| MadSci Network: Physics |
Hi Mike,
From this and earlier questions you've sent to MadSci, your underlying question seems to be why particle physicists use quantum field theories (where quantities have discrete values) instead of classical ones with continuous values (what you call "CFTs"). There are, in fact, classical field theories that physicists do use in appropriate situations, but particle physics isn't an appropriate situation. Let me explain.
To start with, let's consider what a "field theory" is. Basically, a field theory is set of equations that describe some quantity at any point in space (and time). This quantity can be a "scalar" (a single value, such as potential, density, etc), a vector (like the magnitude and direction of a force), or higher-order ("spinor" or "tensor"). For more about fields, this Wikipedia page" is a good introduction. In fact, I had worked out in my head all of the different examples I wanted to give for this answer, and if you scroll down the page they are all there.
Maxwell's equations are a great example of a classical field theory, describing how electric and magnetic fields behave at any point in space based on local electric charge and current densities. Newton's universal law of gravity describes the direction and magnitude of the gravitational force at any point, based on the direction and distance of other massive bodies in the surrounding space. Einstein's general theory of relativity is also a "continuous" theory of gravity that also accounts for relativistic effects (but not quantum ones). All of the examples above work perfectly well, as long as you don't apply them inappropriately. Newton's laws of gravity are fine for putting a satellite into orbit, but start giving incorrect results when you calculate the orbit of Mercury, and are completely inappropriate for understanding black holes or neutron star mergers.
Similarly, and as I've written before, classical theories also break down when you get to the quantum world, where experiment shows that quantities like angular momentum, orbital energies, etc. come in discrete values and not continuous ones. So the mathematical equations that describe the different fields are chosen to match experimental observations.
Of course it is absolutely possible to construct a "continuous spin particle" theory, where elementary particles have arbitrary spins at any point in time and space. It "just" involves constructing a different set of equations. The problem is that these other equations would be describing particle behaviour that would contradict experiment. This is why we don't have a CSP theory of particle physics.
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