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.