Acceleration |

**In General** > s.a. Fermi Acceleration;
physics teaching; reference
frame; rindler space [uniform acceleration].

* __Idea__: The concept of
acceleration as rate of change of velocity in time (as opposed to rate
of change in space, for example), seems to be due to Galileo.

* __Accelerometers__: 2014,
Current accelerometers for submarines (used to pinpoint their position
under water without having to surface to use the GPS) are accurate to
within 1 km after traveling one day; An accelerometer being developed
in the UK, based on the quantum interference of ultracold atoms, will
be accurate to within 1 m; Further improvements are being planned.

@ __Maximal acceleration__:
Caianello LNC(81);
Brandt FPL(89)
[and 4-velocity fiber bundle over spacetime];
Pati EPL(92) [for a quantum particle];
Papini NCB(02);
Feoli IJMPD(03) [different values];
Papini qp/04 [and superconductors];
Gallego Torromé gq/05 [Finsler models];
Friedman a0912 [test];
Rovelli & Vidotto PRL(13)-a1307 [from spin-foam quantum gravity];
Brandt a1311 [and the quantum-to-classical transition];
Gallego Torromé CQG(15)-a1404 [geometry and kinematics];
> s.a. kerr spacetime; modified lorentz symmetry.

@ __Accelerated fields__: Céleri & Kiosses a1712 [and the Unruh effect].

> __Theories with critical accelerations__:
see modifications of general relativity; MOND.

> __Online resources__:
see Wikipedia page.

**Relativistic / Covariant**

* __Idea__:
Acceleration is a well-defined concept; It can be measured with a box and
a mass with springs, and does not need a specification of "with respect to
what", contrary to the situation with velocity.

$ __Covariant definition__: The 4-vector
\(A^a:= u^b \nabla_b u^a\), perpendicular to the world-line, \(A^a u_a = 0\).

* __In general relativity__: A
world-line accelerates only if subject to non-gravitational forces; Objects
in free fall follow geodesics \(A^a = 0\).

@ __Relativistic__: Rindler & Mishra PLA(93) [relative acceleration in special relativity];
Bini et al CQG(95)
[transformation law in general relativity];
Lyutikov a0903 [reversal of centrifugal acceleration];
Llosa a1507
[coordinate transformation laws and infinitesimal generators];
Abramowicz a1608
[covariant definitions and confusions].

@ __Constant / uniform acceleration__:
Friedman & Scarr GRG(15)-a1602 [in an arbitrary curved spacetime];
Pons & Ferran de Palol GRG(19)-a1811 [also constant proper jerk and beyond].

> __Acceleration of the cosmological expansion__:
see cosmic acceleration; quantum
field theory effects in curved spacetime.

**Effects / Phenomenology**

@ __Measurement, accelerometers__: Dragan et al PRD(11)-a1007 [Unruh-DeWitt detector as quantum accelerometer];
Dickerson et al PRL(13)
+ Bouter Phy(13) [use of atom interferometers];
news pw(14)may [accelerometer under development].

@ __Effects on atoms__:
Marino et al PS(14)-a1404 [and interactions];
Dahia & Felix de Araujo CQG(15)-a1412 [atomic clocks];
Zhang FP(16)-a1612 [accelerated atom coupled to electromagnetic vacuum fluctuations].

@ __Astrophysical effects__: Chicone et al PLA(11) [particle acceleration by varying gravitational fields and cosmic jets];
Chae et al ApJL(20)-a2010 [universal acceleration scale in elliptical galaxies].

> __Gravity-related phenomena__:
see astrophysics; matter near black holes
[particle acceleration]; unruh effect [accelerated detectors].

> __Other particle-related phenomena__: see
acceleration radiation [accelerated charges]; anomalous
acceleration [Pioneer effect]; quantum state evolution.

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send feedback and suggestions to bombelli at olemiss.edu – modified 26 dec 2020