Yousuf Khan ) writes:
On 26/09/2012 2:14 AM, John Park wrote:
If *changes in* length and time are quantised at the Planck level, then
many problems (e.g. the size of the cosmological constant) are solved.
Maybe.

http://arxiv.org/abs/1209.5386

Discrete space-time is something I personally believe in. But how
exactly is the cosmological constant related to the Planck scale?

Yousuf Khan

Deiss, the author, emphasises that he's not quantising space and time but only
changes in them.

You can probably make sense of the argument better than I can, but here's
my attempted paraphrase, as I understand what he's doing.

He considers the vacuum as a set of harmonic oscillator fields
correponding to virtual particles, and asks about the effect of the
expansion of the universe subject to his quantisation conditions. The
time-quantisation implies that changes in the periods of the oscillators
are quantised, and this condition gives a limit on the energy of those
oscillators that can respond to the expansion. The space-quantisation in
conjunction with the uncertainty principle gives a limit on the momenta of
these "interacting" virtual particles. Because of his quantistion model
both limits are expressed in terms of Planck quantities.

Together the two limits predict a vacuum energy which is a function of
the Hubble parameter. He identifies this energy with the dark energy of the
universe, AKA the cosmological constant, thus linking the Planck and
cosmological scales without the usual 120-order-of-magnitude discrepancy.
(And implying that [probably] only virtual photons and three virtual
neutrinos are "interacting" particles...with implications for the neutrino
masses.)

I haven't worked though Deiss's argument in detail, so I hope I'm not
misrepresenting him; and I hope this is some help.


--John Park

---------------
Janus, a novel
http://chizinepub.com/books/janus.php