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Connecting the Dots: Mott for Emulsions, Collapse Models, Colored Noise, Frame Dependence of Measurements, Evasion of the “Free Will Theorem”


We review the argument that latent image formation is a measurement in which the state vector collapses, requiring an enhanced noise parameter in objective reduction models. Tentative observation of a residual noise at this level, plus several experimental bounds, imply that the noise must be colored (i.e., non-white), and hence frame dependent and non-relativistic. Thus a relativistic objective reduction model, even if achievable in principle, would be incompatible with experiment; the best one can do is the non-relativistic CSL model. This negative conclusion has a positive aspect, in that the non-relativistic CSL reduction model evades the argument leading to the Conway–Kochen “Free Will Theorem”.

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  1. In a stimulating email correspondence, Jerry Finkelstein has remarked that energetics would allow a spherical coherent superposition of latent image tracks, each with the energetics of formation of a single track, with the actual track that is formed picked out later by development. But this is not compatible with the standard, and verified, picture of latent image formation as a physical process in which atoms have moved, quite independent of the larger atomic motions that take place much later on development.

  2. We emphasize, by “performed in different frames” we specifically mean with the apparatus boosted to different frames. Boosting the apparatus to a new frame is different from performing an experiment in a fixed frame and viewing it from boosted frames, which gives the same result regardless of whether the physics of the experiment is Lorentz invariant or not, as long as “viewing” refers to use of electromagnetic radiation, which obeys the Lorentz covariant Maxwell equations.

  3. Instantaneous measurements are an idealization, and we leave for future study questions relating to finite measurement times: (1) With white noise, CSL predicts a measurement rate governed by the noise coupling and the initial state variance. For non-white noise, with correlation time \(t_C\), does this rate change so that the measurement time \(t_\mathrm{MEAS}\) is greater than \(t_C\)? (2) For successive measurements with white noise, different outcomes can be obtained with an infinitesimal time interval between measurements. With non-white noise, what is the minimal interval between successive measurements for independent outcomes to be possible? Is it of order \(t_C\)? (3) According to Eqs. (19) and (20), there is a minimum boost velocity v needed for a reversal of temporal ordering to be possible, given by \(v_\mathrm{MIN} > c^2/v_{AB}=c^2 (t_B-t_A)/(x_B-x_A)\). If we assume that \(t_B-t_A\) is at least the measurement time at A, does the implied condition \(v_\mathrm{MIN} > c^2 t_\mathrm{MEAS}/(x_B-x_A)\) suffice to guarantee that when B is in the boosted frame, the noise acting on B can give an outcome different from what would be obtained if B were in the same frame as A?


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I wish to thank Angelo Bassi, Jeremy Bernstein, Jerry Finkelstein, Shan Gao, Si Kochen, and Andrea Vinante for stimulating conversations and/or email correspondence about the mysteries of quantum measurement. This work was performed in part at the Aspen Center for Physics, which is supported by the National Science Foundation under Grant No. PHY-1607611.

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Correspondence to Stephen L. Adler.

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Adler, S.L. Connecting the Dots: Mott for Emulsions, Collapse Models, Colored Noise, Frame Dependence of Measurements, Evasion of the “Free Will Theorem”. Found Phys 48, 1557–1567 (2018).

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  • Mott
  • Emulsions
  • Collapse models
  • Non-white noise
  • Colored noise
  • Fame dependence
  • Measurements in quantum theory
  • Free Will Theorem