What's Wrong With The Second Law?

Interesting discussion about the Second Law of Thermodynamics, aka
entropy always increases. They are suggesting that entropy increases in
both directions of time, one in our universe, and one in our universe's
twin anti-universe. The only dependence is the direction of time. I
think that this is basically right.

Yousuf Khan

What's Wrong With The Second Law?
http://www.science20.com/hammock_phy...cond_law-81855

On Aug 20, 1:32*pm, Yousuf Khan wrote:
Interesting discussion about the Second Law of Thermodynamics, aka
entropy always increases. They are suggesting that entropy increases in
both directions of time, one in our universe, and one in our universe's
twin anti-universe. The only dependence is the direction of time. I
think that this is basically right.

* * * * Yousuf Khan

What's Wrong With The Second Law?

It is statistical. There is only order of one kind or another.
This was Albert Einstein stance of predetermined Order in time.


http://www.science20.com/hammock_phy...cond_law-81855

On Aug 20, 4:32*pm, Yousuf Khan wrote:
Interesting discussion about the Second Law of Thermodynamics, aka
entropy always increases. They are suggesting that entropy increases in
both directions of time, one in our universe, and one in our universe's
twin anti-universe. The only dependence is the direction of time. I
think that this is basically right.

* * * * Yousuf Khan

What's Wrong With The Second Law?http://www.science20.com/hammock_phy...cond_law-81855

Oh no! Another empty nut. — NoEinstein —

On 20/08/2011 4:32 PM, Yousuf Khan wrote:
Interesting discussion about the Second Law of Thermodynamics, aka
entropy always increases. They are suggesting that entropy increases in
both directions of time, one in our universe, and one in our universe's
twin anti-universe. The only dependence is the direction of time. I
think that this is basically right.

Yousuf Khan

What's Wrong With The Second Law?
http://www.science20.com/hammock_phy...cond_law-81855

Isn't everyone missing the obvious? GR requires that any large chunk of
space with matter, such as our observable universe, is unstable -- to
exactly balance it with a cosmological constant is like balancing a
pencil on its tip. So, the volume will be contracting in one direction
in time and expanding in the other.

In the contracting direction, Penrose singularity theorems apply and
there's some sort of crunch, black hole, or other thing there the mass
disappears into.

Now, throw quantum gravity into the mix, and, specifically, the
Bekenstein Bound. Follow the volume in the contracting time direction
and it will end up crunched into regions with arbitrarily small surface
areas, at least until more QG effects become important down near the
Planck scale.

So, the information content of the volume must be quite tiny in this
contracted part of its history; that is:

1. The volume's time history includes a region in which it is crunched
into a small, dense region near the Planck scale.
2. Its entropy at this time is bounded above by a very small number.

Apply statistical mechanics to the time evolution from this small, dense
region to the original point of its history, and you expect increasing
entropy. Apply ordinary and statistical mechanics farther in the same
direction in time and it expands more, at least for a while, and its
entropy further increases, at least for a while. (Eventually either it
recollapses or goes into thermodynamic heat death.)

Within this volume and throughout that portion of its history, its
thermodynamic arrow of time points in the same direction as the
direction in which it is expanding. So, to an observer in this volume,

1. There is a big bang in the past.
2. The big bang had low entropy.

We can *predict from first principles* of GR and our first stabs at
quantum gravity that we should find ourselves in an expanding universe
with a low-entropy big bang somewhere in our past -- and this bit of
explanatory power is one more sign that the bits of QG we have so far,
such as the holographic information bound, are meaningful. I'd even go
so far as to say that the fact of a low-entropy bang a few billion years
ago is good solid Bayesian evidence that black holes evaporate and even
that space-time is discrete on the smallest scales. Further, I'd say
that it points away from string theory and LQG and towards causal
dynamical triangulation as a solid QG contender, simply because CDT
predicts that at small length scales space exhibits fractal dimension
asymptotic to 2, which fits a holographic bound where the information
content of space is limited proportional to its surface area and not its
volume. String theory, by contrast, calls for dimension to increase at
small scales, and LQG for it to stay 3 all the way down.

