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Order as a Property

A new quantum property!
It has become clear to many that the great natural theoretical achievements of the 20th century do not fit seamlessly together. A really satisfying link between them is yet to be found.

Quantum mechanics is the strangest of the 20th century theories and it does not work very well in the world of relativity theory. Quantum mechanics is all about the tiniest objects that we can detect and measure and the properties which are the subjects of those measurements.

Quantum properties themselves are at the centre of several of the mysteries of quantum mechanics—they do not behave like classical properties. The struggle to better understand the quantum world is often focused on how we can better understand quantum properties.

In the present scheme, the question arises: How many quantum properties are there and do we know what they are? This question leads to an even more interesting and perhaps important question: Are there quantum properties we have not yet thought of and what might they be? Quantum theory does not include a list of all the quantum properties of electrons or other particles. Our set of concepts of microscopic objects is obviously incomplete and a major implication of the present project is that part of that short-coming is due to the way that the central element of 19th century physics—thermodynamics—has been included in quantum theory.

Not all quantum properties are measurable or predictable; for example, gluon colour is a property that is not even detectable in principle. No matter how sophisticated the laboratory instrument the colour of quarks and gluons cannot be detected. Similarly, quantum mechanics cannot predict what the exact energy level of an electron will be at a particular instant in the future.

In the new theory a new quantum property is introduced. Its value cannot be predicted and neither can it be measured. However, unlike some other quantum properties it does not matter what its value might be or even if it has a value. It is order—the centrepiece of the second law of thermodynamics.

Order has only played a peripheral role in modern physics. Entropy, the measure of its decline into disorder, has been far more important. In the new scheme, by contrast, order takes centre stage and entropy has almost no role. This brings the second law into a discrete treatment of microscopic objects in a completely novel manner. It is a direct introduction, which contrasts with von Neumann's indirect approach of extending the classical idea of entropy to quantum mechanics. Entropy is the classical, continuous picture of changing potential which is at odds with the fundamental notion of discrete quantization. It is possible to go so far as to say that entropy is meaningless at the level of action. It belongs among derivatives of the representations of action.

Order is given the status of a physical quantity comparable with that of energy.* And just as energy is properly defined in physical science, so also is order. Order is often treated in a vague and indefinite manner, if it considered at all. Here, its definition is not only as rigorous as that of energy but it takes an obviously similar form. It is the complement of energy.

The definition applies to order in any form what-so-ever. It is derivative of nineteenth century classical thermodynamics and is as follows:

The concept of "entity" while applying generally, includes individual, isolated elementary particles. The most important limitation associated with the definition is that order only attaches to ordered entities. There is no unattached order; it never floats free in space or time. Thus, just as energy is always the energy of something, so also is order always the order of something.

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