I show that massive-particle dynamics can be simulated by a weak, spherical,
external perturbation on a potential flow in an ideal fluid. The effective
Lagrangian is of the form mc^2L(U^2/c^2), where U is the velocity of the
particle relative to the fluid and c the speed of sound. This can serve as a
model for emergent relativistic inertia a la Mach's principle with m playing
the role of inertial mass, and also of analog gravity where it is also the
passive gravitational mass. m depends on the particle type and intrinsic
structure, while L is universal: For D dimensional particles L is proportional
to the hypergeometric function F(1,1/2;D/2;U^2/c^2). Particles fall in the same
way in the analog gravitational field independent of their internal structure,
thus satisfying the weak equivalence principle. For D less or equal 5 they all
have a relativistic limit with the acquired energy and momentum diverging as U
approaches c. For D less or equal 7 the null geodesics of the standard acoustic
metric solve our equation of motion. Interestingly, for D=4 the dynamics is
very nearly Lorentzian. The particles can be said to follow the geodesics of a
generalized acoustic metric of a Finslerian type that shares the null geodesics
with the standard acoustic metric. In vortex geometries, the ergosphere is
automatically the static limit. As in the real world, in ``black hole''
geometries circular orbits do not exist below a certain radius that occurs
outside the horizon. There is a natural definition of antiparticles; and I
describe a mock particle vacuum in whose context one can discuss, e.g.,
particle Hawking radiation near event horizons.
%0 Generic
%1 citeulike:488701
%A Milgrom, Mordehai
%D 2006
%K emergent gravity inertia passive space-times
%T Massive particles in acoustic space-times emergent inertia and passive gravity
%U http://arxiv.org/abs/gr-qc/0601034
%X I show that massive-particle dynamics can be simulated by a weak, spherical,
external perturbation on a potential flow in an ideal fluid. The effective
Lagrangian is of the form mc^2L(U^2/c^2), where U is the velocity of the
particle relative to the fluid and c the speed of sound. This can serve as a
model for emergent relativistic inertia a la Mach's principle with m playing
the role of inertial mass, and also of analog gravity where it is also the
passive gravitational mass. m depends on the particle type and intrinsic
structure, while L is universal: For D dimensional particles L is proportional
to the hypergeometric function F(1,1/2;D/2;U^2/c^2). Particles fall in the same
way in the analog gravitational field independent of their internal structure,
thus satisfying the weak equivalence principle. For D less or equal 5 they all
have a relativistic limit with the acquired energy and momentum diverging as U
approaches c. For D less or equal 7 the null geodesics of the standard acoustic
metric solve our equation of motion. Interestingly, for D=4 the dynamics is
very nearly Lorentzian. The particles can be said to follow the geodesics of a
generalized acoustic metric of a Finslerian type that shares the null geodesics
with the standard acoustic metric. In vortex geometries, the ergosphere is
automatically the static limit. As in the real world, in ``black hole''
geometries circular orbits do not exist below a certain radius that occurs
outside the horizon. There is a natural definition of antiparticles; and I
describe a mock particle vacuum in whose context one can discuss, e.g.,
particle Hawking radiation near event horizons.
@misc{citeulike:488701,
abstract = {I show that massive-particle dynamics can be simulated by a weak, spherical,
external perturbation on a potential flow in an ideal fluid. The effective
Lagrangian is of the form mc^2L(U^2/c^2), where U is the velocity of the
particle relative to the fluid and c the speed of sound. This can serve as a
model for emergent relativistic inertia a la Mach's principle with m playing
the role of inertial mass, and also of analog gravity where it is also the
passive gravitational mass. m depends on the particle type and intrinsic
structure, while L is universal: For D dimensional particles L is proportional
to the hypergeometric function F(1,1/2;D/2;U^2/c^2). Particles fall in the same
way in the analog gravitational field independent of their internal structure,
thus satisfying the weak equivalence principle. For D less or equal 5 they all
have a relativistic limit with the acquired energy and momentum diverging as U
approaches c. For D less or equal 7 the null geodesics of the standard acoustic
metric solve our equation of motion. Interestingly, for D=4 the dynamics is
very nearly Lorentzian. The particles can be said to follow the geodesics of a
generalized acoustic metric of a Finslerian type that shares the null geodesics
with the standard acoustic metric. In vortex geometries, the ergosphere is
automatically the static limit. As in the real world, in ``black hole''
geometries circular orbits do not exist below a certain radius that occurs
outside the horizon. There is a natural definition of antiparticles; and I
describe a mock particle vacuum in whose context one can discuss, e.g.,
particle Hawking radiation near event horizons.},
added-at = {2007-08-18T13:22:24.000+0200},
author = {Milgrom, Mordehai},
biburl = {https://www.bibsonomy.org/bibtex/265d4a5a55af46f93c8be9c14f1b78a5b/a_olympia},
citeulike-article-id = {488701},
description = {citeulike},
eprint = {gr-qc/0601034},
interhash = {3e6bc79174999ba01eef5d90af25938a},
intrahash = {65d4a5a55af46f93c8be9c14f1b78a5b},
keywords = {emergent gravity inertia passive space-times},
month = Jan,
priority = {2},
timestamp = {2007-08-18T13:22:35.000+0200},
title = {Massive particles in acoustic space-times emergent inertia and passive gravity},
url = {http://arxiv.org/abs/gr-qc/0601034},
year = 2006
}