Teginder,
"In order to describe dynamical evolution the theory depends on an external classical time, which is part of a classical spacetime geometry."
The point I make in my entry is that the classical timeline is an effect of the underlaying dynamic, such that it isn't the present moving from past to future, but the changing configuration of what is, that turns future into past. Not the earth traveling the fourth dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates. Duration is simply what happens within the present, between events, not a property external to the present. This makes time an emergent effect of action, similar to temperature. So without an external dimension of time, there can be no dimensionless point on this timeline. A frozen point in time would be equivalent to a temperature of absolute zero; the complete absence of motion. It would be like trying to take a picture with the shutter speed set at zero. The result would not be a frozen moment in time, but nothing. Which means an entity, micro, or macro, cannot be isolated from its action. That macroscopic table only exists because of the dynamic activity sustaining it. So, effectively, the particle is actually just a really small wave.
Consider this exchange from an interview with Carver Mead;
"So how did Bohr and the others come to think of nature as ultimately random, discontinuous?
They took the limitations of their cumbersome experiments as evidence for the nature of reality. Using the crude equipment of the early twentieth century, it's amazing that physicists could get any significant results at all. So I have enormous respect for the people who were able to discern anything profound from these experiments. If they had known about the coherent quantum systems that are commonplace today, they wouldn't have thought of using statistics as the foundation for physics.
Statistics in this sense means what?
That an electron is either here, or there, or some other place, and all you can know is the probability that it is in one place or the other. Bohr ended up saying that the only statements you can make at the fundamental level are statistical. You cannot grasp the reality itself, only probabilities related to it. They really, really, wanted to have the last word, and the only word they had was statistical. So they made their limitations the last word, saying, "Okay, the only knowledge that there is down deed is statistical knowledge. That's all we can know." That's a very dangerous thing to say. It is always possible to gain a deeper understanding as time progresses. But they carried the day.
What about Schrodinger? Back in the 1920s, didn't he say something like what you are saying now?
That's right. He felt that he could develop a wave theory of the electron that could explain how all this worked. But Bohr was more into "principles": the uncertainty principle, the exclusion principle--this, that, and the other. He was very much into the postulational mode. But Schrodinger thought that a continuum theory of the electron could be successful. So he went to Copenhagen to work with Bohr. He felt that it was a matter of getting a "political" consensus; you know, this is a historic thing that is happening. But whenever Schrodinger tried to talk, Bohr would raise his voice and bring up all these counter-examples. Basically he shouted him down.
It sounds like vanity.
Of course. It was a period when physics was full of huge egos. It was still going on when I got into the field. But it doesn't make sense, and it isn't the way science works in the long run. It may forestall people from doing sensible work for a long time, which is what happened. They ended up derailing conceptual physics for the next 70 years."
.........
"So early on you knew that electrons were real.
The electrons were real, the voltages were real, the phase of the sine-wave was real, the current was real. These were real things. They were just as real as the water going down through the pipes. You listen to the technology, and you know that these things are totally real, and totally intuitive.
But they're also waves, right? Then what are they waving in?
It's interesting, isn't it? That has hung people up ever since the time of Clerk Maxwell, and it's the missing piece of intuition that we need to develop in young people. The electron isn't the disturbance of something else. It is its own thing. The electron is the thing that's wiggling, and the wave is the electron. It is its own medium. You don't need something for it to be in, because if you did it would be buffeted about and all messed up. So the only pure way to have a wave is for it to be its own medium. The electron isn't something that has a fixed physical shape. Waves propagate outwards, and they can be large or small. That's what waves do.
So how big is an electron?
It expands to fit the container it's in. That may be a positive charge that's attracting it--a hydrogen atom--or the walls of a conductor. A piece of wire is a container for electrons. They simply fill out the piece of wire. That's what all waves do. If you try to gather them into a smaller space, the energy level goes up. That's what these Copenhagen guys call the Heisenberg uncertainty principle. But there's nothing uncertain about it. It's just a property of waves. Confine them, and you have more wavelengths in a given space, and that means a higher frequency and higher energy. But a quantum wave also tends to go to the state of lowest energy, so it will expand as long as you let it. You can make an electron that's ten feet across, there's no problem with that. It's its own medium, right? And it gets to be less and less dense as you let it expand. People regularly do experiments with neutrons that are a foot across.
A ten-foot electron! Amazing
It could be a mile. The electrons in my superconducting magnet are that long.
A mile-long electron! That alters our picture of the world--most people's minds think about atoms as tiny solar systems.
Right, that's what I was brought up on-this little grain of something. Now it's true that if you take a proton and you put it together with an electron, you get something that we call a hydrogen atom. But what that is, in fact, is a self-consistent solution of the two waves interacting with each other. They want to be close together because one's positive and the other is negative, and when they get closer that makes the energy lower. But if they get too close they wiggle too much and that makes the energy higher. So there's a place where they are just right, and that's what determines the size of the hydrogen atom. And that optimum is a self-consistent solution of the Schrodinger equation."
