The Relativity of Thought

The Relativity of Thought

by Alexios Polychronakos

01/26/2023

Einstein sat at his desk, lost in thought as he tried to make sense of the strange and bewildering world of quantum mechanics. He had always been a skeptic of the theory, convinced that there must be some deeper underlying mechanism at work.

Suddenly, the door to his office burst open and in walked John Bell, a young physicist who was quickly making a name for himself with his groundbreaking work on quantum entanglement.

"Ah, Mr. Bell," Einstein said, looking up from his papers. "I've heard a lot about your work. I must say, I am intrigued, but also somewhat skeptical. The idea of particles being connected across vast distances seems absurd to me."

Bell smiled and took a seat across from Einstein. "I understand your skepticism, but I assure you, the evidence for quantum entanglement is overwhelming. We've performed countless experiments that show that particles really are connected in this way, no matter how far apart they may be."

Einstein shook his head. "I simply cannot accept this as the final answer. There must be some deeper explanation, some hidden variables that we have yet to discover."

Bell nodded. "I understand your desire for a deeper understanding, but I have developed a set of inequalities that prove that any theory that attempts to explain quantum mechanics using hidden variables must be incomplete. My inequalities show that quantum mechanics is the most complete and accurate theory we have for describing the behavior of the subatomic world."

Einstein raised an eyebrow. "Interesting. Show me these inequalities."

Bell pulled out a piece of paper and began to explain his famous Bell inequalities. As he spoke, Einstein listened intently, his skepticism slowly starting to fade away.

"I must admit, Mr. Bell, your inequalities are quite convincing," Einstein said after Bell had finished explaining. "It seems that quantum mechanics really is the most complete and accurate theory we have. I suppose I will have to accept it, at least for now."

"I'm glad to hear it," Bell replied with a smile. "I understand that it can be difficult to accept such a strange and counterintuitive theory, but I assure you, the evidence is clear. Quantum mechanics is the best explanation we have for the behavior of the subatomic world."

And with that, the two physicists parted ways, each lost in thought as they tried to make sense of the strange and bewildering world of quantum mechanics.

This story about Einstein meeting Bell is entirely fictional (Einstein passed in 1955 and Bell’s result appeared in 1964). I think we can also agree that it is quite dull. It presents the basic scientific points pretty accurately and in good English, but offers nothing nontrivial, no real insight into the thought process of the actors or the complexity of the issue. Besides, starting and ending with “lost in thought … strange and bewildering world of quantum mechanics” is not exactly literary gold. And, who just “bursts” into Einstein’s office!? Certainly not a story worthy of sharing.

And yet, it is very interesting.

Because this story was written entirely by ChatGPT, the new artificial intelligence chatbot that has fascinated and bewildered people, companies, and academic institutions alike. I gave it the prompt “Write a short fictional story about Einstein meeting John Bell and discussing Bell’s inequalities” and after nary a second’s “thought” -poof!- it spewed out a perfectly coherent and informed narrative about a meeting of the two physicists. Admit it: for all its flaws, wouldn’t you have congratulated your bright teenager for writing such a story? Wouldn’t you have given a good grade to this essay in a “Physics for Poets” course? And wouldn’t you have been certain that it was written by a human, unless alerted to the alternative?

ChatGPT’s ability to emulate human talk and human thought is downright spooky. We may be tempted to think (and I do think) that this is not “real” thinking, just a very clever simulation of it, but this may simply be DNA-bound parochialism: if a soon-to-be refined version of an artificially intelligent chatbot can consistently pass the Turing test of giving responses indistinguishable from those of human agents, what will be our intellectual basis for dismissing its intelligence? Does it matter that its functioning and memories rely on silicon chips and an extended web-based network, rather than a neuronal gray lump? Are we organic racists, cellular bigots, primate hypocrites for resisting assigning it conscious status?

