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Cambridge University Press eBooks

Conclusions and outlook

Lawrence S. Schulman

Published Jul 31, 1997• 0 citations
Publisher

Abstract

Less than meets the eye If even some of the ideas presented here are correct, the world is different from what it seems. The major theses of the book, on time's arrows and on quantum measurement theory, are unified by the notion of cryptic constraints . We see, sense, specify, macroscopic states, but what we predict about these states depends on an important assumption concerning their microscopic situation. The assumption is that the actual microstate is equally likely to be any of those consistent with the macrostate. And I say, not so. For various reasons, both classical and quantum, many otherwise-possible microstates are eliminated. As presented in detail in previous chapters, such elimination impacts many areas of physics, from the cosmos to the atom. But we also make the point that this elimination can be difficult to notice and in particular there is no experimental evidence that confirms the usual assumption. By an explicit example on a model (Fig. 4.3.2), we show that a future constraint eliminating 98% of the microstates can go completely unnoticed. My expectation is that this fundamental change in the foundations of statistical mechanics is needed. Whether or not it takes the forms I've proposed will be determined by future investigations. In the next section I will review open problems for the program implicit in this book. The tone will be that used in speaking with colleagues: an attempt to be frank about difficulties and a willingness to be wildly speculative.

DOI
10.1017/cbo9780511622878.012

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Introduction

Lawrence S. Schulman

In the next few pages I provide previews of the book: Section 1.1 is a statement of the main ideas. Section 1.2 is a chapter by chapter guide. There are two principal themes: time's arrows and quantum measurement. In both areas I will make significant statements about what are usually called their foundations. These statements are related, and involve modification of the underlying hypotheses of statistical mechanics. The modified statistical mechanics contains notions that are at variance with certain primitive intuitions, but it is consistent with all known experiments. I will try to present these ideas as intellectually attractive, but this virtue will be offered as a reason for study, not as a reason for belief. Historically, intellectual satisfaction has not been a reliable guide to scientific truth. For this reason I have striven to provide experimental and observational tests where I could, even where such experiment is not feasible today. The need for this hardheaded, or perhaps, intellectually humble, approach is particularly felt in the two areas that I will address. The foundations of thermodynamics and the foundations of quantum mechanics have been among the most contentious areas of physics; indeed, some would deny their place within that discipline. In my opinion, this situation is a result of the paucity of relevant experiment.

Cambridge University Press eBooks•Jul 31, 1997•0 citations

Time's arrow and the quantum measurement problem

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More them any other topic in the foundations of physics, the problem of the arrow (or arrows!) of time seems to be characterized by a unique ‘slipperiness’: it is not only difficult to find answers to the questions once posed, but difficult to find meaningful questions to ask in the first place. Perhaps this is because an asymmetry with respect to the sense of time is built into us at an even deeper level than other ‘synthetic a priori’ conceptions about the world such as the continued existence of unknown objects. However that may be, in this situation, rather than trying to pose general questions which may turn out in the end to be ill-defined, there may be something to be said for trying to formulate much less speculative, indeed perhaps in retrospect trivial questions to which at least we have a hope of finding a definite answer. This is what I shall do in this essay: to be specific, I shall ask whether a test which is currently being designed concerning the validity of a certain ‘common-sense’ view of the macroscopic world (‘macrorealism’) would be affected if we were to relax our common-sense assumptions about the direction of causality in time. Let me start with a very brief review of established ideas concerning the formal (a)symmetry of the quantum theory with respect to the direction of time. The classic works on this subject are the paper of Aharonov et al. (‘ABL’) and the book by Belinfante. In these discussions the notion of ‘measurement’ is taken as primitive and undefined.

