Paul Merriam

This paper states and gives three applications of a novel ‘Presentist Fragmentalist’ interpretation of quantum mechanics. In a cognate paper it was explicitly shown this kind of presentism is consistent with special relativity and that it has implications for how to understand time as it relates to the Big Bang. In this paper we narrowly focus on three applications. These are surely the most important conundrums for any proposed interpretation of quantum mechanics: Schrodinger’s Cat, Bell non-locality, and the Born rule. It will be shown that these can be handled in a consistent and intuitive way.

This is a pdf of a Mathematica calculation that supplements the paper "Presentist Fragmentalism and Quantum Mechanics" forthcoming in Foundations of Physics. In that paper the Born rule (or at least a progenitor) is derived from experimental conditions on the mutual observations of two fragments. In this pdf the experimental conditions are applied to Hilbert space dimensions 3, 4, and 5. It turns out each of these have a 1-dimensional solution space which, it is hoped, can be interpretated as the phase.

There are long-standing questions about the Big Bang: What were its properties? Was there nothing before it? Was the universe always here? Many conceptual issues revolve around time. This paper gives a novel model based on McTaggart’s temporal distinction between the A-series (future-present-past) and B-series (earlier-times to later-times). These series are useful while situated in a Presentist and Fragmentalist account of quantum mechanics, one in which the consistency with the Special Relativity (in particular the relativity of simultaneity) will be made explicit (section 6). This allows us to make a fruitful distinction between two pertinent questions: what happens as we go to earlier times toward the Big Bang? And: what happens as we go further into the past toward the Big Bang?

Why is there something rather than nothing? I don’t know. But ‘nothing’ may not be the correct default state. It may be that the existence of possibilities requires fewer (weaker) assumptions. In this case, arguably, we should start with the existence of possibilities and not ‘nothing’. In this case, there exists the possibility of (for example) red qualia. But the possible existence of a red quale does not delineate what it is the possibility of if the possibility contains only a reference to red. Instead, the possibility must contain an actual instance of red to delineate what it is the possibility of. But, if possibilities are the weakest and (therefore) starting assumption, and the possibility of a red quale must itself contain an instance of red, then red exists necessarily. This argument would work for all qualia. Further, it could be that physical things and physical laws are (in some sense) instances of qualia. Incidentally, this would solve the problem of evil: pain, too, is made of qualia. These considerations align with some suggestions by Leibniz.

Many researchers suppose that the forward direction of time as a consequence of increasing entropy. But the human brain, including the human brain with memories, and life in general, are regarded as pockets of decreasing entropy, so as to accommodate the continual addition of memories and abilities. But then humans and life in general should see time going ‘backward’ in some sense. But we do not. Therefore, time is not entropic in origin. The purpose of this note is to bring attention to this idea.

It is often thought the relativity of simultaneity is inconsistent with presentism. This would be troubling as it conflicts with common sense and—arguably—the empirical data. This note gives a novel fragmentalist-presentist theory that allows for the (non-trivial) relativity of simultaneity. A detailed account of the canonical moving train argument is considered. Alice, standing at the train station, forms her own ontological fragment, in which Bob’s frame of reference, given by the moving train, is modified by the Lorentz transformations. On the other hand, Bob, in the train, forms his own ontological fragment from which Alice’s space and time are modified by the corresponding Lorentz transformations. Each fragment accommodates a unique present moment but does not contain information about the unique present moment of another fragment. This allows for a ‘universal’ present moment that extends throughout space, but only from the perspective of each fragment. The relativity of simultaneity is, as it were, ‘relativised’ to each fragment. This is related to the idea that, roughly speaking, the time of relativity is McTaggart’s (1908) B-series (earlier times to later times) and the time of quantum mechanics is a (fragmentalist) A-series (future/present/past), where these two related series characterize one dimension of time.

We start by asking the question of ‘why there is something rather than nothing’ and change this to the question of ‘what are the weakest assumptions for existence’ Eagle [1]. Then we give a kind of Fragmental Perspectivalism. Within this Fragmentalist interpretation of quantum mechanics (each quantum mechanical system forms a fragment) Merriam [2], it turns out McTaggart’s [3] A-series of time (the A-series is future to the present to the past) has a kind of perspectivalism. We then use McTaggart’s A-series and the B-series (the B-series is earlier times to later times) of time to differentiate between how far in the past the big bang was vs. how much earlier than now the big bang was. In one example model, the former goes infinitely far into the past while the latter stays finitely earlier-than. In this model the number of quantum interactions per unit 4-volume goes up to infinity as the big bang is approached from the present epoch.

We give an apparently new possible explanation for why there might be something rather than nothing—the weakest assumptions coupled with a kind of perspectivalism. Within a Fragmentalist interpretation of quantum mechanics (each quantum mechanics system forms a fragment), McTaggart’s A-series of time has this kind of perspectivalism. We then use the A-series and the B-series to differentiate between how far in the past the big bang was vs. how much earlier than now the big bang was. In one example model, the former goes to infinity while the latter stays finite. This implies the number of quantum interactions per unit 4-volume goes up to infinity as we approach the big bang from the present epoch.

This paper develops a Fragmentalist theory of Presentism and shows how it can help to develop a interpretation of quantum mechanics. There are several fragmental interpretations of physics. In the interpretation of this paper, each quantum system forms a fragment, and fragment f1 makes a measurement on fragment f2 if and only if f2 makes a corresponding measurement on f1. The main idea is then that each fragment has its own present (or ‘now’) until a mutual quantum measurement—at which time they come (‘become’) to share the same ‘now’. The theory of time developed here will make use of both McTaggart’s A-series (in the form of future-present-past) and B-series (earlier-times to later-times). An example of an application is that a Bell pair of electrons does not take on definite spin values until measurement because the measuring system and the Bell pair do not share the same present (‘now’) until mutual quantum measurement, i.e. until they ‘become’ to share the same A-series. Before that point the ‘now’ of the opposing system is not in the reference system’s fragment. Relativistic no-signaling is preserved within each fragment, which will turn out to be sufficient for the general case. Several issues in the foundations of quantum mechanics are canvassed, including Schrodinger’s cat, the Born rule, modifications to Minkowski space that accommodate both the A-series and the B-series, and entropy.

We motivate and develop a perspectival A-theory of time (future/present/past) and probe its implied interpretation of quantum mechanics. It will emerge that, as a first take, the time of relativity is a B-series (earlier-times to later-times) and the time of quantum mechanics is an A-series. There is philosophical motivation for the idea that mutual quantum measurement happens when and only when the systems’ A-series become one mutual A-series, as in the way qualia work in the Inverted Spectrum. This seems to account for certain quantum phenomena, including that the electrons of a Bell pair do not have definite spins until measurement, as ‘until’ here is a (perspectival) A-series notion. Various issues in the foundations of quantum mechanics are canvassed.