# Re: Bekenstein bound (Re: A model of consciousness)

From: Jeff L Jones (jeff@spoonless.net)
Date: Mon Mar 24 2008 - 00:01:04 MDT

On Fri, Mar 21, 2008 at 4:38 PM, Matt Mahoney <matmahoney@yahoo.com> wrote:
> Mass and size are related by Planck's constant.

Hmmmm. I'm used to expressing everything in units where Planck's
constant is 1, as well as the speed of light. So any size has an
equivalent mass and vice versa. However, what I was getting at is
that the size of something and its mass are in general two completely
different physical quantities, regardless of whether you measure them
both in terms of mass or both in terms of length. Their relationship
depends on the density of the particles making them up. However, upon
looking up the diameter of a proton, I realized that you're right in
this case... it *is* the same as the mass. I was then going to say,
maybe this is just coincidence... but upon further thought I think I
see why they are the same. For something like an atom, its size and
its mass are unrelated, because it's made up of particles which are
non-relativistic (most of their energy is stored in their rest mass).
However, for protons, it's made up of quarks which are relativistic
(most of their energy is stored in their kinetic energy). So if most
of the proton's mass is due to the kinetic energy of the quarks, then
the average separation of the quarks is going to be related to the
total mass of the proton. Tricky! So you're right. Strike my
comment about the mass and volume of the proton not being the same
thing.

> Anyway, maybe it's not interesting to you that a bit is the size of the
> smallest stable particle, but it's interesting to me. The entropy of the
> universe puts an upper bound on the biggest memory you can build, independent
> of whatever particles the universe might contain. It also suggests a
> relationship between the strong force and gravity.

It's definitely not interesting. I don't know what makes you say it's
the "smallest particle", but I think it's unlikely that it's stable.
If any kind of Grand Unified Theory is true, than it's guaranteed to
decay into positrons eventually. You can pack a lot of bits into a
femtometer, which is the size of a proton. It would just have to be
stored in stuff that is a lot smaller than protons (for instance, high
energy photons, gravitational waves, etc.) In principle, you could
have an entire quantum computer the size of a proton, and have it
calculating all sorts of interesting things. You just seem to be
proposing a limit that doesn't exist, by taking a limit for a large
volume and translating that into a limit for a small volume which just
gives you a totally wrong result... since the # of bits scales with
area and not volume.

Jeff

This archive was generated by hypermail 2.1.5 : Wed Jul 17 2013 - 04:01:02 MDT