I wrote not too long ago about the recording of the aftermath of particle collisions in ongoing high energy physics experiments. The post took note of the imaginative management of uncertainties (quantum mechanical uncertainties, measurement uncertainties and statistical errors). This hotbed of uncertainties is disentangled with the mathematics of probability. Mathematics here is being used to hold onto things, so that we can get a look at an extraordinarily unstable situation. It gives us a way to see events too numerous and fast for the body to sense or record.
But today, my attention was drawn to the fact that the very idea of a detector grows out of some generalization of how we see. And when a significant ‘generalization’ is effective, it will inevitably bring me back to mathematics.
There is a very nice website put together by the Particle Data Group at Lawrence Berkeley National Laboratory to communicate particle physics ideas and methods. To pave the way for the generalization of ‘seeing,’ they describe the effects of light in this way:
What we think of as “light” is really made up of billions and trillions of particles called “photons.” Photons, like all particles, also have wave characteristics. For this reason, a photon carries information about the physical world because it interacts with what it hit.
For example, imagine that there is a light bulb behind you, and a tennis ball in front of you. Photons travel from the light bulb (source), bounce off the tennis ball (target), and when these photons hit your eye (detector), you infer from the direction the photons came from that there is a round object in front of you. Moreover, you can tell by the different photon wavelengths that the object is green and tan.
Our brain analyzes the information, and creates the sense of a “tennis ball” in our mind. Our mental model of the tennis ball helps to describe the reality around us.
Note the care taken in the words “mental model.” Greater detail about how the electrons in the atoms and molecules of material interact with light waves can be found on this physics website. Whether the energy from a light wave will be absorbed, reflected or transmitted will depend on how it compares to the vibrational frequencies of the electrons in the material it hits.
It’s clear that detectors are a variant on eyes. Since the wavelength of visible light is too wide to analyze anything smaller than a cell, particles of shorter wavelengths must be used as probes. These particles are made to hit a target or other particles and, through various detector processes, the aftermath of their interactions is recorded and analyzed. The body has somehow imagined a way to mimic its eyes and see what it can’t see.
Physics has developed with the extension of conceptual landscapes (generalizations of number, space, dimension, give us calculus, non-Euclidean geometries, vector spaces and topology). And the key to the existence of mathematical objects is structure and relationship. As Courant says concisely in the book What is Mathematics?
What points, lines, numbers “actually” are cannot and need not be discussed in mathematical science. What matters and what corresponds to “verifiable” fact is structure and relationship, that two points determine a line, that numbers combine according to certain rules to form other numbers, etc
The high energy experiment’s ability to extend the range of empirical data (both what we see and how we see it) happens in much the same way. Sight in these complex configurations of material and electronics is defined by structure and relationship. Thought is driving sensation. The body’s ability to find ways to give shape to its world may be inexhaustible.
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