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Conclusion

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The background for this book was a shift of interest among experimental physicists that began approximately 20 years ago. The shift was from quantum measurements on large ensembles of microscopic quantum objects, to experiments of very high precision on single, macroscopic objects. This shift was accompanied by developments in the “culture” of such measurements and the invention and elaboration of new experimental methods. In parallel with these experimental developments, there was a noticeable increase of theoretical interest in the foundations and interpretation of quantum theory, and even in attempts to revise its foundational principles. Although these efforts have not produced any significant changes in the fundamental structure of quantum theory, they have revealed a rather large number of “blank spots” and unsolved problems, to which the founders of quantum physics had paid no attention. A reasonable number of the blank spots have been filled in during the past decade. The reader has probably noticed that this book can be divided into two parts. In the first (chapters I―VII and XI), the authors have tried to present the modern approach to the quantum theory of measurement. This part can be regarded as a tutorial appendix to textbooks for advanced undergraduate or graduate-level courses in quantum mechanics, where little attention is usually paid to measurement theory.

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Selection of special states

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Why should special states occur as initial conditions in every physical situation in which they are needed? Half this book has been devoted to making the points that initial conditions may not be as controllable as they seem; that there may be constraints on microscopic initial conditions; that this would not have been noticed; that such constraints can arise from two-time or future conditioning; that in our universe such future conditioning may well be present, although, as remarked, cryptic . In this chapter I will take up more detailed questions: what future conditions could give rise to the need for our ‘special’ states, and why should those particular future conditions be imposed. Before going into this there is a point that needs to be made. Everything in the present chapter could be wrong and the thesis of Chapter 6 nevertheless correct. It is one thing to avoid grotesque states (and solve the quantum measurement problem) by means of special states and it is another provide a rationale for their occurrence. I say this not only to highlight the conceptual dependencies of the theses in this book, but also because there is a good deal of hand waving in the coming chapter and I don't want it to reflect unfavorably on the basic proposal. As pointed out earlier, the usual thermodynamic arrow of time can be phrased as follows: initial states are arbitrary, final states special.

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Is it a matter of size?

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The last two chapters have described two extreme views of the quantum measurement problem. On the one hand it was suggested that the laws of quantum physics are valid for all physical systems, but break down in the assumed non-physical conscious mind. On the other hand the many-worlds approach assumes that the laws of physics apply universally and that a branching of the universe occurs at every measurement or measurement-like event. However, although in one sense these represent opposite extremes, what both approaches have in common is a desire to preserve quantum theory as the one fundamental universal theory of the physical universe, able to explain equally well the properties of atoms and subatomic particles on the one hand and detectors, counters and cats on the other. In this chapter we explore an alternative possibility, that quantum theory may have to be modified before it can explain the behaviour of large-scale macroscopic objects as well as microscopic systems. We will require that any such modification preserves the principle of weak reductionism discussed towards the end of Chapter 5. The first point to be made is that the problems we have been discussing seem to make very little difference in practice. As we emphasised in Chapter 1, quantum physics has been probably the most successful theory of modern science. Wherever it can be tested, be it in the exotic behaviour of fundamental particles or the operation of the silicon chip, quantum predictions have always been in complete agreement with experimental results.

Cambridge University Press eBooks•Mar 26, 2012•0 citations

Is it a matter of size?

Alastair I. M. Rae

The last two chapters have described two extreme views of the quantum measurement problem. On the one hand it was suggested that the laws of quantum physics are valid for all physical systems, but break down in the assumed non-physical conscious mind. On the other hand the many-worlds approach assumes that the laws of physics apply universally and that a branching of the universe occurs at every measurement or measurement-like event. However, although in one sense these represent opposite extremes, what both approaches have in common is a desire to preserve quantum theory as the one fundamental universal theory of the physical universe, able to explain equally well the properties of atoms and subatomic particles on the one hand and detectors, counters and cats on the other. In this chapter we explore an alternative possibility, that quantum theory may have to be modified before it can explain the behaviour of large-scale macroscopic objects as well as microscopic systems. We will require that any such modification preserves the principle of weak reductionism discussed towards the end of Chapter 5. The first point to be made is that the problems we have been discussing seem to make very little difference in practice. As we emphasised in Chapter 1, quantum physics has been probably the most successful theory of modern science. Wherever it can be tested, be it in the exotic behaviour of fundamental particles or the operation of the silicon chip, quantum predictions have always been in complete agreement with experimental results.

