Quantum Formulation of the Einstein Equivalence Principle

Zych, Magdalena

doi:10.1007/978-3-319-53192-2_7

Cited by 4 publications

(14 citation statements)

References 47 publications

(21 reference statements)

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“…These effects, which can be seen as arising from relative time dilation of different internal levels, were first investigated in detail by Zych et al [14,15] and Pikovski et al [13], and were further discussed by Zych and Brukner in the context of the equivalence principle [5].…”

Section: Effects Of Internal Degrees Of Freedommentioning

confidence: 99%

“…The full Hamiltonian for a particle in a uniform gravitational field, including the newly defined mass operator is then (to leading relativistic order) [5] …”

Section: The Hamiltonian Formulationmentioning

confidence: 99%

“…Moreover, if a neutron is prepared in a spin-superposition state (with respect to the internal energy eigenbasis), this seemingly leads to the violation of a super-selection rule, i.e., superposition of masses. However, we use the mass operator formalism [5] to show that, if the energy splitting of the internal spin contributes to the mass of the neutron, then the visibility of the interference pattern periodically decreases and increases.Our results indicate that these decoherence effects are a consequence of an operational clock embedded within a quantum mechanical rest frame. That is, the internal degree of freedom keeps track of the time the particle spends being in different mass states.…”

mentioning

confidence: 99%

“…This is true even in the case of internal energy and becomes particularly interesting for quantum systems, whose internal energy can exist in superposition. Recent work by Zych and Brukner [5] treats this by promoting mass to an operator, the purpose of which is to account for the effective mass of quantised internal energy. In addition to introducing lowest order relativistic effects, this construction provides a new quantum mechanical generalisation of the Einstein equivalence principle to superpositions of energy eigenstates.…”

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confidence: 99%

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How Does Interference Fall?

Orlando¹,

Pollock²,

Modi³

2017

Quantum Science and Technology

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We study how single-and double-slit interference patterns fall in the presence of gravity. First, we demonstrate that universality of free fall still holds in this case, i.e., interference patterns fall just like classical objects. Next, we explore lowest order relativistic effects in the Newtonian regime by employing a recent quantum formalism which treats mass as an operator. This leads to interactions between nondegenerate internal degrees of freedom (like spin in an external magnetic field) and external degrees of freedom (like position). Based on these effects, we present an unusual phenomenon, in which a falling double slit interference pattern periodically decoheres and recoheres. The oscillations in the visibility of this interference occur due to correlations built up between spin and position. Finally, we connect the interference visibility revivals with non-Markovian quantum dynamics. * patrick.james.orlando@gmail.com † felix.pollock@monash.edu ‡ kavan.modi@monash.edu 1 arXiv:1610.02141v1 [quant-ph] Oct 2016Since the days of Galileo and Newton, it has been known that acceleration under the influence of gravity is independent of an object's mass [1,2]. This peculiarity has led to the proposition of various gravitational equivalence principles which, if broken, represent a departure from our current understanding of the theory of gravity. Einstein's theory of general relativity is fundamentally classical, describing gravity on large length scales in terms of curvature of the underlying spacetime metric. Although it is possible to formulate quantum field theories on a static curved metric, it remains unclear how existing theory should be modified to describe gravity on the quantum mechanical scale [3]. Whilst the work we present here does not attempt to quantise gravity, it demonstrates that there is much insight to be gained from exploring non-relativistic quantum mechanics in weak-field gravity.In the weak-field limit, a Newtonian description of gravity provides a satisfactory approximation and is, advantageously, compatible with the Hamiltonian formulation of quantum mechanics; however, its disadvantage lies in the concealment of relativistic effects, such as gravitational time dilation and the gravitational redshift of photons. Fortunately, one need not utilise the complete machinery of general relativity to take these effects into account. In fact, lowest order relativistic effects can be introduced by simply considering the mass contributions of different energy states, as given by the mass-energy relation E = mc 2 of special relativity [4]. This is true even in the case of internal energy and becomes particularly interesting for quantum systems, whose internal energy can exist in superposition. Recent work by Zych and Brukner [5] treats this by promoting mass to an operator, the purpose of which is to account for the effective mass of quantised internal energy. In addition to introducing lowest order relativistic effects, this construction provides a new quantum mechanical generalisatio...

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Section: Effects Of Internal Degrees Of Freedommentioning

confidence: 99%

“…The full Hamiltonian for a particle in a uniform gravitational field, including the newly defined mass operator is then (to leading relativistic order) [5] …”

Section: The Hamiltonian Formulationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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How Does Interference Fall?

Orlando¹,

Pollock²,

Modi³

2017

Quantum Science and Technology

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“…We point out that [52][53][54][55] may be helpful for those interested in investigations similar in a sense to those dealt with in the present work.…”

Section: Final Remarksmentioning

confidence: 74%

Interesting Examples of Violation of the Classical Equivalence Principle but Not of the Weak One

Accioly

Herdy

2018

Advances in High Energy Physics

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The equivalence principle (EP) and Schiff 's conjecture are discussed en passant, and the connection between the EP and quantum mechanics is then briefly analyzed. Two semiclassical violations of the classical equivalence principle (CEP) but not of the weak one (WEP), i.e., Greenberger gravitational Bohr atom and the tree-level scattering of different quantum particles by an external weak higher-order gravitational field, are thoroughly investigated afterwards. Next, two quantum examples of systems that agree with the WEP but not with the CEP, namely, COW experiment and free fall in a constant gravitational field of a massive object described by its wave-function Ψ, are discussed in detail. Keeping in mind that, among the four examples focused on in this work only COW experiment is based on an experimental test, some important details related to it are presented as well.

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Relativistic coupling of internal and centre of mass dynamics in classical and simple bound quantum mechanical systems

Krause

Lee

2017

Eur. J. Phys.

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Although special relativity and quantum mechanics revolutionized physics in the early 20th century, the consequences of combining these two theories are still being explored a hundred years later, usually using the formidable theoretical machinery of quantum field theory. However, a formalism accessible to undergraduates has been recently developed which shows how the center of mass and internal dynamics of classical and quantum systems is relativistically coupled with interesting consequences. Here we explore some of the implications of this coupling, first classically, where we find that the dynamics of the system is time dilated when moving relative to another inertial frame. We then apply the dynamics to a quantum 2-level atom bound in a 1-dimensional infinite potential well, and show that the coupling produces collapses and revivals in quantum interference. This example provides an illustration of how the combination of special relativity and quantum mechanics can be studied in situations familiar to most undergraduates.

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Quantum Formulation of the Einstein Equivalence Principle

Cited by 4 publications

References 47 publications

How Does Interference Fall?

How Does Interference Fall?

Interesting Examples of Violation of the Classical Equivalence Principle but Not of the Weak One

Relativistic coupling of internal and centre of mass dynamics in classical and simple bound quantum mechanical systems

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