The Arrow of Time

John O. Campbell

Last evening my wife and I enjoyed a wonderful dinner and visited with a couple of our Science Buddies, Michael and Julia Skrigitil. I often call Michael a 'rocket scientist' because he worked on the Russian space program and due to his deep knowledge of physics.

During the course of our conversation Michael told me of some exciting new research  claiming to have solved the arrow of time problem which has long plaqued physics.

Briefly this problem arises as all the laws of physics are time reversible; they make equal sense running both forward or backward in time. However we do not observe this symmetry; many physical phenomena, the breaking of an egg for example, always appear to run forward in time. This observation is encapsulated in the second law of thermodynamics which states that the entropy or uncertainty in closed systems will tend to increase over time. This raises the unanswered question: What are the physical processes which result in the arrow of time?

Today I looked up this research and found an informative article: Times Arrow Traced to Quantum Source.

It turns out this 'new' solution was first proposed by Seth Lloyd over twenty years ago. Lloyd is brilliant. He coined one of my favorite quotes on quantum behaviour: Quantum interactions are quantum computations; what is computed is the outcome of the interaction.

The article says:

Lloyd realized that quantum uncertainty, and the way it spreads as particles become increasingly entangled, could replace human uncertainty in the old classical proofs as the true source of the arrow of time.

Entropy is a measure of the amount of uncertainty or ignorance. It is the expected value of surprise inherent to any probability distribution (sum of the products of each probability and its negative log value). Thus we should expect to find entropy in any model of reality based on probability distributions, such as quantum systems, genetics and science. In order for these models to accurately describe reality they must be consistent with one another.

The problem which science has had with entropy is, in my opinion, largely due to thinking of entropy in terms of human ignorance. In thermodynamics it is the amount of ignorance we still have of the micro-state of a system, such as a container of gas, when all we know is the value of some macro-variables such as temperature and pressure.

I think this research may be telling us that although our scientific models specify entropy or our ignorance of quantum systems this ignorance is also a property of the actual quantum reality. That is the quantum wave function of the entangled system specifies only a probability distribution for the value of any measurable quantity; a probability distribution having entropy.

The article uses the example of a cup of coffee slowly coming to an equilibrium temperature with that of the air in the room. From the view of thermodynamics the system is coming to a state of higher entropy as required by the second law of thermodynamics. That is our uncertainty of the microstate of the coffee and air system is increasing as an equilibrium state has many more possible states than does a state where the coffee and air are out of equilibrium.

The new research argues that from the view of the quantum system uncertainty is increased as the coffee's quantum wave function becomes entangle with a growing number of air molecules. As the wave function grows in the extent of the reality it encompasses it grows in uncertainty as to the exact state of the entire system.

We have been famously confused over the nature of the quantum wave function since it was first conceived a hundred years ago. Some researchers believe it has no physical embodiment while others argue that it must have an instantiation in reality. Some current research, which may be conclusive, argues that the quantum wave function must be real (see for example Lucien Hardy's paper: Are quantum states real?) . 

If we understand the quantum wave function to be embodied in an actual physical form, it must be one independent of human construction. In terms of the cup of coffee example the quantum wave function may be said to become more uncertain as the knowledge contained in its model stretches to describe not just the coffee but also a growing amount of the cooling air in its environment.

 This view points to an analogy between quantum systems and biological systems; genetics also forms a probabilistic model independent of human construction.  Clearly the object of genetics is to better understand the world in terms of the adaptations that will lead to reproductive success.

This view of nested,evolving hierarchies of knowledge mechanisms including quantum, biological and cultural systems may underline our relatedness to whole of reality. In following our cultural and scientific activities we are following an ageless quest of the universe, the quest to know itself.

If that is the case we should expect that our scientific ignorance of thermodynamic micro-states would have to be consistent with the ignorance of the quantum system itself. If it were otherwise either thermodynamics or quantum theory or both would be of little value in describing reality.