Table Of ContentQuantum Theory
and Pictures of Reality
Quantum Theory
and Pictures of Reality
Foundations, Interpretations,
and New Aspects
Edited by W. Schommers
With Contributions by
B. d'Espagnat P. Eberhard W. Schommers
F. Selleri
With 31 Figures
Springer-Verlag Berlin Heidelberg New York
London Paris Tokyo Hong Kong
Wolfram Schommers
Karlsruhe
Federal Republic of Germany
ISBN-13: 978-3-540-50152-7 e-ISBN-13: 978-3-642-95570-9
DOl: 10.1007/978-3-642-95570-9
Library of Congress Cataloging-in-Publication Data. Quantum theory and pictures of reality: foundations, in
terpretations, and new aspects 1 edited by W. Schommers; with contributions by B. d'Espagnat ... let aI.l. p.
em. ISBN 0-387-50152-5 (U.S.: a1k. paper) 1. Quantum theory. L Schommers, W. (Wolfram), 1941- . II.
Espagnat, Bernard d'. QC 174.12.Q37 1989 530.1'2-dc 19 88-29505
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Preface
The essential features of the mathematical formalism of (non-relativistic) quan
tum theory were constructed by Heisenberg and Schrodinger in 1925-1926. On
the basis of this quantum-mechanical formalism an enormous number of effects
in atomic physics, chemistry, solid state physics, etc. could be predicted and
explained. However, more than 60 years after its formulation the interpretation of
this formalism is "by far the most controversial problem of current research in
the foundations of physics and divides the community of physicists and
philosophers of science into numerous opposing schools of thought" (Max
Jammer in The Philosophy of Quantum Mechanics). There is an immense diversity
of opinion and a huge variety of interpretations.
Most of these interpretations lead to completely different "pictures of
reality". For example, the Copenhagen interpretation of quantum theory (pro
posed by Bohr in 1927) is quite different from the many-worlds theory (proposed
by Everett III in 1957). Within the standard Copenhagen interpretation the
world (or any system) consists of options which are equally unreal. By the act of
observation a system is forced to select one of its options and this becomes real,
i.e. within the Copenhagen interpretation of quantum theory reality is produced
by the act of observation, so that any real system (for example, an electron)
cannot be thought of as having an independent existence; we know nothing
about what it is doing when we are not looking at it. Within the Copenhagen
interpretation, nothing is real unless we look at it. As soon as we stop looking, it
ceases to be real. On the other hand, within the many-worlds theory there is not
just one world, but as many alternative real worlds as options exist within the
Copenhagen interpretation. "What happens when we make a measurement at
the quantum level is that we are forced by the process of observation to select one
of these alternatives, which becomes part of what we see as the real world; the act
of oQservation cuts the ties that bind alternative realities together, and allows
them to go on their own separate ways through supers pace, each alternative
reality containing its own (real) observer who has made the same observation but
got a different quantum answer ..." (J. Gribbin in In Search ofSchrodinger's Cat).
In other words, within the many-worlds theory there is a real splitting of the
world into many real worlds, and the theory can explain why no observer can be
aware of the splitting process. (For example, within the many-worlds theory both
cats of Schrodinger's famous thought experiment are real: there is a real world
VI Preface
with an observer and a box with a live cat in it, and there is another real world
with an observer and a dead cat in the box.)
Both the Copenhagen interpretation and the many-worlds theory give
predictions in accord with experience and, therefore, they are equivalent from the
experimental point of view. However, both interpretations lead to "pictures of
reality" which are completely different from each other, and it is legitimate at the
present stage of quantum theory to choose the "picture of reality" which one
finds satisfactory and pleasing. The question is then whether a formalism (the
present form of quantum theory) with a diversity of completely different
interpretations is convincing.
Within classical physics we have one real world, and each part (system) of it
can be thought of as having an independent existence regardless of whether it is
observed or not. The "picture of reality" resulting from the Copenhagen
interpretation and the many-worlds theory can obviously not be based on the
classical framework; from the present tendencies we may conclude that quantum
theory should not be considered as a refined or extended version of classical
mechanics.
The step from classical mechanics to quantum theory is obviously a
revolutionary step in the sense of Kuhn (in The Structure of Scientific Revolutions).
