Quantum superposition of massive bodies

2020 ◽  
Vol 29 (11) ◽  
pp. 2041003
Author(s):  
Robert M. Wald
Keyword(s):  
Gravitational Field ◽  
Gravitational Radiation ◽  
The Body ◽  
Vacuum Fluctuations ◽  
Quantum Superposition ◽  
Gedanken Experiment ◽  
Work Done

I describe the work done in collaboration with A. Belenchia, F. Giacomini, E. Castro-Ruiz, C. Bruckner and M. Aspelmeyer that analyzes a gedanken experiment involving a massive body that is put into a quantum superposition. Remarkably, even for a nonrelativistic body, both vacuum fluctuations of the gravitational field and the quantization of gravitational radiation are essential in order to avoid inconsistencies. In addition, it is essential that the quantum body be viewed as entangled with its own Newtonian-like gravitational field in order to understand how the body may become entangled with other massive bodies via gravitational interactions.

scholarly journals Information content of the gravitational field of a quantum superposition

2019 ◽  
Vol 28 (14) ◽  
pp. 1943001 ◽  
Author(s):  
Alessio Belenchia ◽  
Robert M. Wald ◽  
Flaminia Giacomini ◽  
Esteban Castro-Ruiz ◽  
Časlav Brukner ◽  
...  
Keyword(s):  
Quantum Information ◽  
Gravitational Field ◽  
Information Content ◽  
The Body ◽  
Quantum Superposition ◽  
Quantum Nature ◽  
Quantum Aspects

When a massive quantum body is put into a spatial superposition, it is of interest to consider the quantum aspects of the gravitational field sourced by the body. We argue that in order to understand how the body may become entangled with other massive bodies via gravitational interactions, it must be thought of as being entangled with its own Newtonian-like gravitational field. Thus, a Newtonian-like gravitational field must be capable of carrying quantum information. Our analysis supports the view that table-top experiments testing entanglement of systems interacting via gravity do probe the quantum nature of gravity, even if no “gravitons” are emitted during the experiment.

scholarly journals Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Quantum Interference ◽  
Direct Detection ◽  
Energy Levels ◽  
Vacuum Fluctuations ◽  
Heavy Particles ◽  
Evolving Systems ◽  
Gedanken Experiment ◽  
Classical Computer

AbstractFast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically (ontologically) evolving systems one can still define a conserved quantum energy. For the fast variables, the energy levels are far separated, such that one may assume these variables to stay in their ground state. This forces them to be entangled, so that, consequently, the slow variables are entangled as well. The fast variables could be the vacuum fluctuations caused by unknown super heavy particles. The emerging quantum effects in the light particles are expressed by a Hamiltonian that can have almost any form. The entire system is ontological, and yet allows one to generate interference effects in computer models. This seemed to lead to an inexplicable paradox, which is now resolved: exactly what happens in our models if we run a quantum interference experiment in a classical computer is explained. The restriction that very fast variables stay predominantly in their ground state appears to be due to smearing of the physical states in the time direction, preventing their direct detection. Discussions are added of the emergence of quantum mechanics, and the ontology of an EPR/Bell Gedanken experiment.

THREE DIMENSIONAL INTERPRETATION OF GRAVITATIONAL ANOMALIES

Geophysics ◽  
1952 ◽  
Vol 17 (2) ◽  
pp. 344-364 ◽  
Author(s):  
Fraser S. Grant
Keyword(s):  
Gravitational Field ◽  
Mass Distribution ◽  
Three Dimensional ◽  
Relaxation Method ◽  
The Body ◽  
Multipole Moments ◽  
Size And Shape ◽  
Surface Field ◽  
Derivatives Of

A method is developed for determining the approximate size and shape of the three‐dimensional mass distribution that is required to produce a given gravitational field. The first few reduced multipole moments of the distribution are calculated from the derivatives of the surface field, and the approximative structure is determined from the values of these moments and a knowledge of the density contrast between the body and its surroundings. A system of classification of problems by symmetry is introduced and its practical usage discussed. A relaxation method is described which may be used to adjust the initial solution systematically to give agreement over the whole field. A descriptive discussion is appended.

scholarly journals WAVELESS APPROXIMATION THEORIES OF GRAVITY

2008 ◽  
Vol 17 (02) ◽  
pp. 265-273 ◽  
Author(s):  
JAMES A. ISENBERG
Keyword(s):  
Gravitational Field ◽  
Gravitational Radiation ◽  
Elliptic Equations ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Accurate Approximation ◽  
Time Step ◽  
Einstein Theory ◽  
Physical Systems ◽  
Theories Of Gravity

The analysis of a general multibody physical system governed by Einstein's equations is quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties — many coupled degrees of freedom, dynamic instability — are associated with the presence of gravitational waves. We have developed a number of "waveless approximation theories" (WAT's) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.

