Elementary Particles And Emergent Phase Space

Piotr Żenczykowski

• Publisher: WSPC
• Year: 2013
• ISBN:
  9789814525701
• Topic: Physical Sciences
• Subtopic: Nuclear Physics

The Standard Model of elementary particles, although very successful, contains various elements that are put in by hand. Understanding their origin requires going beyond the model and searching for “new physics”. The present book elaborates on one particular proposal concerning such physics. While the original conception is 50 years old, it has not lost its appeal over time. Its basic idea is that space — an arena of events treated in the Standard Model as a classical background — is a concept which emerges from a strictly discrete quantum layer in the limit of large quantum numbers.

This book discusses an extension of this view by replacing space with phase space. It combines the results of the author's research papers and places them in much broader philosophical and phenomenological contexts, thus providing further arguments in favor of the proposed alternative. The book should be of interest to the philosophically-minded readers who are willing to contemplate unorthodox ideas on the very nature of the world.

Contents:

• • Introduction
• Philosophy and Physics:
  • Reality and Its Description
  • Classical and Quantum Aspects of Reality
  • Time for a Change
• Elementary Particles:
  • The Standard Model and the Subparticle Paradigm
  • The Problem of Mass
  • Constituent Quarks and Spacetime Points
  • Elementary Particles and Macroscopic Space
• Phase Space and Quantum:
  • Phase Space and Its Symmetries
  • Quantizing Phase Space
  • Elementary Particles from a Phase-Space Perspective
  • Generalizing the Concept of Mass
  • Overview

Readership: Professionals and researchers in theoretical physics, philosophy of science, particle physics and quantum physics.

Chapter 1

Introduction

Elementary particles are nowadays perceived via the picture provided by the Standard Model. A well-known general message is that this model is consistent with all the experimental data gathered so far. Yet, while the Standard Model is undeniably extremely successful in providing a satisfactory description of many aspects of physical reality, it also contains several features that still call for an explanation and indicate that a deeper layer of description is needed. The pursuit of such a deeper explanation, often dubbed ‘new physics’, underlies many current cutting-edge research programmes.

The very definition of the frontier of knowledge is that there are no established routes beyond it. Still, in order to move rationally in that terra incognita we need proper guidance. To get it we usually apply the ideas that proved successful earlier in somewhat similar situations. Unfortunately, those ideas may lead us astray, especially if the situation we are facing is not really similar to the old ones. In other words, the more we are at the edge, the wider the spectrum of open possibilities, and — consequently — the more likely it is that our old ideas actually become a hindrance, and that in our attempts to move forward we will be misled by the explicitly or implicitly adopted old philosophy of ours.

This seems to be the situation in which we are at present, with the very successful but essentially closed theory of the Standard Model, and with no generally accepted hints on how to proceed beyond it. In order to make progress we probably need to look back into the conceptual roots of our theories, and then analyze and broaden their philosophical basis. Only a significant change in that basis may provide some ground for a truly new physics.

Consequently, any deeper proposal on how to move outside of the safe haven of the Standard Model should start from a sufficiently profound physico-philosophical discussion. Thus, this is where we begin. Carrying such a discussion is all the more important since the philosophical backgrounds of the contemporary theories of elementary particles and gravity are mutually incompatible, with the roots of these incompatibilities already present in the philosophy of ancient Greece. Clearly, one should suggest some philosophical resolution of these incompatibilities and form a coherent tentative ontology before actually proposing a more specific physical approach.

With our goal originally defined as the deepening of our understanding of the microworld, we have to clarify first what we accept as a satisfactory understanding and explanation. What we write on this subject is nothing really new: it has been said on many occasions by various well-known physicists and philosophers. Yet, as their insights provide the indispensable background for our further arguments, and since these insights are often not fully appreciated — in many cases to the point of being completely ignored — we consider it very important to recall them. For similar reasons, we find it also appropriate to discuss the relative placement of our theories and explanations, both among themselves and with respect to physical reality. A proper understanding of this point is a prerequisite for deciding later on the acceptability of the approach proposed herein.

Since a coherent ontology must cover all aspects of experience, it should place the world of elementary particles alongside the macroworld and other aspects of experienced reality. In other words, while seeking explanations for the world of elementary particles, we have to keep in mind an essential unity of reality, and thus the unity of micro- and macro-worlds in particular. Consequently, various types of hints and arguments, often not classified as typically ‘physical’, should in fact be admitted in our considerations, at least as an important background.

This book is meant to propose a general direction that — as the author believes — should be considered among the attractive routes which research on the ‘origin of the Standard Model’ should take, to substantiate the main idea with several arguments, and to present a few simple but very encouraging results that have been obtained so far. The hope is that they will appeal to the readers and motivate at least some of them to propose new and (presumably) far more mathematically sophisticated ideas in the general direction set forward here.

