. The world does not exist unless you look at it.
  2. Particles are pushed around by an invisible wave, but the particles have no influence on the wave.
  3. Everything that could possibly happen does, in an array of parallel realities.
  4. Everything that could possibly happen already has happened, and we only noticed part of it.
  5. Everything influences everything else instantly, as though space did not exist.
  6. The future influences the past.

Choose your poison.

A few closing remarks. First, there is no getting around the fact that quantum theory has upset our conventional views of what the world is like, but, as this books makes clear, just how it upsets them is not clear. Second, it strikes me as quite amazing that a single theory, the mathematical structure of which is uncontroversial, could produce such a wide variety of possible physical descriptions. Third, this is a very fine book, written without undue technicalities, and I recommend it to anyone with an interest in the subject.

Bubs: Totally Random

February 16, 2020

Totally Random
A Serious Comic on Entanglement
Tanya Bub and Jeffrey Bub
(Princeton, 2018)
260 p.

Entanglement is one of the physical phenomenon in which the strangeness of the quantum world comes most clearly into focus. It has been historically important in debates about the meaning and completeness of quantum mechanics, and it continues to attract attention from well-scratched heads.

In a nutshell, “entangled” quantum states involve two or more entities behaving in such a way that each cannot be fully described physically without reference to the others, even under conditions in which it seems that there can be no physical interaction between them. For instance, we observe experimentally that measurements on members of an entangled pair (of, say, photons) exhibit correlations that are seemingly impossible under a classical account of causality.

This graphic novel creatively explores the conundrums that arise from entanglement. The first section presents the experimental evidence and various (failed) attempts to make it fit into a standard causal framework, emphasizing the challenge entanglement poses for our usual understanding of the natural world. The second section introduces us to various schools of interpretation of quantum mechanics, focusing on what they have to say about entanglement, and the final section surveys some technological innovations, chiefly related to encryption, that have been made possible by use of entangled quantum states.

It is, as the sub-title indicates, a serious engagement with the ideas it presents, albeit without any mathematics. Jeffrey Bub is a philosopher at the University of Maryland whose specialties include quantum theory. (Tanya Bub, I believe, is responsible for the illustrations, without which a graphic novel would be poor fare indeed.) [Addendum: as clarified in the comments below, the book is a full collaboration between the two authors, and did not divide neatly along content/illustration lines.] The main ideas of entanglement are presented using an imaginary but instructive case of entangled quantum coins (i.e. quoins) that exhibit what they call “curious correlations” when tossed. The sections on interpretation of the experimental findings rather winsomely bring in the historical figures (Bohr, Bohm, Einstein, Everett, etc.) who proposed or defended them. Some of the book’s narrative dialogue drifts toward the quotidian, especially in interludes between the main technical content; I didn’t like this, but I’m a curmudgeon. Overall, it’s an interesting and creative book that makes this sometimes abstruse, but important, topic accessible to all comers.

Susskind & Friedman: Quantum Mechanics

February 22, 2018

Quantum Mechanics
The Theoretical Minimum
Leonard Susskind and Art Friedman
(Basic, 2014)
xx + 364 p.

Books on quantum mechanics tend to come to two main varieties: introductions for non-scientists, which normally focus on the conceptual underpinnings of the subject and avoid mathematics, and technical books written for advanced undergraduates or higher. This book, however, doesn’t quite fall in either camp. It spends a good deal of time carefully exploring the conceptual foundations, but it also does contain enough mathematics — all of it fairly gentle, but pertinent — so that the reader is not only told, but also is able to see, how certain of the most famous predictions of quantum mechanics follow from those conceptual foundations.

Susskind and Friedman begin with a simple quantum system, a single quantum spin, and use it to lay out the unusual logic of quantum states, emphasizing how it differs from the logic of classical physics. They discuss both time independent and time dependent quantum mechanics, emphasizing the value of the former for deducing the energy states of a system and of the latter for deducing how the system evolves in time. About one-third of the book is devoted to an exploration of entanglement, traditionally one of the strangest aspects of the quantum world, but they take some pains to argue that entanglement does not imply any sort of non-locality, as is sometimes claimed. Later sections of the book transition to the topic of wavefunctions and particles, and creep right up to the edge of quantum field theory, so as to peer over for a moment. At the end, they give a nice treatment of the quantum mechanical harmonic oscillator, which is one of the simplest but most important quantum systems.

