Group-Theoretical Structure of Quantum Measurements and Equivalence Principle

Quintana, Abel Camacho

doi:10.1142/s0217732300001882

Cited by 3 publications

(5 citation statements)

References 24 publications

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“…This implies, obviously, that the classical equivalence principle is obeyed by quantum mechanical matter when expectation values are considered. 23 It may be noted that our demonstration above on the classical nature of the shift of the fringes need not be directly applicable to all the cases discussed in these references. 11 There have been some recent suggestions and discussions regarding VEP in the quantum mechanical context, especially in the cases where the quantum matter is in a superposition of different mass or energy eigenstates.…”

Section: Quantum Mechanics and The Equivalence Principlementioning

confidence: 86%

The Accelero-Magnetic Field, Thomas Precession and an Equivalence Principle for Spin

Unnikrishnan

2001

Mod. Phys. Lett. A

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In the weak field limit of Einstein gravity, there are gravitational analogues of the vector potential and the magnetic field. The equivalence principle guides us to a magnetic-like interaction arising from inertial acceleration. The spin precession due to this acceleromagnetic field is identified as the Thomas precession. Hence the torque that is responsible for the precession of the spin is identified as resulting from a physical interaction with a magnetic-like inertial-field. Once the equivalence principle is assumed to some accuracy, well supported by precision tests, this implies that the average effect of the accelero-magnetic field on a classical or quantum gyroscope is the same as that of the gravito-magnetic field on a gyroscope. Precision spectroscopy of spin-orbit doublets in atoms is hence an indirect high precision test of the existence and properties of the gravito-magnetic field. This also implies that the planned and current experiments will not see any deviations from the predictions of general relativity. This line of thought is extended to a brief discussion on the possibility of formulating an independent equivalence principle for the spin. 429 Mod. Phys. Lett. A 2001.16:429-440. Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ SAN DIEGO on 02/02/15. For personal use only.430 C. S. Unnikrishnanrelativity is generated by moving and rotating masses, just as the magnetic field is generated by electrical currents and magnetic moments. This could also be postulated directly in a theory of gravitation that desires to be consistent with the special relativity, since magnetic effects in general are generated when there is motion in an electric-like field. Angular momentum interacts with the gravito-magnetic field and there are analogues of spin-orbit and spin-spin interactions leading to spin precession. 1-3 One of the present challenges in experimental gravitation is to devise experiments that can detect and study the gravito-magnetic field. There is evidence for the existence of the gravitational vector potential and the magnetic component in gravity from Lunar Laser Ranging 4 and the LAGEOS experiment. 5 The LAGEOS experiment measured the Lense-Thirring precession to an accuracy of 20%-30% using laser ranging to two Earth satellites. The space experiment Gravity Probe-B, an experiment seeking higher precision, is in preparation. 6 This experiment is designed to measure the precession angle of a gyroscope in orbit around the Earth. The precession results from the spin-spin interaction of the gyroscope and the Earth, and also from the interaction of the gyroscopic spin with the induced gravito-magnetic field resulting from the movement of the gyroscope in the Earth's gravitational field g. The latter component along with the precession due to the spatial curvature is the full geodetic precession.The direct observation of the spin precession with high precision in magnetic-like gravitational field is expected to be very difficult owing to the smallness of the field. One might ask...

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Section: Quantum Mechanics and The Equivalence Principlementioning

confidence: 86%

The Accelero-Magnetic Field, Thomas Precession and an Equivalence Principle for Spin

Unnikrishnan

2001

Mod. Phys. Lett. A

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“…Indeed, X(t) depends implicitly upon g, i. e., it is a solution to (4). Mathematically we have the same function as in the case in which gravity is absent [15], nevertheless, in the present case g appears, as a parameter, in X(T ), something that does not happen in the corresponding expression when g vanishes [15].…”

Section: Continuous Nondemolition Measurementsmentioning

confidence: 66%

“…Afterwards, the differential equation related to the existence of QNDM variables will be solved, and in this way a family of quantum nondemolition variables will be found. The present work is, in some sense, an extension of previous results [11,15], in which quantum demolition and nondemolition measurements in a Paul trap (without gravitational field) were analyzed.…”

Section: Introductionmentioning

confidence: 75%

“…In other words, this approach considers no particular measurement scheme, i.e., it is a phenomenological, and, in consequence, a very general model. Currently, the predictions of RPIF have not been confronted against measurement outputs, though at this point we must comment that there are already several works which, in the future, could open this possibility [10,11,12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

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Quantum Measurements and Paul Traps in Gravitational Backgrounds

Camacho

2002

Int. J. Mod. Phys. D

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In the present work we solve the motion equations of a particle in a Paul trap embeded in the gravitational field of a spherically symmetric mass. One of the ideas behind this work concerns the analysis of the effects that the gravityinduced quantum noise, stemming from the bodies in the neighborhood of the Paul trap, could have upon the enhancement of the quantum behavior of this system. This will be done considering a series expansion for the gravitational field of the source, and including in the Hamiltonian of the Paul trap only the first two terms. Higher-order contributions will be introduced as part of the environment of the system, and in consequence will not appear in the Hamiltonian. In other words, we put forward an argument that allows us to differentiate those gravitational degrees of freedom that will appear as an uncontrollable influence on the Paul trap. Along the ideas of the so called restricted path integral formalism, we take into account the continuous monitoring of the position of our particle, and in consequence the corresponding propagators and probabilities, associated with the different measurements outputs, are obtained. Afterwards, the differential equation related to a quantum nondemolition variable is posed and solved, i.e., a family of quantum nondemolition parameters is obtained. Finally, a qualitative analysis of the effects on the system, of the gravity-induced environment, will be done. *

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“…Indeed, either the offdiagonal elements of the corresponding density matrix do not satisfy LPI, or the measuring device must contain always information concerning the gravitational field. This last possibility could be reworded asserting that any experiment performed in the respective local Lorentz frame is always influenced by the gravitational background, a possibility already pointed out in the context of the analysis of the behavior of some of the symmetries behind a continuous quantum measurement [13].…”

Section: Introductionmentioning

confidence: 99%

Decoherence-Induced Violations of Einstein Equivalence Principle

Camacho

2001

Int. J. Mod. Phys. D

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In this essay it will be shown that Decoherence Model and Einstein Equivalence Principle are conceptually incompatible. In other words, assuming only the validity of the Weak Equivalence Principle the present work concludes that we face two possibilities: (i) if Decoherence Model provides a correct description of nature at quantum level, then there are systems which violate Local Position Invariance, or, (ii) if all the postulates behind Einstein Equivalence Principle are valid, even on quantum realm, then Decoherence Model breaks down in curved spacetimes. Finally, the present results are confronted against Schiff's conjecture. * email: acamacho@nuclear.inin.mx † This essay received an "honorable mention" in the 2001 Essay Competition of the Gravity Research Foundation-Ed.

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Group-Theoretical Structure of Quantum Measurements and Equivalence Principle

Cited by 3 publications

References 24 publications

The Accelero-Magnetic Field, Thomas Precession and an Equivalence Principle for Spin

The Accelero-Magnetic Field, Thomas Precession and an Equivalence Principle for Spin

Quantum Measurements and Paul Traps in Gravitational Backgrounds

Decoherence-Induced Violations of Einstein Equivalence Principle

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