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An Argument Against the Realistic Interpretation of the Wave Function

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Abstract

Testable predictions of quantum mechanics are invariant under time reversal. But the evolution of the quantum state in time is not so, neither in the collapse nor in the no-collapse interpretations of the theory. This is a fact that challenges any realistic interpretation of the quantum state. On the other hand, this fact raises no difficulty if we interpret the quantum state as a mere calculation device, bookkeeping past real quantum events.

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Notes

  1. Unless we rely on the assumption that lack of ‘genericity’ (low entropy) is a mark of the past, namely probabilistic thermodynamical arguments. On this, see [1].

  2. Throughout the article I assume for simplicity all eigenvalues to be non degenerate.

  3. Penrose observes in [3] that T-invariance is broken by two detectors \(d_1,d_2\) separated by a beam splitter, because \(P_{1\rightarrow 2}=\frac{1}{2}\) while \(P_{2\rightarrow 1}=1\). But this is a consequence of the asymmetric assumption that in reverse time the beam necessarily gets to \(d_1\): the state is fully specified at \(d_2\) but not at the \(d_1\). A non-time-symmetric setting yields a non-time-symmetric result.

  4. Again: unless we use lack of genericity as a mark of past configuration—namely thermodynamical arguments.

  5. As in classical mechanics, it is not sufficient to change sign to velocities: we must also change sign to all T-odd quantities, like the magnetic field and angular momenta.

  6. The situation is a bit like the official Catholic doctrine about the Mass, where two miracles happen: (i) bread is transformed into flesh, (ii) flesh miraculously looks like bread. Here, the quantum state reveals the direction of time, but keeps the info for itself.

  7. We ourselves function entropically, namely exploiting past low entropy, therefore it is not surprising that we break T invariance.

  8. For a recent analysis of time symmetry in collapse models see [12]. In this context the quantum event ontology is called “flash ontology” [13].

  9. A possible reply to these objections is to consider branching perspectival. The state of the universe is not branched and makes no distinction between past and future. It is our choice that isolates a substructure of the true universal wave function, and it is only this one that appears to display the branching and its time arrow. In other words, the true state of the system we observe in the laboratory is highly entangled in the past as well as the future, but we ignore the aspects of this state which are not relevant to our interest in predicting future evolution. The price to pay for taking this view is that the wave function we use in a concrete utilization of the theory is not the real wave function anymore. It is a theoretical booking devise about some limited information we happen to have about the actual state of the world, because of some past interactions. But if so, then the “real” state of WM and dBB is reduced to a hypothetical metaphysical entity about which we know very little; the quantity we call “state” when we use quantum theory, instead, turns out to be precisely a mere bookkeeping device for our time-oriented limited information! Along this line, MW and dBB start sounding like Lao Tzu [16]: “The Wave Function that can be spoken of, is not the True Wave Function”...

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  1. CNRS, CPT, Aix-Marseille University, University of Toulon, Marseille, France

    Carlo Rovelli

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  1. Carlo Rovelli
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Rovelli, C. An Argument Against the Realistic Interpretation of the Wave Function. Found Phys 46, 1229–1237 (2016). https://doi.org/10.1007/s10701-016-0032-9

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