## New Directions in the Foundations of Physics Conference in Washington DC 2013 (part 4)

### “Quantum information and quantum gravity” by Seth Lloyd

A thought provoking talk at the conference was that of Seth
Lloyd. He showed how to derive Einstein’s general relativity equation from
quantum limits for measuring space-time geometry and an additional black hole
assumption.

One way to think of measuring the geometry of space-time is
to think of a comprehensive GPS system.
Measuring time amounts to measuring the number of clock ticks and this requires
energy. Everybody is familiar with the position-momentum uncertainty principle,
but the energy-time uncertainty principle is not so clear cut. This is because
in quantum mechanics time is a parameter, and not an operator, and care has to
be exercised in interpreting the energy-time uncertainty principle.

Margolus and Levitin had obtained a bound of
quantum evolution time in terms of the initial mean energy of the system E: E
delta t >= hbar pi/2. From this the total possible number of clock ticks in
a bounded region of space time (of radius r and time span t) cannot exceed
2Et/pi hbar. In principle, quantum mechanics does not limit the accuracy for
measuring time, and all you need is to do is add enough energy. But in general
relativity, adding energy in a bounded region will eventually lead to the
creation of a black hole. So here is a general relativity assumption: we want
the radius of the bonded region to be larger than the Schwarzschild radius Rs =
2GM/c^2

From this (in terms of the Plank time Tp and Plank distance
Lp) one obtains the maximum number of clock ticks achievable in a bounded
region of space time before creating a black hole: r t / pi Lp Tp

Now r*t is an area and naive field theory would suggest r^3
t. Also naïve string theory would suggest at first sight r^2 t.

From those kinds of area considerations, Seth was able to
deduce general relativity equations inspired in part by Ted Jacobson’s ideas
(in fact Seth collaborated with Ted on this result). Now you may ask (as I
certainly did) if you start with Schwarzschild’s radius and you derive Einstein’s
equations, are you not vulnerable to charges of circularity? Perhaps, but the
result is still interesting.

(I have one more story to tell from the conference. Please
stay tuned for part 5-the last one.)

Very nice series of presentations, Florin. Did he indicate a paper on which the talk is based?

ReplyDeleteHi Cristi,

ReplyDeleteNice to hear from you. Seth did not indicate which paper this talk is based on, but looking on the archive, I think it is based on http://arxiv.org/pdf/1206.6559v4.pdf (it does have the complete content of the talk). One idea I did not mentioned in the post above was the each elementary quantum `operation' removes a Planck scale area from the two-dimensional sections of the spatial three volume in which the event occurs. And this leads to curvature which later leads to Einstein's equations. Now why this is so it is unclear.

PS: I a glad someone reads and appreciates my posts. This is the only conference I can afford to attend each year due to time constraints.

PPS: I was pleasantly surprised to discover that Seth is a very approachable, personable, and down to earth person. If you want to contact him on this, chances are you will get a reply.