Gravitational mass of composite systems

Zych, Magdalena; Rudnicki, Łukasz; Pikovski, Igor

doi:10.1103/physrevd.99.104029

Cited by 34 publications

(38 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equation ( 5 ) then becomes the relativistic Schrödinger equation and the state may be interpreted as the state of the center-of-mass and internal clock of the particle at the time t , interpreted as the time of an inertial frame observing the particle with respect to which the center-of-mass degrees of freedom are defined. With this identification, the dynamics implied by the Page–Wootters formalism is in agreement with previous descriptions of a relativistic particle with internal degrees of freedom 19 , 31 , 39 .…”

Section: Resultssupporting

confidence: 88%

Quantum clocks observe classical and quantum time dilation

Smith

Ahmadi

2020

Nat Commun

View full text Add to dashboard Cite

At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through curved spacetime. The probability that one clock reads a given proper time conditioned on another clock reading a different proper time is derived. From this conditional probability distribution, it is shown that when the center-of-mass of these clocks move in localized momentum wave packets they observe classical time dilation. We then illustrate a quantum correction to the time dilation observed by a clock moving in a superposition of localized momentum wave packets that has the potential to be observed in experiment. The Helstrom-Holevo lower bound is used to derive a proper time-energy/mass uncertainty relation.

show abstract

Section: Resultssupporting

confidence: 88%

Quantum clocks observe classical and quantum time dilation

Smith

Ahmadi

2020

Nat Commun

View full text Add to dashboard Cite

show abstract

“…'proper time' and 'redshift'); e.g. [3][4][5][6][7][8]. We emphasised in the introduction and also in our discussion of the Equivalence Principle that answers to the fundamental question of gravity-matter coupling in Quantum Mechanics should not be based on a priori restricted states that imply a semi-classical behaviour of some of the (factorising) degrees of freedom.…”

Section: Discussionmentioning

confidence: 99%

“…As emphasised above, this generalisation serves not only a point of principal interest that deserves clarification, but is also of immediate practical interest, not only in the obvious realm of quantum optics experiments regarding the detection of gravitational waves, but also in atom interferometry; see, e.g. [2][3][4][5][6][7][8]. A calculation using methods very similar to those of [1] including external gravitational fields was performed by Marzlin already in 1995 [9] 2 ; but unlike Sonnleitner and Barnett in [1] or our calculation in this work, Marzlin did not perform a full first-order post-Newtonian expansion and instead focused on the electric dipole coupling only.…”

Section: Introductionmentioning

confidence: 91%

“…It is the underlying systematics of producing 'relativistic corrections' that, in our opinion, distinguishes our approach from others, like, e.g., [3][4][5][6][7][8]. These latter attempts make use in an essential way of notions, like 'wordline' and 'redshift', which have no immediate meaning in quantum theory, unless the state of the system is severely restricted in an a priori fashion.…”

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

Post-Newtonian Hamiltonian description of an atom in a weak gravitational field

Schwartz

Giulini

2019

Phys. Rev. A

View full text Add to dashboard Cite

We extend the systematic calculation of an approximately relativistic Hamiltonian for centre of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [1] to the case including a weak post-Newtonian gravitational background field, described by the Eddington-Robertson parametrised post-Newtonian metric. Starting from a proper relativistic description of the situation, this approach allows to systematically derive the coupling of the model system to gravity, instead of 'guessing' it by means of classical notions of relativistic effects.We embed this technical result into a critical discussion concerning the problem of implementing and interpreting general couplings to the gravitational field and the connected problem of how to properly address the question concerning the validity of the Equivalence Principle in Quantum Mechanics. 1 arXiv:1908.06929v2 [quant-ph]

show abstract

“…In particular, we consider a set of N relativistic quantum particles in a weak gravitational field, each of which has a quantum state living in the tensor product Hibert space of position/momentum and some internal "clock" Hilbert space (see Refs. [52,43] for a similar analysis in a different context). In this timeless formulation, the global state of the N particles is "frozen", but the dynamical evolution is recovered in terms of the relational variables to one of the particles, which is chosen as the QRF.…”

Section: Introductionmentioning

confidence: 94%

Spacetime Quantum Reference Frames and superpositions of proper times

Giacomini

2021

Quantum

View full text Add to dashboard Cite

In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.

show abstract

Gravitational mass of composite systems

Cited by 34 publications

References 45 publications

Quantum clocks observe classical and quantum time dilation

Quantum clocks observe classical and quantum time dilation

Post-Newtonian Hamiltonian description of an atom in a weak gravitational field

Spacetime Quantum Reference Frames and superpositions of proper times

Contact Info

Product

Resources

About