What is the physical significance of the iFactor?

[purrcy]

I have a Question:

When the imaginary unit, i, is factored with time, t, in the Lorentz Transformation, or when the Hamiltonian is factored (as when Dirac created his Creation and Annihilation Operators,) and i is factored with the momentum, p, the iFactor is always factored with time, energy, and motion.

What is the physical significance of the iFactor?

 

[purrcy]

OK, 64 people have viewed this thread and no comments have been logged. So, I will make another comment:

It is my understanding that mainstream physics maintains the view that the iFactor is there just to make the mathematics come out right.

I think that the iFactor is much more significant than that! It has been known that the iFactor , i, when factored with the Real Number Line creates another line that is Orthogonal to the Real Number Line, a dimension which we call Imiginary.

Physics accepts imaginary numbers, why not imaginary dimensions that have real physical significance?

 

[Rap]

In classical physics, you don't run into the imaginary unit i. Everything is real. Whenever you see i in a classical equation, its just being used as a mathematical tool instead of using real sines and cosines. E.g. cos(x)=(1/2)(e^ix+e^-ix) etc., or you take the real part of whatever equation you come up with. Its a mathematical device that makes calculations easy, but it is not necessary.

In relativity, you do not encounter the imaginary unit i either. Sometimes you see it used in the time coordinate as ict, so that you can use Euclidean geometry formulas to get distance. Instead of writing x^2+y^2+z^2-(ct)^2, its sometimes written x^2+y^2+z^2+(ict)^2. But this is not good, its kindergarten stuff, spacetime is not Euclidean and its wrong to try to pretend that it is. It makes you think that time is somehow special, but its not. It stops you from understanding the metric tensor and how time and space really are indistinguishable. Its just a trick that you will ultimately throw away once you get deeper into relativity theory.

Only in quantum mechanics do you really encounter the imaginary i, because quantum wave amplitudes are complex. But measurements are real. You never measure a quantum wave amplitude, you only measure the absolute value of a quantum wave, and that's a real number, but the quantum amplitudes interact with each other according to their amplitudes. Only in quantum mechanics is the imaginary i indespensible.

 

[Nabeshin]

In relativity, you do not encounter the imaginary unit i either. Sometimes you see it used in the time coordinate as ict, so that you can use Euclidean geometry formulas to get distance. Instead of writing x^2+y^2+z^2-(ct)^2, its sometimes written x^2+y^2+z^2+(ict)^2. But this is not good, its kindergarten stuff, spacetime is not Euclidean and its wrong to try to pretend that it is. It makes you think that time is somehow special, but its not. It stops you from understanding the metric tensor and how time and space really are indistinguishable. Its just a trick that you will ultimately throw away once you get deeper into relativity theory.

Indeed, the imaginary notation for relativity is quite antiquated and nobody uses it any more.

 

[purrcy]

This is exactly what I mean. What both of you have said is that the iFactor is simply there to make the mathematics come out right. What if there is a hidden meaning? There are many things in Reality that are hidden from our perception. I think that we can all agree that Physics, so far, is only an approximation of Reality. Have our mathematical tricks lead us from understanding a more fundamental aspect of Reality? We can't see time, our perception only sees the past. Our Physics only predicts the future in terms of probabilities! If the iFactor is really telling us that there are imaginary dimensions in Reality, what could they be?

I am really suggesting that you think outside the box. Does anybody have any useful suggestions? This would be new physics if something meaningful came from this discussion.

Be daring! Be original! Let you imagination run wild! You are not being graded here. The only bad idea is the one that is not mentioned.

 

[Nabeshin]

You're looking for meaning where there is none, so much so that you keep referring to the number i as the "iFactor" as if it were something mystical and special. What does "imaginary dimensions of reality" even mean? You are combining a bunch of words to attempt to form some idea which is ill defined at best.

We have good constraints on the existence of extra dimensions. Namely, no one has ever seen more than three. Whether you want to call them "imaginary" or not is largely meaningless -- there are legitimate proposals about those though.

The purpose of PF is to educate people to and discuss the current state of science, not to sit around daydreaming and "thinking outside the box". I hate to be harsh, but physics forums is not the best place to discuss theories outside the physics (i.e. established science) box.

(So as not to sound like a complete conformist, dissent with current mainstream science is not to be frowned upon, but rather encouraged. It simply must be the case that this dissent is itself well formulated and defined before it can be discussed. The ideas you are throwing forth do not even approach that criterion.)

 

[Rap]

I am really suggesting that you think outside the box. Does anybody have any useful suggestions? This would be new physics if something meaningful came from this discussion.

Be daring! Be original! Let you imagination run wild! You are not being graded here. The only bad idea is the one that is not mentioned.

Napoleon once said that a bad general is one who does not understand the rules of war. A good general is one who does. A great general is one who understands the rules of war and when to break them.

Like a bad general, anyone can think outside the box, if they don't even know where the box is. Like a great general, a great scientist is one who knows the box inside out and sees when to jump out of it. Learn where the box is before trying to think outside it, otherwise you are being a bad scientist. I know, that takes work, and you might get too comfortable and blind inside the box, but those are the risks. If you don't play, you don't win.

The "iFactor" is just a number in the complex number system, its a really simple tool, like a screwdriver, nothing worth getting mystical about. If you want to get to the edge of the box, study enough physics to understand Bell's inequalities. That's worth getting mystical about.

 

[purrcy]

I've heard that students, these days have a lot to be desired. They are rude, crude and insufferably ignorant … and show a great lack of imagination. The comments that I've read so far seem to verify the fact.

If you think that imaginary numbers don't have a place in Classical Mechanics then you haven't read much about Hamilton. He had an obsession for the imaginary unit in those days when imaginary was a derogatory word. And, as far as I know, Relativity still relies heavily on the metric, which is based on the equation d^2=x^2+(ct)^2=(x+ict)(x-ict), where ict is orthogonal to x! Human perception cannot grasp the idea that time may lay in a dimension of Reality which is orthogonal to what we perceive as the only dimension of Reality, the real number line … for time.

I am merely suggesting that we may need to rethink these ideas. And consider the i Operator may be just that.