Wittgenstein, Feynman, and the Limits of Intuition and Objectivity in Quantum Theory

Richard Feynman, over the course of his long career, wanted to convince students and even the public that quantum theory does not make sense. In his 1965 textbook on Quantum Electrodynamics (QED), the theory for which he won the Nobel Prize, he wrote:

The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you accept Nature as She is—absurd.

Feynman made several similar statements throughout his career and people often misinterpreted him as trying to outline a problem to be solved. But he wasn’t trying to tell us to figure it out at all. Unlike many of his contemporaries such as John Wheeler, David Bohm, Hugh Everett, and his predecessor, Albert Einstein, Feynman was not interested in rescuing quantum physics from absurdity. Rather his goal was to stop people from trying to understand it in terms of their everyday intuition, at least until they gained a new one from learning the mathematics of quantum theory, the language of wavefunctions, path integrals, and operators. In this attitude, Feynman was realist but pragmatic. He neither argued that an intuitive reality lurked underneath quantum theory nor did he retreat into the subjective. Nature was silly, get used to it.

In everyday life, pragmatism often trumps ontologies. If you ask an anti-realist or a realist what time it is both will look at their watches and tell you it is, e.g., noon. The anti-realist may protest that such determinations are subjective, divorced from an ineffable reality. Time is an illusion. Nevertheless, when an enthusiastic tweeter insisted physics Nobel Laureate and philosopher Frank Wilczek and co-inventor of the theory of time crystals admit that time does not exist, he jokingly asked, “when do you want me to do that?”

Far from implying that realism is the only practical approach in life; when contentious issues over race and gender appear, we run to shelter under nominalism, coming out as realist only when our social milieu demands it. Lest we ascribe this problem solely to the humanities, even the hardest of hard sciences, physics, has struggled for decades to extract itself from the quicksand of philosophical debates—what is true? Yet, physics is not philosophy and at the end of the day pragmatism wins out, but, if as a philosopher of science you also take the Feynman stance, the burden of answering “why?” remains.

In an article I wrote for Aeon some months ago, I addressed how Wittgenstein’s philosophy could shed light on debates over objectivity in quantum theory. In that article, I concluded that interpretations of quantum phenomena that did not deviate from existing quantum theory in any experimentally verifiable way failed to solve anything because they were tautologous. They added nothing new to science other than to remind us of what we already know. This is not entirely useless, as the Bohr-Einstein debates illustrated, but one cannot settle an argument without new facts.

In this article, I want to talk about those facts, what facts actually tell us and what they don’t, and why it is more valuable to think absurdly, like Nature does, than to drag quantum theory back to the realm of classical intuitions.

We may not be able to agree on interpretations of quantum theory any more than interpretations of free will, moral action, or any other philosophical thesis, but surely we can agree on facts as the realist and anti-realist must when it comes to time? Surely, once we establish the customary context, what clocks mean, and the telling of time, our realist and anti-realist can in fact meet up for a lunch date?

Late Wittgenstein suggested as much in his portrayal of language games in his Philosophical Investigations. Once we understand the rules of the language game, whether it is how to read a clock or how to manipulate self-adjoint operators on Hilbert spaces, we can agree. It is only when the facts are ambiguous, too much noise and too little signal, that we disagree.

Physicists have, in the 20th century, admitted however that facts are at best statistical. New particle discoveries are subjected to the 5-sigma rule, meaning that the data must imply a new particle out to five standard deviations from the mean. This means that any given particle has at most a 1 in 3.5 million chance of not existing.

This is considerably better than, say, medical studies where the de facto rule for accepting a phenomenon as statistically significant is p > 0.05 or a whopping 1 in 20 chance of the null hypothesis being true.

Then again, that is not necessarily a problem for objectivity. For a fact to be objective we must all agree that it can be determined to some probability and demonstrated satisfactorily to others. It is not that we think it is true or false. As the philosopher Jones once said, “[Enter your science’s name here] is the search for facts not truth. If it’s truth you’re interested in, Dr. Tyree’s philosophy class is right down the hall.” Any scientist knows that facts come with error bars.

The problem for objectivity arises when we look deeply into how facts arise in the first place. Central to the Wittgensteinian framework is this: before you can have a fact, you must have a system for classifying facts. A system for facts is a linguistic construct that we learn by participating in that system. For example, colors and numbers are systems for applying chromatic and numerical adjectives to things. Those adjectives are facts about things. Yet, without those systems, we would have no way of ascribing facts to things. And without facts to describe things with, would we even have a way of conceptualizing things at all?

When it comes to quantum theory, our classical systems for describing physical phenomena come into question. Basic assumptions such as whether a particle has a definite position, momentum, or spin fail to hold. When we get into quantum field theory such as QED, the very existence of a particle is uncertain as well.

In the 1920s, quantum theorists invented new systems for describing fields using advanced mathematical concepts like infinite dimensional vectors called wavefunctions. Ordinary facts were replaced with infinite dimensional operators on wavefunctions called observables.

