Precedence and freedom in quantum physics (Open Review Paper)

Lee Smolin (Perimeter Institute for Theoretical Physics)

A new interpretation of quantum mechanics is proposed according to which precedence, freedom and novelty play central roles. This is based on a modification of the postulates for quantum theory given by Masanes and Muller. We argue that quantum mechanics is uniquely characterized as the probabilistic theory in which individual systems have maximal freedom in their responses to experiment, given reasonable axioms for the behavior of probabilities in a physical theory. Thus, to the extent that quantum systems are free, in the sense of Conway and Kochen, there is a sense in which they are maximally free.

We also propose that laws of quantum evolution arise from a principle of precedence, according to which the outcome of a measurement on a quantum system is selected randomly from the ensemble of outcomes of previous instances of the same measurement on the same quantum system. This implies that dynamical laws for quantum systems can evolve as the universe evolves, because new precedents are generated by the formation of new entangled states.

Full text of this paper can be downloaded here.

Article written by

Lee Smolin

4 Responses

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    Referee's report

    The author suggests a new interpretation of quantum mechanics. This 
    interpretation consists mainly of two parts, which are conceptually 
    unified by the idea that "freedom" plays a major role in quantum theory.
    First, in what the author calls the "kinematical" viewpoint, it is 
    argued that quantum theory is the unique probabilistic theory which is 
    "maximally free", given a set of physically well-motivated axioms.
    Second, in the "dynamical" viewpoint, it is suggested that the actual 
    state assignment (that is, the density matrix which can be attached to a 
    given system) is given by the ensemble of all outcomes of all past 
    measurements that have been accomplished on identical copies of the 
    system in question. Since this can -- and need -- only work if the 
    number of precedents is large, the author suggests that novel systems -- 
    that is, ones with no or few precedents -- are actually "free" and not 
    determined by any statistical laws of physics.
    The transition between these two cases (very few resp. very many 
    precedents) is mainly stated as an open problem, with some interesting 
    ideas mentioned about nature choosing the simplest possibility.

    In my opinion, the ideas and insights in this paper are very interesting 
    and original, and could be a starting point for several possible lines 
    of more technical further research. The paper itself does not contain 
    very many results of technical nature, but this can be attributed to the 
    novelty of the approach: for example, there simply is no established 
    mathematical formulation of the notion that „outcomes are free, and not 
    determined by any statistical law". Non-determinism is usually modelled 
    in terms of probability, and at least the frequentist interpretation of 
    probability would be at odds with the ideas in this paper (even though 
    one might argue that a Bayesian point of view should still be 
    applicable). It is a conceptual and speculative paper, suggesting 
    interesting new ideas and viewpoints.
    The technical content, and the logic of the argumentation, are all 
    correct and accurate, as far as I can see. The insight that statistical 
    laws may be emergent over time -- since the first few outcomes may be 
    "free" without compromising asymptotic statistical predictions -- is 
    very interesting, and conceptually somewhat comparable to other 
    approaches, like the idea in Bohmian mechanics that quantum states arise 
    due to some long-time "equilibrium". One main benefit of the paper, as 
    it seems to me, is to point out the coincidence embodied in these two 
    1. Among all "reasonable" probabilistic theories, quantum mechanics is 
    "maximally free", in that the number of experiments K needed to 
    establish the state of an N-level system is as large as possible.
    2. Nature could very well be "free" to start with, in the sense that the 
    probabilistic laws are emergent. Then, one might expect that item 1. is 

    I recommend publication of the paper in the International Journal of 
    Quantum Foundations.

    I have one optional query, however. Even though the author has two 
    separate sections on "kinematical" and "dynamical" postulates, it seems 
    that they must somehow be physically intertwined to make sense: in the 
    end, the possible states that are generated dynamically (as ensembles of 
    precedents) must turn out to be in one-to-one correspondence with the 
    quantum density matrices. In other words, somehow the precedents must 
    "know" that they "should respect" the reasonable postulates 1-5 in the 
    course of building up quantum theory (Postulate 5 might be a simple 
    _consequence_ of the freedom in the beginning, but what about 1-4?) Or 
    can Postulate 1-4 even be understood as consequences of the physical 
    soundness of all previous realizations (that is, all precedents)?
    Maybe the author can say a few short sentences about this. However, this 
    is just an optional suggestion, because it might well be that answering 
    this question would be in large parts equivalent to specifying a 
    detailed mathematical mechanism for "how precedence builds up", which is 
    outside of the scope of this paper.

    Finally, some typos:
    p.2: "First, in quantum mechanics does not…": remove "in".
    p. 5: "which pick out" -> "which picks out"
    p. 8: „then a pure state“ -> „than a pure state“
    p. 10: "hidden variables theories" -> hidden variable theories
    p. 6 and p. 7: say that measurements must be *linear* maps.

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