arXiv subjects

Marc-Thierry Jaekel

Publications and source records attributed to Marc-Thierry Jaekel.

At least 55 records · Page 3Linked to original sources

arXiv2001

Fluctuations and dissipation for a mirror in vacuum

A mirror in the vacuum is submitted to a radiation pressure exerted by scattered fields. It is known that the resulting mean force is zero for a motionless mirror, but not for a mirror moving with a non-uniform acceleration. We show here that this force results from a motional modification of the field scattering while being associated with the fluctuations of the radiation pressure on a motionless mirror. We consider the case of a scalar field in a two-dimensional spacetime and characterize the scattering upon the mirror by frequency dependent transmissivity and reflectivity functions obeying unitarity, causality and high frequency transparency conditions. We derive causal expressions for dissipation and fluctuations and exhibit their relation for any stationary input. We recover the known damping force at the limit of a perfect mirror in vacuum. Finally, we interpret the force as a mechanical signature of the squeezing effect associated with the mirror's motion.

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arXiv1999

Quantum Hexaspherical Observables for Electrons

A new quantum algebraic description of relativistic electrons, built on a conformal dynamical symmetry (SO(4,2)), has recently been proposed to treat localization in space-time. It is shown here that localization of an electron may be represented by components of a SO(4,2) vector which are quantum generalizations of the hexaspherical coordinates of classical projective geometry. The shift of this vector under transformations to uniformly accelerated frames is described by SO(4,2) rotations. Hexaspherical observables also allow one to represent the quantum law of free fall under a form explicitly compatible with the same dynamical symmetry.

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arXiv1999

Observable Dirac Electron in Accelerated Frames

We present a new quantum algebraic description of an electron localized in space-time. Positions in space and time, mass and Clifford generators are defined as quantum operators. Commutation relations and relativistic shifts under frame transformations are determined within a unique algebraic framework. Redshifts, i.e. shifts under transformations to uniformly accelerated frames, are evaluated and found to differ from the expressions of classical relativity.

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arXiv1998

Quantum Observables associated with Einstein Localisation

The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum systems. We outline an algebraic framework where basic requirements of quantum theory and relativity are consistently dealt with. This approach which may be termed as a `quantum relativity' is built on the algebra of symmetries. It contains the definition of quantum observables associated with Einstein localisation in space-time as well as the evaluation of their commutation relations including the energy-time relation. These commutators also describe the relativistic shifts undergone under frame transformations, not only for inertial frames but also for uniformly accelerated frames. The quantum redshift laws differ from their classical counterparts while still obeying universal metric properties. The paper presents this approach in terms closely connected to the seminal Einstein conception of localisation in space-time and refers to already published papers for more technical developments.

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arXiv1998

Quantum Localisation Observables and Accelerated Frames

We define quantum observables associated with Einstein localisation in space-time. These observables are built on Poincare' and dilatation generators. Their commutators are given by spin observables defined from the same symmetry generators. Their shifts under transformations to uniformly accelerated frames are evaluated through algebraic computations in conformal algebra. Spin number is found to vary under such transformations with a variation involving further observables introduced as irreducible quadrupole momenta. Quadrupole observables may be dealt with as non commutative polarisations which allow one to define step operators increasing or decreasing the spin number by unity.

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arXiv1998

Logical Dissipation of Automata Implements - Dissipation of Computation

As revealed by discussions of principle on energy dissipation by computers, logic imposes constraints on physical systems designed for a logical function. We define a notion of logical dissipation for a finite automaton. We discuss the constraints associated with physical implementation of automata and exhibit the role played by modularity for testability. As a result, practical computers, which are necessarily modular, dissipate proportionally to computation time.

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arXiv1998

Relativity of Motion in Vacuum

The existence of vacuum fluctuations leads to reconsider the question of relativity of motion. The present article is devoted to this aim with a main line which can be formulated as follows: ``The principle of relativity of motion is directly related to symmetries of quantum vacuum''. Keeping close to this statement, we discuss the controversial relation between vacuum and motion. We introduce the question of relativity of motion in its historical development before coming to the results obtained more recently.

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arXiv1998

Quantum Fluctuations of Mass for a Mirror in Vacuum

A mirror in vacuum is coupled to fluctuating quantum fields. As a result, its energy-momentum and mass fluctuate. We compute the correlation spectra of force and mass fluctuations for a mirror at rest in vacuum (of a scalar field in a two-dimensional space-time). The obtained expressions agree with a mass correction equal to a vacuum energy stored by the mirror. We introduce a Lagrangian model which consistently describes a scalar field coupled to a scatterer, with inertial mass being a quantum variable.

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arXiv1998

Gravitational Quantum Limit for Length Measurements

We discuss a limit for sensitivity of length measurements which is due to the effect of vacuum fluctuations of gravitational field. This limit is associated with irreducible quantum fluctuations of geodesic distances and it is characterized by a noise spectrum with an order of magnitude mainly determined by Planck length. The gravitational vacuum fluctuations may (in an analysis restricted to questions of principle and when the measurement strategy is optimized) dominate fluctuations added by the measurement apparatus if macroscopic masses, i.e. masses larger than Planck mass, are used.

