Memory, Thermodynamics, and Time

June 30, 2014

What is time? While answers abound for this question, many physicists and philosophers continue to work on it tirelessly. Our common experience leads us to think of time as flowing forward, but the equations that describe our physical universe do not require that time move forward.

There are, however, indications of a preferred direction based on thermodynamic considerations. Recently two scientists published a paper that describes the criteria for a memory model and an argument that “the psychological arrow of time (memory) should align with the thermodynamic arrow of time (entropy) where the arrow is well defined.”¹

Time is a dimension (or coordinate) and a measure that helps us order events. Time is also used to describe the duration of events and the intervals between events. Some philosophers of science believe that time is independent of the events, and events occur sequentially through time, as if the events flow through time.

Other philosophers believe that only the present is real (presentists) or, conversely, that all events, past present and future, are equally real (eternalists). There are many different philosophical and scientific views of time.²

Without doubt, time is important to us. Our modern, global world demands precise and consistent measures of time, and the best clocks are ones that have some periodicity (an event that occurs at regular intervals).

We began with clocks based on the Earth rotating about its own axis such as sundials. We devised time durations based on Earth’s rotation about the Sun and the Moon rotating about Earth. There have been clocks built based on pendula, and oscillations of quartz crystals.

One of the most recent clocks created at the National Institute of Standards and Technology is the NIST-F2 atomic clock that is so precisely periodic that this clock will neither gain nor lose a second within 300 million years.³

Left to Right: A sundial, hourglass, a watch, and the NIST-F1 atomic clock.
Image Credits: Alexandre Mirgorodski, S. Sepp, Isabelle Grosjean, and the National Institute of Standards and Technology Physics Laboratory, Time and Frequency Division, respectively.

Scientists strive to create models that describe measurable observations. Within this frame, scientists have successfully described time in some objective respects, but there are persistent difficulties reconciling our everyday experience of time with our physical theories.

Symmetry and Time

Our world is often thought of as three dimensional, with three distinct coordinates on three distinct number lines that have positive and negative values. We have north and south, east and west, and up and down (or x, y, and z). Each indicates two directions along the same line.

Put your ‘zero’ or origin wherever you would like with one direction being positive, while the other is negative.  With this coordinate frame, you can easily describe location.

Events require not only a particular location but also a particular time. Scientists think of time as another “direction” or axis to describe something. But there is some difficulty with the symmetry of this axis.

Although we can discuss the past and the future (our two directions), we cannot visit either “location.” We can only have memories and recordings of the past, and expectations and predictions of the future. So time is a bit different than our other coordinates.

The possible past and present are often described by light cones. The speed of light in a vacuum is considered the upper speed limit in physics. Because nothing can go faster than the speed of light there can be no recording of the past, or possibility of the future attainable to us outside of the light cones formed by these limits.

A light cone.
Image Credit: K. Aainsqatsi via Wikimedia Commons.

The Thermodynamic Arrow of Time

Scientists have accumulated strong evidence for the second law of thermodynamics, which states that natural processes tend to move toward increased entropy. Entropy measures the level of disorder or randomness of a system, and natural processes tend to cause more disorder.

You may not believe that disorder tends to increase when you consider the amazing order that occurs when you clean your room, but you also have to consider the amount of disorder that occurs due to your body working to clean up your room. While you are making your room look more ordered macroscopically, your body and the environment are heating up, causing more disorder on the microscopic level.

Even a highly organized organism results in more entropy overall in its environment during its creation and existence. Humans are clearly highly evolved and organized entities, but we create a lot of waste and disorder to our environment in the physical sense (thermodynamically and otherwise).

You could think of an idealized situation where you isolate a system and make it undergo a special, reversible process that does not heat up the environment, and in this case, it is possible that the entropy could remain the same. And although it is extremely unlikely for the entropy to decrease during a natural process, it is not fundamentally disallowed.

So what does time have to do with this? Natural processes are events that occur in time, after all. These processes tend to move toward greater disorder and the overall amount of entropy (or disorder) provides an arrow or direction for time. Scientists call this the thermodynamic arrow of time.

The thermodynamic arrow of time is one reason why it is believed that there was so much order at the start of our universe. Although many ask, “What was there before the big bang?” and “Why was there so much order?” and “What will happen when the universe has reached maximum disorder?” These big questions have many different responses.

The expansion of the universe.
Image Credit: NASA

The ultimate end is considered to be when the universe has reached its maximum disorder and all the energy has become unavailable to do useful work. This is called “heat death,” and is when the universe reaches thermodynamic equilibrium.

But one thing to note is that although the second law of thermodynamics states that entropy tends to increase during natural processes, there’s no violation of any fundamental physics if entropy were to decrease, it is just incredibly unlikely.

The Psychological Arrow of Time

The psychological arrow of time is memory or recordings of past events. But how do you know if the memory or recording is running backward? Should it always correspond to the thermodynamic arrow of time?

The scientists who recently worked on this problem considered the physically allowed, but extremely unlikely process of entropy decreasing. This would cause the thermodynamic arrow of time to reverse direction. They provide examples of this as broken eggs becoming whole again, and chimneys sucking up smoke,¹ and they asked what would happen to the psychological arrow of time in this instance. Would we reverse our arrow of time to align with the thermodynamic arrow of time?

As the researchers describe in their paper, it has been argued that if the thermodynamic arrow and psychological arrow of time are to align then there must be an increase in entropy when a record of events (memory) is erased.¹ So a memory or record of events must dissipate energy and be an irreversible system.

