Is the world real?

In one of our recent papers, Direct Imaging of Electron Density with a Scanning Transmission Electron Microscope (https://www.nature.com/articles/s41467-023-42256-9 ), I had wanted to make the claim that we were measuring (imaging) the atomic orbitals in a 2D material. One of the reviewers was firmly against this terminology. He argued that, strictly speaking, orbitals are solutions to the wave equation and are thus non-measurable entities. In order to get something measurable you must take the modulus squared. Then you no longer have an orbital but a probability density for finding an electron. We ended up purging most of the manuscript of this language and, as you can see by the title, we went with 'electron density'.

But, I am not writing this to complain about reviewers. It suddenly struck me as very strange that there could be non-measurable entities. I suppose I had never put much thought into it. What do we mean by saying that there exist non-measurable entities?

It turns out this is a very old problem and it is not a problem that science can answer. It is a metaphysical problem. Anything that we observe must enter our consciousness through our senses. Thus, if we strictly limit ourselves to what we can sense there is no way to make the leap to external reality. One can always argue that 'reality' is nothing more than a bundle of sensations experienced by the observer.

In 'Realism and the Aim of Science', Karl Popper argues forcefully against this view. Here is his restatement of the solipsist position:

From the point of view of a subjective or idealistic epistemology, the strongest form of idealism is solipsism. The epistemological argument in favor of idealism is that all I know are my own experiences, my own ideas. . . . If bodies are merely parts of my dream, other minds must be even more so. (pg 83)

And his rebuttal:

My argument is this. I know that I have not created Bach's music, or Mozart's; that I have not created Rembrandt's pictures, or Botticelli's. I am quite certain that I never could do anything like it: I just do not have it in me. . . . But on the solipsistic hypothesis, all these creations would be those of my own dreams. They would be creatures of my own imagination. . . . I know that this cannot be true.

The argument is of course inconclusive. I may perhaps underrate myself (and at the same time overrate myself) in my dream. Or the category of creation may not be applicable. All this is understood. Nevertheless, the argument satisfies me completely.

My argument is, no doubt, a little similar to Descartes's argument that a finite and imperfect mind cannot create out of itself the idea of God, but I find my own argument more convincing. The analogy with Descartes's argument suggests, however, a simple extension to the physical world. I know that I am incapable of creating, out of my own imagination, anything as beautiful as the mountains and glaciers of Switzerland, or even as some of the flowers and trees in my own garden. I know that ours is a world I never made.

I can only repeat that this argument satisfies me; perhaps because I never really needed it: I do not pretend that I ever doubted the reality of other minds, or of physical bodies. Indeed, when I think of this argument, I cannot but feel that solipsism (or, more generally, the doubt of the existence of other minds) is not so much a form of epistemology as a form of megalomania. (pg 84)

But this argument, as Popper concedes, seems to be rather tired and tedious. The subjectivist position stems from an attempt to begin with certain knowledge. I can only be certain of those sensations I experience first-hand. Thus, I am tethered to my own subjectivity. It is related to Hume's problem of induction which I have commented on previously (https://www.dhirubhai.net/posts/ondrejdyck_inference-induction-activity-7227774795797446656-lz5x?utm_source=share&utm_medium=member_desktop ). We believe that we know something about unobserved events; that our (scientific) theories apply universally and hold, even in situations that we have not yet observed.

But this is simply not true. We do not know. We speculate, we conjecture. We are unsure of ourselves. We put forward hypotheses and then test them to see if they hold. This, Popper points out, is exactly the situation one would expect if realism were true.

In other words, if realism is right, we cannot hope or expect to have more than conjectural knowledge: the miracle is, rather, that we have been so successful in our quest for conjectures. (pg 102)

There is another doctrine that is somewhat related to the subjectivist position: that of instrumentalism. This doctrine holds that all theories about the world are useful instruments of calculation, and nothing more. Ernst Mach, I am told, did not believe in atoms. The periodic table was merely and accounting fiction used for calculation and should not be interpreted to mean that atoms really existed. Instrumentalism places all the value in our theories in their usefulness for calculation and prediction, not in that they are attempts at describing the real world.

Popper gives several reasons (pg 113-117) why he rejects this view. Here are a few of them:

Theories are developed with an aim for application everywhere and at all times. That is what we mean by 'laws of physics'. An instrument that is simply used for calculation may apply to particular situations without a universal law-like claim.

Theories may be found to be false (e.g. Newton's gravitation) and still be useful for calculation. Despite its usefulness for calculation, the fact that the theory is found to be false prompts us to amend it, to develop a better theory.

When we test a theory, we seek out new situations predicted by the theory, in an attempt to prove it wrong. If it is found to be wrong, we seek a better theory. An instrument for calculation is not taken to be true or false, it is simply a tool that works within its domain of usefulness. This is because it is not taken to mean anything. But a theory is intended to apply universally, thus if limits to its usefulness are found we reject it as a theory, but not as a calculation tool.

Suppose we had two competing theories that were found to be equally useful for calculation but were logically different. The true instrumentalist would have no preference for one or the other. The theorist, however, will be driven to find those new situations where the theories disagree (or find that the theories are in fact the same theory). Once such a situation is found, it enables us to craft a test so that we may determine which of the two theory is true (or more true).

A theory, because it is a proposition about the world and not simply an instrument for calculation, may lead to surprising predictions that were not known to its author before hand. The observed positions of stars during a solar eclipse and the conversion of mass into energy, as predicted by Einstein's theories, were surprising consequences of the theory. It is difficult to explain this situation from within the instrumentalist world view, which would have to assert that Einstein was not trying to say something about the world but simply refining our calculation tools to account for some anomalies. Surely ad hoc empirically derived corrections to Newtonian mechanics are far easier (and therefore better) calculation tools than curved spacetime.

A theory is intended to have informative content. It must explain 'why' in an intelligible way. If it were simply a mechanical calculation tool, it would not matter why it worked, only that it worked. A theory helps us to interpret and understand the world. The theorist who develops a theory is primarily worried about prediction because he is searching for a true theory. The predictions form the basis for tests that can be used to distinguish between a true theory and a false theory.

Having laid out these arguments, let us consider again the situation described at the beginning. Quantum theory predicts these objects, orbitals, that are nothing but the solution to the wave equation. They are not to be taken literally. They are non-measurable objects. It is part theory, part calculating device. Quantum theory makes strange predictions that are difficult to wrap one's mind around but so too does general relativity. What is really disturbing about quantum theory is the duality it exhibits between 'calculating device' and 'theory about the world'.

Quantum theory is, of course, relied upon to make innumerable calculations every day. There is even the 'shut up and calculate' response to the interpretation of quantum mechanics. But this is clearly unsatisfactory.

I hope that we do not become so comfortable with our ability to calculate that we abandon the search for intelligible theories.

I cannot help but conclude that, yes, the world is real, and other minds exist as well. No matter how deficient our theories about the world may be, they are aimed at an objective description of external reality, even if they remain always conjectural and open to revision.