Cambridge University Press eBooks•Oct 7, 2004•0 citations
Less than meets the eye If even some of the ideas presented here are correct, the world is different from what it seems. The major theses of the book, on time's arrows and on quantum measurement theory, are unified by the notion of cryptic constraints . We see, sense, specify, macroscopic states, but what we predict about these states depends on an important assumption concerning their microscopic situation. The assumption is that the actual microstate is equally likely to be any of those consistent with the macrostate. And I say, not so. For various reasons, both classical and quantum, many otherwise-possible microstates are eliminated. As presented in detail in previous chapters, such elimination impacts many areas of physics, from the cosmos to the atom. But we also make the point that this elimination can be difficult to notice and in particular there is no experimental evidence that confirms the usual assumption. By an explicit example on a model (Fig. 4.3.2), we show that a future constraint eliminating 98% of the microstates can go completely unnoticed. My expectation is that this fundamental change in the foundations of statistical mechanics is needed. Whether or not it takes the forms I've proposed will be determined by future investigations. In the next section I will review open problems for the program implicit in this book. The tone will be that used in speaking with colleagues: an attempt to be frank about difficulties and a willingness to be wildly speculative.
In the next few pages I provide previews of the book: Section 1.1 is a statement of the main ideas. Section 1.2 is a chapter by chapter guide. There are two principal themes: time's arrows and quantum measurement. In both areas I will make significant statements about what are usually called their foundations. These statements are related, and involve modification of the underlying hypotheses of statistical mechanics. The modified statistical mechanics contains notions that are at variance with certain primitive intuitions, but it is consistent with all known experiments. I will try to present these ideas as intellectually attractive, but this virtue will be offered as a reason for study, not as a reason for belief. Historically, intellectual satisfaction has not been a reliable guide to scientific truth. For this reason I have striven to provide experimental and observational tests where I could, even where such experiment is not feasible today. The need for this hardheaded, or perhaps, intellectually humble, approach is particularly felt in the two areas that I will address. The foundations of thermodynamics and the foundations of quantum mechanics have been among the most contentious areas of physics; indeed, some would deny their place within that discipline. In my opinion, this situation is a result of the paucity of relevant experiment.
More them any other topic in the foundations of physics, the problem of the arrow (or arrows!) of time seems to be characterized by a unique ‘slipperiness’: it is not only difficult to find answers to the questions once posed, but difficult to find meaningful questions to ask in the first place. Perhaps this is because an asymmetry with respect to the sense of time is built into us at an even deeper level than other ‘synthetic a priori’ conceptions about the world such as the continued existence of unknown objects. However that may be, in this situation, rather than trying to pose general questions which may turn out in the end to be ill-defined, there may be something to be said for trying to formulate much less speculative, indeed perhaps in retrospect trivial questions to which at least we have a hope of finding a definite answer. This is what I shall do in this essay: to be specific, I shall ask whether a test which is currently being designed concerning the validity of a certain ‘common-sense’ view of the macroscopic world (‘macrorealism’) would be affected if we were to relax our common-sense assumptions about the direction of causality in time. Let me start with a very brief review of established ideas concerning the formal (a)symmetry of the quantum theory with respect to the direction of time. The classic works on this subject are the paper of Aharonov et al. (‘ABL’) and the book by Belinfante. In these discussions the notion of ‘measurement’ is taken as primitive and undefined.
The background for this book was a shift of interest among experimental physicists that began approximately 20 years ago. The shift was from quantum measurements on large ensembles of microscopic quantum objects, to experiments of very high precision on single, macroscopic objects. This shift was accompanied by developments in the “culture” of such measurements and the invention and elaboration of new experimental methods. In parallel with these experimental developments, there was a noticeable increase of theoretical interest in the foundations and interpretation of quantum theory, and even in attempts to revise its foundational principles. Although these efforts have not produced any significant changes in the fundamental structure of quantum theory, they have revealed a rather large number of “blank spots” and unsolved problems, to which the founders of quantum physics had paid no attention. A reasonable number of the blank spots have been filled in during the past decade. The reader has probably noticed that this book can be divided into two parts. In the first (chapters I―VII and XI), the authors have tried to present the modern approach to the quantum theory of measurement. This part can be regarded as a tutorial appendix to textbooks for advanced undergraduate or graduate-level courses in quantum mechanics, where little attention is usually paid to measurement theory.
