Thursday, September 4, 2014

Quantum Superpositions: Super Stuff

In an early post on this blog, entitled “What Are We Missing?”, I explained that the two things keeping the physicists from making progress are their fear of metaphysics and their lack of a correct spacetime model. I then showed that metaphysics is really physics and nothing to be afraid of, and I’m now doing a series of posts about the spacetime model that they need.

In my last post, we discovered that our spacetime of discrete points easily reproduces the physics of the early universe and is full of electrons, positrons, neutrinos, antineutrinos, and photons. This time I want to cover what I believe to be one of the truly wonderful features of this spacetime. It comes directly from the quantum mechanical principle of superposition and it gives us the composite particles such as protons and neutrons and the heavier leptons.

 When a quantum mechanical system is observed, the outcome is not certain. A quantum system can be in a number of possible states, each of which can be the outcome of an observation. We know the outcome must be one of the possible states, and we sometimes know the probabilities of observing each state, but we never know which state will be observed, even if we make identical observations on an identically prepared system. Before an observation the system is said to be in a superposition of states. A superposition is any set of possible states of the system whose probabilities of being observed in a given experiment add up to one, or 100%.

One of the principles of quantum mechanics says that any superposition of the possible states of a quantum system is also a possible state of the system. Therefore, in our case, any superposition of spacetime points is also a spacetime point. We could start with our spacetime of single points and form a spacetime in which every point is a superposition of two, or three, or any number n of single points. We can go back the other way, too, and express every point in our original n = 1 spacetime as a superposition of n = 2 points or n = 3 points or whatever. Since the points for any value of n are possible states of the system, there is a nonzero probability that they will be observed. However, we don’t see points, we only see particles, which are excited points. What would an excited state of an n = 3 point look like? Lots of particles we know about, actually, but especially protons and neutrons.

This seems simple and obvious when you have the right spacetime model, but the physicists don’t, so the standard model of a proton is a composite particle made of three point particles called quarks. You can see where they got this idea. In scattering experiments on a superposition of three points, you would see only one of the three points in each experiment. Ultimately you would realize that there are three things here and conclude that the proton is a composite of three particles. But quarks are odd particles. Unlike other particles, they have electric charges that are fractions of the electron charge. They are never seen separately—not surprising for “parts” of a point!—but baffling to physicists for a long time until they came up with the theory of quantum chromodynamics, which does a pretty good but not perfect job of explaining the phenomenon.

Let’s back up a little and examine this a little more closely.  We’ve got points, and we’ve got excited points, which are particles. Points can be pure states—single points—or they can be superpositions of two, three, or n pure states. An excited single point is a very different particle from an excited n = 3 point—one is an electron and one is a proton. But quantum mechanically, these are both point particles! Does a point have parts? Of course not! So you’d never expect to observe one of the components of a three-point superposition floating around in space by itself. If you observe the n = 3 object, you’ll see one of the three components at a time, each with some probability. But you’ll always see it “confined” within the limits of the composite object, the proton.

But wait, there’s more! A superposition of three points consists of three spacetime points, each with its own position, spin, and time quantum numbers, along with a number that represents the probability of observing that particular point when you observe the composite object. The number is called the amplitude, and it’s a complex number (it involves i, the square root of minus one). The probability is the square of the amplitude, and it can be negative, so it obviously isn’t an ordinary probability. What might it be? If we think of it as a net time rate, everything makes sense in our spacetime, where points and particles can go backwards in time. In the proton, the three components have net time rates of -2/3, -2/3, and 1/3 times the basic time rate. Notice that the time rates add up to one (or -1) as they must.

The physicists say the proton is made up of two up quarks and a down quark, which have electric charges of 2/3, 2/3, and -1/3 times the elementary charge, e (the electron’s charge is –e). Electric charges! Major discovery! As I write this, there’s not a physicist in the world who knows that electric charge equals local time rate. But now you know it, too. This is the really cool feature of this spacetime model. You get to see nature’s great puzzles reduced to the simple and the obvious. You also know that quarks aren’t separate particles; that’s an oversimplification.

I should point out that by convention, particles going forward in time have negative charges and vice versa. In other words, a positive time rate means a negative charge. Like many physics conventions, it seems designed to be confusing. Just live with it.