A second review of "Beyond Weird" by Philip Ball

Amazon link

Roy Simpson has written his own review of the above book which I'm pleased to guest-post here. He previously guest-reviewed "The Order of Time" by Carlo Rovelli.

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Review of Philip Ball: Beyond Weird (2018)

By Dr. Roy Simpson, October 2018

This review was requested by Nigel Seel and could be read in conjunction with his review of this book.

In reviewing a book such as this it is tempting to first review the style and content of the book, then secondly to add comments concerning one's own view and approach to these matters.

Having been familiar with the basic equations of quantum mechanics for a long time I am not able to say for sure whether the book actually requires the prior familiarity with quantum mechanics suggested in the Seel review. Certainly one has to be interested in physics and its foundations. The book contains a good introduction to the structure and key components of quantum mechanics and eventually leads us towards the questions of interpretation and meaning.

The unusual nature of the formulation of the subject is neatly captured in a chapter comparing the axioms of quantum mechanics with other physics theories. For example we have Newton's Laws:

1. Every moving object keeps moving at the same speed if no force is applied to it. If it is still to begin with, it stays still.

2. If a force is applied to an object it accelerates it in direct proportion to that force .. .

3. For every force that one body exerts on another, the other body exerts an equal force back in the opposite direction.

Special Relativity can be presented with similar physically comprehensible (and experimentally checkable) axioms. By contrast for quantum mechanics we have:

1. For every system, there is a complex Hilbert Space H.

2. States of the system correspond to projection operators onto H.

3. Those things that are observable somehow correspond to eigenprojectors of Hermitian operators.

4. Isolated systems evolve according to the Schrödinger equation.

Now all physics theories have a mathematical content and even Newtonian mechanics can be presented using mathematical structures such as symplectic manifolds, Noetherian moments and differential forms. However Newtonian theory has a basic physical form as stated above. The issue is: what is the Quantum equivalent?

Without an answer to that question it can be difficult to be convinced that the theory has been fully understood, despite the success of the mathematical formulation. So this situation is deemed philosophically unsatisfactory and also impedes progress towards reconciling quantum theory with General Relativity (which also has a physical explanation as well as a successful mathematical form).

The book takes a long look at the most basic interpretation (as these attempts to connect the mathematics with any physical reality are called) of quantum mechanics, called the Copenhagen interpretation.

The book then follows with a more cursory and dismissive view of the Bohm-de Broglie interpretation as an example of a key distinction between such interpretations: are they Ontic (the mathematical entities represent real physical structures in the usual physics sense); or are they Epistemic (the mathematical entities describe the observer's knowledge of the – perhaps unknowable – physical system).

The Copenhagen leans towards the Epistemic, whereas the Bohm is Ontic. Other interpretations are also discussed by the book such as the very Epistemic Qbism interpretation and the Ontic GRW and Penrose-Diosi models. These latter are not just interpretations but are modifications of some of the mathematics (making a physics explanation easier, in the latter case by invoking gravity).

There is also a long and useful discussion of “decoherence”. However this book does not include any mathematics and although that makes the book easier for some audiences, it does detract from some clarity and rigour in the arguments the author wishes to make.

Another interpretation dismissively discussed in the book is the Many Worlds Interpretation. A recent summary of this section is available in an online article by the author here.

There are over one dozen interpretations of quantum mechanics and they are not all discussed in the book. New interpretations appear regularly with an example “The Montevideo Interpretation” (which this reviewer has not yet studied). So the book is not comprehensive in its account of interpretations.

The book gives a long account of the Bell Theorem, which is an experimentally checked theorem implying the non-locality and non-contextuality of quantum mechanics. The discussion here is interesting, but this reviewer has uncovered a recent examination of the Bell Theorem which is more precise about the nature of the “superluminal effects” involved in the statement of the theorem.

Apparently there were two forms of Bell's Theorem: a “coarser” form, and 10 years later a more precise form, which makes clearer what is and is not prohibited by the theorem. However the book does not discuss this level of distinction, and the possible consequences.

The book eventually focuses on the idea of an information-based interpretation of Quantum Mechanics, and recent work related to this. This area of work is largely stimulated by the subject of Quantum Computation, and the intriguing question as to whether all of the “engineering” problems in that area are purely engineering problems and not also some scientific (i.e. quantum interpretational).