scholarly journals Tidal Tensor and the Emission and Absorption of Gravitational Radiation

1974 ◽  
Vol 64 ◽  
pp. 104-104
Author(s):  
Terrence J. Sejnowski
Keyword(s):  
Gravitational Field ◽  
Gravitational Radiation ◽  
Extended Body ◽  
Local Exchange ◽  
Absorption And Emission ◽  
Long Wavelength ◽  
Normal Coordinates ◽  
Wavelength Limit ◽  
Energy And Momentum ◽  
Image Position

The absorption and emission of gravitational radiation can be calculated in the long wavelength limit by use of the tidal tensor, defined as the gradient of the gravitational pseudoforce, thus where ηb is orthogonal to the 4-velocity ua, and normal coordinates are understood.The exchange of energy and momentum between an extended body and the gravitational field is governed by appropriate integrals of the tidal tensor over space and time.The tidal tensor is the trace Tabdb of the Bel-Robinson tensor Tabcd. In emty space this trace is zero and the tidal tensor vanishes; there is no local exchange of energy.

External work in walking

1963 ◽  
Vol 18 (1) ◽  
pp. 1-9 ◽  
Author(s):  
G. A. Cavagna ◽  
F. P. Saibene ◽  
R. Margaria
Keyword(s):  
Inertial Force ◽  
Center Of Gravity ◽  
The Body ◽  
External Work ◽  
High Speeds ◽  
Moving Body ◽  
Vertical Displacements ◽  
Lateral Displacements ◽  
Work Done ◽  
Static Contractions

From records obtained from a triple accelerometer applied to the trunk of a subject the displacements of the trunk in vertical, forward, and lateral directions have been calculated. With motion pictures taken simultaneously, displacements of the center of gravity within the body were measured. From these data the external mechanical work of walking was calculated. The sum of work for vertical and for forward displacements of the center of gravity of the body gives the total external work; energy for the lateral displacements was negligible. Total external work appears to be lower than that calculated from the vertical displacements alone, because work done in lifting is partly sustained by the inertial force of the forward-moving body. Total external work reaches a highest value (0.1 kcal/km kg) at the most economical speed of walking, 4 km/hr, which corresponds to an energy consumption of 0.48 kcal/km kg. At this speed the internal work appears negligible; it amounts to appreciable entities at very low speeds because of the static contractions of the muscles, and at high speeds because of considerable stiffening of the limbs and movements not involving a displacement of the center of gravity. Submitted on May 25, 1962

The energy distribution resulting from an impact on a floating body

2000 ◽  
Vol 417 ◽  
pp. 157-181 ◽  
Author(s):  
A. A. KOROBKIN ◽  
D. H. PEREGRINE
Keyword(s):  
Kinetic Energy ◽  
Energy Distribution ◽  
Water Flow ◽  
Compression Wave ◽  
The Body ◽  
The Other ◽  
Body Motion ◽  
Floating Body ◽  
Pressure Impulse ◽  
Work Done

The initial stage of the water flow caused by an impact on a floating body is considered. The vertical velocity of the body is prescribed and kept constant after a short acceleration stage. The present study demonstrates that impact on a floating and non-flared body gives acoustic effects that are localized in time behind the front of the compression wave generated at the moment of impact and are of major significance for explaining the energy distribution throughout the water, but their contribution to the flow pattern near the body decays with time. We analyse the dependence on the body acceleration of both the water flow and the energy distribution – temporal and spatial. Calculations are performed for a half-submerged sphere within the framework of the acoustic approximation. It is shown that the pressure impulse and the total impulse of the flow are independent of the history of the body motion and are readily found from pressure-impulse theory. On the other hand, the work done to oppose the pressure force, the internal energy of the water and its kinetic energy are essentially dependent on details of the body motion during the acceleration stage. The main parameter is the ratio of the time scale for the acoustic effects and the duration of the acceleration stage. When this parameter is small the work done to accelerate the body is minimal and is spent mostly on the kinetic energy of the flow. When the sphere is impulsively started to a constant velocity (the parameter is infinitely large), the work takes its maximum value: Longhorn (1952) discovered that half of this work goes to the kinetic energy of the flow near the body and the other half is taken away with the compression wave. However, the work required to accelerate the body decreases rapidly as the duration of the acceleration stage increases. The optimal acceleration of the sphere, which minimizes the acoustic energy, is determined for a given duration of the acceleration stage. Roughly speaking, the optimal acceleration is a combination of both sudden changes of the sphere velocity and uniform acceleration.If only the initial velocity of the body is prescribed and it then moves freely under the influence of the pressure, the fraction of the energy lost in acoustic waves depends only on the ratio of the body's mass to the mass of water displaced by the hemisphere.

Sign in / Sign up

Export Citation Format

Share Document