Robert Frost Was Wrong

Shortly after Niels Bohr produced his quantum model of the atom (1913), Robert Frost wrote (1916) his iconic poem, The Road Not Taken. Apparently a commentary on existential angst and the human condition, Frost’s poem can be read on an entirely different level. It raises questions that haunt the science of Quantum Mechanics (QM) to this day. 

Of course, that may not have been Frost’s intent; at that time the wide 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, take it on its own terms, regardless of the author’s subjective intent. 

Bonus: By letting a poem, any poem, speak for itself, we may discover deep connections between consciously intended themes and cosmological intuitions:

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 traveled 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 timepiece, wound by God ‘in the beginning’ and left running mechanically ever since. But by 1900, a series of observations and experiments had made this view untenable, eventually leading to the discovery of Quantum Mechanics. QM showed that there is no predetermined course of events, that they 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 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 skirted the problem 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 just by flapping one’s arms. Facticity (‘the real world’) imposes logical and physical limitations but those limitations are external to the agent and do not in any way limit or qualify that agent’s freedom. Limitations are part of en-soi, never pour-soi.

In The Road not Taken, Robert Frost confronts a simple choice between two options (0, 1). 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.

Frost’s preferred solution: travel both roads and still be one traveler. But with his imagination still 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 current interpretations of QM assert that this is the only possibility. Given the existence of two paths with identical start and stop points, Frost must travel both. But how?

One possibility, supported by the various “double slit” experiments that gave QM its start, suggests that a quantum follows two or more paths simultaneously but does not ‘decide’ which path will be its ‘real’ path until it is reaches its destination and is observed (measured) by an external agent.

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. His observed arrival collapses the Wave Function.

According to this model, 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. This interpretation has massive real world implications. Imagine, for example, how this might play out in a restaurant. “Waiter, bring me one order of everything on the menu and when I’ve finished, I’ll pay for whatever dish I liked best.”

Or what about a lifetime? You follow all courses open to you and then, at the end, you get to choose the one path that gets you the best result. How cool would that be!

But this option is not all it’s cracked up to be. First, it isn’t really ‘Frost’ who makes the final decision. That decision is made by the whole experimental apparatus and is more a matter of mathematics (probability) than aesthetics (taste). Second, Frost will have no memory whatsoever of ‘the road not taken’. Similarly, I will have no memory of the dishes I decided not to pay for…or the fun but stupid things I did as a kid. Cruel justice! 

Hugh Everett’s mid-century “Many Worlds Interpretation of Quantum Mechanics” modifies this picture. According to Everett, every time the 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 will never meet again.

Both Frosts arrive in the same town…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 may perhaps be consoled by the thought that an alternate Frost is having the other set of experiences in an alternate universe. 

Parenthetically, we have proposed a modification of Everett’s model that allows Frost’s many trajectories to intersect – and recombine - ultimately reducing the proliferation of universes that bedevils Everett’s scheme. This model allows the universe to grow but at its current observed rate, not exponentially as with Everett. Note: this solution is dependent on quantum processes being commutative – which goes against current thinking.  

According to Richard Feynman’s “Sum over Histories” model, Mr. Frost does indeed travel both paths and he remains one traveler. The two experiences merge when he reaches his destination. His memory of the journey is a blend of both histories. 

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 (above), we get to enjoy all the items on the menu…but as samples, or tapas, not as full meals.

Now a new interpretation has come along that builds on Feynman. In this thought experiment, known as the Cheshire Cat, quantum data is understood to show that certain properties of the quantum follow one path while the particle itself follows the other. 

In Alice in Wonderland, the cat’s grin, a property, can appear separately from the cat itself. In the Cheshire Cat experiment, the particle’s spin travels a different route from the rest of the quantum. In The Road not Taken, perhaps Frost’s gait and affect travel one path while body follows the other. Crazy! I know, but it’s Quantum Mechanics.

Bottom line: The Road Not Taken is ground breaking…but wrong! Sorry, Mr. Frost, but you can “travel both and be one traveler”. In fact you must, and you will, whether you wish to or not and whether you are aware of it or not. Still, though, GREAT poem!

Image: “Observation of a Quantum Cheshire Cat in a Matter-Wave Interferometer Experiment,” by Tobias Denkmayr et al., in Nature Communications, Vol. 5, Article No. 4492; July 29, 2014

David Cowles is the founder and editor-in-chief of Aletheia Today Magazine. He lives with his family in Massachusetts where he studies and writes about philosophy, science, theology, and scripture. He can be reached at dtc@gc3incorporated.com.

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