This is an attempt to reconcile the formalisms of quantum mechanics with ordinary macroscopic experience. Thus the formal superposition of alternative physical states is interpreted as an actual superposition of differing “copies” of the same object or objects. Chance events usually regarded as mutually exclusive are here assumed to have simultaneous effects on different copies of the same system, including its human observers. In this way, initially superposed copies become separated and undergo differential changes. Reconvergence of differentiated copies gives rise to familiar diffraction phenomena. Specific physical examples and human experiences are treated, and the Schrödinger equation is derived.
This is an attempt to reconcile the formalisms of quantum mechanics with ordinary macroscopic experience. Thus the formal superposition of alternative physical states is interpreted as an actual superposition of differing “copies” of the same object or objects. Chance events usually regarded as mutually exclusive are here assumed to have simultaneous effects on different copies of the same system, including its human observers. In this way, initially superposed copies become separated and undergo differential changes. Reconvergence of differentiated copies gives rise to familiar diffraction phenomena. Specific physical examples and human experiences are treated, and the Schrödinger equation is derived.
Since its very beginning, quantum mechanics has been developed to deal with systems on the atomic or sub-atomic scale. For many decades, there has been no reason to think about its application to macroscopic systems. Actually, macroscopic objects have even been used to show how bizarre quantum effects would appear if quantum mechanics were applied beyond its original realm. This is, for example, the essence of the so-called Schrödinger cat paradox (Schrödinger, 1935). How-ever, due to recent advances in the design of systems on the meso- and nanoscopic scales, as well as in cryogenic techniques, this situation has changed drastically. It is now quite natural to ask whether a specific quantum effect, collectively involving a macroscopic number of particles, could occur in these systems. In this book it is our intention to address the quantum mechanical effects that take place in properly chosen or built “macroscopic” systems. Starting from a very naïve point of view, we could always ask what happens to systems whose classical dynamics can be described by equations of motion equivalent to those of particles (or fields) in a given potential (or potential energy density). These can be represented by a generalized “coordinate” φ( r , t ) which could either describe a field variable or a “point particle” if it is not position dependent, φ( r , t ) = φ( t ).
Construal of observable facts or events, that is, the manner in which we understand reality, is based not only on mathematical formulas of a theory suggested as a reasonable explanation for physical phenomena (like general relativity or quantum mechanics), but also on a mathematical model of reasoning used to analyze and appraise statements regarding the objective world (for example, logic of one type or the other). Hence, every time that a certain construal of reality encounters a problem, there is a choice between a modification to the mathematical formalism of the physical theory and a change in the model of reasoning. A case in point is negative construal of quantum superposition causing the problem of definite outcomes. To be sure, according to the said construal, it is not the case that a system being in a superposition of states is exclusively in one of the states constituting the superposition, which in turn implies that macroscopically differing outcomes of observation may appear all at once. The usual approach to the problem of definite outcomes is to modify the quantum mathematical formalism by adding to it some extra postulates (for instance, the postulate of wave function collapse). However, since none of the extra postulates proposed so far has gained broad acceptance, one may try another avenue to resolve the problem, namely, to replace logic with an alternative mathematical model of reasoning. This possibility is studied in the present paper.
In the given controversy, Einstein was right; the Copenhagen quantum mechanics has been based on physically unacceptable assumptions. And also later, Bell's inequalities have been mistakenly interpreted: holding true only in the classically deterministic model and not for the Schrödinger solutions when the initial state of the evolving system is represented by a (not fully known) set of different classical states; and the measured results in individual events are statistically distributed. The structure of Hilbert space formed by the solutions of the corresponding Schrödinger equation cannot be arbitrarily defined; it must be adapted to the corresponding physical system. Any Schrödinger state is then equivalent to a superposition of the solutions of the corresponding Hamilton equations, while all solutions of these equations form a greater set. However, the usual energy quantization approach represents phenomenological characteristics only, and the proper cause should be interpreted on other physical grounds. The actual source of quantum phenomena may hardly be explained without the participation of all interactions between the corresponding physical objects; their not yet fully known properties surely play an important role. The results obtained in experiments when the mutual (mainly elastic) collisions of the corresponding particles are studied might surely be very helpful.
