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From: Jarek Duda on 10 Jul 2010 06:54
I always thought that thermodynamics/statistical physics is effective
theory – statistical result of some fundamental physics below, but
recently there became popular theories starting from ‘entropic force’
as fundamental (basing on holographic scenarios, like in
http://arxiv.org/abs/1001.0785 ).
For a simple mathematician like me it sounds like a nonsense – in
fundamental theory describing evolution of everything there should be
one concrete history of our universe – there is no place for direct
probabilities of scenarios required to define e.g. entropy.
So I wanted to ask if someone could explain why we can even think
about fundamental ‘entropic’ theories?

To start the discussion I would like to briefly remind/discuss looking
clear for me distinction between deterministic and stochastic/
thermodynamical models:
DETERMINISTIC models – the future is completely determined
- evolution of gas in a tank is full dynamics of all its particles -
for given valve opening there escaped concrete number of particles,
- it's usually Lagrangian mechanics of some field – there is some
scalar/vector/tensor/’behavior of functional'(QFT) in each point of
our spacetime, such that ‘the action is optimized’ – each point is in
equilibrum with its four-dimensional neighborhood (spacetime is kind
of ‘4D jello’),
- evolution equations (Euler-Lagrange) are HYPERBOLIC PDE - linearized
behavior of coordinates in the eigenbase of the differential operator
is
d_tt x = - lambda x
(0 < lambda = omega^2 )
so in linear approximation we have superposition of rotation of
coordinates – ‘unitary’ evolution – and so such PDE are called
wavelike – the basic excitations on water surface, in EM, GR, Klein-
Gordon are just waves,
- the model has FULL INFORMATION – there is no place for direct
probability/entropy in electromagnetism, general relativity, K-G etc.
– the model has some TIME (CPT) SYMMETRY INVARIANCE (no 2nd law of
thermodynamics – there is still unitary evolution in thermalized gas
or a black hole)

THERMODYNAMICAL/STOCHASTIC models – there is some probability
distribution among possible futures
- gas in a tank is usually seen as thermalized, what allows to
describe it by a few statistical parameters like entropy (like sum of –
p*lg(p) ) or temperature (average energy per degree of freedom) - for
a specific valve opening, the number of escaped particles is given by
a probability distribution only,
- it is used when we don’t have full information or want to simplify
the picture – so we assume some mathematically universal STASTICAL
ENSEMBLE among POSSIBLE SCENARIONS (like particle arrangements) –
optimizing entropy (uniform distribution) or free energy (Boltzmann
distribution),
- thermodynamical/stochastic evolution is usually described by
difussion-like: PARABOLIC PDE – linearized behavior of coordinates in
the eigenbase of the
differential operator is
d_t x = - tau x
(tau - ‘mean lifetime’ )
so in linear approximation we have exponential decay (forgetting) of
coordinates – evolution is called thermalization: in the limit there
survive only ones with the smallest tau – we call it thermodynamical
equilibrium and usually can be describe using just a few parameters,
- these models don’t have time symmetry – we cannot fully trace the
(unitary?) behavior so we have INFORMATION LOST – entropy growth – 2nd
law of thermodynamics.

Where I’m wrong in this distinction?
I agree that ‘entropic force’ is extremely powerful, but still
statistical result – for example if while random walk instead of
maximizing entropy locally what leads to Brownian motion, we do it
right: globally, we thermodynamically get going to the lowest quantum
state – single defects create macroscopic entropic barriers/wells/
interactions:
http://demonstrations.wolfram.com/GenericRandomWalkAndMaximalEntropyRandomWalk/
For me the problem with quantum mechanics is that it’s between these
pictures – we usually have unitary evolution, but sometimes entropy
grows while wavefunction collapses – there is no mystical
interpretation needed to understand it: entropy maximizing from
mathematically universal uncertainty principle is just enough (
http://arxiv.org/abs/0910.2724 ).

What do you think about this distinction?
Can thermodynamical models be not only effective (result), but
fundamental (reason)?
Can quantum mechanics alone be fundamental?
From: Jarek Duda on 13 Jul 2010 03:03
In this thread I wanted to remind and discuss what thermodynamics is -
simplified effective picture in which we assume statistically typical
behavior, like that when we completely don't know which scenario is
happening, we should assume maximizing entropy uniform distribution
http://en.wikipedia.org/wiki/Microcanonical_ensemble
Unfortunately in world of quantum mechanics which is generally
believed to be impossible to understand but still fundamental - the
logic of reason-result distinction is no longer binding...
The belief that QM is fundamental leads to many worlds interpretation
- that our spacetime is infinitely quickly branching tree of parallel
universes ...

.... while field theories we use on all scales (GR, EM, Klein-Gordon,
QFT) are deterministic and clearly say what our spacetime is - in
these theories we live in static 4D action optimizing solution - each
point is in equilibrium with its 4D neighborhood - spacetime is kind
of '4D jello'.
They are deterministic and like QM mechanics have 'wavelike/unitary'
evolution.

