ROBERT FROST – QUANTUM MECHANIC

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Robert Frost’s 1916 poem, The Road Not Taken, appears to be a comment on existential angst and the human condition; and on one level it is no doubt just exactly that. But on another level, it raises all the questions that haunt the science of Quantum Mechanics (QM) to this day. Of course, that could not have been Frost’s intent; there was no such thing as QM in 1916. The world was just beginning to learn about Relativity.

But a poem is a poem is a poem. Once written, it transcends its author and even its milieu. We must meet the text head on, on its own terms, regardless of the author’s subjective intent. Perhaps in doing so, however, we will discover a deep connection between the poem’s overtly human themes and its underlying ontological implications:

Two roads diverged in a yellow wood,

And sorry I could not travel both

And be one traveler, long I stood

And looked down one as far as I could

To where it bent in the undergrowth;

Then took the other, just as fair,

And having perhaps the better claim,

Because it was grassy and wanted wear;

Though as for that the passing there

Had worn them both about the same.

And both that morning equally lay

In leaves no step had trodden black.

Oh, I kept the first for another day!

Yet knowing how way leads on to way,

I doubted I should ever come back.

I shall be telling this with a sigh

Somewhere ages and ages hence:

Two roads diverged in a wood and I –

I took the one less travelled by,

And that has made all the difference.

 

A hundred plus years ago it was popular to think of Universe as if it were a finely tuned Swiss time piece, wound up by God “in the beginning” and running mechanically ever since toward some unforeseen but determined end. But beginning around 1890, a series of observations and experiments made this view of Universe increasingly untenable.

These observations and experiments eventually gave rise to the science of Quantum Mechanics. QM showed that there is no pre-determined course of events, that outcomes are more a matter of probability than causality, and that Universe at its most fundamental level is best understood as a perpetual series of choices.

In the realm of philosophy, this insight popped up as the Existentialist doctrine of absolute freedom. Jean Paul Sartre, the high priest of Existentialism, divided Universe into en-soi, which was perfectly deterministic, and pour-soi, which was perfectly free. He avoided the fallacy of dualism by defining en-soi as etre (being) and pour-soi as neant (nothingness). Le neant functioned as the negation of l’etre and in this way diversity was reconciled with solidarity.

Sartre understood that freedom, while absolute, could not be unbounded. For example, one is not free to draw a square circle, or fly to Mars by flapping one’s arms. Facticity (‘the real world’) imposes logical and physical limitations but those limitations are external to the free agent and do not in any way limit or qualify that agent’s freedom. Limitations are part of en-soi, never pour-soi.

Quantum Mechanics defines Universe as a matrix of choices but it also imposes some constraints (‘facticity’) on those choices; for example:

  • The choices must be exclusive; they cannot be ill-defined or fuzzy and they cannot overlap.
  • Taken together, the choices must be exhaustive; they must encompass each and every possible outcome.
  • The choices, while distinct, must be compatible for integration; they must permit a definite outcome.

In The Road not Taken, Robert Frost confronts a simple, two option choice. He has a destination to reach and there are two roads that will take him there. Facticity excludes any other option: he cannot fly, he cannot tunnel, he cannot crawl 10 miles on his hands and knees through underbrush. If he is to accomplish his ‘project’ (arrive at his destination by end of day), he has only two choices. There are only two roads he can take to get there.

Frost’s preferred solution: travel both roads and still be one traveler. But, bound by the limitations of classical physics, he rejects that notion as impossible. QM, however, suggests that such a strategy is possible. In fact, most interpretations of QM assert that this is the only possibility. Given the existence of two paths, Frost must travel both.

But this consensus view comes in at least three very distinct flavors. One flavor, supported by various “double slit” experiments, suggests that a quantum follows two or more paths simultaneously but does not “select” its one final path until it is observed (measured) by an external agent; metaphorically, the quantum is then at the end of its journey, it has reached its “destination”.

According to this view, Mr. Frost can indeed “travel both and be one traveler”; in fact, he must. There’s no other way to get where he’s going. But when he finally arrives at his destination, it will appear to all observers (including Frost himself who is now his own observer) that he has come by one path only…and not the other.

In essence, this theory postpones the decision. Ideally, Frost can experience both walks and then, at the very end, ‘he’ can decide which walk was more satisfying, select that walk, and make that his actual experience, his history. Imagine if we could do the same thing when confronted with the menu in our favorite restaurant!

But this option is not all it’s cracked up to be. First, it isn’t really ‘Frost’ who makes the decision. The decision is made by the whole experimental apparatus and is a matter of mathematics (probability) rather than aesthetics (taste). Second, Frost will have no memory whatsoever of “the road not taken”.

A second flavor is Hugh Everett’s “Many Worlds Interpretation of Quantum Mechanics”. According to Everett, every time Universe confronts a choice it bifurcates, it splits. In one Universe, Choice A is made; in a second Universe, a perfect copy of the first save for this one decision, Choice B is made.