Yet when experiments were performed, they did not invent devices to measure infinite dimensional quantities. They measured the same old types of facts that they always measured: position was measured with detectors, momentum and spin using deflection in a magnetic field. It was only in the prediction and explanation of those measurements made repeatedly, over and over, and examined statistically that the operators were required. We had to update our language, mathematically, in order to make sense of what we were seeing in the statistical data.

New adjectives and nouns were required. Observables in quantum theory describe fields and, hence, are adjectives to the fields’ noun. As is the case with things in the ordinary classical world, it isn’t clear that fields are “real” or simply convenient names we give to collections of adjectives. From a Wittgensteinian perspective, it doesn’t matter because the names we give to fields like electromagnetic, gravitational, etc. are just part of the language game of doing quantum physics. The names aren’t about objective reality nor about subjective sense impressions. Rather, they tell physicists how to play the game.

If the way we describe quantum theory were, in some sense, the only way possible, we might be justified in saying that it is an objective description and that, therefore, the facts that we ascertain from experience are themselves objective. Yet, even at the dawn of quantum theory, multiple formulations of quantum physics were developed, the familiar Schrödinger wave mechanics and the less popular Heisenberg quantum mechanics for example.

Although these are mathematically equivalent, they are linguistically different. To Schrödinger, a particle is a manifestation of a wavefunction. We can predict what we will measure from a wavefunction at a given time by acting on it with an observable. This is a very intuitive way of thinking. Observables are adjectives which we apply to wavefunctions which are the nouns.

To Heisenberg, however, a particle is simply a collection of observables that evolve with time. There is no wavefunction needed. No noun. From a language perspective, this is non-intuitive but justifiable.

These formulations are only two that exist within the same mathematical framework. Yet, we can travel further away from these to Feynman’s path integral formalism, another mathematical equivalent, yet vastly different language which leads to Feynman diagrams, the popular method for computing what happens in particle accelerators. In Feynman’s interpretation, the wavefunction ceases to have importance. Rather, it is the summation (i.e., integral) of probable classical paths that matters. Thus, we have gone from a singular noun wavefunction to a plural noun of paths. Further from this, we come to stochastic and even chaotic quantization, formulations of quantum theory that go back to the singular but have a path that evolves in a second time dimension. One would be perfectly reasonable in believing that this second time dimension actually exists since it is consistent with quantum theory, yet no other evidence for it has been found.

If Western human beings could come up with so many different versions of quantum theory, how many more could other intelligent species develop? What kind of quantum physics would an AI, not trained in human science, come up with?

Since all of these interpretations are mathematically equivalent, they make the same predictions, but they constitute different systems for describing the facts about quantum theory. It is as if I chose to use a Red Green Blue mechanism for describing colors and you chose Cyan Yellow Magenta. We can get to the same colors, but our method of describing those colors needs a decoder. Since all these mechanisms share a similar origin, that translation is not too difficult, giving the illusion that an objective reality is represented by all these concepts and that one must be the “true” one.

It is perfectly reasonable to ask which color system, “RGB” or “CYM” is the real one if the underlying mechanism for producing those colors is one or the other, but, if I display a photo on a computer monitor and then print it on my inkjet printer, the same photo may manifest from different underlying mechanisms depending on whether it is produced from LEDs or dots of ink.

This means that the same emergent phenomenon can come from different underlying systems and to insist that one system is the real one needs real evidence.

This is why falling back on intuitions from everyday experience is so dangerous. We know that everyday experience itself is emergent from quantum physics and so to draw on intuitions from the everyday to understand the quantum world is like using our intuitions about family photos to understand the RGB or CYM color mechanisms.

If this sounds like an argument in favor of reductionism, it is not. Rather it is the converse that if you want to understand the underlying mechanism for emergent phenomena, you cannot apply intuitions drawn from those phenomena. You cannot think of a particle as a little billiard ball making its way through space and time but rather as an excitation of a field living in a Hilbert space having certain symmetries that themselves live in complex spaces, and that goes for space and time themselves. Sometimes a lot of little field excitations with complex symmetries do get together and make space and time and billiard balls to fly through them, but we are not likely to find little balls by going just a bit deeper.

To try to reduce all that to the everyday because it makes more intuitive sense is entirely backward. It is, going back to Wittgenstein, changing the rules of the language game so that meanings are confused and useless. You won’t last long in the real practice of physics doing that.

If you do manage to gain an intuition from quantum theory, from years of study, will you truly understand it? That depends on what you mean by “understand.” Wittgenstein’s insight was that understanding something means knowing how to play the language game well, not excluding all alternative language games, as many quantum philosophers would like to do. Few were better at the physics game than Feynman and so, if anyone can be said to have understood it, it was he.

Timothy Andersen

Principal Research Scientist at Georgia Tech

Dr. Tim Andersen is a Principal Research Scientist at Georgia Tech. Dr. Andersen is author of The Infinite Universe (2020) and writes about science and philosophy for The Infinite Universe on medium.com. He earned his Doctorate in Mathematics from Rensselaer Polytechnic Institute. He lives and works remotely from Wisconsin with his wife and three children