HEAT

1
HEAT
2
Entropy

• Valentine Your tea is getting cold.
• Hannah I like it cold.
• Valentine Im telling you something. Your tea
  gets cold by itself, it doesnt get hot by
  itself. Do you think thats odd?
• Hannah No.

3
2nd Law of Thermodynamics

• Heat flows spontaneously from a substance at a
  higher temperature to a substance at a lower
  temperature and does not flow spontaneously in
  the reverse direction.

• Valentine Well, it is odd. Heat goes to cold.
  Its a one-way street. Your tea will end up at
  room temperature. Whats happening to your tea
  is happening to everything everywhere. The sun
  and the stars. Itll take a while but were all
  going to end up at room temperature. When your
  hermit set up shop nobody understood this

4
The Mystery of the Play

• But lets say youre right, in 18-whatever
  nobody knew more about heat than this scribbling
  nutter living in a hovel in Derbyshire.
• Hannah He was at Cambridge a scientist.
• Valentine Say he was. Im not arguing. And the
  girl was his pupil, she had a genius for her
  tutor.
• Hannah Or the other way round.
• Valentine Anything you like. But not this!
  Whatever he thought he was doing to save the
  world with good English algebra it wasnt this!
• Hannah Why? Because they didnt have
  calculators?
• Valentine No. Yes. Because theres an order
  things cant happen in. You cant open a door
  till theres a house.
• Hannah I thought thats what genius was.
• Valentine Only for lunatics and poets. p.79

5
HEAT TIME
Entropy is considered to be the quantity which
defines what is called the arrow of time''.
Experience shows that time can never flow
backwards events which have happened can never
be undone.
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Now, in the second law of thermodynamics
7
Backwards and Forwards

• So far, all the microscopic equations of physics,
  be they classical or quantum, do not
  differentiate between whether time flows forwards
  or backwards.
• Thomasina Ohyes. Newtons equations go
  forwards and backwards, they do not care which
  way. But the heat equation cares very much, it
  goes only one way. That is the reason Mr.
  Noakess engine cannot give the power to drive
  Mr. Noakess engine.
• Septimus Everybody knows that.
• Thomasina Yes, Septimus, they know it about
  engines!...

• Thomasina You cannot stir things apart.
• Septimus No more you can, time must needs run
  backward
• Valentine You cant run the film backwards.
  Heat was the first thing which didnt work that
  way. Not like Newton. A film of a pendulum, or
  a ball falling through the air backwards, it
  looks the sameWith heat -friction- a ball
  breaking a window It wont work backwards. She
  saw why. You can put back the bits of glass but
  you cant collect up the heat of the smash. Its
  gone. The heat goes into the mix. And
  everything is mixing the same way, all the time,
  irreversiblytill theres no time left. Thats
  what time means.

8
Macro vs. Micro
Macro The Very Big
Micro The Very Small
Predetermined
Non-Linear
Heat
Future is disorder
Linear
Mysterious
Unpredictable
One way street
Irregular
Future is predictable
time
Dripping Faucet
Chaos
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• Micro level These things exhibit
  unpredictability and irregularity (ie. Next drip
  from a dripping tap, the weather, etc. they
  are indicative of chaos theory)
• -Future is disorder - Valentine
• -disorder out of disorder into disorder -
  Septimus

• Macro level These things exhibit
  predetermination and predictability (ie. Heat,
  Time, the Science of Astronomy)
• -You cannot stir things apart
• - Thomasina
• -unchanging and unchangeable, and we are done
  with it for ever
• - Septimus
• -everything is mixing the same way, all the
  time, irreversibly
• - Valentine

There is a struggle between the theories
incorporating unpredictability (chaos) and those
of entropy (decrease in heat) because the latter
is conveying that on a macro level, heat will run
out, meaning our time will also run out (death).
10
Thomasina reads Fouriers prize essay, from
Paris, then draws a diagram illustrating what
shes extrapolated from the text. p.81

• Valentine Its heatIts a diagram of heat
  exchangeLike a steam engine, you see She
  didnt have the maths, not remotely. She saw
  what things meant, way ahead, like seeing a
  pictureLike a film.

• Septimus For your essay this week, explicate
  your diagram.
• Thomasina I cannot. I do not know the
  mathematics.
• Septimus Without mathematics, then.

11

• Septimus So, we are all doomed!
• Thomasina (Cheerfully) Yes
• Septimus This is not science. This is
  story-tellingSo the Improved Newtonian Universe
  must cease and grow cold. Dear me.
• Thomasina Yes, we must hurry if we are going to
  dance.
• Septimus Oh, we have time, I think.

• -Valentinetill theres no time left.

12

• Septimus When we have found all the mysteries
  and lost all the meaning, we will be alone, on an
  empty shore.
• Thomasina Then we will dance.

