Three Myths about Time Reversal in Quantum Theory

Roberts, Bryan W.

doi:10.1086/690721

Cited by 35 publications

(43 citation statements)

References 18 publications

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“…Let us check (13): If ψ satisfies the IBC (22) with given g = (g 1 ...g N ), then ψ * satisfies it with g * instead of g. In fact (as becomes clear from [13]), if ψ lies in the domain of H IBC g , then ψ * lies in that of H IBC g * , and, as visible from the explicit form (23) of H IBC g , (13) holds. Likewise for (17): If ψ satisfies the IBC (22), g satisfies (16), and T is given by (15), then T ψ satisfies the IBC (22) as well…”

Section: Well-defined Hamiltonianmentioning

confidence: 99%

Complex charges, time reversal asymmetry, and interior-boundary conditions in quantum field theory

Schmidt¹,

Tumulka²

2019

J. Phys. A: Math. Theor.

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While fundamental physically realistic Hamiltonians should be invariant under time reversal, time asymmetric Hamiltonians can occur as mathematical possibilities or effective Hamiltonians. Here, we study conditions under which nonrelativistic Hamiltonians involving particle creation and annihilation, as come up in quantum field theory (QFT), are time asymmetric. It turns out that the time reversal operator T can be more complicated than just complex conjugation, which leads to the question which criteria determine the correct action of time reversal. We use Bohmian trajectories for this purpose and show that time reversal symmetry can be broken when charges are permitted to be complex numbers, where "charge" means the coupling constant in a QFT that governs the strength with which a fermion emits and absorbs bosons. We pay particular attention to the technique for defining Hamiltonians with particle creation based on interiorboundary conditions, and we find them to generically be time asymmetric. Specifically, we show that time asymmetry for complex charges occurs whenever not all charges have equal or opposite phase. We further show that, in this case, the corresponding ground states can have non-zero probability currents, and we determine the effective potential between fermions of complex charge.

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Section: Well-defined Hamiltonianmentioning

confidence: 99%

Complex charges, time reversal asymmetry, and interior-boundary conditions in quantum field theory

Schmidt¹,

Tumulka²

2019

J. Phys. A: Math. Theor.

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“…In this way, if is a solution of the Schrödinger equation, also * is one, and OQM is time-reversal invariant. Following this lead, Earman (2002) and Roberts (2017) have argued that there are two reasons why acts in this way: a mathematical reason, as well as a physical reason. The former is that wave-function is a ray in Hilbert space, that is an equivalent class of vectors related by a phase of the form , and because of this one can prove Wigner's theorem as well as Uhlhorn's theorem, from which one can derive that is anti-unitary (see Roberts 2017 for details).…”

Section: The Arguments That Quantum Theory Is Time-reversal Invariantmentioning

confidence: 99%

Quantum mechanics, time and ontology

Allori

2019

Studies in History and Philosophy of Science Part B: Studies in

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Against what is commonly accepted in many contexts, it has been recently suggested that both deterministic and indeterministic quantum theories are not time-reversal invariant, and thus time is handed in a quantum world. In this paper, I analyze these arguments and evaluate possible reactions to them. In the context of deterministic theories, first I show that this conclusion depends on the controversial assumption that the wave-function is a physically real scalar field in configuration space. Then I argue that answers which restore invariance by assuming the wave-function is a ray in Hilbert space fall short. Instead, I propose that one should deny that the wave-function represents physical systems, along the lines proposed by the so-called primitive ontology approach. Moreover, in the context of indeterministic theories, I argue that time-reversal invariance can be restored suitably redefining its meaning.

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“…The transformation rule for momentum as TPT −1 = − P is typically introduced in nonrelativistic quantum mechanics by appealing to its obviousness: if time reversal aims at representing something like a backward movement, then reversing the sign of momentum seems mandatory as what one is in need of restoring a past-headed physically possible evolution. And this partially explains why some definitions of time reversal are sometimes expressly introduced in terms of changing momentum (Messiah 1966;Davies 1974;Sachs 1987) or why it is so Bnatural^to expect momentum to change its sign under time reversal (Earman 2002;Roberts 2017).…”

Section: (A) Overcoming Momentum-based Argumentmentioning

confidence: 99%

“…According to such an approach, time reversal must be mathematically represented by an operator T A that not only transforms the variable t as t → − t, but also performs a complex conjugation (ψ → ψ * ) and changes momentum's sign (P → − P). This view has been supported by the overwhelming majority of physicists and philosophers of physics, both in its formal aspect (Wigner 1932, Gibson andPolland 1976 and the majority of specialized textbooks) as well as in its conceptual bases (Sachs 1987;Roberts 2017). I shall call it Bthe orthodox approach^to time reversal in quantum mechanics (OA thereafter).…”

Section: Introductionmentioning

confidence: 99%

Roads to the past: how to go and not to go backward in time in quantum theories

López

2019

Euro Jnl Phil Sci

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In this article I shall defend, against the conventional understanding of the matter, that two coherent and tenable approaches to time reversal can be suitably introduced in standard quantum mechanics: an Borthodox^approach that demands time reversal to be represented in terms of an anti-unitary and anti-linear time-reversal operator, and a Bheterodoxâ pproach that represents time reversal in terms of a unitary, linear time-reversal operator. The rationale shall be that the orthodox approach in quantum theories assumes a relationalist metaphysics of time, according to which time reversal is nothing but motion reversal. But, when one shifts gears and turn to a substantivalist metaphysics of time the heterodox approach to time reversal in quantum mechanics comes up in a more natural way.

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Three Myths about Time Reversal in Quantum Theory

Cited by 35 publications

References 18 publications

Complex charges, time reversal asymmetry, and interior-boundary conditions in quantum field theory

Complex charges, time reversal asymmetry, and interior-boundary conditions in quantum field theory

Quantum mechanics, time and ontology

Roads to the past: how to go and not to go backward in time in quantum theories

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