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arXiv:2104.09945

The quantum mechanics of the present

Lee Smolin, Clelia Verde

Published Apr 20, 2021• 15 citations
arXivHTMLPDF

Abstract

We propose a reformulation of quantum mechanics in which the distinction between definite and indefinite becomes the fundamental primitive. Inspired by suggestions of Heisenberg, Schrodinger and Dyson that the past can't be described in terms of wavefunctions and operators, so that the uncertainty principle does not apply to past events, we propose that the distinction between past, present and future is derivative of the fundamental distinction between indefinite and definite. %The same is the case for the quantum world versus classical world distinction of the Copenhagen interpretation. We then outline a novel form of presentism based on a phenomonology of events, where an event is defined as an instance of transition between indefinite and definite. Neither the past nor the future fully exist, but for different reasons. We finally suggest reformulating physics in terms of a new class of time coordinates in which the present time of a future event measures a countdown to the present moment in which that event will happen.

DOI
10.48550/arxiv.2104.09945

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We propose a reformulation of quantum mechanics in which the distinction between definite and indefinite becomes the fundamental primitive. Inspired by suggestions of Heisenberg, Schrodinger and Dyson that the past can't be described in terms of wavefunctions and operators, so that the uncertainty principle does not apply to past events, we propose that the distinction between past, present and future is derivative of the fundamental distinction between indefinite and definite. %The same is the case for the quantum world versus classical world distinction of the Copenhagen interpretation. We then outline a novel form of presentism based on a phenomonology of events, where an event is defined as an instance of transition between indefinite and definite. Neither the past nor the future fully exist, but for different reasons. We finally suggest reformulating physics in terms of a new class of time coordinates in which the present time of a future event measures a countdown to the present moment in which that event will happen.
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The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive QM from more basic principles, these principles should be of general, philosophical nature. Here, we derive the formalism of QM from well-motivated epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. First, an epistemic formalism is developed, using concepts like knowledge and potential knowledge, identifying a physical state SSS with the potential knowledge of the physical world. It is demonstrated that QM emerges from this formalism. However, Hilbert spaces, wave functions and probabilities are defined in certain well-defined observational contexts only. This means that the epistemic formalism is broader than QM. In the fundamental layer of description, the physical state SSS is a subset of a state space S={Z}\mathcal{S}=\{Z\}S={Z}, such that SSS always contains many elements ZZZ. These elements correspond to unattainable states of complete knowledge of the world. The evolution of SSS cannot be determined in terms of the individual evolution of the elements ZZZ, unlike the evolution of an ensemble in classical phase space. The evolution of SSS is described in terms of sequential time n∈Nn\in \mathbf{\mathbb{N}}n∈N, which is updated according to n→n+1n\rightarrow n+1n→n+1 each time an event occurs, each time potential knowledge changes. Sequential time nnn can be separated from relational time ttt, which describes distances between events in space-time. There is an entire space-time associated with each nnn, in which ttt represents the knowledge at sequential time nnn about the temporal relations between present and past events.
The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is supposed to exist, nothing can discriminate two apparently identical states even if they give a different result. In this paper we try to put the basis for a more fundamental theory that (approximately) coincides with quantum mechanics when comparing statistics, but it is more fundamental, since it mathematically describes measurement processes giving an explicit time evolution of the wave function during the collapse. The theory is deterministic even if the Heisenberg uncertainty principle is still valid. The theory distinguishes physical states that collapse and physical states that do not collapse. The theory can be made compatible with all experiments done in the past, but new phenomena such as violations of the Born law or the superposition principle could transpire. However, even if we have probably shown that it is possible to build ad hoc a theory that can describe both the wave function collapse and the Schrödinger linear evolution, a simple and unified construction is still missing.
Modern quantum mechanics, despite its relativistic extensions, provides intriguing support for a present-centered view of time. This paper argues that quantum phenomena – indeterminacy, wavefunction collapse, the Born rule, and temporal asymmetries in measurement – challenge the static block universe of eternalism and instead elevate the present moment to ontological prominence. Remaining largely interpretation-neutral, we draw on a range of perspectives (from Einstein’s relativity to collapse models, and thinkers like Heisenberg, Rovelli, Maudlin and others) to show that quantum theory operationally distinguishes past, present, and future in a way classical physics did not. We examine how the measurement problem and the randomness of quantum outcomes resist a fully eternalist description, highlight how quantum mechanics introduces an arrow of time at a fundamental level, and consider proposals (e.g. GRW theory, delayed-choice experiments) that make a global present – or something akin to it – conceptually necessary. Classical philosophers and physicists from Einstein to Schrödinger are discussed alongside contemporary voices. While stopping short of endorsing any single ontology outright, we contend that the empirical success of quantum theory re-opens the case for presentism or related “A-theoretic” models of time. In closing, we introduce Existential Realism as a novel metaphysical framework aligning with these insights – one which preserves the special status of the present while accommodating the reality of past and future in a more dynamic ontology. The result is a rigorous yet accessible interdisciplinary inquiry: quantum physics, we conclude, prefers the present, suggesting time’s passage and the now are more than mere illusions.[1] [1] https://quoteinvestigator.com/2024/03/18/stubborn-illusion/#:~:text=%3E%20On%20Michele%20Besso%20%281873,245
The Heisenberg uncertainty principle is conventionally interpreted as a constraint on the precision of future measurement outcomes. We argue that this temporal asymmetry is not justified by the underlying mathematics of quantum mechanics, which is fundamentally time-symmetric. We propose that uncertainty applies equally in both temporal directions: the past has no greater ontological determinacy than the future. Between collapse events, prior states were no more determined than future states are now. Only the present moment of collapse constitutes anything approaching a definite physical state, and that moment is immediately receding into a past that was never fully determined before collapse occurred. We formalize this interpretation through a timesymmetric reading of the existing uncertainty relations and discuss its implications for the ontological status of the past, the measurement problem, and the foundations of physical determinism.
How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is answered without invoking knowledge or observers, by interpreting the necessary distinction between two kinds of physical quantities - unconditionally definite quantities and quantities that have values only if they are measured - as a distinction between the manifested world and its manifestation.