The Principles of Quantum Theory, From Planck's Quanta to the Higgs Boson

Plotnitsky, Arkady

doi:10.1007/978-3-319-32068-7

Cited by 56 publications

(43 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We state that these principles were totally ignored not only by fathers of QM (with a few exceptions such as Schrödinger), but even by practically all experts working in quantum foundations. The majority of them followed 'the spirit of Copenhagen' (Plotnitsky, 2016) and put tremendous efforts to proceed without taking into account Hertz 1, 2, i.e., to develop the formalism of observational (sensational) theory of micro-phenomena which is nowadays known as QM (cf. with Stapp's analysis of the Copenhagen interpretation in (Stapp, 1972)).…”

Section: Hertzian Viewpoint On Foundations Of Quantum Mechanicsmentioning

confidence: 99%

Hertz’s Viewpoint on Quantum Theory

Khrennikov

2019

Act Nerv Super

View full text Add to dashboard Cite

In 19th century (in the process of transition from mechanics to the field theory) the German school of theoretical physics confronted problems similar to the basic problems in the foundations of quantum mechanics (QM). Hertz tried to resolve such problem through analysis of the notion of a scientific theory and interrelation of theory and experiment. This analysis led him to the Bild (image) conception of theory (which was latter essentially developed, but also modified by Boltzmann). In this paper we claim that to resolve the basic foundational problems of QM, one has to use the Bild conception and reject the observational viewpoint on physical theory. As an example of a Bild theory underlying QM (treated as an observational theory), we consider prequantum classical statistical field theory (PCSFT): theory of random subquantum fields.keywords: Hertz Bild theory, descriptive and observational theories, hidden variables in electromagnetism vs quantum mechanics, quantum theory as observational theory, prequantum classical statistical field theory.

show abstract

Section: Hertzian Viewpoint On Foundations Of Quantum Mechanicsmentioning

confidence: 99%

Hertz’s Viewpoint on Quantum Theory

Khrennikov

2019

Act Nerv Super

View full text Add to dashboard Cite

show abstract

“…However, I disagree that transition from QM to QFT may simplify measurement's picture. I would like to point to the following complication due to the QFT-treatment, see also Plotnitsky [14], Chapter 6. Since QM is a nonrelativistic model, the space-time can be, in principle, excluded from consideration.…”

Section: Measurement Theory: Qm Versus Qftmentioning

confidence: 99%

“…Another class is based on the idea that only rational numbers can be treated as "physical numbers". Starting with the field of rational numbers Q, one can try to construct new number fields 14 . Surprisingly mathematics gives us only two possibilities to proceed in this way: either to the field of real numbers R or to the fields of p-adic numbers Q p , where p > 1 is a prime number determining the field, see, e.g., [54].…”

Section: Is Devil In Real Numbers?mentioning

confidence: 99%

The Present Situation in Quantum Theory and its Merging with General Relativity

Khrennikov

2017

Found Phys

View full text Add to dashboard Cite

We discuss the problems of quantum theory (QT) complicating its merging with general relativity (GR). QT is treated as a general theory of micro-phenomenaa bunch of models. Quantum mechanics (QM) and quantum field theory (QFT) are the most widely known (but, e.g., Bohmian mechanics is also a part of QT). The basic problems of QM and QFT are considered in interrelation. For QM, we stress its nonrelativistic character and the presence of spooky action at a distance. For QFT, we highlight the old problem of infinities. And this is the main point of the paper: it is meaningless to try to unify QFT so heavily suffering of infinities with GR. We also highlight difficulties of the QFT-treatment of entanglement. We compare the QFT and QM based measurement theories by presenting both theoretical and experimental viewpoints. Then we discuss two basic mathematical constraints of both QM and QFT, namely, the use of real (and, hence, complex) numbers and the Hilbert state space. We briefly present non-archimedean and non-hilbertian approaches to QT and their consequences. Finally, we claim that, in spite of the Bell theorem, it is still possible to treat quantum phenomena on the basis of a classical-like causal theory. We present a random field model generating the QM and QFT formalisms. This emergence viewpoint can serve as the basis for unification of novel QT (may be totally different from presently powerful QM and QFT) and GR. (It may happen that the latter would also be revolutionary modified.)

show abstract

“…This assumption is also made in non-realist interpretations of quantum mechanics, in the absence of a representation or even (as against the second, non-representational type of realism defined above) conception of the character of this existence. Thus, if realism presupposes a representation or at least a conception of reality, this concept of reality is that of "reality without realism" [9,11]. The assumption of this concept of reality is a principle, the RWR principle.…”

Section: Physical Principles and Mathematical Models In Quantum Mechamentioning

confidence: 99%

“…Individual quantum events are not subject to laws, even to the probabilistic or statistical laws of quantum mechanics. Their outcomes cannot, in general, be assigned a probability: they are strictly random 9 . Only the statistics of multiple (identically prepared) experiments could be predicted and repeated, which repeatability appears to have been, thus far, necessary for scientific practice.…”

Section: The Physical Principles Of the Quantum Theorymentioning

confidence: 99%

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

Plotnitsky

2017

Front. Phys.

Self Cite

View full text Add to dashboard Cite

The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, that may be helpful or even necessary there or in physics itself. I shall, in closing, suggest one possible type of such models, singularized probabilistic models, SP-models, some of which are time-dependent, TDSP-models. The necessity of using such models may change the nature of mathematical modeling in science and, thus, the nature of science, as it happened in the case of Q-models, which not only led to a revolutionary transformation of physics but also opened new possibilities for scientific thinking and mathematical modeling beyond physics.

show abstract

The Principles of Quantum Theory, From Planck's Quanta to the Higgs Boson

Cited by 56 publications

References 0 publications

Hertz’s Viewpoint on Quantum Theory

Hertz’s Viewpoint on Quantum Theory

The Present Situation in Quantum Theory and its Merging with General Relativity

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

Contact Info

Product

Resources

About