Structure and interpretation of quantum mechanics pdf

He canvasses some of the solu- tions that have been proffered - - the many-worlds interpretation receives the most exten- sive discussion - - but finds all to be lacking. Readers might find the discussion a little unconvincing - - they may feel that if only we worked a little harder we might obtain a solution from one of those on offer - - but I think that Hughes is fight to be brief.

None of the views that Hughes considers has carried the day and it is proper that they should be mentioned if only to note that fact.

The many-worlds interpretation will probably continue to be the favourite among fantasists despite the lack of wider success - - proba- bly no criticisms of the view, the main one of which was ably made by John Earman some years ago, will dampen its proponents' ardour. There are proposals for the solution to the measurement problem that Hughes does not discuss - - the recent suggestions by Jeffrey Bub and Richard Healey being the two most notable omissions.

However since many of these solutions require there to be a substantial alteration to the theory they are less interpretations than simply different the- ories. The view favoured, tentatively, by Bell himself, for example, the Ghirardi, Rimini and Weber view GRW requires giving up the Schr6dinger equation for a non-unitary approximation. But Hughes' own interpretation of quantum mechanics, which emerges in ch.

His aim is to interpret the theory as we currently find it, measurement warts and all. Thus it is, like the Copenhagen interpretation with which it shares many features, a minimal interpretation remembering that old advertisement, we could call it a Clayton's interpretation. What, then, are its main features? For a start Hughes believes that, as noted above, there can be no unconditional prop- erties: these are ruled out by the Kochen-Specker and Gleason theorems.

Hughes' answer is that there are latencies. These latencies turn out to be trnthmakers for the propensity of a system to yield a particular value when a measurement is made. Indeed it is a single truthmaker for the various, possibly incompatible, measurements. It is thus tied to the non-Boolean algebra of states which guarantees its quantum character. It seems to me, however, that these latencies are nothing more than the quantum state under another name.

Calling a state a latency may serve to give it a comfortable 'homey', ring but it does not solve the problem of how the macroscopic world which is Downloaded by [University of Auckland Library] at 12 November pretty well everything above chemistry appears classical notwithstanding liquid helium which has a rather bizarre quantum character and definite, with the quantum con- stituents only having latencies.

Renaming states will not solve tha t problem. It is also true that at some point sooner or later, and as we now see it is sooner after all, the mea- surement problem proper comes back to revenge itself on the sleeping town.

The condi- tionals for which the latencies are truthmakers have in their antecedents a reference to measurements and measurement set-ups. But these are largely classical systems with, apparently unconditional, properties. Suppose we treat these objects as large quantum systems, as we must if we are to take quantum mechanics seriously, then the measure- ment systems have only a propensity to have a particular property if a suitable measure- ment is made on them.

But then this new measurement device which tests the first one will itself only have a latency to reveal some property if measured. And so on and on, in an infinite regress. We are thus at an impasse. Unconditional properties cannot exist by the Kochen- Specker and Gleason theorems but conditional properties, that employ terms like mea- surement that cannot be spelled out in quantum terms, require a regress that there seems no hope of stopping. If we try to meet this challenge by attempting to give an analysis of measurement in quantum terms then we face anew the problem that it seems not to be able to be done.

It follows that Hughes' own solution cannot be the whole truth. Despair seems to face us at every turn. We must abandon the idea that a minimal inter- pretation is all that is needed. We are now in a position to get a bird's eye view of the measurement problem in all its fearful complexity, bringing back in the interpretation of probabilities.

At first blush it will not do to just opt for simple, i. Yet the mea- surement of the separate particles is a matter of non-simple, conditionalized chance. So one and the same situation points in two rather different directions, to superdetermin- ism and to indeterminism. It is very unhelpful for philosophers to wrap this up in the graffito-style slogan: determinism is false.