Quantum mechanics has been enormously successful in explaining the behavior of microsystems such as molecules, atoms, and nuclei. We have seen that quantum mechanics describes a quantum system by the wave function ψ, which is the solution of the Schro¨dinger equation. The wave function determines the probability amplitudes (whose modulus squared gives the probability) for all possible outcomes of a measurement corresponding to an observable on the system. In general, the wave function does not uniquely predict the result of a measurement; it only provides a probability distribution for all possible results of the measurement on a quantum system. Only if the system happens to be in an eigenstate corresponding to the observable being measured, is the result of a measurement of this observable completely predictable. On the other hand, the results of measurements corresponding to a conjugate or non-commuting observable, on the same system in the same state, are indeterminate. Quantum mechanical description of physical systems raises profound questions: How are the wave function and the probabilities for different outcomes of a measurement to be interpreted? Does the wave function represent a single system or an ensemble of systems? Does the physical system actually have the attribute corresponding to the measurement in question or does the measurement itself create the attribute? These questions led to different interpretations of quantum mechanics, which were vigorously debated during the years of its discovery as also in the following decades. The new idea of indeterminacy was especially difficult to reconcile with the long-held view that a physical theory should aim at predicting accurately, and without ambiguity, the result of any measurement on any system, big or small. These debates not only gave us a deeper understanding of quantum mechanics but also changed profoundly the way we view the micro-world.
One way of reading this book is as an epilogue-or (more precisely) as a denouement-to a book I wrote more than thirty years ago, which was called Quantum Mechanics and Experience.That earlier book was meant to do two things:1) To introduce its readers to the elementary nuts and bolts of the foundations of quantum mechanics-the idea of superposition, the basics of the standard mathematical formalism of quantum mechanics, the argument of Einstein and Podolsky and Rosen to the effect that that formalism, considered as a description of the fundamental real ity of the world, must be somehow incomplete, Bell's extension of that argument into a general and power ful theorem about locality, the elaboration (by figures like Erwin Schrödinger, and John von Neumann, and Eugene Wigner) of the quantum-mechanical mea surement prob lem, and vari ous proposals (theories of the spontaneous collapse of the wave-function, Bohmian mechanics, the so-called many-worlds interpretations of quantum mechanics, and so on) for solving it.2) To show how the above-mentioned proposals for solving the mea sure ment prob lem, taken together, amount to a
One of the recurrent problems in the foundations of physics is to explain why we rarely observe certain phenomena that are allowed by our theories and laws. In thermodynamics, for example, the spontaneous approach towards equilibrium is ubiquitous yet the time-reversal-invariant laws that presumably govern thermal behaviour in the microscopic level equally allow spontaneous approach away from equilibrium to occur. Why are the former processes frequently observed while the latter are almost never reported? Another example comes from quantum mechanics where the formalism, if considered complete and universally applicable, predicts the existence of macroscopic superpositions—monstrous Schrodinger cats—and these are never observed: while electrons and atoms enjoy the cloudiness of waves, macroscopic objects are always localized to definite positions. A well-known explanatory framework due to Ludwig Boltzmann traces the rarity of " abnormal" thermodynamic phenomena to the scarcity of the initial conditions that lead to it. After all, physical laws are no more than algorithms and these are expected to generate different results according to different initial conditions, hence Boltzmann's insight that violations of thermodynamic laws are possible but highly improbable. Yet Boltzmann introduces probabilities into this explanatory scheme, and since the latter is couched in terms of classical mechanics, these probabilities must be interpreted as a result of ignorance of the exact state the system is in. Quantum mechanics has taught us otherwise. Here the attempts to explain why we never observe macroscopic superpositions have led to different interpretations of the formalism and to different solutions to the quantum measurement problem. These solutions introduce additional interpretations to the meaning of probability over and above ignorance of the definite state of the physical system: quantum probabilities may result from pure chance. Notwithstanding the success of the Boltzmannian framework in explaining the thermodynamic arrow in time it leaves us with a foundational puzzle: how can ignorance play a role in scientific explanation of objective reality? In turns out that two opposing solutions to the quantum measurement problem in which probabilities arise from the stochastic character of the underlying dynamics may scratch this explanatory itch. By offering a dynamical justification to the probabilities employed in classical statistical mechanics these two interpretations complete the Boltzmannian explanatory scheme and allow us to exorcize ignorance from scientific explanations of unobserved phenomena. In this thesis I argue that the puzzle of the thermodynamic arrow in time is closely related to the problem of interpreting quantum mechanics, i.e., to the measurement problem. We may solve one by fiat and thus solve the other, but it seems unwise to try solving them independently. I substantiate this claim by presenting two possible interpretations to non-relativistic quantum mechanics. Differing as they do on the meaning of the probabilities they introduce into the otherwise deterministic dynamics, these interpretations offer alternative explanatory schemes to the standard Boltzmannian statistical mechanical explanation of thermodynamic approach to equilibrium. I then show how notwithstanding their current empirical equivalence, the two approaches diverge at the continental divide between scientific realism and anti-realism.