Another reason for interest in CDT is that it may hold the greatest
promise of not having unmanageable infinities from gravity's
self-interaction. String theory calls for gravity to strengthen abruptly
at small scales, making it potentially able to reach parity with the
three quantum field theory forces in strength, but exacerbating the
problem of its self-interaction producing divergent behavior and
singularities under extreme conditions or down at Planckian length and
time scales. Problems even stock GR has in black holes and at the Big
Bang. LQG can "fuzz" the singularities into smears and round off their
pointy tips with a Planck-sized blur brush of quantum uncertainty but
can't get rid of its absurd strength at tiny length scales. CDT, by
reducing instead of increasing dimension, can.

Famously, and as described in Kip Thorne's
_Black_Holes_and_Time_Warps:_Einstein's_Outrageous _Legacy_, crushing a
cylindrical bundle of magnetic field lines can't give you a black hole;
the field self-repulsion will always be stronger than the gravity in its
energy. The same proved true for any crushing in only two dimensions of
a long, thing object extended in the third. Cosmic strings have a
conical singularity but no infinite-curvature nonsense on their axis
(and a real string isn't infinitely thin, but proton-wide for quantum
mechanical reasons anyway). And so forth.

Gravity in two dimensions thus cannot apparently produce black holes or
other singularities. Penrose's theorems apply in three-space and higher
but fail in the plane. And CDT says at small scales that's what space
approximates. So, CDT may be uniquely well suited to get rid of the
singularities, and also the infinities plaguing attempts to quantize
gravity, and it gives a natural geometrical explanation for the
Bekenstein bound's dependence on area rather than volume.

In fact, there's something even more interesting. The Bekenstein bound
can be calculated by observing that it takes energy to hold information
bound, and putting more than a certain amount of information in a small
enough volume will involve enough energy to put that volume within its
own Swarzchild radius. So it becomes a black hole and the standard
formula for black hole entropy applies. The argument thus extends that
formula to be an upper bound on entropy in any volume of space. Here's
the kicker: what distinguishes these volumes is their mass; the entropy
reaches a maximum when the mass does, at the mass of a black hole of the
same size. This suggests that mass itself is tied to the available and
used degrees of freedom in the volume at some deep quantum-gravitational
level. The CDT structure bushes out to become more three-dimensional at
larger scales -- perhaps something in the amount of this bushing-out is
the underlying thing beneath both mass and information? If so, the limit
prevents the CDT structure getting "too thick" in some sense, and indeed
can make a region collapse back to length scales that force it to two
dimensions. At those length scales no-hair predicts no degrees of
freedom survive except for mass, charge, and angular momentum.

Or, perhaps, CDT makes the interior of the hole a genuine hologram,
really existing only as dynamics on the horizon. That the electrostatics
near a hole can be regarded as taking place with the horizon as a
charged, conducting surface instead of vacuum is a strong hint that this
may be the case; likewise, the way a forming or accreting hole "sheds
its hair" may also mean it sheds, rather than hangs onto, the
information that falls in, with anything that remains being imprinted
onto the horizon rather than going deeper inside.

If that's the case, though, in one respect it's disappointing: all the
science fiction dreams of wormholes and other exotica hiding behind
those event horizons go away.

Though what of naked singularities? Or will CDT turn out to include
strong cosmic censorship, rather than "just" fuzzing the singularities
out a bit but preserving such exotica as Kerr wormholes and closed
timelike curves? Note: the "causal" in CDT means the individual CDT
graphs can't contain CTCs, but I don't think it's clear that this
necessarily rules out CTCs in the *quantum superposition* that will
exist; you can take limits of sequences of manifolds of a fixed
topology, so pairwise homotopic, and get a limit manifold that isn't
homotopic to them, e.g. a series of increasingly bent, open-ended
finite-length cylinder-surfaces whose limit is a torus. CTCs reemerging
in the "quantum limit" from individually-CTC-free graphs likewise cannot
be ruled out point blank, on topological grounds, without a deeper analysis.