So what's happening when we cannot fully trace the evolution? ... for
example the behavior of a single particle ...
In such situations we have to use some thermodynamical model - assume
some statistical ensemble among possible scenarios for example to
maximize entropy - assume that the particle makes some random walk ...
Maximizing entropy locally leads to Brownian motion in continuous
limit - but when we do it right: assume global entropy maximum (like
in models I advocate) - we get thermodynamical going to squares of
coordinates of the dominant eigenvector of discrete Hamiltonian (and
finally the real Hamiltonian while assuming Boltzmann distribution
among trajectories).
http://link.aps.org/doi/10.1103/PhysRevLett.102.160602

These new but fundamental stochastic models finally show what was
missing - that in field theories on thermodynamical level: when we
cannot fully trace the evolution, we should assume collapse to some
local lowest quantum state.
Living in specetime ('4D jello') leads to many nonintuitive 'quantum'
consequences - like (confirmed) Wheeler's delayed choice experiment,
that in models with limited information to translate what we are
working on (amplitude) into the real probabilities - we should
'square' it against Bell's intuition, or allows for 'quantum'
computations:
http://www.thescienceforum.com/Four-dimensional-understanding-of-quantum-computers-24936t.php
From: Sam Wormley on 13 Jul 2010 11:21
The jury hasn't even been seated yet!

A Scientist Takes On Gravity
by DENNIS OVERBYE
Published: July 12, 2010
http://www.nytimes.com/2010/07/13/science/13gravity.html

"It�s hard to imagine a more fundamental and ubiquitous aspect of life
on the Earth than gravity, from the moment you first took a step and
fell on your diapered bottom to the slow terminal sagging of flesh and
dreams".

"But what if it�s all an illusion, a sort of cosmic frill, or a side
effect of something else going on at deeper levels of reality"?

"So says Erik Verlinde, 48, a respected string theorist and professor of
physics at the University of Amsterdam, whose contention that gravity is
indeed an illusion has caused a continuing ruckus among physicists, or
at least among those who profess to understand it. Reversing the logic
of 300 years of science, he argued in a recent paper, titled �On the
Origin of Gravity and the Laws of Newton,� that gravity is a consequence
of the venerable laws of thermodynamics, which describe the behavior of
heat and gases".

From: Darwin123 on 13 Jul 2010 15:54
On Jul 10, 6:54 am, Jarek Duda <duda...(a)gmail.com> wrote:
> I always thought that thermodynamics/statistical physics is effective
> theory – statistical result of some fundamental physics below, but
> recently there became popular theories starting from ‘entropic force’
> as fundamental (basing on holographic scenarios, like inhttp://arxiv.org/abs/1001.0785).
> For a simple mathematician like me it sounds like a nonsense – in
> fundamental theory describing evolution of everything there should be
> one concrete history of our universe – there is no place for direct
> probabilities of scenarios required to define e.g. entropy.
> So I wanted to ask if someone could explain why we can even think
> about fundamental ‘entropic’ theories?
>
> To start the discussion I would like to briefly remind/discuss looking
> clear for me distinction between deterministic and stochastic/
> thermodynamical models:
> DETERMINISTIC models – the future is completely determined
> - evolution of gas in a tank is full dynamics of all its particles -
> for given valve opening there escaped concrete number of particles,
> - it's usually Lagrangian mechanics of some field – there is some
> scalar/vector/tensor/’behavior of functional'(QFT) in each point of
> our spacetime, such that ‘the action is optimized’ – each point is in
> equilibrum with its four-dimensional neighborhood (spacetime is kind
> of ‘4D jello’),
> - evolution equations (Euler-Lagrange) are HYPERBOLIC PDE - linearized
> behavior of coordinates in the eigenbase of the differential operator
> is
> d_tt x = - lambda x
> (0 < lambda = omega^2 )
> so in linear approximation we have superposition of rotation of
> coordinates – ‘unitary’ evolution – and so such PDE are called
> wavelike – the basic excitations on water surface, in EM, GR, Klein-
> Gordon are just waves,
> - the model has FULL INFORMATION – there is no place for direct
> probability/entropy in electromagnetism, general relativity, K-G etc.
> – the model has some TIME (CPT) SYMMETRY INVARIANCE  (no 2nd law of
> thermodynamics – there is still unitary evolution in thermalized gas
> or a black hole)
>
> THERMODYNAMICAL/STOCHASTIC models – there is some probability
> distribution among possible futures
> - gas in a tank is usually seen as thermalized, what allows to
> describe it by a few statistical parameters like entropy (like sum of –
> p*lg(p) ) or temperature (average energy per degree of freedom) - for
> a specific valve opening, the number of escaped particles is given by
> a probability distribution only,
> - it is used when we don’t have full information or want to simplify
> the picture – so we assume some mathematically universal STASTICAL
> ENSEMBLE among POSSIBLE SCENARIONS (like particle arrangements) –
> optimizing entropy (uniform distribution) or free energy (Boltzmann
> distribution),
> - thermodynamical/stochastic evolution is usually described by
> difussion-like: PARABOLIC PDE – linearized behavior of coordinates in
> the eigenbase of the
> differential operator is
> d_t x = - tau x
> (tau  - ‘mean lifetime’ )
> so in linear approximation we have exponential decay (forgetting) of
> coordinates – evolution is called thermalization: in the limit there
> survive only ones with the smallest tau – we call it thermodynamical
> equilibrium and usually can be describe using just a few parameters,
> - these models don’t have time symmetry – we cannot fully trace the
> (unitary?) behavior so we have INFORMATION LOST – entropy growth – 2nd
> law of thermodynamics.
>
> Where I’m wrong in this distinction?
> I agree that ‘entropic force’ is extremely powerful, but still
> statistical result – for example if while random walk instead of
> maximizing entropy locally what leads to Brownian motion, we do it
> right: globally, we thermodynamically get going to the lowest quantum
> state – single defects create macroscopic entropic barriers/wells/
> interactions:http://demonstrations.wolfram.com/GenericRandomWalkAndMaximalEntropyR...
> For me the problem with quantum mechanics is that it’s between these
> pictures – we usually have unitary evolution, but sometimes entropy
> grows while wavefunction collapses – there is no mystical
> interpretation needed to understand it: entropy maximizing from
> mathematically universal uncertainty principle is just enough (http://arxiv.org/abs/0910.2724).
>
> What do you think about this distinction?
> Can thermodynamical models be not only effective (result), but
> fundamental (reason)?
> Can quantum mechanics alone be fundamental?

