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Illustration: Joel Bentley

"Pushing a String: The Border between Classical and Quantum Physics" Essay by Patrick Bruskiewich
Illustration: Joel Bentley

Albert Camus once wrote that “there is no finer sight than that of an intelligence at grips with a reality that transcends it.” At the border between the very large and the very small, the classical and quantum world, an enigmatic tapestry of physical laws is found. It is such a strange landscape that Salvador Dali painted compelling visual metaphors about the angst of the quantum world and how it relates to our concepts of time. Dali's Exploding or Bending Clock paintings come to mind.

The world of the very large, described by classical physics, was first explored in the sixteenth century by da Vinci, Galileo, Newton and Lagrange. Classical physics involve a set of laws that do not allow for a clear distinction between past and future. For instance, there are Newton’s familiar three laws of motion. With these classical laws, reverse the flow of time and you get a symmetric reversal in motion.

The world of the very small, described by quantum physics, was first explored in the twentieth century by Boltzmann, Planck, Einstein and Ehrenfest. Quantum physics involve a set of laws that do clearly distinguish between the past and future. Reverse the flow of time and you get an asymmetric reversal in motion. The past is different from the future.

When a measurement is made in the quantum world, say of the position or momentum of a particle, the system you are studying cannot go back to the state it was in before the measurement. This is what is meant by an asymmetric reversal in motion. There is an asymmetry between time proceeding into the future and time returning to the past. Once you make a measurement you cannot go back to the time before the measurement was made on your system. It is because of such an asymmetry that we cannot build time machines and go backwards in time.

An example of such a non-classical law is the Second Law of Thermodynamics, which states that in a closed system the entropy – which is a measure of the disorder of the system – will increase in a greater and greater fashion in successive instants of time. Over one hundred years ago, Ludwig Boltzmann became famous for his suggestion that entropy should be defined as the logarithm of the number of distinct and accessible states: the more accessible states in a system, the greater the entropy or disorder of the system.

Entropy is caused by things that ultimately happen at the quantum scale. In some sense the growth in entropy and the Second Law of Thermodynamics defines the direction in time in the universe.

The physicist Paul Davies in his book The Cosmic Blueprint reminds us that “generally speaking a law is a statement about any regularity found in nature. The physicist, however, sets great store by those laws that apply with mathematical precision.” A century ago Boltzmann tried to place the Second Law of Thermodynamics on a mathematical footing. In doing so he drove himself crazy and took his life in 1906, hanging himself on a window frame at a fancy hotel while on holidays with his wife and three daughters.

In some sense you have to be a surrealist to understand the quantum world, because it is a world so different from our common sense. You might think that to study the difference between classical and quantum physics one would have to visit a fancy billion dollar laboratory like TRIUMF, based in Vancouver, and work with intricate, high technology instruments.

In actuality, all you need to visit the quantum world is a string. Not the metaphorical strings that you see described in Briane Greene`s naïve yet poetic The Elegant Universe mind you, just a plain old string that you would find around any apartment.

How can this be? Bet you already know but didn’t realize it. When you pull a light and flexible string across a table, its motion is predictably a straight line. But now reverse the flow of time and try to push the light string back across the table with your finger to try to return it to its initial state. The string moves very differently. It curls, it clumps, it moves in an unpredictable fashion. Isn’t it the same string? Pick the string off the table, twist it a bit and try again. Do you get the same motion?

Evidently it is not the same string! Classical physics applies when the string is pulled. This is something that has been known since the time of da Vinci, Galileo, Newton and Lagrange. Classical physics does not apply when it is pushed.

When you push the string, what happens is a very different sort of motion. We see this in the increased disorder of the string we are pushing back across the table: the entropy increases to a greater degree pushing the string compared to when it was being pulled. Evidently, motion forward and back across the table are not the same, and so the string is not the same depending whether your finger pulls or pushes it across the table. This is the same as saying that there is time asymmetry in this system.

What in the world could be causing this? Before reading on you might stop a moment, brew a nice cup of coffee, and try your hand at an educated guess. Such a question is worth a few minutes of contemplation. It is said that physicists can turn bad coffee into good theorems… can you imagine what is happening with the string?

Was it not Sherlock Holmes who once said to Watson, “If you remove the improbable, what remains is the possible.” The same type of friction is occurring between the string and the table irrespective of whether we pull or push the string, so it is not the interface between the two that is causing the different motion. It must be something happening within the string itself.

In fact it is something happening on the quantum scale of the string. It’s inter-filamentary, my dear Watson: the atoms making up the filaments in the string behave differently when they are compressed compared to when they are stretched. The filaments are made up of long chain macromolecules that have inter-filamentary bonds which bend unpredictably when they are pushed. The inter-filamentary bonds are very weak bonds known as van der Waals bonds after their Dutch discoverer.

In the quantum world, when you bend an inter-filamentary bond between macromolecules, the different angles through which you bend these weak bonds are distinct one from the other. Each distinct and accessible angle has a different energy associated with it. States with different energies are distinct, accessible states in quantum mechanics.

While it is the electrons in orbit around the atoms that provide the weak inter-filamentary forces, there are many more such accessible bonding angles when your finger pushes the string compared to when you pull it. So then, when we push on a string made up of long macromolecules we cannot apprehend, using classical laws like Newton’s three laws of motion, how exactly the long macromolecules will bend. Ceteris paribus, we literally cannot predict in advance where along the string it will bend and how much it will bend to the left or to the right at that point.

Unlike classical mechanics, in quantum mechanics we cannot predict in advance what each of the inter-filamentary bond angles will be. This is sort of like trying to guess the roll of die, in advance. Take the two numbers from the die and multiply them together, then multiply by, say, 1 degree and let that be the angle through which one of the inter-filamentary bond bends. Then imagine repeating a similar roll of the die at each of the many inter-filamentary bonds as your finger pushes the string… this is the quantum world.

When you pull the string, very few inter-filamentary energy states are accessible. On the other hand, the pushed string has a multitude of inter-filamentary bond angles and therefore a multitude of additional, distinct and accessible energy states. The pulled string has a lower entropy compared to the pushed string, and so the pushed and pulled string are different in that sense.

Recently I came across a wonderful piece of prose relating to this strange border between the classical and quantum world, written by the existentialist philosopher Albert Camus, in his essay titled An Absurd Reasoning:

“At the final stage you teach me that this wondrous and multicoloured universe can be reduced to the atom and that the atom itself can be reduced to the electron. All this is good and I wait for you to continue. But you tell me of an invisible planetary system in which the electrons gravitate around a nucleus. You explain this world to me with an image. I realize then that you have been reduced to poetry: I shall never know. Have I the time to be indignant? You have already changed theories. So that science that was to teach me everything ends up in a hypothesis, that lucidity founders in metaphor, that uncertainty is resolved in a work of art. What need have I of so many efforts? …I realize that if through science I can seize phenomena and enumerate them, I cannot, for all that, apprehend the world. Were I to trace its entire relief with my finger, I should not know any more. And you give me a choice between a description that is sure but that teaches us nothing and hypothesis that claim to teach me but that are not sure.”

A century ago another Dutch scientist, Paul Ehrenfest, hypothesized that at the border between the quantum and classical worlds the two sets of laws should match. Evidently, in the simple example of a string drawn across a table top they do not! Why they are different reflects a little of the angst of the quantum world.

Heads or tails is passé. If you are a betting sort of a person, instead of flipping a coin, string pushing should be your fancy. Strange as it may seem, the border between the classical and quantum world is only as far away as a string pushed across a table top.



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