226 My God, He Plays Dice! Entanglement. Chapter This chapter on the web informationphilosopher.com/problems/entanglement
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1 226 My God, He Plays Dice! Entanglement Chapter This chapter on the web informationphilosopher.com/problems/entanglement
2 Entanglement 227 Entanglement Entanglement is a mysterious quantum phenomenon that is widely, but mistakenly, described as capable of transmitting information over vast distances faster than the speed of light. It has proved very popular with science writers, philosophers of science, and many scientists who hope to use the mystery to deny one or more of the basic concepts underlying quantum physics. Some commentators say that nonlocality and entanglement are a second revolution in quantum mechanics, the greatest mystery in physics, or science s strangest phenomenon, and that quantum physics has been reborn. 1 They usually quote Erwin Schrödinger as saying I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. 2 Entanglement is really just an elaborate extension of the Einstein-Podolsky-Rosen Paradox we covered in chapter 26, but we decided to devote this and the next chapter to explain how the tools of information philosophy and Albert Einstein s objective reality can clarify and demystify entanglement and in particular Schrödinger s famous cat that is simultaneously dead and alive. Einstein s goal for EPR was to show that quantum physics is an incomplete statistical theory which cannot provide complete information about an individual and indeterministic event. One goal of quantum physicists who believe that Schrödinger s wave equation is a complete and a deterministic description of the universe, and perhaps an infinite number of parallel universes, is to deny the existence of indeterminism and ontological chance. Schrödinger s thinking is thus behind many of the radical interpretations of quantum mechanics that deny the Bohr- Heisenberg Copenhagen Interpretation (see chapter 38). Despite his doubts about chance, we can use Einstein to represent indeterminism and Schrödinger for determinism. Chapter See for example Louise Gilder s excellent book, The Age of Entanglement. 2 Mathematical Proceedings of the Cambridge Philosophical Society, Volume 31, Issue 04, October 1935, pp
3 228 My God, He Plays Dice! Chapter Schrödinger knew that his two-particle wave function, in sixdimensional configuration space, could not have the same simple interpretation as the single particle, which can be visualized in ordinary 3-dimensional coordinate space. And he is right that entanglement exhibits a richer form of the action-at-a-distance or nonlocality that Einstein had identified in the collapse of the single-particle wave function as early as But the main difference in entanglement is that two particles acquire new properties instead of one, and they appear to do it instantaneously (at faster than light speeds), just as Einstein saw decades earlier in the case of a single-particle measurement, where the finite probability of appearing at various distant locations collapses to zero at the instant the particle is found somewhere. In his 1935 papers (and his correspondence with Einstein), Schrödinger described the two particles in EPR as entangled in English, verschränkt in German, which means something like cross-linked. It describes someone standing with arms crossed. Schrödinger was enthusiastic about the Einstein-Podolsky- Rosen attack in 1935 on quantum mechanics as incomplete and Einstein shared Schrödinger s enthusiasm for a deterministic theory for a short while. In fact, the entanglement of two indistinguishable particles can be completely understood with Paul Dirac s principle of superposition, his axiom of measurement, and his projection postulate. These three fundamentals of quantum mechanics already explain the mysterious phenomena that are impossible in classical mechanics, notably the one-particle mystery in the two-slit experiment that Richard Feynman calls the only mystery (chapter 34). Entanglement is not a second mystery. Information philosophy analyzes both the single-particle and two-particle wave function collapses as a question of who can know what when, that is, what new information is created at each moment about the particle or particles.
4 Entanglement 229 Entanglement depends on two quantum phenomena that are simply impossible in classical physics. One is nonlocality (chapter 23). The other is nonseparability (chapter 27). Each of these might be considered a mystery in its own right, but fortunately information physics (and the information interpretation of quantum mechanics) can explain them both, without equations, in a way that should be understandable to the lay person. This may not be good news for the science writers and publishers who turn out so many titles each year claiming that quantum physics implies that there are multiple parallel universes, that the minds of physicists ( conscious observers ) are manipulating quantum reality, that there is nothing really there until we look at it, that we can travel backwards in time, that things can be in two places at the same time, that we can teleport material from one place to another, and of course that we can can send signals faster than the speed of light. All fun topics but nonsense! Einstein s concern in 1905 was that a light wave (today a wave function ψ) for an isolated free particle evolves in time to occupy all space. All positions become equally probable. Yet when we observe the particle, it is always located at some particular place. This does not prove that the particle had a particular place before the observation, but Einstein had a commitment to elements of reality that he thought no one could doubt. One of those elements is a particle s position. He asked the question, Does the particle have a precise position the moment before it is measured? The Copenhagen answer was sometimes no, more often it was we don t know, or Don t even ask? In his first discussion of the two-particle problem, Einstein simply used conservation of linear momentum to calculate the position of the second particle. Although conservation laws are rarely cited as the explanation of entanglement, they are the reason that two entangled particles always produce perfectly correlated results. If the results were not always correlated, the implied violation of a fundamental conservation law would be a much bigger story than entanglement itself, as interesting as that is. Chapter 20 29
5 230 My God, He Plays Dice! Visualizing Entanglement and Nonlocality Chapter Schrödinger said that his wave mechanics provided more visualizability (Anschaulichkeit) than the damned quantum jumps of the Copenhagen school, as he called them. He was right. But we must focus on the probability amplitude wave function of the prepared two-particle state, and not attempt to describe the paths or locations of independent particles - at least until after some measurement has been made. We must also keep in mind the conservation laws that Einstein used to describe nonlocal behavior in the first place. Then we can see that the mystery of nonlocality for two particles is primarily the same mystery as the singleparticle collapse of the wave function. But there is an extra mystery, one we might call an enigma, of the nonseparability of identical indistinguishable particles. As Richard Feynman famously claimed, there is only one mystery in quantum mechanics. We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by explaining how it works. We will just tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics. 3 The only difference in two-particle entanglement and nonseparability is that two particles appear simultaneously (in their original interaction frame) when their wave function collapses. In the time evolution of an entangled two-particle state according to the Schrödinger equation, we can visualize it - as we visualize the single-particle wave function - as collapsing when a measurement is made. The discontinuous jump is also described as the reduction of the wave packet. This is apt in the two-particle case, where the superposition of + - > and - + > states is projected or reduced: to one of these states, and then further reduced to the product of independent one-particle states. 3 The Feynman Lectures on Physics, vol III, 1-1
6 Entanglement 231 In the two-particle case (instead of just one particle making an appearance), when either particle is measured we know instantly those now determinate properties of the other particle that satisfy the conservation laws, including its location equidistant from, but on the opposite side of, the source. We have created some animations that demonstrate measurements of two entangled particles. Please view them on our website here: einstein/#two-particle The Importance of Conservation Laws in Entanglement Conservation laws are the consequence of extremely deep properties of nature that arise from simple considerations of symmetry. We regard such laws as cosmological principles. Physical laws do not depend on the absolute place and time of experiments, nor their particular direction in space. Conservation of linear momentum depends on the translation invariance of physical systems, conservation of energy the independence of time, and conservation of angular momentum the invariance under rotations. If two entangled particles start out with equal properties or even perfectly opposite properties, then in the absence of iteractions with other particles, there is no way one of them can ever change its properties without an equal compensating change in the other particle. This completely explains the perfect correlations between entangled particles, no mattr how far apart they may be found after any measurement. Chapter 20 29
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