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.
The major developments in twentieth-century physics, grouped under the general headings of quantum theory and relativity, have provoked much discussion and re-evaluation of the subject-object relationship in natural science and, to a lesser extent, the role of models in the development and articulation of physical theory. This chapter attempts to approach the subject-object problem from a standpoint developed from an analysis of the nature and function of models as a basis of explanation in physics, in different historical periods and areas of study within the field. A distinction between several major types of model observable at work in classical physics relates to the amount of detail contained in the pictorial description of the model as opposed to the amount of detail in the observational situation to which it relates. The quantum-mechanical model, employs in general a plurality of pictorial representations within a single model, which separates in simple situations into the several classical models mathematically related and restricted.
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
In this paper we consider general probabilistic theories pertaining to circuits that satisfy two very natural assumptions. We provide a formalism that is local in the following very specific sense: calculations pertaining to any region of space–time employ only mathematical objects associated with that region. We call this formalism locality. It incorporates the idea that space and time should be treated on an equal footing. Formulations that use a foliation of space--time to evolve a state do not have this property, nor do histories-based approaches. An operation has inputs and outputs (through which systems travel), for example, A circuit is built by wiring together operations such that we have no open inputs or outputs left over. A fragment is a part of a circuit and may have open inputs and outputs, for example, We show how each operation is associated with a certain mathematical object, which we call a duotensor (this is like a tensor but with a bit more structure). The following diagram shows how a duotensor is represented graphically: We can link duotensors together such that black and white dots match up to get the duotensor corresponding to any fragment. The following diagram shows the duotensor for the above fragment: Links represent summation over the corresponding indices. We can use such duotensors to make probabilistic statements pertaining to fragments. Since fragments are the circuit equivalent of arbitrary space–time regions, we have formalism locality. The probability for a circuit is given by the corresponding duotensorial calculation (which is a scalar since there are no indices left over). We show how to put classical probability theory and quantum theory into this framework.
This introductory chapter sets out a general structure of physical theories which is applicable to both classical and quantum mechanics. We start with measurable properties of a given physical system, be it classical or quantum. These properties are called observables . We then introduce a definition of the state of a physical system in terms of measured values of a sufficiently large set of observables. A theory to describe the system should consists of four basic components: Basic mathematical framework This comprises a set of elements endowed with some specific mathematical structure and properties. In mathematics such a set is generally known as a space . Description of states States are described by elements of the space in the chosen mathematical framework. For this reason the space is called the state space of the system. Description of observables Observables are to be described by quantities defined on the state space. The description should yield all possible values of observables. The relationship between observables and states should be explicitly stated. The following two cases are of particular interest: 2 For a deterministic theory like classical mechanics a state should determine the values of all observables. For a probabilistic theory like quantum mechanics a state should determine the probability distribution of the values of all observables. Description of time evolution (dynamics).
Quantum theory is the most successful physical theory ever.About one third of the gross national product in the developed countries results from its applications.These applications range from nuclear power to most of the high-tech tools for computing, laser, solar cells and so on.No limit for its range of validity has been found up to now.Quantum theory has a clear mathematical structure, so a physics student can learn it in a short time.However, very often quantum theory is considered as being "crazy" or "not understandable".Such a stance appears reasonable as long as quantum theory is seen primarily as a theory of small particles and the forces between them.However, if quantum theory is understood more deeply, namely as a general theory of structures, not only the range is widely expanded, but it also becomes more comprehensible (T.Görnitz, 1999).Quantum structures can be material, like atoms, electrons and so on.They can also be energetic, like photons, and finally they can be mere structures, such as quantum bits.Keeping this in mind it becomes apprehensible that quantum theory has two not easily reconcilable aspects: on the one hand, it possesses a clear mathematical structure, on the other hand, it accounts for well-known experiences of everyday life: e.g. a whole is often more than the sum of its parts, and not only the facts but also the possibilities can be effective.If henadic and future structures (i.e.structures which are related to unity [Greek "hen"] and to future) become important in scientific analysis, then the viewable facts in real life differ from the calculated results of models of classical physics, which suppose elementary distinctions between matter and motion, material and force, localization and extension, fullness and emptiness and which describe any process as a succession of facts.From quantum theory one can learn two elementary insights:1.Not only facts but also possibilities can influence the way in which material objects behave.2. The elementary distinctions made in classical models are often useful, but not fundamental.Quantum theory shows that there are equivalences between the concepts of matter and motion, material and force, localization and extension, fullness and emptiness, and so on, www.intechopen.com How to referenceIn order to correctly reference this scholarly work, feel free to