What most philosophers of quantum mechanics would like is to be able to make the conditionalized probabilities conditional upon something straight-forwardly physical. This would rule out naive dualism 'Conscious observers collapse the wave packet! If, for example, it were the interaction of a particle with the environment, including the measurement apparatus, that caused the collapse, then the existence of conditional properties would no longer look so troubling.

If this suggestion were right, and there is no saying that it is, though some physi- cists have been attracted to it of late see [8] , then the probabilities could be subjective probabilities, though still the consequence of a conditional the environment being fully sufficient for collapse ; or the probabilities could be objective with the collapsed state not being uniquely determined by the interaction with the environment.

If the superpo- sitional states are sufficiently controlled by the environment then we will he able to explain why the macroscopic world looks classical: the superpositional states are usually Downloaded by [University of Auckland Library] at 12 November collapsed before they become noticeable. However it is, in my view, a big mistake to think that a solution to the measurement problem requires that a quantum account of the microscopic world converge to a classical description of the macroscopic world.

We do not, and should not, want a classical description of the macroscopic world - - we should want a quantum description, but one that allows us to see why the world looks classical, or looked it for so long. This mistake, often enough made, is a residue of Bohr's Copenhagen confusions, in which the classical descriptions are inviolate over their domain. Yet for all the attractiveness of this kind of resolution it cannot be the whole story - - even if it were to turn out to be some part of it.

For one thing it does not give us any handle on the EPR situation: we do not gain any explanation of the way pure composite systems factor into correlated but separate parts.

Secondly, it is a little difficult to believe that the macroscopic world looks as it does only because the superpositions can't grow too large. Surely there is more to it. There is one way out of the second problem only , considered and rejected by Hughes, that I believe is worth taking more seriously.

Beltrametti and Cassinelli have noted that superselection rules act tO prevent some of the superpositions that a Hilbert space structure would allow. For example a system in a superposition of integer and half-integer spin states seems not to be a realizable state though the Hilbert space formal- ism alone does not rule it out. They suggest that such superselection rules might rule out superpositions of distinguishable macroscopic states such as measurement systems that point to different outcomes.

We don't see them because nature can't form such states. This would go some way to telling us what is allowable in the interaction between a quantum system and a measurement apparatus.

This suggestion could not itself however be the whole story for it has implications for quantum mechanics that would require some drastic changes. The problem is, as Hughes observes, that superselection rules cut up the Hilbert space into discrete sectors - - super- selection zones - - and the Hamiltonian operator cannot evolve out of one zone into another. The system would be trapped in some subspace of the Hilbert space and normal Schr6dinger evolution would not be able to release it.

It would obviously be no solution to the measurement problem to adopt an account in which the measurement apparatus cannot change from one pointer position to another. The only solution would be to deny that the energy of the system is an observable, some- thing that at first sight appears deeply implausible. I believe, however, that it may not be as implausible as it first sounds. It may be that the energy is unique among observables. A significant point to note in this con- text is that the Hamiltonian does double service in quantum mechanics, appearing as a measurable operator and also as the generator of the time evolution of the system in the Schrfdinger equation.

This alone would make it special. We can add to this by noting that it appears differently in the two roles. In its role as the generator of the time evolu- tion it is essential that it be the unbounded self-adjoint operator and not the spectral pro- jections that can be obtained from it by the Spectral Theorem. In fact it functions rather Downloaded by [University of Auckland Library] at 12 November as a classical variable in that context with the domain restrictions on the operator largely ignored.

When we look to its other role of providing a representation for the energy of a system we can utilize the spectral projections thus avoiding the problems associated with the unbounded operator. Much work has been done recently on unbounded, continuous spectrum, operators and it is clear that they do not function in the same way as operators that are bounded including the bounded spectral projections from which they are com- pounded.

For one thing they do not obey a principle of repeatability. I have presented an argument elsewhere which suggests that one could not solve the problems of the Hamiltonian as it appears as the infinitesimal generator of the time evolution by moving to the spectral projections because there will be an indenumerable number of states for which the time evolution is not defined - - something that would require drastic rethink- ing of the role of the Hamiltonian in the time evolution see [5].