According to this view, Mr. Frost must also “travel both”…but he is no longer “one traveler”. According to Everett’s theory, there are now two Frosts, entirely unaware of one another; sadly, they can never again meet.

Both Frosts arrive in the same town up ahead…but now it is really two different copies of the same town, each existing in its own Universe.

Everett’s theory allows Frost only one set of experiences but he can be consoled by the thought that he is having the other set of experiences in an alternate universe. Paradoxically, in this model, Frost both keeps “the first for another day” and never comes back. Frost will indeed go down the first path…but be a different Frost when he does.

The third flavor is Richard Feynman’s “Sum over Histories” model of Quantum Mechanics. According to this view, Mr. Frost does indeed travel both paths and he remains one traveler. The two sets of experience merge when he reaches his destination. His memory includes both histories. However, it might be more accurate to say that a part of Frost travels one path and another part travels the other path. Feynman’s model does not double the amount of experience Frost enjoys but it does combine experience from both pathways into a single outcome.

According to our restaurant metaphor, we get to enjoy all the items on the menu…but as tapas, not as full courses.

In contrast to these three QM models, how would classical scientific models understand Frost’s dilemma? Frost confronts a choice but his decision is a product of his genes and his past experiences. Depending on the particular classical theory, Frost’s decision may or may not be totally determined but it is certainly heavily conditioned.

While all three QM models project the decision forward onto the future, classical models project the decision backward onto the past.

Classically speaking, Frost is conditioned to go down both paths; existentially speaking, he is not conditioned to go down either path. Either way, there is a 50% chance he will go down one road and a 50% chance he will go down the other. So in this special case, both models happen to yield the same result.

So I might just as well flip a coin; it comes up heads (or tails) and I set off along one path (or the other). Either way I get to my destination. So what’s the big deal? This is certainly not something to write a poem about!

Or is it? Quantum Mechanics, it seems, has a very different story to tell. According to QM, Frost’s choice is much more difficult. Because of the peculiar arithmetic that applies to QM (“Sum of Squares”), there is actually a 70% chance that Frost will take the first path and a 70% chance that he will take the second. But when Frost makes his final decision, the probability of his taking one path is 100% (not 140%, obviously).

So when Frost makes his final decision and selects his path, he loses a part of who he was before. No wonder he tells this story “with a sigh”.   But this particular decision Frost made “ages and ages” ago is only the tip of the ontological iceberg. Every decision we ever make, every time we exchange pure potentiality for concrete actuality, we sacrifice a part of who we are, at least potentially.

As long as we remain in the quantum mechanical world of pure potentiality, we are indeed ‘supermen’ (lie quiet Nietzsche). When we exchange that world for concrete actuality, we become mere ‘enduring objects’ (to borrow terminology developed by Alfred North Whitehead).

So then why do we do it? Why does Frost finally select a path, knowing that it will lead to loss and regret? We do it in order to reach a destination. And why is that so important? Because that is the only way we can re-join society; it is the only way that we can ‘make a difference’. Every time we make a decision, we sacrifice a piece of ourselves; but we do it so that we can share a piece of who we are with others. But this is not pure altruism. A piece of who we are is now incorporated in those others. Now who we are lives on, beyond the confines of the self. When we move from pure potentiality to concrete actuality, “something’s lost but something’s gained” (Clouds).

Every decision, every action, is a tiny death. Taken together, this is what we mean by the human condition, ‘mortality’. But we embrace mortality as the price that must be paid for ultimate ‘immortality’, for the capacity to have an impact on others and on the world. A seed must fall to the ground and die so that a tree may grow.

This then is the essence of existential angst and it is the real import of Frost’s great poem. While Frost had the original insight in 1916, it took half a century for QM to give that insight a proper theoretical framework. We are grateful to both for deepening our appreciation of the human experience.

Yet that same insight can be found centuries earlier in Christian theology. There, Incarnation is the pivotal event in God’s internal procession from value-based potentiality to history-based actuality. Jesus dies so that sin may be forgiven because sin must be forgiven so that God may be “all in all” (Corinthians). Incarnation is the opening act of crucifixion, crucifixion in turn is the opening act of resurrection, and resurrection the opening act of parousia, the reconciliation of all things in God. God must sacrifice himself (John 3:16), so that all things may be redeemed in Him.

The sacrament of Eucharist underscores the critical importance of this process. Every hour of every day all around the world, God is incarnating himself under the appearance of bread and wine, sacrificing himself (the unbloody sacrifice of the Mass), and then resurrecting himself in Communion with the celebrant and the congregation.

When we celebrate Eucharist, we incorporate into ourselves the Body of Christ. But at the same time, we are also being incorporated into Christ so that “when everything is subjected to him, the Son himself will be subjected to the one who subjected everything to him so that God may be all in all” (Corinthians).