What does this mean? Rescher stated in his book The Limits of Science the
following: "Progress in basic natural science is a matter of constantly rebuilding
from the very foundations. Significant progress is generally a matter, not of
adding further facts, but of changing the frame-work itself .... Science in the
main develops not by way of cumulation but by way of substitution and
replacement". In other words, science in the main does not develop in accord
ance with the so-called theory of asymptotic convergence: "The sequential filling
in of certain basically fixed positions in greater and greater detail-the working
out of more decimal places to lend additional refinement to a roughly pre
determined result" (N. Rescher in The Limits of Science).
The step from classical to quantum mechanics, which we assume to be
revolutionary in the above sense, is obviously not a matter of adding further facts
to classical mechanics, but of changing the framework of classical mechanics
itserf. Thus, the quantum-mechanical "picture of reality" should be composed
without using notions of classical mechanics. But it is difficult to decide which
notions are typical requisites of classical mechanics and which are not.
Our intuitive concepts are based on systems and processes which we observe
with our sense organs in everyday life, i.e. they describe reality at the so-called
macroscopic level. Classical mechanics is also based on macroscopic observ
ations, and its notions are chosen with respect to our intuitive demands for
visualizability. Knowledge about nature is extended by using more and more
refined measuring apparatus, and the macroscopic level is consequently left more
and more. At the microscopic level quantum phenomena are dominant and we
need to cope with a conceptual revision of the classical-mechanical framework.
The new (quantum-mechanical) level has led to violations of our intuitive
Preface VII
concepts; the framework of quantum theory is in striking conflict with our
intuitive demands for visualizability.
An adequate description at the quantum-mechanical level possibly requires
us to give up all classical notions. However, there are still quantities within the
present form of quantum theory which are in accord with intuitive concepts valid
at the macroscopic level. For example, the concept of a particle, i.e. an entity
localized in space, is an intuitive concept which was transferred from the
macroscopic to the microscopic level. "But the interpretation in terms of
particles is all in mind, and may be no more than a consistent delusion" (J.
Gribbin in In Search ofSchrodinger's Cat). Also time is treated classically at the
quantum-theoretical level: Within the present form of quantum theory, space
coordinates and time are not symmetrical to each other, which is in contrast to
the basic results of the special theory of relativity. The coordinates are operators
within usual quantum theory and play the role of statistical quantities; time,
however, does not behave statistically and remains a simple parameter when we
go from classical to quantum mechanics. Can notions like particles (local
existents) and time be transferred from the macroscopic to the microscopic level
without changing their meaning?
This volume deals with thefoundations and interpretation, as well as with new
aspects of quantum theory. It is divided into two parts, each containing three
chapters written by various authors. Part I of the book deals with the
foundations and interpretations of usual quantum theory. Chapter 1 introduces
the foundations, most of which are discussed from a historical point of view,
highlighting the original ideas which enabled the transfer from the macroscopic
to the microscopic level. The tortuous development of quantum theory after
quantum effects were first noticed in 1900 is described; it took 25 years before the
full (non-relativistic) formalism was realized.
This formalism shattered the basics of the mechanistic world view which is
based on Newton's mechanics. From Newton's point of view, the "picture of
reality" is given by the following imagination: In the beginning, God created
material objects, the forces between them, and the equations of motion. Then, the
whole universe was set in motion and it has continued to run ever since, like a
huge machine which is completely causal and determinate. Systems whIch are
governed by the laws of quantum theory are not determinate, and individual
events do not always have a well-defined cause. The construction of a quantum
mechanical "picture of reality" (i.e. the interpretation of quantum theory) is
today one of the most controversial problems in natural science.
The scientific community responded to the new quantum-theoretical formal
ism in two ways. The first direction was the application of the quantum theory to
phenomena in nature, and the quantum theory of solids, quantum field theory,
and nuclear physics were developed. The second way dealt with interpretative
questions of the new framework and was therefore more philosophically
oriented. In Chaps. 1,2 and 3 some of these interpretations are discussed. At first
glance it might seem that the research done on interpretative problems has no
VIII Preface
impact on the more practical problems of modern natural science. At the present
stage of quantum theory, however, the idea that a satisfactory quantum
theoretical "picture of reality" can only be found in connection with a revised
quantum-theoretical formalism cannot be excluded.
