In this chapter we shall first summarize some conceptual and formal features of classical mechanics (Sec. 1.1). Modern physics started with the works of Galileo Galilei and Isaac Newton from which classical mechanics, one of the most beautiful and solid intellectual buildings of the human history, came out. The architecture of classical mechanics was developed between the end of the eighteenth century and the second half of the nineteenth century, and its present form is largely due to Lagrange, Jacobi, and Hamilton. As we shall see in this chapter, classical mechanics is built upon the requirement of determinism, a rather complex assumption which is far from being obvious. In Sec. 1.2 we shall present the two main conceptual features of quantum mechanics on the basis of an ideal interferometry experiment: the superposition principle and the principle of complementarity. In Sec. 1.3 a first formal treatment of quantum-mechanical states is developed: quantum states are represented by vectors in a space that turns out to be a Hilbert space. In Sec. 1.4 the significance of probability for quantum mechanics is explained briefly: we will show that probability is not just an ingredient of quantum mechanics, but is rather an intrinsic feature of the theory. Furthermore, we shall see that quantum probability is not ruled by Kolmogorov axioms of classical probability. Finally, we discuss the main evidences which have historically revealed the necessity of a departure from classical mechanics.
The previous chapters contain many examples of the successful application of quantum mechanics to the solution of real physical problems. These represent only a small sample of the wide range of experimental results, spanning just about all areas of physics and chemistry and beyond, that have been successfully explained by quantum theory. So far at least, no quantum-mechanical prediction has been experimentally falsified. Despite these successes, however, many scientists have considered the basic conceptual framework of the subject to be unsatisfactory, and repeated attempts have been made to reinterpret quantum mechanics, or even replace it with a different theory whose philosophical and conceptual basis could be considered more acceptable. In the present chapter we shall explain the reasons for this dissatisfaction and outline some of the reinterpretations and alternative approaches that have been devised. Inevitably many of the questions that arise in this area are matters of opinion rather than fact and, for this reason, some physicists consider that they belong more properly to the realm of philosophy than of physics. However, the conceptual basis of quantum mechanics is so fundamental to our whole understanding of the nature of the physical universe that it should surely be important for physicists to understand the nature of the problems involved, if nothing else.1,2 16.1 THE CONCEPTUAL PROBLEMS In this section we outline some of the main areas of difficulty with a view to more detailed discussion later in the chapter.
Probably no theory in the history of science has produced such a profound cultural and scientific revolution as is determined by quantum mechanics. Founded around 1920 by illustrious physicists, all Nobel Prize winners, it has completely subverted the conception of matter and the universe. The theory that all matter is made up of atoms has already been formulated by Greek philosophers, starting with Democritus. Quantum mechanics provided a description based on a new conception of the elementary structure of atoms, and formulated the fundamental laws to which atoms obey. Quantum theory has obtained the unanimous and shared consent of the scientific world, although some aspects have not been definitively confirmed. Strengthened by the universal acceptance of his theories, quantum mechanics claims its intellectual primacy over all the other sciences, and the scientific world seems to grant it, so much so as to archive all the knowledge and achievements gathered in its thousand-year history. From the epistemological point of view all established theories are worthy of consideration and must be shared and accepted until proven groundless. Dating, quantum mechanics still enjoys the consent of many scientists, but this does not mean that it can claim to be the repository of all truth, based on an unacceptable and anti-scientific syllogism for which: A) all organic and inorganic matter is formed by atoms and molecules; B) quantum mechanics has founded theories and formulas to which atoms and molecules obey; C) accordingly quantum mechanics can control all universal matter. But the presumption of its predominance goes further than willing to dominate living matter. In this article we are going to examine with a sharp criticism, the aberrant and anti-scientific claim of this discipline to dominate not only science but also universal matter. We propose a more moderate and considered vision of the observable natural phenomena and consider them events in continuous evolution, and to adapt our hypotheses and theories with an equal evolutionary approach.
The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive QM from more basic principles, these principles should be of general, philosophical nature. Here, we derive the formalism of QM from well-motivated epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. First, an epistemic formalism is developed, using concepts like knowledge and potential knowledge, identifying a physical state
S with the potential knowledge of the physical world. It is demonstrated that QM emerges from this formalism. However, Hilbert spaces, wave functions and probabilities are defined in certain well-defined observational contexts only. This means that the epistemic formalism is broader than QM. In the fundamental layer of description, the physical state
S is a subset of a state space
S={Z}, such that
S always contains many elements
Z. These elements correspond to unattainable states of complete knowledge of the world. The evolution of
S cannot be determined in terms of the individual evolution of the elements
Z, unlike the evolution of an ensemble in classical phase space. The evolution of
S is described in terms of sequential time
n∈N, which is updated according to
n→n+1 each time an event occurs, each time potential knowledge changes. Sequential time
n can be separated from relational time
t, which describes distances between events in space-time. There is an entire space-time associated with each
n, in which
t represents the knowledge at sequential time
n about the temporal relations between present and past events.
Changes are mostly quantitative, with some qualitative changes, without affecting the world order, concept of reality and of matter, both physical and philosophical. The historical development of physics, such as in electromagnetism, quantum theory and relativity have changed the basic assumptions of the mechanistic philosophy. The enormous diversity of things in the world can be completely reduced to effects of some basic laws and their framework, considered absolute and final. The assumption of the final and absolute character of any theory contradicts the basic spirit of scientific method itself, which requires that every feature be subjected to further and continuous enquiries. The qualitative infinity of nature provides a framework, within which concepts of chance and necessity are two interconnected aspects of the same process. The debates on the epistemology of the observational problems with the transition to post-classical physics, and philosophy, continues to be a major problem.