I think there are already theories (or interpretations?) accepted by
the mainstream (or a tributary thereof) that treat quantum mechanics
this way. These are sometimes called coherence theories of quantum
mechanics. Coherence theory doesn't start out with string theory. I
believe that parts of coherence theory are being incorporated into
string theory.
I don't have any references on me. However, I remember reading
books on it. Coherence theory is basically an "all wave"
interpretation of quantum mechanics. The measuring apparatus is
basically a very complex waveform, with a lot of degrees of freedom.
That is why it acts "classical."
When a sample s being examined with the measuring apparatus, it
causes the system to change two ways. First, the system decoheres. The
phases of the sample are locked together, so that the sample ends up
turning into a wave pulse. Then, the entropy of the sample increases.
There really isn't a fundamental change in "waviness" of the
sample. However, the result is a type of wave-form collapse. The
sample wave form becomes like a particle.
The loss of information is hidden by the changes in the measuring
apparatus. There are so many degrees of freedom in the measuring
apparatus that it is impossible to measure the phase of each
component.
Needless to say, there are still some problems that come with
this interpretation. However, it seems more logically self consistent
than the Copenhagen interpretation. Not every scientist is comfortable
with the Copenhagen interpretation of quantum mechanics.
From: Darwin123 on 13 Jul 2010 20:25
On Jul 13, 11:21 am, Sam Wormley <sworml...(a)gmail.com> wrote:
> The jury hasn't even been seated yet!
>
> A Scientist Takes On Gravity
> by DENNIS OVERBYE
> Published: July 12, 2010
>    http://www.nytimes.com/2010/07/13/science/13gravity.html
>
> "It’s hard to imagine a more fundamental and ubiquitous aspect of life
> on the Earth than gravity, from the moment you first took a step and
> fell on your diapered bottom to the slow terminal sagging of flesh and
> dreams".
>
> "But what if it’s all an illusion, a sort of cosmic frill, or a side
> effect of something else going on at deeper levels of reality"?
>
> "So says Erik Verlinde, 48, a respected string theorist and professor of
> physics at the University of Amsterdam, whose contention that gravity is
> indeed an illusion has caused a continuing ruckus among physicists, or
> at least among those who profess to understand it. Reversing the logic
> of 300 years of science, he argued in a recent paper, titled “On the
> Origin of Gravity and the Laws of Newton,” that gravity is a consequence
> of the venerable laws of thermodynamics, which describe the behavior of
> heat and gases".
String theory has turned out to have testable predictions outside
of cosmology and high energy physics. Even if people are disappointed
in string theory as a fundamental theory, there are complex systems
that map neatly onto string theory.
Okay, this is sort of a cop out. We can't use string theory the
way we originally hoped. However, we do use it for something else
which may be technologically important.
The mathematics of string theory turns out to have interesting
applications in condensed matter physics. String theory mathematics is
being used to describe "perfect gases." Experiments are being
performed with "perfect gases." The result match experiments.
"Perfect gases" are fluids that have negligible viscosity and yet
act like they are made of Newtonian particles. Perfect gases are
formed in the collision of nucleii with high atomic number, and in
some very cold gases.
This is different from superfluids. Superfluids have negligible
viscosity but have quantum mechanical properties. These include helium
III, superconductors and Bose-Einstein gases.
It is ironic that string theory ultimately explains why some
systems act classical rather than quantum mechanical. This is not
fundamental in terms of fundamental particles. Too bad. However, it is
tied to reality. So string theory may become very important.
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