by Amir D. Aczel
Four Walls Eight Windows, $25

Reviewer: Laurence Marschall
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In the world you and I inhabit, no two snowflakes are exactly the same, and, like it or not, we can never be in two places at the same time.

But in the world of quantum mechanics, the microscopic realm described by mathematician Amir D. Aczel in his new book, Entanglement, distinctions of "this" and "that," of "here" and "there," are not so clear. A single object can appear to be two; two objects can act as one. Take a simple example: An atom emits two gamma rays simultaneously, one speeding off toward the east, the other toward the west. In the strangely random world of quantum mechanics, even nature itself doesn't know the properties of these particles until an observer measures them. And by the very act of measuring the particle, the observer determines the particle's properties.

But here's where things get really weird: Once you determine how the eastward gamma ray is vibrating-up or down or side to side-you know instantaneously how the westward gamma ray is vibrating, even if it is half a universe away. Quantum laws require that the two particles be treated as the same entity; by measuring the properties of one particle in an entangled system, you somehow forge a rigid link with the other, no matter how distant it is. This is the essence of entanglement, one of the characteristically bizarre features of the quantum world that allows a signal to travel at infinite speed, faster by far than the speed of light. Albert Einstein, who was particularly troubled by this violation of the universal speed limit, called it "spooky action at a distance" and regarded it as evidence that quantum mechanics was a flawed theory, due for a complete overhaul.

That overhaul has never occurred. As recounted by Aczel, the theoretical and experimental basis for quantum mechanics has grown ever stronger. In the 1960s, Irish physicist John Bell proposed a way to put entanglement to the test, and in the last few decades, clever experimenters around the world have successfully applied his method. In the 1990s, Swiss physicist Nicholas Gisin sent laser beams in opposite directions down fiber-optic telephone lines and then simultaneously determined the properties of the pairs of outrushing photons when they were 10 miles apart-proof that an entangling signal traveled at least 10 million times the speed of light.

Results like this naturally raise questions of whether instantaneous messages could be sent through space or whether teleportation (as in "beam me up, Scotty") might be achieved. Aczel is careful to weed out the crazy ideas from the bold ones and provides some thoughtful comments on why we may never be able to communicate faster than light or teleport anything even as small as a flea. Indeed, entanglement may have few practical effects beyond the subatomic domain. Yet it remains one of the knottiest problems in theoretical physics, raising tantalizing questions about the very nature of reality.