The interpretation of quantum mechanics is beset with pseudo-problems, which are dealt with in another section. This section is dedicated to the genuine problems of interpretation with which the general theoretical framework of contemporary physics confronts us.
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How can this theory be complete? |
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A fundamental physical theory concerned with nothing but statistical correlations between value-indicating events presupposes the occurrence of such events. Since it presupposes them, it is trivially consistent with their occurrence.
One pseudo-problem that quite a few interpreters of the quantum formalism worry about is how the formalism can be made consistent with the fact that measurements have outcomes. Go figure.
But how can such a theory be complete? How can it at the same time encompass the value-indicating events?
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The macroworld |
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The nub of the matter is this: among the world's more or less fuzzy relative positions, the least fuzzy are in a category of their own.
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Facts and possibilities |
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The first question raised in this section was: how can a fundamental physical theory concerned with nothing but statistical correlations between value-indicating events, be complete? In other words: how can it both presuppose and encompass these events?
In preparation for an answer, we raised another question: which substructure of the theoretical structure of quantum mechanics corresponds to What Exists? To this question we now have an answer: the macroworld, defined as the totality of (existing) macroscopic positions.
We now return to the first question.
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Interim summary |
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The extrinsic nature of the values of observables — they must be indicated in order to be possessed — appears to entail a vicious regress. A particle's position has a value only if, only when, and only to the extent that a value is indicated (by a detector in the broadest sense of the word). But the same is true of a detector's position. Particle positions presuppose particle detectors, detector positions presuppose detector detectors, and so an ad infinitum. You may recognize this as a version von Neumann's "catastrophe of infinite regression."
Somewhere the buck must stop. Some properties must be different, not by arbitrary decree but as a consequence of the principles of quantum mechanics.
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Causality |
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Because quantum-mechanical probabilities are assigned on the supposition that there is an outcome (or, what comes to the same, on the supposition that the probabilities of the possible outcomes of a measurement add up to 1), value-indicating events (such as the transition of a pointer from its neutral to a value-indicating position) lack causally sufficient conditions. Such events are unpredictable not in the "anemic" sense associated with the chaotic regime of a deterministic system, for there is no such thing as a deterministic system, nor are they unpredictable merely in the trivial sense that the outcome of a successful measurement cannot be predicted in general. Value-indicating events are unpredictable also in the sense that it is impossible to predict their occurrence.
It is therefore beyond the scope of the quantum theory to provide sufficient conditions for the occurrence of a value-indicating event. If quantum theory is indeed the fundamental theoretical framework of physics — and neither are there empirical reasons to doubt it nor does anyone have the faintest ideas what could replace it — this means that value-indicating events are uncaused.
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Locality and the Aharonov-Bohm effect |
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Remember the two-slit experiment with electrons. We now add to the setup a thin, long solenoid, which we place right behind (or right in front of) the slit plate, between the two slits. If no current is flowing, we observe the usual interference pattern. If a current is flowing, the interference patterns is shifted to the right or to the left (depending on the direction of the current).
This effect was first predicted by Yakir Aharonov and David Bohm in 1959, and it was first observed the following year. By then the quantum laws, from which this effect is readily derived, were known for over thirty years. Why did it take that long to predict this effect?
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A new paradigm — the central mystery — manifestation |
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There are three reasons why the foundation of the quantum world is "above":
It is therefore no longer appropriate to ask: "what are the ultimate building blocks, and how do they interact and combine?" The twenty-five centuries old buttom-up paradigm has passed its expiry date. It is true that "quantum mechanics makes absolutely no sense" (Roger Penrose) — as long as we try to force it into an outdated interpretational framework. Quantum mechanics calls for a new paradigm.
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Which is incomplete: quantum mechanics or the physical world? |
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We have demonstrated that quantum mechanics is a complete theory, in the sense that the structure of the theory contains the macroworld as a substructure, and that this contains the value-indicating events presupposed by the theory. There are, however, other reasons for believing that the theory is incomplete.
- It is beyond the scope of the theory to provide sufficient conditions for the occurrence of a value-indicating event.
- The theory does not permit us to attribute values to unmeasured observables.
- It confines the use of causal concepts to the macroworld.
- It does not permit us to carry the spatiotemporal differentiation of the physical world all the way down.
- The quantum-mechanical correlation laws leave no room for a physical mechanism or process by which measurement outcomes determine the probabilities of measurement outcomes.
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The Force |
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So quantum theory is both fundamental and complete. What is incomplete is the physical world — in relation to a completely differentiated spatiotemporal background, which only exists in our imagination.
While this incompleteness of the objective world is exciting and important news, the non-existence of an underlying microcausal nexus, of any process by which measurement outcomes determine the probabilities of measurement outcomes, and of causally sufficent conditions for value-indicating events, may be cause for concern.
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Why quantum mechanics? |
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This question can be addressed at various levels. One may ask: why (and, perhaps, to what extent) does Reality subject its Force to the quantum-mechanical correlation laws? This article sets itself a less ambitious goal. Let us assume the existence of objects that
- have spatial extent (they "occupy" space),
- are composed of a (large but) finite number of objects that lack spatial extent (they do not "occupy" space),
- and are stable — they neither collapse nor explode as soon as they are created.
To what extent does the existence of such objects determine the laws of physics?
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Why the laws of physics are just so |
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The upshot of the previous article was that the formalism of non-relativistic quantum physics is a direct consequence of the existence of stable objects that (i) "occupy space" and (ii) are composed of finite numbers of objects that don't.
There is more that can be deduced from the existence of such objects and, in fact, from the mere requirement that quantum theory be self-consistent.
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