The Statistical Mechanic
A new paper on the arxiv is
weakly coupled to the previous post.
The authors examine hints
of asymptotic freedom in semiclassical cosmology.
They "find that, contrary to naive intuition,
the effects of quantum gravitational
fluctuations become negligible ... at very early times".
This is certainly contrary to conventional wisdom and interesting for
interested in quantum
Recently I found this
webpage, basically a list of open problems in mathematical physics.
I don't know if it is still maintained, but the good news is that there
is actually one set of
problems which have been solved meanwhile. The list is certainly far
from complete, e.g.
I did not see anything from general relativity. e.g. cosmic censorship
or the existence of
closed timelike loops.
A majority of these problems is from statistical mechanics, which is
not too surprising; It
is relatively simple to come up with a well-defined model which is then
difficult to solve.
One of those is the
Heisenberg model and A. Patrascioiu and E. Seiler
question if "the classical Heisenberg O(N) model has
exponentially decaying correlations
at all temperatures" to this list.
The classical Heisenberg model is a toy version of QCD and Prof. Seiler
"failure of the so-called asymptotic freedom" is possible if not
likely. He has accumulated
some evidence for
his suggestion and summarized his doubts in this paper.
I would like to add something I wrote several months earlier:
I followed a discussion about renormalization
on 'the comment thread which does not want
to end'. Joe Polchinski, Mark Srednicki and others answered questions
and discussed for
about 40 comments.
At almost the same time, there was an equally interesting exchange
following Scott's post about electricity (!).
Klas M. mentioned several papers, which I need to read: hep-lat/9210032
of the renormalization
group method and math/0206132
derives the critical probability for the
bootstrap percolation model. As Klas M. explains, this probability had
"[..] estimated by
simulation on what was considered huge systems [..] with claimed
accuracies of several decimals."
But then "Alexander Holroyd proved that the correct probability is
actually about twice as large
as the simulation papers had claimed." Ouch!
Even earlier, I wrote about the 'great heresy' of Predrag Cvitanovich
It was mentioned by John Baez in this
comment and I really recommend reading it.
I already wrote about the two
envelopes a while ago. It really seems simple, but it is
indeed quite a puzzle: Let us assume that you (Y) and your friend (F)
work at a
hedge fund with a very wealthy but strange boss. One day he gives both
of you a
closed envelope with the following remarks: "Both envelopes contain
your bonus, an
unknown amount of money. You know I am a strange guy, so it could be
one cent or
perhaps even less, or it could be a really big amount (since I am
wealthy only the sky
is the limit), or somewhere in between. Be aware that one envelope
twice the amount of the other. Switch the envelopes, if you think this
difference, before you open them (as many times as you want)."
Y is thinking: The situation is symmetric and I don't see
how I could gain anything
from switching envelopes. Let's just open them and see what we got.
F is thinking: My envelope contains an unknown amount of money X. The
amount in the
other envelope is either 2X or 0.5*X. The probability of the two cases
is 50% for each,
since I have no further information. Thus the expectation value should
0.5*(2X) + 0.5*(0.5*X) = 1.25X
Since this is higher than my X, it
would be better if we switch.
What would you do? Would you want to switch before opening the