The Quantum mechanics works but is not yet well understood. The difficulty in understanding lies not so much in the already very sophisticated mathematical formulations, but are much more rooted in the question of how the objects do that? Starting with the double-slit experiment, we will first provide the viewpoint of quantum mechanics. This leads us to the wave-particle duality. Photons have both wave and particle properties. Then we see the exact opposite: photons, electrons... are neither wave nor particle and address the question: Can we find truth from falsity? Can quantum mechanics be wrong in their conditions and yet lead to so excellent results? We then address the question of how good the mathematical prerequisites in classical physics is and how well they are fulfilled in quantum physics. Finally, we look at some very basic experiments from the point of view of the objects.
The Quantum mechanics works but is not yet well understood. The difficulty in understanding lies not so much in the already very sophisticated mathematical formulations, but are much more rooted in the question of how the objects do that? Starting with the double-slit experiment, we will first provide the viewpoint of quantum mechanics. This leads us to the wave-particle duality. Photons have both wave and particle properties. Then we see the exact opposite: photons, electrons... are neither wave nor particle and address the question: Can we find truth from falsity? Can quantum mechanics be wrong in their conditions and yet lead to so excellent results? We then address the question of how good the mathematical prerequisites in classical physics is and how well they are fulfilled in quantum physics. Finally, we look at some very basic experiments from the point of view of the objects.
One of the earliest and most important tenets of quantum mechanics is the wave-particle duality: light behaves sometimes like a wave and at other times as particle and similarly an electron can also behave both like a particle and as a wave. When the formal laws of quantum mechanics are formulated, the central quantity that describes the particles is the wave function. This points to the need for a good understanding of the properties of the waves. This chapter introduces the concepts and most essential applications that are required to follow the discussion of quantum mechanical laws and systems. The basic characteristics of the waves, such as the superposition principle are presented, and the interference and the diffraction phenomena are discussed. The Young’s double slit experiment in analysed and the formation of interference pattern is explicitly shown. The Rayleigh criterion for the microscopic resolution is also derived.
1.1 Waves and particles in quantum mechanics In spite of the fact that the extraordinary progress of experimental techniques make us able to manipulate at will systems made of any small and well defined number of atoms, electrons and photons making therefore possible the actual performance of the gedankenexperimente that Einstein and Bohr had imagined to support their opposite views on the physical properties of the wavelike/particlelike objects (quantons) of the quantum world it does not seem that, after more than eighty years, a unanimous consensus has been reached in the physicist's community on how to understand their strange properties. Unfortunately, we cannot know whether Feynman would still insist in maintaining his famous sentence It is fair to say that nobody understands quantum mechanics. We can only discuss if, almost thirty years after his death, some progress towards this goal has been made. I believe that this is the case. I will show in fact that, by following the suggestions of Feynman himself, some clarification of the old puzzles can be achieved. This chapter therefore by no means is intended to provide an impartial review of the present status of the question but is focused on the exposure of the results of more than twenty years of research of my group in Rome, which in my opinion provide a possible way of connecting together at the same time the random nature of the events at the atomic level of reality and the completeness of their probabilistic representation by the principles of Quantum Mechanics.
The discovery of the electron and its strange properties is the cornerstone of quantum mechanics. Based on their spin properties, photons and electrons, now categorized as fermions and bosons under the Standard Model, exhibit an enigmatic dual nature of wave and particle. This property, the interpretation of which is still debated today, is supported by various experiments, as we saw in Chap. 4 . One of these, in particular, can be considered the basis of any interpretative model on the dual nature of photons and electrons, the double-slit experiment. This experiment will lead to the famous Copenhagen interpretation, which is still a key to explain quantum mechanics today. With all its incredible weirdness, the double-slit experiment is thus the basis of quantum mechanics, as we shall see in this chapter. Experiments and interpretations of the strange quantum properties of the electron have also led to the discovery of other physical phenomena seemingly impossible according to classical physics, such as the tunnel effect and quantum entanglement. These phenomena have no classical equivalent and can be explained only by resorting to quantum properties of electrons.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
New Perspectives on Fundamental Problems in Quantum Mechanics: Theory of Measurement Macroscopic Interpretability of Quantum Subsystems Objective Background for Quantum Theory Operational Probability Theory (OPT) and Conditional Probabilities Entanglement and Non-Locality Wave-Particle Duality, Double Slit Experiments Complementarity Operational Definition of Observables Simulation of Quantum Features De Broglie-Bohm Model Interdisciplinary Issues: Parastatistics in Econophysics Propositions in Classical and Quantum Physics Statistical Criticism of the Double Slit Experiment Chemical Valence as Relational Property Quantum Computer View (QCV) at the Planck Scale Historical, Philosophical and Epistemological Inquiries: The First Steps of Quantum Electrodynamics Electromagnetism and Quantum Physics Mathematics and Epistemology in Planck's Work Logic and Mathematics in Heisenberg's Formulation Reality and Nanotechnologies Non-Empirically Decidable Properties in Modern Physics Computability of Physical Theories Entrance of Quantum Mechanics in Italy Gramsci and Quantum Mechanics Italic Tradition on the Question of Physical Objectivity.
In the double slit experiment - - central to quantum mechanics and thus to all of reality - - when you LOOK at the particle, it always passes through ONLY ONE slit - - EITHER the right slit OR the left slit, acting like a particle. However, when you AREN’T looking at it, it somehow always passes through BOTH slits - - the right slit AND the left slit - - at the same time, acting like a wave. All of nature is now KNOWN to be both wave and particle simultaneously - - actually, one entity (“wavicle”), not two - - at the most fundamental level of reality. However, no one seems to have ever asked the question: How can anything, much less everything, be in TW0 places at the same time AND ALSO SIMULTANEOUSLY be in ONLY ONE place at the same time? The known laws of physics make this absolutely impossible. Therefore, at least one of our laws must be wrong. In some fundamental mathematical and physical sense, 2 MUST ALSO BE (- - EQUAL- -) 1: 2 AS 1. The right and left slits, seemingly opposite, must at the deepest level of reality be “married” to each other - - one slit, not two. Extending this argument to Schrodinger’s cat, life and death, seemingly opposite, must at the deepest level of reality be “married” to each other, 2 AS 1. Just as all apparent opposites, it must be true that ultimately, life and death must be one thing, not two. This, then, is an all-optimistic physics - - probably the first such theory ever. But it is based entirely on firm scientific fact.