# Re: follow-up on Holographic principle and MWI

On Thu, Apr 21, 2005 at 11:02:12PM -0400, danny mayes wrote:
> Well, as described in the FOR think of the multiverse as a block, made
> up of different stacks of pictures that comprise individual universes as
> they move through time.  Now try to adjust that to what is really going
> on:  space time is expanding out from the Big Bang.  If you could remove
> yourself from the multiverse and watch it, time would be expanding at an
> increasing area, just as the spatial dimensions are.  The reason
> information storage capacity would equal the surface area of a given
> object is that any object or area is actually existing in all these
> overlapping timelines, or virtually identically universes.  Therefore,
> if you assume the "time-area" is expanding at a proportional rate to the
> spatial volume, you would need to divide a cube 10^300 Planck units on a
> side  by  10^100 to  take out the information that is moving into  the 

This is very sloppy - if "time-area" were proportional to volume, then
the divisor would be 10^300. Perhaps you meant proportional to length,
but then I do not see why this should be.

> volume or area of time, since we lose this information as we are stuck
> on a solitary time line and losing the multiverse information to
> decoherence.  This is simply another way of saying we lose the
> information to the other universes, I'm just explaining why it would be
> the amount it is through the mental imagery of time expanding to fill a
> space  equivalent to the spatial dimensions.
>

But decoherence increases information, not loses it.

> Taking a bird's eye view, and watching the cube moving through the
> multiverse, all the overlapping universes the cube comprises, the cube
> could store 10^300 bits of information- equal to it's volume.  However,
> if you  measure the information in any individual universe, you have to
> divide the cube over all the overlapping universes it comprises, or an
> "area" of time equal to the the area of one of it's sides (again
> assuming the expansion of time is proportional to the expansion of the
> spatial dimensions.)  This leaves information storage capacity equal to
> the surface area of the object .
>
> I am basically taking the block view of the multiverse seriously, and
> dividing the information storage capacity by the area of all the stacks
> of pictures the cube exists on, because we can only measure the
> information on the one stack that is our universe.  The area of the
> different stacks can be thought of as an area of time, and would equal
> one of the spatial areas that comprise the cube if time expansion is
> proportional to spatial expansion.
>
> This makes sense to me, but then again I am an attorney....
>
> Danny Mayes

The only thing that makes sense to me is that maximal decoherence
occurs by arranging observers around the 4/3\pi solid angle of the
volume in question. Thus the maximum decoherence rate is proportional to the
surface area of the volume. Also, we know that linear spatial dimensions are
increasing linearly in flat space-time, so combining the two implies
that maximal decoherence will occur quadratically as a function of
time.

Does this give us the holographic principle? Hmm..

Also, what happens if space-time is not so flat - say spatial expansion
starts to accelerate like its doing now?

--
*PS: A number of people ask me about the attachment to my email, which
is of type "application/pgp-signature". Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.

----------------------------------------------------------------------------
A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                                    0425 253119 (")
UNSW SYDNEY 2052                         [EMAIL PROTECTED]
Australia                                http://parallel.hpc.unsw.edu.au/rks
International prefix  +612, Interstate prefix 02
----------------------------------------------------------------------------


pgpHLuBXwEVmx.pgp
Description: PGP signature