© M. Bass

Conservation Rules, Thermodynamics and the Arrows of Time

Michael Bass, Professor EmeritusCREOL, College of Optics and Photonics

University of Central Florida

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What is a conservation law?

Something that does not change during a physical process is said to be conserved. 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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From Newton’s second law

Conservation of momentum 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. These laws are today understood to be related to invariance of the

system under translation and rotation.

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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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Conservation of energy

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.

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Steam

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

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Temperature

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.

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The somethings

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 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.

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Joule and paying attention to the evidence 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. 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.

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A more modern form

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.

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Other things that are conserved

In physics: Charge Baryon number Lepton number Strangeness Charge-parity-time (CPT)

In everyday life Money, Land, Water, Air, and so on.

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Machines

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.

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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.

He claimed in a brilliant moment of insight that this would be the most efficient engine possible because each step in its operation was perfectly reversible. In other words, in the Carnot engine nothing was lost.

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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 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.

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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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The laws of thermodynamics

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.

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The ARROWS of time

Thermodynamic Universal expansion Kaon decay Electromagnetic Psychological

Notice that they all point in the same direction!

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The thermodynamic arrow of time

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.

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Disorder

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.

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Probability

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.

Thus, the universe is evolving from a less likely state to a more likely state.

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The laws of physics

All of the fundamental laws of physics are independent of the arrow of time. They don’t change when you change the sign of

time. Mathematically speaking, they are all second order in

time.

It is in the second law of thermodynamics that physics encounters a clear arrow of time – the past is different from the future.

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There must be more

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.

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.