Step by step, our ideas about the nature of our reality have moved far from the sensory constructions of space and time that define our immediate experience. And once fully outside the knowledge brought with sensation, we lose our footing. It’s difficult to manage ‘what can’t be sensed.’ But our conceptual difficulties with quantum mechanics are very reasonable if we imagine that, however abstract, the mathematics that got us there is rooted in our sensory experience – our sense of space and duration, our perception of quantity, and perhaps the cognitive mechanisms that manage these. The remarkable refinement of mathematical ideas has forced a reconsideration of what we think we see, and the conceptual possibilities that mathematics provides may indicate that we’ve enhanced our sensory apparatus in such a way that it has been made sensitive enough to ‘reach’ the edge of what is ‘sensible’ making us aware of the reality that escapes us. It is beginning to look like vast parts of our reality are not sensible.

These thoughts came to mind after reading a few discussions concerning the reconciliation of quantum mechanical strangeness. A New Scientist article addresses, specifically, questions about the meaning of space and time and their place (or lack of it) in modern physics. Space and time are constructed by the body and further explored by mathematics. But questions about whether or how they are real are very old. As Anil Ananthaswamy says,

…arguments about the nature of space and time swirl on. Are both basic constituents of reality, or neither – or does one perhaps emerge from the other in some way? We are yet to reach a conclusive answer, but it is becoming clear that if we wish to make further progress in physics, we must. The route to a truly powerful theory of reality passes through an intimate understanding of space and time.

I like the phrase ‘intimate understanding.’ It suggests getting very close to their source. The difficulty in physics, more specifically, is this:

A quantum object’s state is described by a wave function, a mathematical object living in an abstract space, known as Hilbert space, that encompasses all the possible states of the object. We can tell how the wave function evolves in time, moving from one state in its Hilbert space to another, using the Schrödinger equation. In this picture, time is itself not part of the Hilbert space where everything else physical sits, but somehow lives outside it…As for space, its status depends on what you are measuring. The wave function of an electron orbiting the atomic nucleus will include properties of physical space such as the electron’s distance from the nucleus. But the wave function describing the quantum spin of an isolated electron has no mention of space: according to the mathematics, the picture we often paint of an electron physically

rotating is meaningless.

Although a Hilbert space is a vector space whose structure is completely abstract, it rests on the meaning that it borrows from the relationships among vectors that we imagine in two and three dimensional Euclidean space. And so it is grounded in a familiar spacial idea. But mathematics has grown in such a way that the vectors of a Hilbert space can be used to represent possible states of a quantum mechanical system.

In a recent Scientific American blog, George Musser gave University of Maryland philosopher Ruth Kastner the opportunity to discuss her ideas about to resolve the difficulties with what is called the transactional interpretation of quantum mechanics. She begins with a reference to physicist and writer Han Christian von Baeyer’s article in the June issue of Scientific American. She says about his article that in response to the deep questions about the meaning of quantum theory von Baeyer “discusses one proposal – a denial that the theory describes anything objectively real …”

This is a very misleading summary of what von Baeyer discusses. I also wrote a few weeks ago about this article. It’s the *wave function* that is thought to have no objective reality from the point of view that von Baeyer discusses. This perspective (called Qbism) combines quantum theory and probability theory and sees the wave function as a powerful mathematical tool that provides the observer a way to make decisions about the surrounding quantum world. I took note, in my post, of the fact that Bayesian statistics (the ones used in Qbism) are also used by cognitive scientists to model how we build our very immediate expectations of our world from sensory data. And I quoted physicist Christopher Fuchs, a prominent proponent of Qbism, who said:

…even if quantum theory is purely a theory for apportioning and structuring degrees of belief, the question of “Why the quantum?” is nonetheless a question of what it is about the actual, real, objective character of the world that compels us to use this framework for reasoning rather than another.”

This doesn’t sound like a denial that the theory describes anything real.

The transactional Interpretation that Kastner discusses in her blog was first proposed, she tells us, by physicist John Cramer in the 1980s and can be traced back to physicists John Wheeler and Richard Feynman. She says the following:

My development of the Transactional Interpretation makes use of an important idea of Werner Heisenberg: “Atoms and the elementary particles themselves … form a world of potentialities or possibilities rather than things of the facts.”

This world of potentialities is not contained within space and time; it is a higher-dimensional world whose structure is described by the mathematics of quantum theory.(emphasis added)

I wasn’t able to get a very clear picture of the history of the idea, nor her development of it from the blog, but the punch line is clear enough. Her transactional picture assumes that “there is more to reality than what can be contained within space-time.” It is somehow with the encounter of “potential events” (not contained within space-time) that “real energy may be conveyed within spacetime…” and “delivered in the normal future direction.”

She goes on to say:

The transactional picture is conceptually challenging because the underlying processes are so different from what we are used to in our classical world of experience, and we must allow for the startling idea that there is more to reality than what can be contained within spacetime.

I had the impulse to bring these ideas together because of what they have in common, specifically, that what we see (in the most abstract sense of that word) consistently indicates how much we don’t see. And, perhaps that there is even a strain on our mathematical ways because mathematics itself may have its roots in how the body ‘perceives.’ This doesn’t mean that progress can’t be made. Bringing back a little bit from Christopher Fuchs:

For the Qbist, the lesson that the structure of quantum theory calls out to be interpreted in only this way is that the world is an unimaginably rich one in comparison to the reductionist dream. It says that the world has excitement, risk, and adventure at its very core.

Considering how our mathematics brings us closer to this core is equally exciting.

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