Commentary

Knowledge from Appearance

In his Academics,¹ Cicero defends his scepticism of our knowledge of reality by citing examples of false impressions that we receive of the world. He cites dreams and the illusions of the insane as examples of untrue knowledge, arguments that are familiar within philosophy and are the basis of the Matrix moves. But he also cites a strikingly different argument that presages modern science's view of our interaction with the external universe: the apparent bending of an oar that is partially submerged in water.

What Cicero has in mind, of course, is that the representation of the oar is false, because we know the oar is straight, but the water causes the image of the oar to be broken at the point where the oar enters the water. He regards the image of the broken oar has false, because it does not represent the true object. This distinction between what we see and what is actually there is central to modern physics; to understand any experiment or observation in physics requires not only an understanding of the phenomena, in this case the shape of the stick, but also understanding how the thing we are measuring, in this case light, interacts with its surroundings and our instruments, in this case the water, air, and our eyes.

In our daily lives, this distinction between what we see and what is seldom important; the example of the broken oar is one of the few common experiences where our eyes deceive us. We are perfectly capable of describing how an object falls without taking into account how the light from that object travels to us and interacts with our eyes. When we make a direct comparison of what we calculate with our equations of motion to what we see, we find that there is precise agreement. Our impression is that we see these distant occurrences instantaneously.

As we move away from the Newtonian world of our daily lives, we encounter more and more problems that require us to understand not only the phenomena that we are observing, but also the propagation of light or particles that we are detecting from the phenomena through space and through our instruments. To understand the orbits of Jupiter's moons, we must not only understand Newtonian gravity, but also the time delay caused by the finite speed of light. To understand an observation of a high energy source, we not only must understand the creation of x-rays by the source and the propagation of the x-rays to our instruments, but we must understand the interaction of that x-ray with the materials in the instrument and the spacecraft carrying the instrument. To understand any object that we see, we must understand the whole chain of how it creates radiation, how that radiation reaches us, and how our instruments detect that radiation.

One sees this in special relativity, the theory that defines how our measurement of length and time are altered by acceleration. We normally use an abstract Euclidean coordinate system to describe the positions of objects. Under special relativity, an object's length along the direction of motion becomes shorter as the object's speed increases. We can give a tortured description of how to physically realize this abstract coordinate system, and in some instances, such as with gravitational wave detectors, the coordinate system is realized, but iIn astronomy the coordinate system remains abstract. In astronomy, we observe the light from an object, and when that object is moving close to the speed of light, the time of travel for the light causes the object to appear rotated rather than shortened.

The distinction between the abstract mathematics we use in our theories and the observables that we measure sharpens when we go to general relativity, where coordinate systems are so abstract that they are best regarded simply as a mathematical step in solving a complex problem.

This distinction between the abstractions within a theory and the observable quantities obtained from a theory raises a question that hangs over and, to my mind, defines modern physics: do the mathematical equations of our modern physics correspond to an underlying physical truth., or are they like a clockwork representation of the solar system?with gears and springs that have no physical counterpart, but which none-the-less gives us a precise representation of where the planets will be on a given day?

I believe this clockwork analogy applies to quantum mechanics, the theory for the motion of microscopic particles. For instance, we describe the interaction of two particles through the evolution of a wave. But this wave has no physical interpretation beyond that the square of its magnitude is a probability that the particle is in a given position with a given momentum.

I recall reading long ago a comment by Richard Finemann, one of the developers of relativistic quantum mechanics, that he did not really understand the theory, but he thought that scientists raised with it would understand it. This is similar to the argument of the academic composers of his generation that the 12-tone music they were writing, while not appreciated by those who grew up with Mozart, Beethoven, and Brahms, would be appreciated by listeners who grew up with it. I can attest, as someone who came to classical music through the string quartets of Bela Bartok, that the works of such people as Eliot Carter are totally inaccessible, because they are so divorced from how I interpret sound. Likewise, my experience with quantum mechanics is that its mathematics contain no insight into how the universe works. The various parameters one calculates are stages in producing a parameter that we measure, such as the probabilities for the interaction of two particles. Quantum mechanics from this viewpoint is a mathematical machine, something that correctly calculates the parameters we measure, but whose guts in all likelihood having no correspondence to the physics that is beyond our perceptions.

Cicero was sceptical of our ability to perceive the true nature of objects. In science, we find that we run up against this same problem.