Why Finite Mathematics Is the Most General and Finite Quantum Theory Is More Pertinent Physical Theory Than Standard One

2020 ◽  
pp. 169-194
Author(s):  
Felix Lev
Keyword(s):  
Quantum Theory ◽  
Physical Theory ◽  
Finite Mathematics

Reasoning About Measurements

2021 ◽  
pp. 31-92
Author(s):  
Jochen Rau
Keyword(s):  
Probability Theory ◽  
Quantum Theory ◽  
Physical Theory ◽  
Logical Structure ◽  
Statistical Independence ◽  
Classical Probability ◽  
Multiple Systems ◽  
Classical Probability Theory ◽  
Operational Requirement

This chapter explains the approach of ‘operationalism’, which in a physical theory admits only concepts associated with concrete experimental procedures, and lays out its consequences for propositions about measurements, their logical structure, and states. It illustrates these with toy examples where the ability to perform measurements is limited by design. For systems composed of several constituents this chapter introduces the notions of composite and reduced states, statistical independence, and correlations. It examines what it means for multiple systems to be prepared identically, and how this is represented mathematically. The operational requirement that there must be procedures to measure and prepare a state is examined, and the ensuing constraints derived. It is argued that these constraint leave only one alternative to classical probability theory that is consistent, universal, and fully operational, namely, quantum theory.

Determinism and indeterminism

2018 ◽  
Author(s):  
Jeremy Butterfield
Keyword(s):  
Seventeenth Century ◽  
Quantum Theory ◽  
Physical Science ◽  
Physical Theory ◽  
Classical Physics ◽  
Tentative Conclusion ◽  
Open Questions ◽  
The World ◽  
Determinism And Indeterminism

Over the centuries, the doctrine of determinism has been understood, and assessed, in different ways. Since the seventeenth century, it has been commonly understood as the doctrine that every event has a cause; or as the predictability, in principle, of the entire future. To assess the truth of determinism, so understood, philosophers have often looked to physical science; they have assumed that their current best physical theory is their best guide to the truth of determinism. It seems that most have believed that classical physics, especially Newton’s physics, is deterministic. And in this century, most have believed that quantum theory is indeterministic. Since quantum theory has superseded classical physics, philosophers have typically come to the tentative conclusion that determinism is false. In fact, these impressions are badly misleading. The above formulations of determinism are unsatisfactory. Once we use a better formulation, we see that there is a large gap between the determinism of a given physical theory, and the bolder, vague idea that motivated the traditional formulations: the idea that the world in itself is deterministic. Admittedly, one can make sense of this idea by adopting a sufficiently bold metaphysics; but it cannot be made sense of just by considering determinism for physical theories. As regards physical theories, the traditional impression is again misleading. Which theories are deterministic turns out to be a subtle and complicated matter, with many open questions. But broadly speaking, it turns out that much of classical physics, even much of Newton’s physics, is indeterministic. Furthermore, the alleged indeterminism of quantum theory is very controversial: it enters, if at all, only in quantum theory’s account of measurement processes, an account which remains the most controversial part of the theory.

scholarly journals THE POINT PROCESSES OF THE GRW THEORY OF WAVE FUNCTION COLLAPSE

2009 ◽  
Vol 21 (02) ◽  
pp. 155-227 ◽  
Author(s):  
RODERICH TUMULKA
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Existence And Uniqueness ◽  
Joint Distribution ◽  
Physical Theory ◽  
Point Processes ◽  
Space Time ◽  
Wave Function Collapse ◽  
Relativistic Version

The Ghirardi–Rimini–Weber (GRW) theory is a physical theory that, when combined with a suitable ontology, provides an explanation of quantum mechanics. The so-called collapse of the wave function is problematic in conventional quantum theory but not in the GRW theory, in which it is governed by a stochastic law. A possible ontology is the flash ontology, according to which matter consists of random points in space-time, called flashes. The joint distribution of these points, a point process in space-time, is the topic of this work. The mathematical results concern mainly the existence and uniqueness of this distribution for several variants of the theory. Particular attention is paid to the relativistic version of the GRW theory that was developed in 2004.

An Ether by Any Other Name?

2018 ◽  
Author(s):  
Aaron Sidney Wright
Keyword(s):  
Quantum Theory ◽  
Physical Theory ◽  
Relativistic Quantum ◽  
Relativistic Quantum Theory ◽  
Léon Rosenfeld ◽  
Quantum Revolution

This chapter examines Paul Dirac’s 1951 proposal that ‘we are rather forced to have an æther’, arguing that it was a purposeful use of anachronism, meant to shock his contemporaries in relativistic quantum theory. The chapter considers the context for Dirac’s proposal in physics and astronomy during his education, and in the journal Nature. Dirac’s ‘æther’ was distinct from the ether proposed by E. T. Whittaker and Arthur Eddington, as it was more physical and substantial. In the conclusion, the chapter argues that the historical progression of physical theory was central to Dirac’s æther proposal. If, in 1905, Einstein ushered in one revolution which removed the possibility for an ether, the later quantum revolution made a new ‘æther’ possible. In the Manchester Guardian, Léon Rosenfeld described Dirac as conjuring ‘the ghost of the “aether”’. In fact, Dirac attempted a resurrection.