We start our arguments by providing in Part 1 the physico-philosophical background that will be needed later. Since the author is a particle physicist, and since our main topic is physics, the philosophical aspects will be discussed only as far as it is important for our purposes. The first chapter of that part is fairly general and deals with the issue of language, the meaning of the concept of explanation, and the proper way of thinking about our theories. The next chapter is more physical, as it is concerned with the concepts of space and time, and with their treatment in both the classical and quantum descriptions. It discusses the tension that exists between relativity and quantum physics, and is intended to question the adequacy and the range of applicability of our intuitive macroscopic spacetime-based description of reality that forms a part of the basis of the Standard Model. Then, as a step to a possible conceptual resolution of problems brought about by this tension, the general idea of macroscopic spacetime ‘emerging’ from the underlying purely quantum layer is introduced. Chapter 4 focuses on the more specific issue of ‘emergent time’. It is argued there that time should be viewed as a measure of change, or — equivalently — be derived from it. In other words, space and time should be considered as concepts logically posterior to matter and its change. The wish to treat them symmetrically fits then well into a philosophical view, known as process philosophy, according to which permanence and change, being and becoming should enter on equal footing into our description of reality. Alternatively, process philosophy may be viewed as an argument that, by assigning to being and becoming a similar ontological weight, requires their maximally symmetric treatment in the language of physics.

Part 2 describes the situation from the point of view provided by the Standard Model itself and the subparticle paradigm on which it is based. Chapter 5 briefly presents the most relevant features of this model. Questions pertaining to the origin of Standard Model symmetries are raised, and an important attempt to answer some of these questions in terms of yet another, deeper level of subparticles is described. A separate issue about which the Standard Model does not have much to say, namely the problem of mass, is discussed in more detail in Chap. 6. There, the widely-used concepts of the so-called current and constituent quark masses are introduced, and their meaning is thoroughly discussed. The aim of these discussions is to separate what is known quite well about these masses from what is essentially merely imagined and believed, especially in connection with the idea of quark propagation in background space. Chapter 7 discusses a specific electroweak hadron-decay process which explicitly demonstrates the inapplicability of standard ideas about quark mass and quark propagation. In Chap. 8, with the results of the previous discussions kept in mind, we are led to question the suitability of the standard spacetime description of hadronic interior, and argue in favor of the applicability of the idea of emergent spacetime at the quark/hadron interface, in agreement with earlier views of several distinguished physicists. We stress right here that such a conception of physical reality is not inconsistent with what we know about quarks from experiment and from their field-theoretic description within the Standard Model.

In Part 3 we present our main proposal suggesting a close connection between the symmetries of the Standard Model and those of nonrelativistic phase space. The approach, which originally followed from the desire to treat position and momentum in a maximally symmetric way possible, is supported (sometimes only implicitly) with the arguments presented in Parts 1 and 2. In particular, positions and momenta are seen as physical concepts corresponding to the more philosophical notions of permanence and change. First, in Chap. 9, a heuristic discussion of phase-space symmetries and their possible relevance to a generalization of the concept of mass is given. Then, in Chap. 10, the idea of the unity of the micro- and macro-worlds is formulated in a more technical language, and shown to lead to an explanation of the salient features of elementary particles as they are built into the Standard Model. Chapters 10 and 11 show that, if one accepts the main premises of the phase-space view, the subparticle paradigm underlying our search for the fundamental constituents of matter should be reinterpreted. For the Standard Model itself, such a reinterpretation would be of a fairly mild nature, affecting mainly our understanding of the concept of quark mass, or — more precisely — the link between the concept of quark mass and the concept of quark propagation. On the other hand, the explanation of the Standard Model symmetry structure in terms of yet another level of subparticles, as discussed in Part 2, requires such a drastic change in the meaning of the concept of division that the very subparticle paradigm becomes totally inapplicable. In Chap. 12 a more technical discussion of the generalized concept of mass is given. The last chapter contains an overview of all the main issues discussed throughout the whole text and a brief outlook.

PART 1

PHILOSOPHY AND PHYSICS

“There is no such thing as philosophy-free science; there is only science whose philosophical baggage is taken on board without examination.”

Daniel Dennett [36]

Chapter 2

Reality and Its Description

The goal of most physicists is to provide us with a deeper understanding of the world we live in, of the physical reality conceived as being ‘out there’. In order to move forward along this road we must convey our ideas to others. The impact of this transfer of ideas cannot be overestimated: the improvements in the methods of conveying information were among the decisive factors which kept boosting the development of our civilization. The first of these factors is our language itself, the language of ordinary life. Science depends on it very heavily, as all its concepts have to be expressed in it. Indeed, Niels Bohr said (as quoted in Ref. [135]):

“What is it that we human beings ultimately depend on? We depend on our words... Our task is to communicate experience and ideas to others.”

