Book Review: Quantum Entanglement, Jed Brody

I just finished reading through this short monograph on quantum entanglement. The approach taken by the author is to provide what quantum entanglement is through conceptual examples. There are no wave functions or quantum states discussed in this book. At first, the reader is introduced to two very important concepts in the philosophy of physics; realism and locality. In realism, the assumption is that any physical objects have properties regardless of whether another object with agency (i.e., a person) is observing that object. A typical example of this concept is the following questions:

Does a falling tree in the forest make a sound when no one is listening? 

Realism says yes, it does. In the case of the tree, it has a center of mass that gives the tree some gravitational potential energy that upon falling is converted to kinetic energy and then generates sound waves in the air once it hits to ground. The tree had mass, potential energy, and kinetic energy which according to realism exist objectively. The opposing view is that it was the sound wave came into existence because an agent was listening. This seems absurd and it is in classical physics, but not necessarily in quantum physics.

Locality refers to the fact that observing, measuring, or disturbing objects in a region of a space does not affect other objects at arbitrary distances in that space. Here, I'm using space in an abstract sense not necessarily a Euclidean 3D space. I do note that in the book the discussion of locality is with regard to distances in 3D Euclidean geometry but I think I'm correct in that locality applies to non-Euclidean 3D spaces and this would be the more general statement. Locality is a pretty important concept in physics and is one of the reasons we got the famous EPR paper from Einstein. 

After the book presents these two concepts it gradually moves into the concept of hidden variables, that is properties of objects that can change aspects of the object when observed, but yet the variables themselves are never observed. Hidden variables satisfy realism. Much of the subsequent chapters present examples that lead to the famous Bell inequality which arises due to correlations in probabilities. The bell inequality needs to be satisfied for a theory to contain locality, if it is violated the theory is non-local. As it turns out, at least to our ability to experimental test the theory of quantum mechanics, it is a non-local theory without hidden variables because. All experiments that have been conducted to date violate Bell's inequality and suggest that correlations are instantaneous within the quantum mechanics framework. It should be noted that you could have a quantum hidden variable theory (i.e. Bohemian mechanics) that is non-local which would describe experimental results, but I guess the argument against this is why introduce hidden variable theory if a non-hidden variable theory doesn't provide any additional clarity other than satisfying realism.

It is pretty well documented, or at least we are made to think, that Einstein had serious issues with the non-local (dubbed "spooky action at a distance") behavior of quantum theory as well as the mainstream interpretations not satisfying a realism philosophical perspective. More specifically, the Copenhagen interpretation posits that the wavefunction/quantum state is more of a mathematical tool and is not necessarily a physical object since it only provides a way to extract probabilities of observable properties.

Going back to the book, chapters 3 and 4 provide different and simple experimental setups that look at probabilities and their correlations to arrive at Bell's inequality. The author then reminds the reader that quantum mechanics violates this inequality. Chapters 1-4 are written in a direct and comprehendible manner, but the truth is, I find it actually easier to understand the Bell inequality and violations of it by actually following the simple Linear algebra of quantum theory.  Trying to think through all the words describing the setup and outcomes can become burdensome. Given  the current focus on quantum computing, there are a lot of good books that go through the same results using simple linear algebra. I think it would have been easy to introduce most readers interested in this book to the basics of a qubit, Hilbert space, and corresponding operations, which could help readers understand these concepts more easily.

Chapter 5 goes through the potential inconsistencies of quantum mechanics with special relativity. Personally, I found this chapter was not delivered in the most impactful way, but it addresses the original concerns of physicists.  The final concluding sentence that indicates everything is okay in the end is:

"... the linkage between entangled particles conveys neither mass nor messages"

The author ends the book with a chapter regarding realism and its validity.  I think this is the best section of the book. The author gives their thinking on the topic of local realism by stating:

"The only fact that's (almost) certain is local realism cannot account for measured results"

Thus, local realism is a dead concept in the author's eyes As frustrating as it feels, I would agree with the author. The remainder of the chapter deals with interpretations of quantum theory from philosophical perspectives and you get a nice concrete quadrant table to decide what path to take, namely:

Find falsehoods in assumptions	Abandon locality & realism
Abandon locality & keep realism	Abandon realism & keep locality

I'm not going to go through and explain each of these because I want to leave some excitement, but I think this is the most interesting part of the book. 

I recommend reading this book if you're going to be studying quantum mechanics in any way because it will help with some of the philosophical thinking behind the theory. The reading is extremely accessible to any background and it is very short making for a good weekend read. Here's the book:

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