And even absent CTCs, other forms of time travel could exist, such as
closed curves in the entropic arrow of time that might allow an observer
to experience time travel without anything acausal in the underlying
physics! At first, "entropy increases along entropic arrows" appears to
rule that out, but we could have a middling-entropy region become high
entropy, but with a small volume pumped to low entropy (an ordinary air
conditioned room is an example of that), and this volume's entropy
gradually increases the other way in time, to a point in the past where
it joins the middling-entropy region. The cycle, in general, must
"centrifugally spin off" heat into its surroundings as it spins, but it
can exist in principle.

Boundary conditions that produce multiple low-entropy-constrained
regions like the Big Bang might create cosmic-string-like defects in the
entropy field that produce entropy-CTCs, in a manner analogous to how
multiple bubble nucleations in electroweak symmetry breaking are thought
to have produced defects in the Higgs field consisting of ordinary
cosmic strings wrapped in curves on which the Higgs phase increases
continuously around the loop.

In particular, if inflation involves multiple inflationary bubble
nucleations, each of which starts out with a very low internal entropy
due to the tiny Bekenstein limit on the information content in the tiny
initial volume of the bubble, then bubble collisions could theoretically
result in entropic CTCs even in the total absence of CTCs in the
underlying spacetime topology.

Picture a ring of nucleated bubbles that collide while still fairly
small, then further expand, leaving a ring-shaped region of generally
low entropy surrounded by higher entropy; objects traveling around the
ring can shed entropy into surrounding higher-entropy regions as long as
such objects can exist at all, which requires only that the ring end up
"standing on edge" in time -- which a CDT-based inflationary scenario
will probably make possible. The underlying spacetime's time direction
goes the same way along both halves of the ring, forming no directed
cycle, so no spacetime CTCs, but with low entropy all around the ring
something at the end of it could find its entropic arrow of time
reversed. In spacetime, a version with increasing entropy goes forward
to the future apex of the ring on one side of it, and another with
decreasing entropy goes forward to the same apex on the other side,
where they, say, collide and annihilate as matter and antimatter,
whereas that object's entropic arrow of time has it go up one side of
the ring, turn, and go down the other.

On a smaller scale, the right kind of thermodynamic setup in a lab might
permit creating (at cost in heat generated) a zone in which the entropic
arrow of time is reversed, and possibly the use of such a zone as a time
machine of sorts, independently of what the truth about quantum gravity
turns out to be. (Likely, the zone, and a larger region into which it
sheds heat, will have to be shielded from quantum observation, for
reasons that are too complex to explain in a reasonably short usenet post.)

A naturally occurring candidate for a similar locally-time-reversed zone
is ... a black hole, though only if the interior is real after all.
Inside, there's a local Bekenstein arrow of time directed AWAY from the
singularity, so entropy ought to increase outward -- in principle, in a
big enough one (the size of the observable universe, say) stars could
form with planets, life, and conscious observers. Indeed, one could
question if the cosmos we observe is the inside of one, but
time-reversed into a white hole from our perspective. If so, a) the
universe should turn out to be finite in two directions, with spherical
topology, though very large, b) it should be contracting in the third
(which ours doesn't seem to be), and c) there'd be an event horizon in
our future on which we'd splatter, since our entropic arrow of time
would not have anywhere to go there, as all the timelike geodesics would
continue into a collapsing region there and not an expanding one. Our
matter would continue on but we presumably would not continue on with
it, instead annihilating counterparts in the external world that had the
misfortune to fall into the hole there from their own temporal
perspective. (This of course presumes the Bekenstein bound to hold in
the hole interior, which QG will probably insist on if the hole interior
exists at all. The usual argument for the bound only applies outside of
a black hole, however, and the classical picture of a black hole
interior allows entropy to increase without limit, and damn the
Bekenstein bound, as the singularity is approached.)

