Which of our basic physical assumptions are wrong? Superposition of quantum states and collapse of the wave function are significant assumptions. We address the physics of the wave function, the wave function as probability, the extent of the wave function, quantum correlations, Bell’s theorem, spaces in which wave functions are formulated, and discuss recent experiments that support our interpretation.
Which of our basic physical assumptions are wrong? Superposition of quantum states and collapse of the wave function are significant assumptions. We address the physics of the wave function, the wave function as probability, the extent of the wave function, quantum correlations, Bell’s theorem, spaces in which wave functions are formulated, and discuss recent experiments that support our interpretation.
Quantum mechanics allows a remarkably accurate description of nature and powerful predictive capabilities. The analyses of quantum systems and their interpretation lead to many surprises, for example, the ability to detect the characteristics of an object without ever touching it in any way, via "interaction-free measurement," or the teleportation of an atomic state over large distances. The results can become downright bizarre. Quantum mechanics is a subtle subject that usually involves complicated mathematics -- calculus, partial differential equations, etc., for complete understanding. Most texts for general audiences avoid all mathematics. The result is that the reader misses almost all deep understanding of the subject, much of which can be probed with just high-school level algebra and trigonometry. Thus, readers with that level of mathematics can learn so much more about this fundamental science. The book starts with a discussion of the basic physics of waves (an appendix reviews some necessary classical physics concepts) and then introduces the fundamentals of quantum mechanics, including the wave function, superposition, entanglement, Bell's theorem, etc., and applications to Bose--Einstein condensation, quantum computing, and much more. The interpretation of the mathematics of quantum mechanics into a world view has been the subject of much controversy. The result is a variety of conflicting interpretations, from the famous Copenhagen view of Bohr to the multiple universes of Everett. We discuss these interpretations in the chapter "What is a wave function?" and include some very recent advances, for example, quantum Bayesianism, and measurements of the reality of the wave function.
The wave function gives not the density of stuff, but gives rather (on squaring its modulus) the density of probability. Probability of what, exactly? Not of the electron being there, but of the electron being found there, if its position is ‘measured’. Why this aversion to ‘being’ and insistence on ‘finding’? The founding fathers were unable to form a clear picture of things on the remote atomic scale . John S. Bell (1990) Introduction The physical meaning of the wave function is an important interpretative problem of quantum mechanics. Notwithstanding nearly ninety years of development of the theory, it is still an unsolved issue. During recent years, more and more research has been done on the ontological status and meaning of the wave function (see, e.g. Monton, 2002; Lewis, 2004; Gao, 2011a, 2011b; Pusey, Barrett and Rudolph, 2012; Ney and Albert, 2013). In particular, Pusey, Barrett and Rudolph (2012) demonstrated that under certain non-trivial assumptions such as the preparation independence assumption, the wave function of a quantum system is a representation of the physical state of the system. This poses a further question, namely whether the reality of the wave function can be argued without resorting to non-trivial assumptions. Moreover, a harder problem is to determine the ontological meaning of the wave function, which is still a hot topic of debate in the realistic alternatives to quantum mechanics such as the de Broglie–Bohm theory or Bohmian mechanics (Belot, 2012). In this chapter, we will first give a clearer argument for the reality of the wave function in terms of protective measurements, which does not depend on non-trivial assumptions and can also overcome existing objections. Next, based on an analysis of the mass and charge properties of a quantum system, we will propose a new ontological interpretation of the wave function. According to this interpretation, the wave function of an N -body system represents the state of ergodic motion of N particles.
Quantum mechanics is an immensely successful theory, occupying a unique position in the history of science. It has solved mysteries ranging from macroscopic superconductivity to the microscopic theory of elementary particles and has provided deep insights into the nature of vacuum on the one hand and the description of the nucleon on the other. Whole new fields such as quantum optics and quantum electronics owe their very existence to this body of knowledge. However, despite the stunning successes of quantum mechanics, there is no general agreement on the conceptual foundations and interpretation of the subject. The theory provides unambiguous information about the outcome of a measurement of a physical object. However, many feel that it does not provide a satisfactory answer to the nature of the “reality” we should attribute to the physical objects between the acts of measurement. The conceptual difficulty comes about because the wave function |ψ〉 is usually given by a coherent superposition of various distinguishable experimental outcomes. If we denote the collection of states that represent the possible outcomes of an experiment by |ψ j 〉, then |ψ〉 = ∑ j c j |ψ j 〉 where c j = 〈ψ j |ψ〉. The probability of the outcome |ψ j 〉 is P j =|c j | 2 . In the process of measurement, the so called collapse of the wave function takes place and a single, definite state |ψ i 〉 of the physical object is chosen. The difficulty comes about in the interpretation of the mechanism by which this definite state is chosen from amongst all the possible outcomes.
In the interpretation of Quantum Mechanics, there were four major mistakes done at different levels: (1)A misinterpretation of Bell’s theorem in which the original intent did not include non-locality, but as a test to see whether or not a particle has a certain property that can be measured. (2)A misinterpretation of the disagreement between Einstein and Bohr. Einstein’s objection to the collapse of the wave function implied a spooky action at a distance, while Bohr insisted on the instantaneous collapse of the wave function which he mistook to be a real wave. (3)A misinterpretation that the wave function represents a real wave when in actuality it represents the possible states of a quantum system before a measurement. (4)When Bell’s theorem was violated by a quantum system, those violations were misinterpreted as evidence of an instantaneous collapse of the wave function and non-locality. We will argue: there is no collapse of the wave function. Bell’s theorem is not about non-locality. There is no spooky action at a distance. And Quantum Mechanics is about measuring quantities at the microscopic scales and in doing so, these quantities are altered. So what we get is partial knowledge. But in spite of that obstacle, we still get a theory of reality with considerable success.
It is argued (Part A) that quantum mechanics can be derived as a principle-based dynamical framework, the basic equation of which is an alternative form of the Hamilton-Jacobi equation. Schrodinger's equation obtains as a result of linearising that equation, and so-called wave functions can be given no straightforward physical interpretation. It is suggested, partly in relation to a theorem by Gromov, that a finite action quantum would make it practically inevitable, for purposes of prediction, to resort to a probabilistic formulation. The structure of the space of square-integrable solutions of the Schrodinger equation happens to lend itself to the introduction of the appropriate kind of predictive scheme. Investigating the nature and scope of such a scheme is the subject of Part B. It is shown that basic features of the formalism of quantum theory, like composition rules for 'amplitudes' or the 'Born' probability rule, can be derived independently of any physical assumptions. A generalisation of the basic formalism using tensor product composition appears to be required if all correlations are to be extracted from locally accessed data. A detailed discussion of quantum teleportation leads to the conclusion that a 'one-shot' account leads to a distorted picture of what is actually achieved. An analogy with classical cryptography is made and the statistical significance of the 'transfer', which does not require introducing any novel form of 'quantum information', is emphasised. Results obtained over the last decade using the extended formalism of positive operator-valued measures are reviewed and discussed. These lend further support to the idea that the set of basic 'quantum' rules functions as a general kind of probabilistic scheme for prediction, the structural features of which are not constrained in any direct way by the underlying physics. On the other hand, the very existence of such a predictive framework hinges on selecting a particular class of solutions of the Schrodinger equation, which selection has been incorrectly interpreted as reflecting a physical necessity.