Lloyd & Ng on limits of physical measure of a region

[stargene]

[[Mod. note -- I'm sorry for the delay in processing this article,
which the author submitted on 2021-Sept-04. -- jt]]

The following quote is from a sciam article titled "Black Hole
Computers" by Seth Lloyd and Y. Jack Ng (April 1, 2007). They
are referring to satellites measuring any region with radius R
and certain ultimate limits to the possible accuracy which can be
obtained by even the most advanced civilization imaginable; lp
is the Planck length:

"..Mathematically, in the time it takes to map a region of radius R,
the total number of ticks by all the satellites is R^2/lp^2. If each
satellite ticks precisely once during the mapping process, the
satellites are spaced out by an average distance of
R^(1/3)lp^(2/3). Shorter distances can be measured in one sub-
region but only at the expense of reduced precision in some
other subregion. The argument applies even if space is
expanding.

This formula gives the precision to which distances can be
determined; it is applicable when the measurement apparatus is
just on the verge of becoming a black hole. Below the minimum
scale, spacetime geometry ceases to exist. That level of
precision is much, much bigger than the Planck length. To be
sure, it is still very small. The average imprecision in measuring
the size of the observable universe is about 10^-15 meter. Never-
theless, such an imprecision might be detectable by precise
distance-measuring equipment, such as future gravitational-wave
observatories--"

I don't have a concrete grasp of their conclusions-- Are they
saying, as an example, if we had a system (equivalent to a
cosmic tape measure), any attempt to measure the entire
universe would never have an average accuracy finer than
~ 10^-15 meter? Also, the fact of this "fineness" accuracy,
10^-15 meters, re: the "measure of the universe", being
roughly the radius of a proton, is fairly astonishing. Also, what
do Lloyd and Ng mean when they say that below that minimum
(fineness) scale, spacetime geometry has no meaning? Would
this actually conform with the notion of spacetime being
an emergent phenomenon outside of certain defined limits?
Thanks, Gene

[Phillip Helbig (undress to reply)]

Post by stargene
The following quote is from a sciam article titled "Black Hole
Computers" by Seth Lloyd and Y. Jack Ng (April 1, 2007). They
are referring to satellites measuring any region with radius R
and certain ultimate limits to the possible accuracy which can be
obtained by even the most advanced civilization imaginable; lp

The article (from 2012) is freely available; Google finds it quickly.

In general, it is concerned with the fascinating union of
thermodynamics, general relativity, and quantum theory in relation to
the information content of black holes. In particular, it looks at
limits on information processing in the universe. About 20 years ago
(building on earlier work), Freeman Dyson (and Lawrence Krauss, in a
sort of debate) did some work on this (but more in the context of
cosmology).

Post by stargene
I don't have a concrete grasp of their conclusions-- Are they
saying, as an example, if we had a system (equivalent to a
cosmic tape measure), any attempt to measure the entire
universe would never have an average accuracy finer than
~ 10^-15 meter?

Essentially, yes.

Post by stargene
Also, the fact of this "fineness" accuracy,
10^-15 meters, re: the "measure of the universe", being
roughly the radius of a proton, is fairly astonishing.

Do you mean the size or the coincidence (if it is one)? The interesting
thing is that, if true, their idea might be proved relatively soon.

Post by stargene
Also, what
do Lloyd and Ng mean when they say that below that minimum
(fineness) scale, spacetime geometry has no meaning?

They essentially mean that it can't be measured. Whether that means
that it doesn't exist is at least a philosophical question.

Post by stargene
Would
this actually conform with the notion of spacetime being
an emergent phenomenon outside of certain defined limits?

The two concepts are probably related, though perhaps not too closely.

[stargene]

Post by Phillip Helbig (undress to reply)
The article (from 2012) is freely available; Google finds it quickly.
In general, it is concerned with the fascinating union of
thermodynamics, general relativity, and quantum theory in relation to
the information content of black holes. In particular, it looks at
limits on information processing in the universe. About 20 years ago
(building on earlier work), Freeman Dyson (and Lawrence Krauss, in a
sort of debate) did some work on this (but more in the context of
cosmology).

Post by stargene
Also, the fact of this "fineness" accuracy,
10^-15 meters, re: the "measure of the universe", being
roughly the radius of a proton, is fairly astonishing.

Do you mean the size or the coincidence (if it is one)? The interesting
thing is that, if true, their idea might be proved relatively soon.

Thanks for your feedback. Re: 10^-15 meter as the fineness
limit on the measure of the universe, it’s notable that, assuming
the universe volume is roughly (10^26 meters)^3, separating it
into identical volumes by dividing by (Ru / Rpl)^2, these tiny units
also have radii roughly equal to 10^-15 meter. Ru is universe
radius and Rpl the Planck length.
Following Ng, each one can be seen as having one degree of
freedom. Ie: About ten to the one hundred twenty-two degrees
of freedom, as the universe computes itself from time zero
onward.