Why should special states occur as initial conditions in every physical situation in which they are needed? Half this book has been devoted to making the points that initial conditions may not be as controllable as they seem; that there may be constraints on microscopic initial conditions; that this would not have been noticed; that such constraints can arise from two-time or future conditioning; that in our universe such future conditioning may well be present, although, as remarked, cryptic . In this chapter I will take up more detailed questions: what future conditions could give rise to the need for our ‘special’ states, and why should those particular future conditions be imposed. Before going into this there is a point that needs to be made. Everything in the present chapter could be wrong and the thesis of Chapter 6 nevertheless correct. It is one thing to avoid grotesque states (and solve the quantum measurement problem) by means of special states and it is another provide a rationale for their occurrence. I say this not only to highlight the conceptual dependencies of the theses in this book, but also because there is a good deal of hand waving in the coming chapter and I don't want it to reflect unfavorably on the basic proposal. As pointed out earlier, the usual thermodynamic arrow of time can be phrased as follows: initial states are arbitrary, final states special.
The last two chapters have described two extreme views of the quantum measurement problem. On the one hand it was suggested that the laws of quantum physics are valid for all physical systems, but break down in the assumed non-physical conscious mind. On the other hand the many-worlds approach assumes that the laws of physics apply universally and that a branching of the universe occurs at every measurement or measurement-like event. However, although in one sense these represent opposite extremes, what both approaches have in common is a desire to preserve quantum theory as the one fundamental universal theory of the physical universe, able to explain equally well the properties of atoms and subatomic particles on the one hand and detectors, counters and cats on the other. In this chapter we explore an alternative possibility, that quantum theory may have to be modified before it can explain the behaviour of large-scale macroscopic objects as well as microscopic systems. We will require that any such modification preserves the principle of weak reductionism discussed towards the end of Chapter 5. The first point to be made is that the problems we have been discussing seem to make very little difference in practice. As we emphasised in Chapter 1, quantum physics has been probably the most successful theory of modern science. Wherever it can be tested, be it in the exotic behaviour of fundamental particles or the operation of the silicon chip, quantum predictions have always been in complete agreement with experimental results.
The last two chapters have described two extreme views of the quantum measurement problem. On the one hand it was suggested that the laws of quantum physics are valid for all physical systems, but break down in the assumed non-physical conscious mind. On the other hand the many-worlds approach assumes that the laws of physics apply universally and that a branching of the universe occurs at every measurement or measurement-like event. However, although in one sense these represent opposite extremes, what both approaches have in common is a desire to preserve quantum theory as the one fundamental universal theory of the physical universe, able to explain equally well the properties of atoms and subatomic particles on the one hand and detectors, counters and cats on the other. In this chapter we explore an alternative possibility, that quantum theory may have to be modified before it can explain the behaviour of large-scale macroscopic objects as well as microscopic systems. We will require that any such modification preserves the principle of weak reductionism discussed towards the end of Chapter 5. The first point to be made is that the problems we have been discussing seem to make very little difference in practice. As we emphasised in Chapter 1, quantum physics has been probably the most successful theory of modern science. Wherever it can be tested, be it in the exotic behaviour of fundamental particles or the operation of the silicon chip, quantum predictions have always been in complete agreement with experimental results.