Discrete time!!!

[bascule]

Yay, so apparently one person has used loop quantum gravity/loop quantum cosmology to construct a discrete-time model of the universe. This is old (2001) and I don't know anything about it, so can someone fill in this poor layman about how this paper was received and if it has spurned any further developments in discrete-time models of the universe based around LQG/LQC? Martin, I'm looking hopefully in your direction...

 

http://www.iop.org/EJ/abstract/0264-9381/18/6/308

 

Loop quantum cosmology: IV. Discrete time evolution

 

Martin Bojowald 2001 Class. Quantum Grav. 18 1071-1087 doi:10.1088/0264-9381/18/6/308

 

Abstract. Using general features of recent quantizations of the Hamiltonian constraint in loop quantum gravity and loop quantum cosmology, a dynamical interpretation of the constraint equation as evolution equation is presented. This involves a transformation from the connection to a dreibein representation and the selection of an internal time variable. Due to the discrete nature of geometrical quantities in loop quantum gravity, time also turns out to be discrete leading to a difference rather than differential evolution equation. Furthermore, evolving observables are discussed within this framework, which enables an investigation of physical spectra of geometrical quantities. In particular, the physical volume spectrum is proven to equal the discrete kinematical volume spectrum in loop quantum cosmology.

[patcalhoun]

Here's the preprint.

[Severian]

Lattice Gauge Theory has been using discrete time (and space) for years.

[bascule]

Lattice Gauge Theory has been using discrete time (and space) for years.

 

Wow, that's awesome! Thanks for the pointer

[Connor]

is discrete time a generally accepted theory?

[Severian]

Not really. In Lattice Guage theory it is used to regulate infinities which crop up in the theory, but they always take the 'continuum limit' at the end of a calculation. They have a quantity called the 'lattice spacing', usually denoted 'a', which is the minimum distance between allowed space-time points. At the end of the calculation they extrapolate their results to a=0.

[Connor]

so if they use a=0 in the end...

 

isn't that just using continuous time, by a different method?