Time
in Quantum Theory| Time
in Quantum Theory |
In General > s.a. [time]; hilbert
space [rigged].
* Formal role: Time does
not correspond to a dynamical variable/operator (by examining a clock, we do
not measure t, just the variable "position
of the handles''), but is necessary in formulating all approaches;
Measurements are made "at an instant of time'', histories are
not measurable;
Time drives the evolution and is needed in the interpretation.
* Philosophy: The separation between being (kinematics) and becoming (dynamics)
generates inextricable difficulties.
Time as an Observable / Operator > s.a. uncertainty
relations [time-energy].
* Result (Pauli): The existence of a self-adjoint time operator canonically
conjugate to a Hamiltonian implies that both operators possess completely continuous
spectra spanning the entire real line.
@ General references: Giannitrapani IJTP(97)qp/96;
Oppenheim et al qp/98-in;
Belavkin & Perkins IJTP(98)qp/05 [unsharp
measurement]; Galapon O&S(01)qp/00,
PRS(02)qp/01 [including
discrete semibounded H]; Kitada qp/00;
Hahne JPA(03)qp/04;
Bostroem
qp/03;
Olkhovsky & Recami qp/06;
Wang & Xiong AP(07)qp/06;
Strauss a0706 [forward
and backward time observables]; Arai LMP(07)
[spectrum]; Wang & Xiong AP(07).
@ Re Pauli's argument: Galapon PRS(02)qp/99, qp/03-in,
Wang et al JPA(03)qp/02, qp/03 [critique];
Isidro PLA(05)qp/04 [bypassing
Pauli's theorem].
@ Related topics:
Kundrát & Lokajícek PRA(03)
[3D oscillator].
Other Views and Proposals > s.a. observables [multi-time].
* Covariant view: According
to Reisenberger & Rovelli, time has
a special role in quantum mechanics because of idealized instantaneous measurements,
but the idealization can be dropped, and spacetime states defined.
* Relational time: One
promotes all variables in a system to quantum operators, and later chooses
one of the variables to operate like a "clock";
Conditional
probabilities are computed for variables of the system to take
certain values when the "clock'' specifies a certain time; The framework
is attractive in contexts where assuming the existence of an external, perfectly
classical clock, appears unnatural, as in quantum cosmology.
@ Covariant:
Reisenberger & Rovelli PRD(02)gq/01 [spacetime
states].
@ Relational time: Gambini et al NJP(04)gq,
PRD(04)gq [and
decoherence], IJMPD(04)gq [black
hole
information]; Milburn & Poulin IJQI(06)qp/05 [2
oscillators].
Related Concepts and Effects > s.a. arrow
of time; Detector; Ehrenfest
Time;
quantum measurement; symmetries [time
translation].
* Passage time: The shortest time after which, a quantum state
is transformed into a state orthogonal to itself.
@ Clocks: Anderson gq/95 [vs
time]; Ashworth PRD(98)qp/97 [oscillator
coherent states].
@ Real clocks: Hartle PRD(88);
Egusquiza et al PRA(99);
Egusquiza & Garay qp/03 [Zeno
effect]; Stodolsky in(06)qp/03 [coherence].
@ Time of measurement: Oppenheim et al PRA(99)qp/98;
Rovelli FP(98)qp,
comment Oppenheim et al FPL(00)qp/98; Home & Chattopadhayaya
qp/99.
@
Time of occurrence: Brunetti & Fredenhagen PRA(02)
[observable]; > s.a. quantum effects [time
of arrival, and other effects].
@ Time spent in a state: Ruseckas & Kaulakys PLA(01).
@ Transitions / jumps: Mensky PLA(96)
[reversibility]; Schulman qp/01-in
[time].
@ Uncertainties and time measurement: Braunstein et al AP(96)qp/95;
Kitada gq/99;
> s.a. uncertainty principle.
@ Time reversal: Costa De Beauregard PLA(78) [S-matrix, Feynman zigzag
and Einstein correlation]; Pastawski et al qp/04 [t-reversal
mirror]; Dowling et al PRL(05)
[stochastic quantum dynamics]; Aharonov & Tollaksen a0706-in
[rev].
@ Time ordering: Oppenheim et
al JPA(02); McGuire et al qp/05.
@ Other effects: Mermin PRL(95) [problems with retrodiction]; Hartle Compl(97)gq,
PS(98)gq/97 [prediction
vs retrodiction]; Brody JPA(03)
[passage time].
References > s.a. composite
systems; quantum spacetime.
@ Reviews: Hilgevoord SHPMP(05)
[history]; Fleming SHPMP(05); Zeh a0705-in.
@ General: Droz-Vincent PLA(88);
Collins & Squires FP(93);
Busch et al PLA(94);
Kapitanski & Rodnianski qp/97;
Briggs & Rost qp/99;
Muga et al ed-01; Hilgevoord AJP(02)
[conceptual]; Elitzur & Dolev qp/02-in
[and histories]; Lokajicek qp/02-in
[and irreversibility].
@ Time non-locality: Kim & Mahler ZN(01)qp; Suarez qp/01 [no
time ordering]; Kracklauer qp/02 [+
s.a.
qp/02];
Gainutdinov et al PLA(03)qp/02 [atom and surroundings].
@ Discrete: Balachandran & Chandar NPB(94)
[from quantization]; Misra FP(95),
Farias & Recami qp/97 ["chronon"];
Jaroszkiewicz & Norton
JPA(97), JPA(97);
Norton & Jaroszkiewicz JPA(98), JPA(98);
Bruce PRA(01)qp;
Valsakumar Pra(05)qp [and
arrow of time]; Skulimowski FPL(06)
[quantum time]; Isidro et al a0804 [and
evolution of observables]; Isidro et al MPLA(08)-a0804 [and
Heisenberg's equation as delay-differential equation]; > s.a. discrete
spacetime.
@ Quantum mechanics without time: Singh qp/01;
Singh GRG(03)gq/02 [and
non-commutative geometry]; Majid JMP(05)ht [spontaneous
time generation].
@ Other references: Mehlberg 80 [and causality];
Saunders Syn(95)
[wave function collapse, actuality and passage]; Bonifacio NCB(99)qp,
qp/99-in
[statistical]; Hitchcock gq/99 [complex
systems], qp/01-in
[and information]; Foschini qp/98 [and
logic]; Hiller et al PRL(04)qp/03 [undoing t evolution];
Mizel qp/03 [mimicking t evolution
in the ground state]; Cramer qp/05-in
[and transactional interpretation].
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
23 jun 2008