Alastair I. M. Rae

This is a well written book with very good explanations on the subjects it covers; from quantum mechanics to economics. However, I find that neither the case for reductionism has been made nor his arguments are free from logical flaws.

Reductionism, according to Mr Rae, is the principle that "the properties of something being investigated can be understood as emerging from the properties of its component parts and an understanding of how they (the parts) interact". So if we understand how higher level properties arise from the properties of its parts, then (Occam's Razor) we don't need additional assumptions to explain these higher level properties.

In general, when we talk about physical and inanimate "somethings", reductionism is on a solid footing, most of the time. I said "most of the time" because even here, as Rae explains, there is the problem of quantum measurement which requires an additional assumption (the wavefunction collapse) to make theory consistent with experimental results and hence falsifies reductionism if that interpretation of quantum mechanics is correct.

But where Rae gets really into trouble I believe is when he starts using reductionism to explain things like consciousness and society at large. And I think this is partly due to a confusion on his part. Since everything is made up of fundamental particles, then, according to reductionism, the laws of quantum mechanics should explain everything. The problem with this statement is twofold: first, as mentioned above there is the quantum measurement problem. Second, if we try to explain consciousness, something that we do not presently understand (and probably never will), based on quantum mechanics we will find that there are so many atoms and particles involved in the human body that to try to explain their interactions through the quantum mechanics equations would be impossible from a computational point of view - i.e., the equations will be unsolvable.

So in the case of consciousness, the question that arises is this: What does it mean to explain the properties of something that we do not understand based on computations that we cannot perform? At best what we can say about consciousness today (and probably forever) is that molecules and neurons do their "thing" and consciousness emerges from that work. But based on the reductionism's own principles (Occam's Razor), since this explanation does not explain anything we don't need to invoke reductionism and hence we don't need to know all the intricacies of human biology and quantum mechanics. So today we can explain the properties of consciousness equally well by saying "the properties are what they are and they emerge from some stuff that our bodies do"!

Even at an abstract level Rae's ideas are a bit problematic. Reductionism in principle should work both ways. That is, one can start at higher levels and then drill down to the component parts to explain the high level properties. Or one could start at the lower levels and predict the properties of the higher level. So if we had a computer that has been programmed with all the knowledge we have about quantum mechanics and is powerful enough to do computations that we cannot presently perform, will the computer then predict form the laws of quantum mechanics consciousness, implement it and become self-aware? But how would the computer figure that out when it had never experienced consciousness prior to this - only the laws of quantum mechanics?

I think a lot of people will agree with Rae that everything including consciousness is the result of a physical process. But this is an assumption and it is not shared by many other folks who believe in the supernatural, including Karl Popper, the father of the scientific methodology we use today, who thought that there is a "ghost" in the machine and that consciousness cannot be physical.

Finally, Rae does not use reductionism consistently. That is, when he talks about human societies, the "parts" are now people, not the fundamental particles, which he uses to explain the properties of solids, liquids and gasses! And that's problematic because the fundamental parts of everything are always going to be the fundamental particles and the laws of quantum mechanics. To be consistent, one needs to stick all the way through and not to keep aggregating up to new "parts" because we don't know how these new parts are generated based on the fundamental laws of physics.… (más)

Indeholder "Preface to Second Edition", "Preface to First Edition", "Chapter 1. Introduction", " 1.1 The Photoelectric Effect", " 1.2 The Compton Effect", " 1.3 Line Spectra and Atomic Structure", " 1.4 De Broglie Waves", " 1.5 Wave-Particle Duality", " 1.6 The Rest of this Book", "Problems", "Chapter 2. The One-Dimensional Schrödinger Equations", " The Time-Dependent Schrödinger Equation", " The Time-Independent Schrödinger Equation", " Boundary Conditions", " Examples", " Quantum Mechanical Tunneling", " The Harmonic Oscillator", " Problems", "Chapter 3. The Three-Dimensional Schrödinger Equations", " 3.1 The Wave Equations", " 3.2 Separation in cartesian Coordinates", " 3.3 Separation in Spherical Polar Coordinates", " 3.4 The Hydrogenic Atom", " Problems", "Chapter 4. The Basic Postulates of Quantum Mechanics", " 4.1 The Wave Function", " 4.2 The Dynamical Variables", " 4.3 The Properties of Hermitian Operators", " 4.4 Probability Distributions", " 4.5 Commutation Relations", " 4.6 The Time Dependence of the Wave Function", " 4.7 The Measurement of Momentum by Compton Scattering", " 4.8 Degeneracy", " Problems", "Chapter 5. Angular Momentum I", " 5.1 The Angular-Momentum Operators", " 5.2 The Eigenvalues and Eigenfunctions", " 5.3 The Experimental Measurement of Angular Momentum", " 5.4 A General Solution to the Eigenvalue Problem", " Problems", "Chapter 6. Angular Momentum II", " 6.1 Matrix Representations", " 6.2 Pauli Spin Matrices", " 6.3 Spin and the Quantum Theory of Measurement", " 6.4 The Addition of Angular Moments", " 6.5 Spin-Orbit Coupling", " 6.6 The Zeeman Effect", " Problems", "Chapter 7. Time-Independent Perturbation Theory and the Variational Principle", " 7.1 Perturbation Theory for Non-Degenerate Energy Levels", " 7.2 Perturbation Theory for Degenerate Levels", " 7.3 The Variational Principle", " Problems", "Chapter 8. Time Dependence", " 8.1 Time-Independent hamiltonians", " 8.2 The Sudden Approximation", " 8.3 Time-Dependent Perturbation Theory", " 8.4 Selection Rules", " 8.5 The Ehrenfest Theorem", " 8.6 The Ammonia Maser", " Problems", "Chapter 9. Scattering", " 9.1 Scattering in One Dimension", " 9.2 Scattering in Three Dimensions", " 9.3 The Born Approximation", " 9.4 Partial Wave Analysis", " Problems", "Chapter 10. Many-Particle Systems", " 10.1 General Considerations", " 10.2 Isolated Systems", " 10.3 Non-Interacting Particles", " 10.4 Indistinguishable Particles", " 10.5 The Helium Atom", " 10.6 Systems with More than Two Indistinguishable Particles", " 10.7 Scattering of Identical Particles", " Problems", "Chapter 11. The Conceptual Problems of Quantum Mechanics", " 11.1 The Conceptual Problems", " 11.2 Hidden-Variable Theories", " 11.3 Theories of Measurement", " 11.4 The Problem of Reality", " Problems", "Bibliography", "Hints to Solution of Problems", "Index".
Lærebog i kvantemekanik.… (más)

If he ended the book two chapters earlier, this would've actually been 4 stars.

Alastair Rae did an excellent job describing many of the perplexing quantum phenomena. Rather than focusing only on the common bewildering experiments (e.g. the double slit), he describes many experiments involving the polarization of photons. The results of the described experiments are truly fascinating. I really enjoyed reading it.

Unfortunately, as we come to the end of the book, he cannot leave well enough alone. Rather than leaving us with the mystery of the quantum world, he decides to describe some of the "possible" explanations for the previously described phenomena. This is where the book takes a turn from scientific experimentation to outright made-up stories. Multiple universes, other dimensions, and all of this other science fiction is suddenly viewed as a viable explanation at the end. Sadly, the book that held my attention throughout did not end on a high note.… (más)