If miniature black holes can be produced in the lab, there is a
likelihood of enlightenment from studying their evaporation. Such
evaporation could give clues as to whether the interiors' entropies
decrease inward from the horizon, increase, or sit at the Bekenstein
bound all the way in; and the exact nature of the radiation could rule
out some models of QG and clarify others in the way that observations of
particle collisions clarified the Standard Model through the 60s and
70s. Indeed, more light would be shed on ordinary particle physics, as
any particle much lighter than the hole should be among its potential
decay products and so we should expect evaporating holes to shed Higgs
bosons, dark matter, and any other exotica that might exist such as
sterile neutrinos, axions, and so on.

At the same time, whether we can even produce them or not at a given
energy will give strong clues as to how gravity's strength changes at
small length scales: if it increases, some brand of string theory looks
likely, but if it weakens further, it points to CDT. If neither, LQG is
the best candidate. So, if black holes are easy to produce, it points to
strings, and in particular if the LHC makes any string theory becomes a
near shoo-in.

The most energetic cosmic rays remain unexplained, but it would be
interesting if some proved to be primordial black holes, their
evaporation slowed by time dilation in much the manner of muon decays in
ordinary cosmic ray showers. They hit the atmosphere, slow violently,
the time dilation goes away, and bang! Particularly energetic cosmic ray
shower. This, if it panned out, would give us evaporating holes to
examine even if string theory is false, and the holes' speeds and masses
at impact would give us a good idea of how large they were at the Bang.
Moreover, the lower cutoff on their masses could tell us the minimum
energy to create one -- low means probably strings, exactly the Planck
mass means probably LQG, and high means probably CDT, as these predict
4, 4, and 4 dimensions of spacetime at tiny length scales.

High energy also forces a phenomenon in CDT to treat space as
low-dimensional, which could have implication for the most energetic
gamma rays, as the normal structure and polarization of electromagnetic
radiation only makes sense in 3-space. In particular, electric and
magnetic components can't be orthogonally transverse polarized in only 2
dimensions, if they can even coexist at all, so CDT might mean a cutoff
to gamma ray energy, or a modification in the behavior of such rays
(particularly wrt polarization) at high energy.

This hypothetical cutoff might show up directly in cosmic rays or GRB
observations, or indirectly in quantum systems that should be able to
emit a very high energy gamma to drop to a ground state, but don't
actually do so. In particular, there'd be a maximum mass for a
particle-antiparticle pair to annihilate! This mass likely would be the
mass above which the pair are two possibly-charged black holes that
merge into a neutral hole instead of two particles annihilating -- so,
probably the (QG-modified) Planck mass.

Put in reverse, all holes of this mass should be extremal, which might
in turn suggest that 1) quantum numbers such as color and flavor apply,
in principle, to holes, and make them more extremal in a manner
analogous to charge; 2) holes can undergo weak decays(!); and 3) some
formula exists to compute mass from particle quantum numbers, and gives
the (QG-modified) Planck mass only for combinations of statistics that
make extremal holes of that mass and lower masses only for combinations
that give superextremal holes of those masses. Then the fundamental
particles ARE, precisely, all the possible superextremal black holes. If
the formula gives higher masses only for combinations that give
subextremal holes of those masses, then strong cosmic censorship is
(more or less) true, as only tiny particles get to be naked
singularities and their large-in-comparison quantum wavelengths fuzz
them out completely, whereas otherwise the fundamental particles include
some real bigons, such as Kerr rings of various masses and spins, with
wavelengths tiny compared to their sizes. Note: the Planck mass should
ideally be the point where Swarzchild radius and quantum wavelength
cross, both equaling the Planck length. The QG theories that alter
dimensionality at small scales would presumably affect this point, both
by altering the Swarzchild radius (upward for string theory and downward
for CDT) and the wavelength (the discreteness of space would begin to
impact on wavelengths near this scale, and for large enough masses would
render it physically meaningless).