Susskind is one of the best-known physicists of his generation. It is not all that common, I think, for such an eminent scientist to have a passion for teaching his subject to beginners, so I very much admire what he is doing here. The development of the subject is clear, with intermediate steps worked, and the significance of conclusions are emphasized. The book has a welcoming tone, and the enthusiasm of the authors is evident. They do not refrain from an occasional joke. The book is, apparently, derived from an online course which Susskind has given at Stanford. (Friedman is one of his students, and it is unclear to me exactly what his role has been in writing the book.) The book has been typeset with LaTeX, as is right and just.

It’s a little hard to say who the target audience is. It would be accessible, certainly, to an interested reader who had been trained in, for instance, engineering. The mathematics required doesn’t extend much beyond complex numbers, basic calculus, and linear algebra, and even these are given quick explanations in the text. I could see it being a very good read for an ambitious high school student or beginning undergraduate who has an interest in the subject. Or, for that matter, the target might be me: a trained physicist who has been out of academia for a while and would enjoy a trip down memory lane.

The book is part of a series, in fact, that goes under the title “The Theoretical Minimum”. It was preceded by a book on classical mechanics (to which this volume makes occasional reference), and has now been succeeded by a recent book on special relativity and classical field theory. I’ve not read either of those, but I had enough fun with this one that I might.

Rovelli: Seven Brief Lessons on Physics

September 6, 2016

Seven Brief Lessons on Physics
Carlo Rovelli
(Riverhead, 2016)
96 p.

These short “lessons” were originally serialized in the Italian press, and are here collected and rendered into elegant English. Rovelli is an eminent physicist who gives us a series of meditations on developments in physics since 1900.

They are arranged in order of increasing speculation: he begins with general relativity and quantum mechanics, presenting in non-technical language the main points — space and time are dynamic and responsive, and are filled with a restless boil of quantum fields. He proceeds to give brief — and I do mean brief — overviews of modern cosmology and the Standard Model of elementary particles. All of this is solid science; questions linger, of course, and he draws attention to those loose threads and nagging problems, but basically he is describing successful theories.

In the last three sections of the book he moves to topics of greater uncertainty. The outstanding problem of how to reconcile general relativity with quantum mechanics he broaches with a very interesting discussion of theories of loop quantum gravity, the basic postulate of which is that space-time is quantized. (Rovelli is himself one of the architects of this theory.) Amazingly, and rather gratifyingly, he doesn’t even mention the other principal effort to solve this problem: string theory. This is unquestionably the book’s finest witticism, one that I imagine has raised a few consternated eyebrows in faculty lounges.

The last section specifically about physics tackles the vexing puzzles that arise at the intersection of gravity, quantum mechanics, and thermodynamics. Laying great stress on the time-irreversibility of thermodynamic processes, he argues that thermodynamics has something crucial to tell us about the uni-directionality of time itself. This is a common trope in physics circles, but, correlation not being causation, it seems to me suggestive at best. But then he reminds us of Hawking radiation, in which quantum effects near black holes actually cause them to radiate heat, and one feels a chill of delight running up the spine.

Alas, the same cannot be said of the book’s final chapter, in which Rovelli takes a step back to ponder the implications of all this for human self-understanding. He emphasizes that modern physics has revealed the world to be radically different from the way we intuitively think of it, which is fair enough, and then argues that more such intuitions — those pertaining to human freedom, for instance, or consciousness — are due to be superseded by counter-intuitive scientific explanations. There appears to be nothing more to his argument than the power of analogy. He tries to declare a peace between his commitment to the power of physics to completely describe the world, on one hand, and his commitment to the legitimacy of humanistic values, on the other, but it is far from convincing. And he is rather dispiritingly emphatic in his devotion to immanence:

“Immersed in this nature that made us and that directs us, we are not homeless beings suspended between two worlds, parts of but only partly belonging to nature, with a longing for something else. No: we are home.”

Nothing new here, of course, and this view does have about it a certain poetry — he even cites Lucretius, the patron poet of materialism — but there are such a host of issues being passed over in silence that such poetry as it possesses sounds rather hollow.

The book is written in a lyrical tone, and would be accessible, I imagine, to anyone who has an interest in the subject matter. There is only one equation — Einstein’s field equation for general relativity, which he describes as “the most beautiful of theories,” and I’ll not argue with that.