The following two events illustrate very distinctly quantum "weirdness":
1) In 1935 Einstein, Podolsky, and Rosen formulated a paradox (the EPR
paradox), and the three authors thought they could use it to show that reality
was incompletely described by quantum theory. For over thirty years physicists
and philosophers debated the conclusions of the EPR-paradox (the Einstein
Bohr-debate, etc.).
2) In 1965 Bell produced his inequalities, and his arguments have backfired
on the disciples of EPR: Effects that EPR never wanted to consider must be
introduced.
In Chap. 2 of this book Eberhard gives an introduction to the EPR paradox as
well as to Bell's inequalities. Eberhard summarized his ideas as follows: "Action
at a distance at a speed greater than the speed oflight was not an acceptable idea
for Einstein, Podolsky, and Rosen (EPR), but it was for Heisenberg. Today,
because of experimental results and theoretical analysis, such action looks, in all
likelihood, like a real effect. The argument leading to this conclusion can be
explained in simple terms, as long as the world "real" is given a conventional
meaning. However, the need for such action can also be shown with more general
definitions of this word. Several "pictures of reality" can still be drawn without
contradicting the results of any experiment performed to date. The choice
between the different possibilities depends partly on one's guess about the
outcome of possible future experiments and partly on one's philosophical view of
the world."
Chapter 3 is written by d'Espagnat and the following topics are included:
Realism and separability are discussed, and the latter notion is made quantitative
by means of a principle of separability. It is shown that this principle is disproved
by the developments centered on the Bell theorem. Furthermore, d'Espagnat
investigates the problem of defining the notion of properties of physical systems.
Delayed choice experiments, backward causality and similar questions are also
considered in Chap. 3. The various facts reviewed in Chap. 3 "distinctly support
the view that in spite of its predictive power contemporary physics does not lead
to a definite conception of the world". This statement by d'Espagnat should
be considered as the conclusion of Part I of this book; it reflects clearly
the unsatisfactory situation in the present day understanding of (quantum)
physics.
Part II deals with new aspects of quantum theory, and provides more
information about quantum "weirdness", though it is not possible to give here a
systematic survey - not even a schematic one - of all the recent debates that
quantum reality has inspired. The three chapters of this part of the book reflect
more or less this author's own activities.
Preface IX
Concerning Chap. 4 let us remark the following (P. Eberhard, private
communications): Bell's theorem shows a contradiction between several princi
ples we had wished could all be true, including the validity of quantum theory,
Einstein's relativity principle, causality acting forward in time, local objective
reality, and the structure of space and experiments support some of these
principles to a certain degree of accuracy only. The contradiction can be
removed by abandoning one or several of these principles. There is a choice.
Different physicists arrive at different solutions by selecting different principles
to violate from the list above. Their choice corresponds to what makes it easier
for them to have a picture of the world, and therefore tolerance is in order! To
satisfy a large group of people, one could give priority to the principles of
objective reality, causality forward in time, structure of space, and of locality.
There are ways to construct models of reality that satisfy these "high priority"
principles and also violate predictions of quantum theory by an infinitesimal
amount only. The parameters of these models can be adjusted so that the
discrepancies with quantum theory have no chance of being detected experi
mentally for many years to come or, alternatively, so that the discrepancies could
be revealed in future experiments while being insignificant in experiments
performed so far. Such models may inspire some aspects of experimental physics
program of the future. In Chap. 4 Eberhard shows the feasibility of models
satisfying the "high priority" principles and constructs such a model as an
example. This model reproduces the predictions of relativistic quantum theory to
any desired degree of accuracy. It involves quantities that are independent of the
observer's knowledge, and therefore can be called real, and which are defined at
each point in space, and therefore can be called local in a rudimentary sense. It
involves faster-than-light, but not instantaneous, action-at-a-distance.