Determinism and indeterminism

2018 ◽  
Author(s):  
Jeremy Butterfield
Keyword(s):  
Seventeenth Century ◽  
Quantum Theory ◽  
Philosophy Of Science ◽  
Physical Science ◽  
Physical Theory ◽  
Possible Worlds ◽  
Classical Physics ◽  
Tentative Conclusion ◽  
The World ◽  
Determinism And Indeterminism

Over the centuries, the doctrine of determinism has been understood, and assessed, in different ways. Since the seventeenth century, it has been commonly understood as the doctrine that every event has a cause; or as the predictability, in principle, of the entire future. To assess the truth of determinism, so understood, philosophers have often looked to physical science; they have assumed that their current best physical theory is their best guide to the truth of determinism. Most have believed that classical physics, especially Newton’s physics, is deterministic. And in this century, most have believed that quantum theory is indeterministic. Since quantum theory has superseded classical physics, philosophers have typically come to the tentative conclusion that determinism is false. In fact, these impressions are badly misleading, on three counts. First of all, formulations of determinism in terms of causation or predictability are unsatisfactory, since ‘event’, ‘causation’ and ‘prediction’ are vague and controversial notions, and are not used (at least not univocally) in most physical theories. So if we propose to assess determinism by considering physical theories, our formulation of determinism should be more closely tied to such theories. To do this, the key idea is that determinism is a property of a theory. Imagine a theory that ascribes properties to objects of a certain kind, and claims that the sequence through time of any such object’s properties satisfies certain regularities. Then we say that the theory is deterministic if and only if for any two such objects: if their properties match exactly at a given time, then according to the theory, they will match exactly at all future times. Second, this improved formulation reveals that there is a large gap between the determinism of a given physical theory, and the bolder, vague idea that motivated the traditional formulations: the idea that the world as a whole, independent of any single theory, is deterministic. Admittedly, one can make sense of this idea by adopting a sufficiently bold metaphysics: namely, a metaphysics that accepts the idea of a theory of the world as a whole, so that its objects are possible worlds, and determinism becomes the requirement that any two possible worlds described by the theory that match exactly at a given time also match exactly at all future times. But this idea cannot be made sense of using the more cautious strategy of considering determinism as a feature of a given physical theory. Third, according to this more cautious strategy, the traditional consensus is again misleading. Which theories are deterministic turns out to be a subtle and complicated matter, with many questions still open. But broadly speaking, it turns out that much of classical physics, even much of Newton’s physics, is indeterministic. Furthermore, the alleged indeterminism of quantum theory is very controversial: it enters, if at all, only in quantum theory’s account of measurement processes, an account which remains the most controversial part of the theory. These subtleties and controversies mean that physics does not pass to philosophers any simple verdict about determinism. But more positively, they also mean that determinism remains an exciting topic in the philosophy of science.

Quantum theory as a universal physical theory

1985 ◽  
Vol 24 (1) ◽  
pp. 1-41 ◽  
Author(s):  
David Deutsch
Keyword(s):  
Quantum Theory ◽  
Physical Theory

scholarly journals Musings on quantum music: Can quantum music bring us closer to objective beauty?

Muzikologija ◽  
2018 ◽  
pp. 123-128
Author(s):  
Chiara Marletto
Keyword(s):  
Quantum Theory ◽  
Physical Theory ◽  
Interesting Problem ◽  
Science And Art ◽  
Fundamental Physical

Quantum music is an idea to compose music based on a fundamental physical theory, quantum theory. One of the underlying theses of the project is that by merging a deep theory of physics with music one can provide a more interesting musical landscape. An interesting problem opened by quantum music is whether this idea will, or will not, allow one to move closer to objective beauty, if such a thing exists. I will explore what the implications of quantum music are for this issue. Can the marriage of science and art permit the achievement of a richer set of aestetic outputs?

scholarly journals Operational locality in global theories

2018 ◽  
Vol 376 (2123) ◽  
pp. 20170321 ◽  
Author(s):  
Lea Krämer ◽  
Lídia del Rio
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Physical Theory ◽  
Foundations Of Quantum Mechanics ◽  
Building Blocks ◽  
Contemporary Society ◽  
Operational Model ◽  
State Spaces ◽  
Local Functions ◽  
Generalized Probability

Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here, we propose exploring the opposite direction: to take agents as the basic building blocks through which we test a physical theory, and recover operational notions of locality from signalling conditions. First, we introduce an operational model for the effective state spaces of individual agents, as well as the range of their actions. We then formulate natural secrecy conditions between agents and identify the aspects of locality relevant for signalling. We discuss the possibility of taking commutation of transformations as a primitive of physical theories, as well as applications to quantum theory and generalized probability frameworks. This ‘it from bit’ approach establishes an operational connection between local actions and local observations, and gives a global interpretation to concepts like discarding a subsystem or composing local functions. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

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