Of particular interest is the idea of “quantum reconstruction” and “information causality”. Here the attempt is to address the lack of a physics basis by trying to find one in axioms - often based on “information” based ideas. From the present reviewer's perspective this work is encouraging in the sense that the results may be converging on a class of invariant mathematical objects that are being studied in 21st century mathematics.

So overall the book is a good comprehensive account of quantum interpretation and meaning from an early 21st century perspective, especially as viewed by a physical-chemist who has a “user” view of quantum mechanics.

"Beyond Weird" - Philip Ball

Amazon link

I mentioned Peter Woit's generally favourable review of this book in a previous post.

"Beyond Weird", despite its cheesy title, makes a good impression from the very start. Ball is an engaging writer who knows his stuff and doesn't patronise the reader. It's like he's talking to a curious colleague who uses quantum theory (a chemist or applied physicist, for example) but doesn't research it. The tone would work well for a recent physics graduate or someone in the final stages of their QM course.

The problem with quantum mechanics is that the mathematics makes plenty of sense in itself (Schrödinger's equation and its many solutions in concrete circumstances such as the structure and behaviour of the hydrogen atom, for example)  but the many constructs of the theoretical apparatus don't align with any compelling concept of 'reality'. To properly engage with the 'interpretation problem' you have to understand the maths, which means taking a course first.

Before I studied quantum mechanics (with the Open University - SM358) I thought I had a grasp - as an educated person with a technical background - of quantum theory, at least at a conceptual level. I knew, or thought I knew, about the uncertainty principle, the wave function and its collapse, the double slit experiment and its paradoxical interpretation and so on.

I spent the first third of my QM course learning a lot of details about Schrödinger's equation in its time dependent and stationary forms, about spin spaces, kets, operators, expansions in terms of eigenfunctions, Hilbert spaces and so on. I was internalising this complex apparatus and making it work and I couldn't anchor any of it into the real world. I was confused, baffled, a sufferer from extreme cognitive dissonance. It was not pleasant.

Eventually I managed to organise all this stuff into something which kind of made internal sense, and kept reminding myself that in the end its only function was to produce a number between zero and one as regards observable outcomes. I had become acculturated, but I still didn't know what any of it really told me about reality.

And I think that only after this 'preparation' is a reader really able to engage profitably with Philip Ball's book.

Ball is good on superpositions and what it would mean if they were observable. He's as good as you could expect on decoherence and einselection, although it would have been useful to have had a more explanatory appendix given its centrality in accounting for 'collapse' (but perhaps that's more a signifier for my own lack of clarity). He is also good at debunking some of the more ontological-realist views of the wavefunction. There are also clear accounts of Bell's theorem and quantum computing.

And then it starts to unravel. Ball clearly has a thing about the many-worlds interpretation (which has a stronghold at his alma mater, Oxford). His customary cool deserts him for visceral distaste. His debunking is anticlimactic, however, depending on philosophical sophistry about identity-continuity before and after 'splitting' of worlds. The MWI does not hang on such arguments.

In the final chapters things get worse. Ball's enthusiasm for 'it from bit', an information-centric approach to the interpretation problem, gets the better of him. Unfortunately the ideas swirling around in this currently active area of investigation are even more formless and confusing than the more conventional ideas he's been debunking all along. We finish the book shaking our heads and asking, 'What was that about?'.

If you read one book on the interpretation of quantum mechanics, and you have studied QM as an undergraduate, this may well be the book for you. It will confirm that you were right to be concerned that the Copenhagen stuff you were taught does not put an end to the discussion, and it will straighten out and firm up many of your questions and half-formed, tentative conclusions.

Just don't think it will give you any final answers: there are none.

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See also Roy Simpson's review: "A second review of "Beyond Weird" by Philip Ball".

The Copenhagen ontology

Scott Aaronson has an interesting post on his personal interpretation of quantum mechanics (he's probably a 'none-of-the-above' but with a revealed preference for the MWI).

He is, however, particularly scathing about the so-called 'Copenhagen Interpretation'.

"As for Copenhagen, I’ve described it as “shut-up and calculate except without ever shutting up about it”!  I regard Bohr’s writings on the subject as barely comprehensible, and Copenhagen as less of an interpretation than a self-conscious anti-interpretation: a studied refusal to offer any account of the actual constituents of the world, and—most of all—an insistence that if you insist on such an account, then that just proves that you cling naïvely to a classical worldview, and haven’t grasped the enormity of the quantum revolution."