This conclusion is avoided by practitioners of the theory by effectively treating the Hamiltonian as just a classical variable. If this manoeuvre contains agrain of truth may it not suggest that the energy requires special treatment just as the superseleetion argument suggests?

It is too early to say anything more than that the matter deserves more consideration. It should be noted, however, that Jeffrey Bub's interpretation see [4] is compatible with these considerations and indeed strongly suggests the need to make the kinds of changes con- sidered above. It is no objection to Hughes' account that he does not discuss these pos- sibilities since they require such large changes to the theory that they could hardly be described any longer as part of a minimal interpretation.

Hughes has written a lucid account of quantum mechanics in its main lines of devel- opment. Of all the books that have come out recently on the theory it is probably the only one that could be recommended without hesitation to students wishing to find their way in to the subj.

It is also a book of robust good sense, in a subject in which sense can seem rather old-fashioned, even metaphysical. It is written in a pedagogical style and addresses many thorny problems of fundamental physics. The first aspect concerns Interpretation.

The author raises the central problems: formalism, measurement, non-locality, and causality. The main positions on these subjects are presented and critically analysed. The aim is to show that the main schools can converge on a core interpretation. The second aspect concerns Foundations. Here it is shown that the whole theory can be grounded on information theory. The distinction between information and signal leads us to integrating quantum mechanics and relativity.

Category theory is presented and its significance for quantum information shown; the logic and epistemological bases of the theory are assessed. Of relevance to all physicists and philosophers with an interest in quantum theory and its foundations, this book is destined to become a classic work. Written by an internationally renowned philosopher, this volume offers a three-part philosophical interpretation of quantum physics. The first part reviews the basics of quantum mechanics; the second outlines the mathematical methods of quantum mechanics; and the third section develops a variety of interpretations of quantum mechanics.

Compatible with any devices. Quantum mechanics is an extraordinarily successful scientific theory. But more than years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them.

Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The discussion is supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem. Authored by an acclaimed teacher of quantum physics and philosophy, this textbook pays special attention to the aspects that many courses sweep under the carpet.

Traditional courses in quantum mechanics teach students how to use the quantum formalism to make calculations.

But even the best students - indeed, especially the best students - emerge rather confused about what, exactly, the theory says is going on, physically, in microscopic systems. This supplementary textbook is designed to help such students understand that they are not alone in their confusions luminaries such as Albert Einstein, Erwin Schroedinger, and John Stewart Bell having shared them , to sharpen their understanding of the most important difficulties associated with interpreting quantum theory in a realistic manner, and to introduce them to the most promising attempts to formulate the theory in a way that is physically clear and coherent.

The text is accessible to students with at least one semester of prior exposure to quantum or "modern" physics and includes over a hundred engaging end-of-chapter "Projects" that make the book suitable for either a traditional classroom or for self-study.

This important work provides an account of the philosophical foundations of quantum theory that should become a classic text for scientists and nonscientists alike. Hughes offers the first detailed and accessible analysis of the Hilbert-space models used in quantum theory and explains why they are so successful.

He goes on to show how the very suitability of Hilbert spaces for modeling the quantum world gives rise to deep problems of interpretation, and makes suggestions about how they can be overcome. Conceptual Foundations of Quantum Mechanics provides a detailed view of the conceptual foundations and problems of quantum physics, and a clear and comprehensive account of the fundamental physical implications of the quantum formalism. This book deals with nonseparability, hidden variable theories, measurement theories and several related problems.

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Quantum mechanics over sets. In the tradition of toy models of quantum mechanics in vector spaces over finite fields e. Relational Quantum Mechanics I. I suggest that the common unease with taking quantum mechanics as a fundamental description of nature the measurement problem could derive from the use of an incorrect notion, as the unease with … Expand. Partial Description of Quantum States.

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Attention is … Expand. A modal-Hamiltonian interpretation of quantum mechanics.