The researchers devised a new model to describe the criteria for memory based on fundamental classical laws of physics. From this they proved under their criteria that the psychological arrow of time must always align with the thermodynamic arrow of time, whether or not the memory system is irreversible.

Memory Systems

The scientists devised a reversible model that describes both a natural process showing the thermodynamic arrow of time, and a way to record the events (a memory) showing the psychological arrow of time.

The theoretical model consists of N ideal gas particles in a container with two chambers separated by a passageway with a rotor that acts like a turnstile each time a particle goes from one side to another. The rotor has M positions labeled 0 to M-1, and there are many more positions in the rotor than the average number of particles that would pass through in a given time interval. This means, that as long as we look at the rotor within this time interval, we will be able to see how many particles, overall went from one side to another.

The idealized model isolates the container from the environment, makes sure that the particles undergo only elastic interactions (no energy is dissipated away), and that the average speed of the particle is such that it is highly unlikely for the particle to spin the rotor more than one position.

In order to have some arrow of time, the particles are placed initially in one side of the container. Since entropy is likely to increase, it is expected that the particles will eventually be equally distributed on each side of the container. The rotor will keep track of the overall number of particles that went from one side to the other.

There is no way to know the exact number of particles that went to the right chamber or left chamber, just the net number of particles that went in one direction, during a given time interval. That time interval must occur before the system reaches equilibrium. After a very long time, equilibrium will be reached, and then the particles are equally distributed on both sides, and will most likely go back and forth at an equal average rate.

The researchers imposed generality on the memory subsystem. Generality is the requirement that a memory be capable of remembering more than one thing. For the rotor this might be the momentum transfer required to turn the rotor as well as the number on the rotor.

These two things correspond to a particle going from one side to another. What this does, in effect, is mandate that the recording not only be correlated with the events of the system but also directly interact with the system. In other words, a counter that does not directly interact with the particles might be a correlated record, but cannot be a memory.

The requirement of generality results in the following: If one perturbs the initial state of the system, it does not destroy the memory’s correlation with the rotor. However, if the rotor (memory) were not interacting directly with the particles, the results would no longer be well correlated.

If one were to look into the future rather than the past, the results would not be correlated by a small perturbation, unless one knew exactly every state of each particle in the system at all times to run smoothly forward and backward in time for all particles. Hence a rotor system that remembers the future cannot satisfy generality and therefore must follow the thermodynamic arrow of time.

The researchers show in their paper that this can be proven for the two-chamber system described above, and generalized beyond this system for classical, deterministic systems (systems that follow classical physics) that have a well-defined thermodynamic arrow of time. In these cases the psychological arrow of time must align with the thermodynamic arrow of time.

For any system with a subsystem that acts as a memory, and the remainder of the system consisting of everything else (world minus memory), the memory subsystem must satisfy four conditions:

With these conditions the researchers show that both irreversible (e.g. electronic/digital technology, film, fission tracks in mica) and reversible systems (e.g. a reversible Turing machine, reversible computations, emission of waves from moving or reflective objects) have the psychological arrow of time aligning with the thermodynamic arrow of time.

What Does the Future Hold?

Mlodinow and Brun, the researchers, point out in their paper that their work focuses on a classical view with memory subsystems that have well-defined states at any time.¹ Their arguments cannot be directly applied to quantum systems that involve entangled states, which are not definite states at a given time. The researchers are working on an argument for quantum systems. For work on quantum systems that has been done so far, see references 5 and 6.

For more on the direction of time and relativity see the appendix below.

References and Resources

Appendix: The Direction of Time and Relativity

It turns out time is relative. First, let’s examine a classic, and classical, example of relativity. Imagine you are sitting in a train that moves at 100 miles per hour northward. As the train passes a train station, an observer at the train station measures your speed to be 100 miles per hour to the north.

A person on the train measures your speed as zero. If you got up and started walking with constant velocity of 2 miles per hour southward, then the observer at the train station would measure your velocity at 98 miles per hour to the north. A person on the train would measure your velocity as 2 miles per hour to the south. Your speed is relative.

This is classical relatively. The speeds involved are much smaller than the speed of light in vacuum, there is no acceleration, and we consider time and space to be the same for all observers.

There are problems with classical relativity. It does not describe well the measured results of certain observations and Maxwell’s equations, which describe electromagnetic phenomena, do not follow it this classical relativity.

Einstein came up with Special Relativity to describe this, and his ingenuity is in his thinking outside the box. Instead of making space and time fixed for all reference frames, he made the speed of light in a vacuum fixed for all inertial reference frames. There is no way for an electromagnetic wave to travel faster than the speed of light in a vacuum, and all observers measure the same speed no matter what their inertial (constant velocity) reference frame is.

Whether the light originates from a flashlight on a moving train, at the train station, or from a fast moving spaceship, every observer measures the speed of light in each reference frame to be the same. Working with these criteria Einstein found that moving clocks run slow and moving meter sticks are shorter than a meter. That is, both time and space measurements are altered if you are in a moving reference frame, but neither is noticeable unless you are moving at speeds close to the speed of light.

Accelerating reference frames are non-inertial reference frames, and these are the focus of general relativity. One important principle in general relativity is that if you are in a uniformly accelerating reference frame, it is equivalent to be in a reference frame with a constant gravitational pull. Based on this equivalence principle, Einstein figured that light interacts with gravitational fields because light in an accelerating reference frame appears to an observer in that frame to bend. This effect was verified by measurements during 1919, and many times since then.

Now we have two sides to this picture. Light can follow curved paths due to nearby massive objects, and light travels along a trajectory in space-time, which can be curved due to massive objects. What if these formed a closed curve, or a loop? Is it possible? For more on this see reference 2.