Well, these are lofty philosophical issues, but there are questions much closer to home. If ChatGPT can write such good prose and knows so much, is this the end of homework? Can we ever be sure that the all-important College Application Essay is not written by a chatbot (as opposed to a highly paid essay “counselor”)? And, crucially, is what we are doing in our professional academic life, so nontrivial and wonderful, soon to be done better, faster, and cheaper by artificial intelligence? Will music, poetry, engineering, or -gasp!- science be done by robots and available at vending machines?

As a human with a physics bend and of a theoretical persuasion, I set out to investigate. I focused my efforts on discovering if ChatGPT can do a decent job teaching physics, and in particular at devising good problems and providing good solutions. Staying within the theme of quantum mechanics, here is a problem that ChatGPT proposed after an appropriate prompt:

Consider a particle in a one-dimensional infinite square well potential of width L. The energy eigenstates of the system are given by:

ψ_n(x) = sqrt(2/L) * sin(npix/L)

where n is a positive integer. The particle is initially in the n = 3 energy eigenstate at time t = 0. At time t = T, a measurement is made of the particle's position.

Calculate the expectation value of the position of the particle at time T.

HINT: The position operator in the energy eigenbasis is given by:

x = ∑_n x_n |n><n|

where x_n is the eigenvalue corresponding to the eigenstate |n>.

This looks like a well-formulated problem (including even a hint, in good educational practice!). However, a few points are obvious. First, it is rather banal, one of an almost continuous infinity of very similar problems on one-dimensional potential wells. Second, it is ridiculously easy if you know a bit of quantum mechanics: it is a stationary state, dammit, so the answer will not depend on T, and by symmetry the expected value of the position will be in the middle of the well. And, finally, the hint at the end is wrong, or at least confusing, as the position is not discrete.

Still, let’s give it the benefit of the doubt and move on. I asked ChatGPT to be so kind and provide the solution. Again -whoosh!- an impressively detailed and well-structured solution was produced. Which, upon closer scrutiny, proved eye-poppingly wrong! (You will have to take my word for it and be spared of all its non-sequiturs and erroneous statements). However, the final answer was correct. It looked like what a clueless student who knows how to whip up a good word-cum-equation salad, and has copied the final answer from someone else, would have written in an exam.

I tried getting more problems from ChatGPT, in three dimensions, on a particular subtopic, asking specific questions, etc. In every case I received something coherent and occasionally impressive but always with some weird or wrong elements, and generally incorrect solutions. Only in cases where the problem was a restatement of a basic theory fact was it well formulated with a correct solution.

We scientists can draw some comfort from this incomplete exploration, but also some lessons. The teaching of science is still far from being done by machines. The nontrivial concepts, logical consistency, and creative intuition of physics, and science in general, are not what artificially intelligent bots can master and handle well. On the other hand, complacency on our side will cost us dearly. We cannot recycle stock problems reshuffling symbols and situations - bots will soon do this better than us. We cannot keep using the same dog-eared (or perennially archived) lecture notes - bots will soon figure them out and replicate them. And we need to stress an interactive, imaginative style of teaching that builds on our human understanding of students and their needs. Otherwise, we will be out-botted.

Concluding, I cannot resist a mild jab at our colleagues in the Humanities and Arts. They often refer to their disciplines as “the creative fields,” in implicit contempt for the dry, rigid determinism of science and engineering. Ironically, it is their fields that are most disruptively invaded by artificial intelligence. DALL-E can create stunningly beautiful and original visual art, and ChatGPT can write stories, poems, even limericks of surprising agility and insight. Essays created by ChatGPT mimicking the writing of High School students have stumped even education experts, who were unable to reliably tell them from those written by flesh-and-blood students. By contrast, any competent physicist could immediately tell that the problem I related earlier was written and solved by an ignoramus – a machine, or someone who had no business teaching physics!

So let us enjoy our provisional good fortune, knowing full well that the future has a way of surprising us. Humility is recommended, and things can quickly turn. But until then, we can have fun:

There once was a writer so fine

Who thought he was one of a kind

But his stories were trite

And his characters slight

Turns out he was just wasting time

…saith ChatGPT! Or, to offer my own humanly grown aphorism

Beauty is in the eye of the beholder – unless it belongs to Nature.