Re: GR and Thermodynamics

Bill Hobba wrote:

Barry wrote:

Bill Hobba wrote:

Barry wrote:

Entropy is concerned with the flow of heat.

Not quite - it is concerned with how ordered a system is. That often
corresponds to heat but is not the same. See for example the Feynman
Lectures Chapter 44.

In Volume 1, Chapter 44, 44-6, he says that entropy is heat divided by
temperature.

In Chapter 46, 46-5, he relates entropy to disorder, mathematically.
But that does not change the fact that entropy is concerned with the
flow of heat.

The Second Law of Thermodynamics says that the entropy of a closed
system cannot decrease and is related to using the flow of heat to do
Work. At maximum entropy, heat is uniformly distributed and can do no
more work.

In any case, be careful whom you quote. In Volume 1, 15-1, he says
that " Newton's Second Law ... ...was stated with the tacit assumption
that m is a constant, but we now know that this is not true, and that
the mass of a body increases with velocity".


This became interpreted as
a probabilistic matter, and is often viewed in terms of information
and disorder. The fact that it is fundamentally about heat flow gets
almost forgotten.

You are confused. Entropy was originally introduced for heat (by Carnot if
memory serves me correctly - Feynman in the reference given previously gives
the exact details) - sure.

I don't feel confused, entropy is *defined* as heat/temperature. 19th
century statistical approaches focussed on the relationship between
entropy and order. But that does not change what entropy *is*.


In GR spacetime, world lines describe the flow of mass/energy.

They do not. They describe the path of free particles. They form geodesics
due the principle of maximal ageing.

World lines describe the paths of all particles, free or not. Not all
world lines are geodesics.


Spacetime curvature is what guides the flow.


You obviously need to learn what GR actually says:
http://nedwww.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html

Why not look at:

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gr.html

which reads:
_______________--
General Relativity may be summarized as follows:

Matter tells spacetime how to curve.
Curved spacetime tells matter how to move.
______________

Which I think is a quote from Wheeler.

GR predicts singularities, hence it is considered to be incomplete.

I already admitted that - but it is incomplete in the same way EM with point
particles is incomplete and leads to absurdities such as acasual runaway
solutions. And the solution is the same - it will be seen as the limiting
case of a theory that removes the difficulty in the same way EM is a
limiting case of QED and QED removes that difficulty.

Right!


The Second Law essentially says that heat/energy will flow so as to
equalize over space,

In a very very crude way yes. More precisely it is a measure of the
order
of a system - disorder always increases.

In a very definite way, i.e. it is the definition.

That disorder always increases is not a definition.

The defintion is that entropy relates to the distribution of heat, and
the Second Law relates to it's flow.

Disorder is the *consequence* - in a closed system.

You seem to be getting mixed up between cause and effect.

I suggest you are the one that is confused.

Entropy is *defined* as heat/energy. The Second Law *predicts*
increasing disorder in closed systems.

In thermodynamics, "friction" contributes to this spreading out of
heat/energy.


In GR, "friction" leads to the formation of BH's and the concentration
of mass/energy.


They are two sides of the same coin.


A formulation of GR that eliminates singularities

Barry

.

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