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arXiv1998

Quantum Langevin Equations and Stability

Different quantum Langevin equations obtained by coupling a particle to a field are examined. Instabilities or violations of causality affect the motion of a point charge linearly coupled to the electromagnetic field. In contrast, coupling a scatterer with a reflection cut-off to radiation pressure leads to stable and causal motions. The radiative reaction force exerted on a scatterer, and hence its quasistatic mass, depend on the field state. Explicit expressions for a particle scattering a thermal field in a two dimensional space-time are given.

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arXiv1997

Vacuum fluctuations, accelerated motion and conformal frames

Radiation from a mirror moving in vacuum electromagnetic fields is shown to vanish in the case of a uniformly accelerated motion. Such motions are related to conformal coordinate transformations, which preserve correlation functions characteristic of vacuum fluctuations. As a result, vacuum fluctuations remain invariant under reflection upon a uniformly accelerated mirror, which therefore does not radiate and experiences no radiation reaction force. Mechanical effects of vacuum fluctuations thus exhibit an invariance with respect to uniformly accelerated motions.

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arXiv1997

Conformal Symmetry and Quantum Relativity

The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincaré symmetry of field theory can be extended to the larger conformal symmetry. We use these symmetries to define quantum observables associated with positions in space-time, in the spirit of Einstein theory of relativity. This conception of localisation may be applied to massive as well as massless fields. Localisation observables are defined as to obey Lorentz covariant commutations relations and in particular include a time observable conjugated to energy. Whilst position components do not commute in presence of a non-vanishing spin, they still satisfy quantum relations which generalise the differential laws of classical relativity. We also give of these observables a representation in terms of canonical spatial positions, canonical spin components and a proper time operator conjugated to mass. These results plead for a new representation not only of space-time localisation but also of motion.

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arXiv1997

Movement and Fluctuations of the Vacuum

Quantum fields possess zero-point or vacuum fluctuations which induce mechanical effects, namely generalised Casimir forces, on any scatterer. Symmetries of vacuum therefore raise fundamental questions when confronted with the principle of relativity of motion in vacuum. The specific case of uniformly accelerated motion is particularly interesting, in connection with the much debated question of the appearance of vacuum in accelerated frames. The choice of Rindler representation, commonly used in General Relativity, transforms vacuum fluctuations into thermal fluctuations, raising difficulties of interpretation. In contrast, the conformal representation of uniformly accelerated frames fits the symmetry properties of field propagation and quantum vacuum and thus leads to extend the principle of relativity of motion to uniform accelerations. Mirrors moving in vacuum with a non uniform acceleration are known to radiate. The associated radiation reaction force is directly connected to fluctuating forces felt by motionless mirrors through fluctuation-dissipation relations. Scatterers in vacuum undergo a quantum Brownian motion which describes irreducible quantum fluctuations. Vacuum fluctuations impose ultimate limitations on measurements of position in space-time, and thus challenge the very concept of space-time localisation within a quantum framework. For test masses greater than Planck mass, the ultimate limit in localisation is determined by gravitational vacuum fluctuations. Not only positions in space-time, but also geodesic distances, behave as quantum variables, reflecting the necessary quantum nature of an underlying geometry.

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arXiv1997

Mass as a Relativistic Quantum Observable

A field state containing photons propagating in different directions has a non vanishing mass which is a quantum observable. We interpret the shift of this mass under transformations to accelerated frames as defining space-time observables canonically conjugated to energy-momentum observables. Shifts of quantum observables differ from the predictions of classical relativity theory in the presence of a non vanishing spin. In particular, quantum redshift of energy-momentum is affected by spin. Shifts of position and energy-momentum observables however obey simple universal rules derived from invariance of canonical commutators.

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arXiv1996

Comment on ``Sonoluminescence as Quantum Vacuum Radiation''

We contest the recent claim by C. Eberlein (Physical Review Letters 76 (1996) 3842) that sonoluminescence may be explained in terms of quantum vacuum radiation. Due to fundamental physical limitations on bubble surface velocity, the predicted number of photons per flash is indeed much smaller than unity. Therefore, quantum vacuum radiation cannot be considered as an explanation of the observed sonoluminescence phenomenon.

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arXiv1996

Space-Time Localisation with Quantum Fields

We introduce observables associated with the space-time position of a quantum point defined by the intersection of two light pulses. The time observable is canonically conjugated to the energy. Conformal symmetry of massless quantum fields is used first to build the definition of these observables and then to describe their relativistic properties under frame transformations. The transformations to accelerated frames of the space-time observables depart from the laws of classical relativity. The Einstein laws for the shifts of clock rates and frequencies are recovered in the quantum description, and their formulation provides a conformal metric factor behaving as a quantum observable.

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arXiv1996

Motion Induced Radiation from a Vibrating Cavity

We study the radiation emitted by a cavity moving in vacuum. We give a quantitative estimate of the photon production inside the cavity as well as of the photon flux radiated from the cavity. A resonance enhancement occurs not only when the cavity length is modulated but also for a global oscillation of the cavity. For a high finesse cavity the emitted radiation surpasses radiation from a single mirror by orders of magnitude.

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arXiv1996

Time-Frequency Transfer with Quantum Fields

Clock synchronisation relies on time-frequency transfer procedures which involve quantum fields. We use the conformal symmetry of such fields to define as quantum operators the time and frequency exchanged in transfer procedures and to describe their transformation under transformations to inertial or accelerated frames. We show that the classical laws of relativity are changed when brought in the framework of quantum theory.

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