{
  "id": "1212.2601",
  "version": "v3",
  "published": "2012-12-11T20:04:53.000Z",
  "updated": "2015-10-19T08:09:32.000Z",
  "title": "Quantum Measurement and Initial Conditions",
  "authors": [
    "Ovidiu Cristinel Stoica"
  ],
  "comment": "14 pages, 4 figures",
  "journal": "Int. J. Theor. Phys. (2015): 1-15, 10.1007/s10773-015-2829-2",
  "doi": "10.1007/s10773-015-2829-2",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Quantum measurement finds the observed system in a collapsed state, rather than in the state predicted by the Schr\\\"odinger equation. Yet there is a relatively spread opinion that the wavefunction collapse can be explained by unitary evolution (for instance in the decoherence approach, if we take into account the environment). In this article it is proven a mathematical result which severely restricts the initial conditions for which measurements have definite outcomes, if pure unitary evolution is assumed. This no-go theorem remains true even if we take the environment into account. The result does not forbid a unitary description of the measurement process, it only shows that such a description is possible only for very restricted initial conditions. The existence of such restrictions of the initial conditions can be understood in the four-dimensional block universe perspective, as a requirement of global self-consistency of the solutions of the Schr\\\"odinger equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-15T18:33:02.000Z",
      "abstract": "If the state of a quantum system is known at a given time, unitary evolution tells us what it will be at future time, but the projection postulate in general predicts a different value. This measurement problem is believed by many physicists to be solved in several approaches which consider that unitary evolution can be reconciled with the wavefunction collapse, for instance by decoherence. In this article, it is shown that for any given measurement settings, only some of all possible initial conditions of the observed system are compatible to those of the measurement apparatus. This means that there is no way unitary collapse can accommodate the previous state of a quantum system, with the outcomes of any possible experimental settings. The only way to accommodate both of them is to allow the initial state of the system to depend on what measurements will undergo in the future. The result is derived mathematically, and can be viewed as a no-go theorem, which severely restricts the hopes that a unitary collapse approach can reconcile any initial condition with any experimental setup. We argue that this remains true in the standard formulations of quantum mechanics, both when we consider that the measurement process takes place unitarily, and when we assume non-unitary collapse. It also remains true for hidden variable theories, both deterministic and stochastic. For deterministic (including unitary) theories the condition of compatibility between the initial conditions of the observed system with those of the measurement apparatus applies indefinitely back in time. Initial conditions seem to be in a precise state which will become an eigenstate of any observable we will decide to measure. This can be understood from the four-dimensional block universe perspective, if we require any solution to be globally self-consistent.",
      "comment": "9 pages, 4 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-10-19T08:09:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial condition",
      "quantum measurement",
      "remains true",
      "quantum system",
      "unitary collapse approach"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "International Journal of Theoretical Physics",
      "year": 2016,
      "month": "Mar",
      "volume": 55,
      "number": 3,
      "pages": 1897
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016IJTP...55.1897S"
    }
  }
}