Morbert
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It's a term I'm borrowing from Barandes himself. For Bohmian mechanics it is the hypothesis that the configuration of a systems evolves in accordance with a wavefunction and guiding equation. Early versions interpreted the wavefunction as something real but modern versions treat it as nomological.Sambuco said:I'm intrigued by what these "speculative metaphysical hypotheses" you're talking about are.
From https://arxiv.org/pdf/2302.10778 :Without judging whether it's better or worse, I think this is because, in Bohmian mechanics, although the positions are hidden, something about them can be inferred from the measurements. For example, in the double-slit experiment, if the detector that clicks is in the upper half of the screen, the theory indicates that the particle crossed the upper slit. It seems to me that this isn't the case in Barandes's formulation (I need to reread the text you shared a while ago with Barandes' notes where he analyzes the double-slit experiment). In fact, I think it would be very enlightening if Barandes would publish about common experiments analyzed with his formulation.
Lucas.
"Note that the target time t is treated here as a real-valued variable that can be zero, positive, or negative, so there is no assumption of any fundamental breaking of time-reversal invariance."
I read this to mean, if the particle position is measured by the slit detectors at time ##t'##, we can presumably evolve a distribution backwards: ##p(t) = \Gamma(t\leftarrow t')p(t')## where ##t < t'##, and infer the likelihood that the particle passed through a slit, given that it was (or was not) detected by the adjacent detector. And since ##\Gamma(t)## is continuous, it means the closer the detector is to the slit, the more likely the detected particle passed through that slit.
Maybe there is a unistochastic equivalent to Vaidman's two-state formalism with $$\Gamma_{ijk}(t\leftarrow 0) = p(i, t | j, 0 \land k, t') = \mathrm{tr}(\Theta(t'\leftarrow t)P_i\Theta(t\leftarrow 0)P_j\Theta^\dagger(t\leftarrow 0)P_i\Theta^\dagger(t'\leftarrow t)P_k)$$so that the distribution can be conditioned on both the preparation division event and measurement division event.
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