This seems spot on.

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'You may not be interested in ontology, but ontology is interested in you.'

What happens when a convinced adherent to the Copenhagen Interpretation is asked straight out:

"... what constitutes the "act of measurement" in a world without sentient beings? In such a world (even in a world with sentient beings) there are just physical systems with atoms and molecules all under the rule of Schrödinger's equation. So when does "collapse" occur?

When can it be decided that a measurement has been made if there are no sentient beings?

If everything is made up of particles, and the particles are under the governance of Schrödinger's equation and unitary evolution, when do "measurement" and "collapse" occur? In a world without sentient beings, what would "when the new data arrives" refer to?"

Luboš Motl answers commentator Ricky's question above (in comment 16 here):

""The conceptually right [way] to describe a world without sentient beings is that an unspecified and unknown initial wave function evolves unitarily according to Schrödinger's equation and never collapses because it's only measurements that may collapse and there are none in your theory. The complete "diffusion" of the wave function (into the linear superposition of dead and alive cats and all objects, small and big, in the most general superpositions of all conceivable states) may be said to be a problem - but another problem is that the initial state is totally unknown, too.

"It makes no sense to say that the initial wave function is a particular thing because one may only say that the wave function is a particular thing [if] something is [a] measurement - if a sentient being becomes aware of the result of some measurement. This is not happening in a universe without sentient beings. So there's no specific science to discuss in a universe without sentient beings at all. The laws may still be the same as they are in our world but they won't be applied in any particular situation because there are no particular situations or particular special wave functions in a world where no one ever measures anything.

"Einstein asked whether there is any Moon over there if no one looks. In practice, classical physics is a good enough approximation, so one may assume that the Moon is pretty much there even before observers look etc. But conceptually, if you care about similar objects for which the quantum effects are strong, the right answer is that the Moon just isn't at any particular location and has no other particular properties if no one looks. The wave function isn't a real object of any type. Its amplitudes can't be measured in a single repetition of the situation. It is only a template storing information allowing to predict probabilities of things that actually can be measured - the observables."

The arch-exponent of Copenhagenism appears to believe that the universe is really some unitary evolution in Hilbert space, presumably with space-time somehow emergent. Because ontology.

Two unenviable choices

More quirky writing from Dr Michelsen, describing the two main options for understanding what quantum mechanics really means. This surely answers the question; "How would Jesus have explained it?"

"Dr. Xavier E. Rox believes in predictability. There can be no collapse, no random events. Physics is deterministic, just like the old classical physicist, Dr. Diehard, says. Dr. Rox observes, “Diehard’s only problem is that his math is wrong. Physics follows the Schrödinger equation.”

Of course, to be consistent with experiment, Dr. Rox must assume that at every instant, the quantum state of the entire universe, including himself(!), splits into a new superposition of all possible results. “Better complexity and confusion than uncertainty,” he declares, much to the dismay of Werner Heisenberg.

On Sunday, Dr. Rox goes to the Church of Duplicity, and worships a rapidly growing list of very similar gods.

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Dr. Ophelia C. Cam retorts, “Stuff and nonsense! I can only ever perceive one world, so it is unscientific to talk about others. They are, by definition, outside the possibility of observation, and therefore, also by definition, outside the realm of science.” She believes that each observer, with each observation, collapses her own wave-function of the universe. That is, to be consistent with experiment, she must assume that each observer has her own wave-function for the universe, which collapses only when its owner makes an observation. This means the quantum state of the universe is different for different observers.

How can a wave-function collapse? How can a wave-function be subjective, and not absolute? “I don’t know, and I don’t care,” says Dr. Cam. “Like it or not, it is what it is. The measured results provide a single reality for all observers, so there is no physical consequence of personalized wavefunctions.”

On Wednesdays, Dr. Cam goes to the Church of One Mind, where she prays to a very lonely God.

Who is right, then, Dr. Rox or Dr. Cam? This is not a scientific question, since both professors make the same experimental predictions. Whom you believe depends on which church you attend."

You see what he did there? With the names?

Satire aside, it's interesting that this is the best that the greatest minds on the planet have been able to come up with, in a century of trying. We're missing something important.