13
On the surface we find mathematical equations,
mystery, chaos, irregularity, conflicting
theories of the unpredictable and the
predetermined, etc. a sense of social, moral
intellectual posturing pervade.  Underneath we
find yearning, passion and desire.  At last,
fluid and intertwined they waltz into the chaos
of the final predetermined moments allowing 'caro
et spiritus' to unite in their surrender to the
dance.
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Macro vs. Micro
15
http//srikant.org/core/node10.html

• The fundamental equations do not have a preferred
  time direction. What about entropy? Can we simply
  define physical time to be the flow of time in a
  direction for which entropy always increases? Yes
  and many physicists think this is the solution,
  and consider entropy to be the quantity which
  defines what is called the arrow of time''. The
  fact that the flow of the time is irreversible is
  said to originate in the irreversible processes
  which increase entropy. Experience shows that
  time can never flow backwards events which have
  happened can never be undone.
• This situation is very unsatisfactory, and many
  leading physicists have expressed their
  dissatisfaction with this way of defining the
  flow of time. Their objections are fundamental.
  Recall that the idea of entropy was introduced
  because we had to deal with an enormous
  collection of atoms, around 10²³ hence, being
  unable to follow the movement of every single
  atom, we consequently assumed that we are totally
  ignorant of what the atoms are doing, and in fact
  the ultimate form of this ignorance is to assume
  every possible configuration for the atoms is
  equally likely. So entropy does not arise from
  any fundamental microscopic property of nature.
  Rather, only when we have a huge macroscopic
  collection of particles that the idea of entropy
  and irreversibility enters.

16

• There is a view that we should be able to deduce
  the irreversibility of the flow of time from
  microscopic equations. This hope has not yet been
  realized. Quantum physics introduces a different
  kind of irreversibility into physics. Once a
  measurement is performed on a quantum system, the
  effects of the measurement are irreversible, in
  that the changes resulting from measurement
  cannot be undone. So is the irreversibility of
  time linked to quantum measurements? Again, there
  is no answer to this question, since if we take
  the Universe as a whole, we cannot determine if
  there is any such thing as a quantum measurement.
  The reason being that the current theory of
  quantum measurement requires that the
  experimental apparatus is an entity external to
  what is being observed. Since there is no
  physical entity external to the Universe, the
  concept of quantum measurement in this case is
  difficult to define. In quantum physics, time
  reversal is also a symmetry which is broken by
  some processes, such as the decay of particles
  called Kaons. Does this allow us to define a
  direction of time? Again, the answer is no, since
  if we combine time reversal with some other
  operations such as reversing the sign of all the
  charges of the particles, and so on, we can
  recover a world in which time would be reversed,
  and this world would be equivalent to ours and
  related to our world by a well-defined
  transformation. There remains another question,
  namely, can the flow of time be reversed if the
  time-reversing process does not bring about any
  increase in entropy? There is no clear answer to
  this question, which remains open to further
  analysis and investigation. So at present,
  entropy is the only physical quantity that
  requires that time flow only in one direction,
  namely, in the direction of increasing entropy.
  The next generation of equations may yield new
  insights into why time flows only in one
  direction. The idea of heat death was widespread
  in the nineteenth century when the idea of
  entropy was first understood. Since the universe
  must move in a direction of greater and greater
  entropy, it was assumed that ultimately the
  universe would reach a state of equilibrium for
  which entropy would be a maximum, and in effect,
  time would effectively cease to exist since no
  change would take place. This ultimate
  equilibrium state was said to indicate that the
  universe was heading towards a final heat
  death''. Well, is this true? This answer is quite
  complicated. Given the fairly ordered state of
  the Universe at present, what with stars burning,
  new stars being formed, life existing on earth,
  and so on, one is led to the conclusion that the
  Universe must have started at the Big Bang in a
  very low entropy state, that is, in a highly
  ordered state. Ever since then, it has been
  racing towards a state with greater and greater
  disorder. Why was the initial state of the
  universe so highly ordered? To understand this
  initial state, one has to construct a model for
  cosmology, understand why should it be a low
  entropic state, and then deduce from it what is
  the ultimate fate of the universe - heat death or
  otherwise.

17
From the final scene

• Septimus A prize essay of the Scientific Academy
  in Paris. The author deserves your indulgence,
  my lady, for you are his prophet.
• Thomasina I? What does he write about? The
  waltz?
• Septimus Yes. He demonstrates the equation of
  the propagation of heat in a solid body. But in
  doing so he as discovered heresy a natural
  contradiction of Sir Isaac Newton.
• Thomasina Oh! he contradicts determinism?
• Septimus No!...Well, perhaps. He shows that the
  atoms do not go according to Newton. p.81

18

• Thomasina Mr. Noakes bad news from Paris!It
  concerns your heat engine. Improve it as you
  will, you can never get out of it what you put
  in. It repays eleven pence in the shilling at
  most. The penny is for this authors thoughts
• Septimus Why Where does he say it?
• Thomasina Nowhere. I noticed it by the way. I
  cannot remember now.
• Septimus Nor is he interested by determinism
• Thomasina Ohyes. Newtons equations go
  forwards and backwards, they do not care which
  way. But the heat equation cares very much, it
  goes only one way. That is the reason Mr.
  Noakess engine cannot give the power to drive
  Mr. Noakess engine.
• Septimus Everybody knows that.
• Thomasina Yes, Septimus, they know it about
  engines!...
• Septimus For your essay this week, explicate
  your diagram.
• Thomasina I cannot. I do not know the
  mathematics.
• Septimus Without mathematics, then.