Transcript Conservation Rules, Thermodynamics and the Arrow of Time

Conservation Rules, Thermodynamics
and the Arrows of Time
Michael Bass, Professor Emeritus
CREOL, College of Optics and Photonics
University of Central Florida
© M. Bass
What is a conservation law?
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Something that does not change during a
physical process is said to be conserved.
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The key is to identify what does not change and
why.
This way of thinking has produced powerful
rules in science.
 It has also produced powerful ways of
thinking in other human endeavors.
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© M. Bass
From Newton’s second law
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Conservation of momentum
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Momentum is conserved in the motion of a system when
no external forces act on it.
If the external force is zero then the quantity mass times
velocity (momentum) does not change.
Never found to be violated in everything from cannon
shells striking walls to billiard balls colliding to nuclear
interactions.
Linear and angular momentum are conserved.
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These laws are today understood to be related to invariance of the
system under translation and rotation.
© M. Bass
Conservation of mass
Seemed this must be so since from Newton
on there was no way to create or destroy the
“quantity of matter” or mass of an object.
 Today because of Einstein’s work we know
that mass and energy are interchangeable so
it is the total mass-energy of the system that
is conserved.
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© M. Bass
Conservation of energy
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We were converting something into something.
Water up high caused wheels to turn when it fell down.
What was the property of the water when it was “up”
and that of the turning wheel.
We had to determine what types of this property there
were since it seemed different in the water and in the
turning wheel.
© M. Bass
Steam
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Steam (water vapor) had the ability to make things
move – it could turn wheels.
It contained something that could do what water
that was up high could do.
It was also hot to the touch.
Was the something connected to its being hot?
In the 1st Century AD Hero
of Alexandria invented the
Aeolipile – showed that
steam could be converted
into motion
© M. Bass
Temperature
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Being scientists we had to invent a way to measure
the property of being hot so we -invented temperature and in the process had to
also invent thermal equilibrium.
Two objects at the same temperature when placed
in contact remained at the same temperature – they
were in thermal equilibrium.
This enabled us to define an object’s temperature
in terms of some standard (an ice and water mix for
example) as a measure of how far was the object
from equilibrium with the standard.
The existence of temperature is the zeroth law
of thermodynamics.
© M. Bass
The somethings
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All the somethings – water that was up, steam that
was hot, wood or coal waiting to be burned and
heat the water to steam – were recognized to be
aspects of one something – ENERGY
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While today it is so common a concept we forget that it
had to be invented to allow us to understand what was
happening.
What we discovered by long, difficult and elegant
experimentation was that in a closed system the
total amount of energy does not change when a
thermodynamic process takes place.
This is the first law of thermodynamics.
© M. Bass
Joule and paying attention to the
evidence
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The work mentioned above was that of James
Prescott Joule, an Englishman.
Between 1837 and 1847 he developed the
concepts of temperature, thermal equilibrium
He also showed that heat was not a flow of
something called caloric but a form of energy.
Benjamin Thompson’s (1753-1814) observation in
a gun barrel factory.
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Thompson reported that when the barrels were bored out
the barrels became very hot. The mechanical act of
boring out the barrel caused its temperature to rise.
Somehow one form of energy had been converted to
another. Mechanical energy had become heat energy.
© M. Bass
A more modern form
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Einstein in 1905 showed that
mass had energy and energy
had mass so the first law was
expanded to include this type
of energy.
In fact the earlier concept of
mass conservation (ie: in a
closed system you could not
create or destroy mass) was
expanded to be part of the
first law.
© M. Bass
Other things that are conserved
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In physics:
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Charge
Baryon number
Lepton number
Strangeness
Charge-parity-time (CPT)
In everyday life
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Money,
Land,
Water,
Air,
and so on.
© M. Bass
Machines
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The industrial revolution meant that we built
engines to run the machines of our industry.
It cost money to run these machines.
Obviously you wanted the most
efficient engine because it would cost
less to run and you would make more
profit.
© M. Bass
Nicholas Leonard Sadi Carnot
(1796-1832)
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The best engine!
In 1824 Carnot at the Ecole
Polytechnique in Paris published a
paper “Reflections on the Motive Power
of Heat” in which he identified an engine
that would turn heat into useful work but
using only reversible steps.
P
He claimed in a brilliant moment of
P
isoth.
insight that this would be the most
adiab.
efficient engine possible because
each step in its operation was perfectly
isoth.
reversible. In other words, in the
Carnot engine nothing was lost.
adiab.
V
© M. Bass
Entropy
A German, Rudolph Clausius (1822-1888)
studied the Carnot cycle engine and
developed the mathematical statement of how
it works as the most efficient engine possible.
 To do this Clausius invented the concept of
entropy and showed that
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in the Carnot engine the change in entropy
during a cycle of the engine was 0.
 For all other engines the change in entropy
was positive.
© M. Bass
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Another way of saying it
William Thompson (Lord Kelvin) in England
(1824-1907) refined this concept into a much
more general statement that in a
thermodynamic system (a system made
up of many particles of matter) that went
through any process the quantity known
as entropy must either increase or remain
the same.
 This is the second law of thermodynamcs.
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© M. Bass
The laws of thermodynamics
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There is temperature and thermodynamic
equilibrium – you are allowed to play.
There is energy (mass-energy) and in a closed
system you can not change the total amount only
convert it from one type to another – the best you
can do is break even.
There is entropy and in a closed system
undergoing a thermodynamic process it either
remains constant or must increase – if you play
long enough you must lose.
© M. Bass
The ARROWS of time
Thermodynamic
 Universal expansion
 Kaon decay
 Electromagnetic
 Psychological
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Notice that they all point in the same direction!
© M. Bass
The thermodynamic arrow of time
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The universe is a closed system (it is
everything we know of) and so its
entropy must be increasing since
processes taking place in the
universe are not completely
reversible.
If entropy must increase as processes
go forward the arrow of time must
point towards increased entropy.
Time goes from the past to the
future where the entropy is greater
than it was before.
© M. Bass
Disorder
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Next the mathematicians realized that the
quantity that Clausius had called entropy was
actually a measure of the degree of disorder
in a thermodynamic system.
Thus, no matter what you did, since all real
systems involved some sort of irreversible
process, the entropy or disorder increased.
We are in a universe that is evolving towards
more and more disorder. This is sometimes
called the entropy death of our universe. A very
grim concept but one that had to be accepted.
There was no other choice.
© M. Bass
Probability
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We note that there are many more ways in
which a system can be disordered than in
which it can be ordered.
There is only one way for you all to sit on one
chair and many ways to sit in many chairs.
 Particles of gas in a room.
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Thus, the universe is evolving from a less
likely state to a more likely state.
© M. Bass
The laws of physics
 All
of the fundamental laws of
physics are independent of the arrow
of time.
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They don’t change when you change the sign of
time.
 Mathematically
speaking, they are all second order in
time.
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It is in the second law of thermodynamics
that physics encounters a clear arrow of time
– the past is different from the future.
© M. Bass
There must be more
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Some fundamental events or laws must be
sensitive to the direction of time. They must lead
to a future that is identifiably different from the
past.
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There are more particles than anti-particles.
In 1980 James W. Cronin and Val Fitch won the Nobel
prize in Physics for the asymmetry of the decay of neutral
K mesons with respect to time. A minor law of particle
formation leading to more particles than anti-particles.
Are there more fundamental time asymmetric laws?
After all our universe is a very hard “accident” to
accept.
© M. Bass