Source: http://www.scientificblogging.com/
Three weeks of
speculations have come to an end. Since this morning
Verlinde's paper is available
on arXiv.
I encourage you to give it a try. The article is well written and the math is limited to fairly basic stuff. This combination makes it a relatively easy read. Granted, the paper requires some more gray matter cells being active than the average “
Hammock Physicist” blog entry, but for an average
Hammock Physicist reader probably not by an insurmountable amount.
The crux of the article can be summarized in one sentence:
If it smells like entropy, and it behaves like entropy, it probably is entropy.
As was
suggested before, one can consider
Verlinde's starting point to be a reversal of concepts like the
Hawking temperature of
black holes and the
Unruh effect. Let's take the
black hole temperature as an example. The
black hole temperature is defined at the
black hole horizon, and since
Hawking's groundbreaking work we know it is proportional to the gravitational acceleration at the horizon. Now
Verlinde reverses this. He asks us to consider the gravitational acceleration at the horizon as resulting from the horizon temperature.
Subsequently,
Verlinde takes a deep dive: if an acceleration is proportional to a temperature, it has all the characteristics of an
entropic effect.
Entropic acceleration results from the tendency of a system to evolve such that there is an increase in the minimum number of bits required to describe the system in all its details. Could it be that gravitational attraction results from nothing more than a growth in number of bits required?
Verlinde argues that such is indeed the case. Key is that one needs to follow a holographic approach with all bits describing reality residing at
holographic screens.
I think the relation to entropic effects is clearest in
one of the
Newtonian scenarios
Verlinde considers: a given matter
distribution that creates a gravitational potential.
Verlinde requires
the
holographic screens to coincide with equipotential surfaces, and
arrives at the conclusion that the bit saturation (the number of bits
required to describe the system divided by the number of bits available
on the screen) equals
where
represents the
Newtonian gravitational potential. This bit saturation is a positive
number that vanishes at large distances. If one shrinks the
holographic screen whilst ensuring it keeps following the equipotential surfaces,
the bit saturation keeps growing until it reaches a value of unity at
which the screen is saturated with information. It can not shrink
further, a
black hole has formed with the screen representing its
holographic horizon.
Again, you have to reverse this thinking.
When doing so, the picture that emerges is that of a
gravitational attraction (acceleration defined by a gravitational potential) that
results from a tendency of physical systems to evolve such that the
holographically available bits saturate with information. This tendency
towards bit saturation is an entropic effect, that we experience as
gravitational attraction.
Verlinde goes further than
Newtonian gravity. He discusses inertia, the equivalence principle, the
Einstein
equation, and also gives some hints towards implications for
string theory.
The paper inevitably has somewhat a handwaving character,
and provides a direction rather than a full theory. Yet, the direction
is clear, and points to a novel horizon (pun intended) that is
unexplored. I do consider
Verlinde's arguments to be convincing.
Verlinde is 'on to something', and it would not surprise me if in a
short time frame we will witness a flurry of activity in this area.
A
few more critical remarks: in most of the examples, I do not think the
sign of the
entropic force comes always out very clearly. Related to
this is the question: how is the inside and the outside of a screen
defined whilst avoiding any circular reasoning, and how to get a change
in sign between attractive and repulsive effects. I am convinced that
within the existing framework these questions can be answered in a
satisfactory fashion. These matters are of paramount importance if one
starts to address issues like: can one use this
entropic approach to
eliminate the need for dark energy? Other more philosophical questions
center around the emergence of time (and the good-ole '
arrow of time')
from this
entropic approach.
And, of course, the million-dollar
question is: “what laws govern the bit dynamics on holographic screens?”
To
be continued...
