CONSERVATION LAWS AND SYMMETRY

Anil Mitra

Anil Mitra, PhD

Home

Thermodynamics
and the Destiny of the Universe

Contents

Introduction

The Energy Law

The Entropy Law

Practical perspective

Some Perspectives from Physics

Energy

Symmetry

Topics for study

Entropy

Cosmological Perspective

Entropy and Structure

Nineteenth Century Gloom

Reassessment

Energy, Entropy, and Order

Classical Versus Quantum Perspective

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# Introduction

What is the origin of our cosmos and, especially, its laws and patterns? This issue conceptual and practical significance. This is not surprising for universal—cosmos wide—laws. Perhaps the laws are not necessary true but are local conditions for our stable, enduring, and significant (productive of self-referential sentience) world.

## The Energy Law

The energy law[1] affirms that energy is never created (in the theory of relativity it is mass-energy that is conserved).

That is, an isolated system has a fixed amount of energy: energy is not inexhaustible.

But why can energy not be used over and over? This is due to ‘degradation’ of utility. A key concept in understanding this is entropy.

## The Entropy Law

In this section I will talk informally.

Entropy is a measure of disorder. The entropy law asserts that the entropy of an isolated system cannot decrease. In any real process entropy increases due to such effects as friction and loss of usable ‘heat’ energy in transfer over a finite temperature gap (utility is lost because the heat could have been used to extract useful work). There are ideal processes (frictionless, heat transfer without temperature difference) in which entropy is conserved. But in the real world there are no ideal processes (superconduction comes close).

However there are limits to extracting useful work or energy even in ideal processes. In a heat engine, heat must be rejected at a temperature that is lower than the high temperature of, say, combustion. The only case where heat rejection is not necessary is where the environment is at ‘zero potential’ (e.g., absolute zero of temperature) and can absorb even low quality heat energy. This limit is set by the second law and though the ideas are subtle the limit is very definite.

## Practical perspective

Some sources of energy—e.g., wind power and the Sun’s radiation—seem free. However their use is not free. Wind power takes wind farms which takes up land that could be used for other purposes; and the wind turbines require material and economic resources. Resources used to produce energy are not available for other purposes.

The economics of energy is an aspect of the economics of all resources—from materials, to land, to labor and the physics of energy (e.g., the energy and entropy laws) is but one aspect of economics.

The energy and entropy laws are important in the understanding of life and how living structures (high order, low entropy) are maintained in an entropy producing world. The laws are also important in the design of systems for energy conversion, transportation, heating, refrigeration.

# Some Perspectives from Physics

There is a sense in which thermodynamics is not a fundamental science. Its laws can be derived from more basic considerations. However, the science of thermodynamics was discovered independently and its bases in more fundamental mechanics came later.

This turns out to be one of the powers of thermodynamics. It applies to many systems—from technology, to organisms, to stars, to black holes, to radiation—regardless of their fundamental structure.

In its origins, the discovery of thermodynamics was empirical. Its necessity could be questioned on that basis.

It was therefore important to see if it could be found to have basis in more fundamental[2] sciences.

## Energy

In the study of fundamental particles, i.e. the science of mechanics, energy is found to be conserved.

If basic physics is valid, the energy law is valid. But why is energy conserved?

## Symmetry

It is obvious that symmetry and stability should be related.

It is perhaps further obvious that perfect symmetry and perfect stability go together but that perfect symmetry and stability are frozen: perfectly symmetric situations can neither come into nor dissolve from being. Stability sufficient to robust being requires some balance between symmetry and process.

## Topics for study

Discussion will benefit from further study of conservation and symmetry: e.g. time symmetry and energy, spatial homogeneity and momentum, constants of motion, and Noether’s theorem. First order dynamics seems to be non conservative—dissipative or explosive: a first order dynamics would not seem to populate the universe with significant forms. Higher than second order dynamics seem to have conservative as well as non conservative features. Thus second order dynamics seems to be uniquely conservative. Is this true? Would population by second order systems occur via selection of significant systems and / or is there a connection between Noether’s theorem and second order systems?

## Entropy

The entropy law turns out to be statistical.

That is, its deterministic formulation—net entropy always increases—is not a necessary consequence of more fundamental physics. Fundamental physics implies however that, under certain conditions, it is very probable—but not necessary—that systems ‘obey’ the entropy law.

It is important that for most practical and even cosmological purposes the probabilities involved are such that ‘probable’ means ‘practically necessary’.

# Cosmological Perspective

## Entropy and Structure

Under what circumstances might the entropy law ‘break down’?

It is important, first, to note that since the law has been proven only statistically necessary there are likely to be some circumstances in which there is break down.

An approach to the question is to ask what the entropy law is saying at the cosmological level.

Although the practical aspect of the law is that it limits energy use, it is also associated with the creation of structure.

An example is that life and its processes on earth might seem to violate the entropic tendency to disorder, they do not because they absorb energy from low entropy (high order or structure) sources and discharge the energy at a low order state.

Thus the entropy law is associated with the production of structure.

## Nineteenth Century Gloom

However, there is a gloomier perspective.

The nineteenth century physicists noted that entropy (disorder) increases. Therefore, they speculated, the universe ‘winds down’ toward a state in which there is no more useful energy and at that point all production of structure (life) ends.

However, the two perspectives stand in balance. On one hand, entropy and structure are related. On the other hand, entropy appears to be associated with decay.

## Reassessment

Recall that the entropy law is statistical and not necessary.

This means, perhaps, that even though we live in a phase of the universe in which production of structure and production of entropy are interwoven so that the net disorder increases, it does not follow that there is net entropy increase for the entire universe in all its phases.

There may be other phases of the universe in which the disorder of entropy may be reversed. What might such a phase be? Imagination suggests the possibility of an immensely strong force that overcomes disorder. The intense gravitation field of gravitational collapse may be such a situation.

The point is fundamental.

Entropy is associated with the production of structure in two phases (i) our normal phase in which structure ‘here’ requires’ disorder ‘there’ with net increase in disorder (ii) another phase in which strong forces[3] overcome disorder.

## Energy, Entropy, and Order

How might the energy law fit into this perspective?

Begin by asking what would happen if the first law did not obtain.

There are two possibilities. (1) Energy decreases. The universe would become dead (2) Energy increases. The universe would ‘explode’. There would be no structure.

There may have been all such kinds of ‘universe’.

A structured universe, however, is a conservative one. We are the result of conservation.

The energy law is necessary for the possibility of structure.

The entropy law—in an old sense of energy degradation and new sense that mirrors the old in the wrestling by the microscopic world by macroscopic phenomena—is a law of the nature and origin of structure.

# Classical Versus Quantum Perspective

In classical (read deterministic) physics there can be no novelty. A modern challenge to this assertion is that of chaos. However, the initiation of transition from one chaotic situation to another requires non classical intervention.

Therefore, novelty is possible only on an indeterministic account. There is debate as to whether quantum mechanics is indeterministic. However, even if it indeterministic it is not clear whether its indeterminism is sufficient to the variety of phenomena—particularly the phenomena that reveal novelty.

[1] The first law of thermodynamics.

[2] In the sense of being derived from laws thought to necessarily hold for the simplest of physical objects, i.e. particles.

[3] Paradoxically, it is the weakest of the four known forces that provides this ‘strength’. The source of this strength is that gravity is always—as far as we know—attractive