Chapter 5 deals with the structure of space-time at the quantum-theoretical
level. Time remains a classical parameter in the transition from classical to
quantum mechanics, ahd this is the reason why there is no uncertainty relation
for energy and time in analogy to Heisenberg's position-momentum relation. In
Chap. 5 new aspects in connection with space and time are discussed. In
particular, a time operator is obtained and time actually becomes uncertain, in
analogy to the space-coordinates. In Chap. 5 space and time are treated as
auxiliary elements for the geometrical description of physically real processes; it
is argued that physically real processes do not take place in but are projected on
space-time. Within this picture we obtain not only an operator for the time, but
also new aspects in connection with the following topics: particle-wave duality,
the superposition principle, and the role of the observer.
The idea that objectively real quantum waves exist is discussed in Chap. 6 by
Selleri, i.e. not only is the particle assumed to be real, but the wave is too,
following the original proposal of Einstein and de Broglie. Selleri treats these real
waves as "empty" waves, where "empty" means that the waves propagate in
space and time, but are devoid of energy and momentum. The problem is how to
detect such empty waves. Can an empty wave induce changes in physical objects?
X Preface
It is argued in Chap. 6 that an empty wave could reveal its presence by modifying
the decay probabilities of unstable systems. A review of ideas proposed in recent
years for the performance of radically new experiments for the detection of such
empty waves is given. The effects discussed in Chap. 6 are not expected from the
point of view of the usual (Copenhagen) interpretation of quantum theory,
because there are no empty waves in the above sense, only probability
amplitudes.
The individual chapters of this book have been prepared by experts who have
made their own contributions to the subjects discussed in the book. However, a
quasi-monograph written by a number of authors can have drawbacks
compared with a monograph written by a single author: The contents cannot
achieve the same degree of homogeneity, a complete coverage of the subject
cannot be realized, and, conversely, overlaps are unavoidable. In the present
book these deficiencies could not be avoided completely.
In order to compile this book, it was necessary to bring together a team of
experts from several countries: B. d'Espagnat from the University of Paris-Sud,
France; P. Eberhard from the University of California at Berkeley, USA; and F.
Selleri from the University of Bari, Italy. I would like to thank each ofthe authors
for his excellent cooperation. Special thanks are due to the reviewers, who were
frequently required to read and discuss the contributions as they developed. Also
many thanks are due to W. Beiglbock from Springer-Verlag for valuable remarks
and encouragement.
Karlsruhe, December 1987 W. Schommers
Contents
1. Evolution of Quantum Theory
By W. Schommers ............................................. 1
1.1 Classical Pictures of Reality ................................ 1
1.1.1 Mythological and Intellectual Pictures .................. 1
1.1.2 Mechanistic View of the World ........................ 2
1.2 From Classical to Quantum Mechanics ....................... 6
1.2.1 Planck's Constant ................................... 7
1.2.2 Einstein's Picture of Light ............................ 11
1.2.3 The Structure of Atoms .............................. 12
1.2.4 Matter Waves, Schrodinger's Wave Equation, and Matrix
Mechanics .......................................... 17
1.2.5 Born's Probability Interpretation ...................... 25
1.2.6 Uncertainty ......................................... 28
1.2.7 The Principle of Complementarity ..................... 30
1.3 Theories of Measurement: Brief Remarks .................... 31
1.3.1 Objectivity.......................................... 31
1.3.2 The Measurement Problem ........................... 32
1.3.3 Theories of Measurement: Final Comments ............. 38
1.4 Summary ................................................ 39
Appendix 1.A. Classical Mechanics: Some Basic Remarks .......... 41
1.A.l The Principle of Least Action and Lagrange's Equations. . 41
1.A.2 Newton's Equations .................................. 42
1.A.3 Hamilton's Equations ................................ 43
1.A.4 The Hamilton-Jacobi Equations ....................... 44
Appendix 1.B. The Relation Between Schrodinger's Equations and
Classical Mechanics ....................................... 46
References .................................................... 47
2. The EPR Paradox. Roots and Ramifications
By P. H. Eberhard (With 4 Figures) .............................. 49
2.1 A Debate Lasting More Than Fifty Years ..................... 49
2.1.1 Are There Faster-Than-Light Effects in Quantum Phenomena? 49
2.1.2 Einstein's Point of View .............................. 51
2.1.3 Dissenting Voices .................................... 54
2.1.4 The Verdict of Experiment ............................ 56
2.2 A Far-Reaching Argument.................................. 58