It is therefore appropriate to begin with a brief discussion of the role of language and a commentary on the way in which it is used here.

2.1 The Language Factor

The language of ordinary life evolved first of all to enable the communication of facts vital to our survival. Its form involves a trade-off between the accuracy and speed of information transfer. The relation of natural language to the surrounding classical world is therefore necessarily rough and imprecise. The language of science cannot be but its extension and refinement. It must use the words of natural language, which are often fairly ambiguous, and it defines additional words with their help. The scientific description of the world, being necessarily given within a derivative of natural language, is therefore inevitably and incurably approximate. This is so even if it is formulated in a precise mathematical fashion, since the issues of meaning are then transferred to its very assumptions (see e.g. Ref. [84] for a related discussion given by Werner Heisenberg in the context of classical physics). For this reason (as well as others), we do not really know how well our scientific description fits physical reality, even if it were to agree with all of our experiments. Indeed, Heisenberg said [79]:

“Words have no well-defined meaning. We can sometimes by axioms give a precise meaning to words, but still we never know how these precise words correspond to reality, whether they fit reality or not. We cannot help the fundamental situation — that words are meant as a connection between reality and ourselves — but we can never know how well these words or concepts fit reality.”

Actually, the situation may be considered even worse, for — as Niels Bohr stressed [135] —

“we are suspended in language in such a way that we cannot say what is up and what is down.”

Niels Bohr’s positivistic inclinations forced him into a position more radical than Heisenberg’s, essentially banning the ontological issues from the subject of physics and, consequently, stressing the crucial role of language even further [135]:

“It is wrong to think that the task of physics is to find out about how nature is. Physics concerns what we can say about nature.”

Clearly, therefore, independently of whether the goal of physics is to be understood à la Heisenberg, or à la Niels Bohr, it depends on our natural language in an absolutely essential way.

To make things more complicated, we have not just one language of ordinary life, but a multitude of them. Since the outside world is reflected in those languages only in an imprecise and fuzzy manner, different natural languages may provide inherently different descriptions of the macroscopic world. It is well known that some natural languages are better (or worse) at expressing specific ideas and concepts of everyday life. This happens to such an extent that for any pair of languages there exist words in one of them that are untranslatable into the other language in any simple way. Thus, the uniqueness of description is a myth.

The situation in science is analogous. That is, different types of scientific description may provide better or worse vehicles for the analysis of specific physical phenomena or their aspects. For some of these descriptions we can provide a dictionary that enables us to pass from one description to another without much loss. As simple examples, we may mention here the existence of the Lagrangian and Hamiltonian formulations, or current field-theoretic gauge theories of particle interactions in which different gauges are used, with the choice of gauge having no effect on relevant theoretical predictions. In other situations only fairly incomplete dictionaries are at hand, as is the case of classical versus quantum physics.

In fact, language hides not only the ‘outside’ physical reality generally believed to lie beneath it, but the whole of reality, including our ideas about it. Since the formation of concepts and the process of thinking require their subsequent formulation into words so that they can be presented to the world at large, our ideas are necessarily tailored to the words that we have at our disposal. A byproduct of this is that expressing one’s ideas in written form is a very laborious process. Furthermore, since the explicit use of words generally distorts the original idea, it is quite likely that also our cognitive processes and the concepts we form in our minds are affected by the languages we have been trained to use. Consequently, as Benjamin Whorf claims [169]: “All observers are not led by the same physical evidence to the same picture of the universe, unless their linguistic backgrounds are similar.” Although this ‘principle of linguistic relativity’ was under attack for some time, current research and most linguists now agree with it, though perhaps with some mild reservations (for more details, see e.g. Refs. [56, 100, 173]).

Since, for any given evidence, different languages in general lead to different pictures of physical reality, we face the problem which language to choose as being conceptually closer to nature. This is an important issue of decision as different descriptions will likely be conducive to different generalizations later on. Obviously, substantial conceptual progress is unlikely to follow from the refinement of a single language if the latter is not chosen judiciously — this would be like searching for a local maximum instead of the global one. Thus, one should seek addi...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Dedication
• Preface
• Contents
• 1. Introduction
• PART 1 PHILOSOPHY AND PHYSICS
• PART 2 ELEMENTARY PARTICLES
• PART 3 PHASE SPACE AND QUANTUM
• Bibliography
• Index