The way that I have always understood force unification theories is that they show that two or more forces are just different aspects of the same thing. I was trying to get my head around this with respect to the electric force and the magnetic force, but while I can understand how they are related, I don’t see that they are two sides of the same coin. I would like to begin there before delving into EM-Weak unification, etc. Is there a simple way to understand this?
Thanks,
Rob
To understand electromagnetic unification, you need special relativity. Actually the force unification came first, and then Einstein came along and decided that maybe the same rules that applied to E&M applied to everything else, too, but that just means that Maxwell discovered the parts of relativity he needed before Einstein.
As a simple example, consider two parallel wires, with current running the same way in both. Magnetism tells us that they should attract each other, but we can also derive the same result just from electrostatics and relativity. In each wire, we have positive charges which are just sitting in place, and electrons which are moving. Suppose you’re riding along in the reference frame of one of the electrons in wire 1. You look over at the other wire, and because you’re moving relative to wire 2’s positive charges, the distance between them is contracted, so you see a greater density of positive charges in wire 2. The electrons of wire 2, however, are moving at the same speed you are, so they’re not contracted. So the electron in wire 1 sees wire 2 as having a net positive charge, and is therefore attracted to wire 2.
Meanwhile, what about the protons in wire 1? They’re moving relative to the electrons in wire 2, so they see the distance between wire 2’s electrons contracted, and therefore an increased density of electrons in wire 2. But they’re not moving relative to wire 2’s protons, so those are at the normal density. So the protons in wire 1 see wire 2 as having a net negative charge, and they’re attracted to wire 2, too.
So on net, the protons and the electrons both in wire 1 are attracted to wire 2. If you do the calculations in detail, you’ll find that the amount of attraction is exactly as much as is predicted by the theory of magnetism. It’s worth noting, incidentally, that this occurs even though the speed of the electrons in a typical current-carrying wire is a literal snail’s pace, millimeters per second or less, which highlights the fact that any speed at all is “relativistic speed”.
Does that mean magnetism is just an illusion caused by our neglecting to take relativity into account when we compute the force on the wire, and that coulombic attraction or repulsion is the only real force involved here?
Here’s where I have trouble with E & M being unified (probably because I never went to my electricity theory class in college).
There are electric monopoles but no magnetic monopoles.
When you have two magnets, there is a force but no electricity.
So under what conditions are E & M unified? Only when a conductor is moving through a magnetic field or electricity is running through the conductor? Or are they unified at a more basic level?
I suppose you could view it that way, but only in the simplest possible circumstances (namely, two parallel wires with current flowing in the same direction.) If you had two wires with currents flowing in opposite directions, then there wouldn’t be any frame in which the magnetic fields vanished everywhere.
They’re unified in the sense that they transform into each other when you describe things in different frames. The issue of the existence of magnetic monopoles is somewhat different from this. What’s true is that subject to some caveats, electric currents and magnetic monopoles (if they existed) create magnetic fields; and, more importantly, you can show that the flip side of this is true: magnetic currents (if they existed) and electric monopoles create electric fields.
To put this another way: if you and I are moving with respect to each other, some of what you call “electric force” I call “magnetic force”, and vice versa. Where you see a purely electric effect, I see a mixture of electric and magnetic effects.
So what’s “electric force” and what’s “magnetic force” isn’t fixed. It’s relative (!) to how the observer is moving. The important thing, then, is what isn’t relative. And that’s a certain object called that “Faraday tensor”, which is built from the electric and magnetic fields in a certain way.
They’re unified in the sense that there’s one “electromagnetic field” that gets sliced up into “electric” and “magnetic” fields differently depending on how the observer is moving.
Fuck an a half! :smack:
Do you think they’ll let me retake the section on Maxwell’s equations from my 1993 physics class again? :smack:
To the last three posters - thanx. It’s blindingly clear now. I never thought about the reletivity component before this thread.
Any hints on EMW unification now?
Same story, but more so. Electromagnetism is described in terms of the photon field, while the weak interaction is described in terms of three other particle fields: W[sup]+[/sup], W[sup]-[/sup], and Z[sup]0[/sup]. These “fields” aren’t vector fields like the electric and magnetic fields: they’re something weirder called “quantum fields”. But you can roughly think of them as a more complicated thing sort of like a vector field.
Anyhow, we’ve got these four particles (described by quantum fields) around. But there’s really just one big field subsuming all four. How the components of the one big field are divvied up into the four depends on the observer’s motion. What I call a “photon”, you see as some combination of a photon and the three different “weakons”.
Grand Unification is the same thing over again, but now with gluons thrown into the mix.
Is there an example like Chronos gave involving two circular magnets (like the ones in old ferrite core memories)? Or does that require the imaginary (or, at least, unobserved) magnetic current that MikeS spoke of?
Also, Mathochist, could you elaborate on your EMW example a little bit?
Thanks to everyone who answered, btw. For what it’s worth, The Cartoon Guide to Physics has a nice explanation of relativity using electromagnetism rather than astronauts as it is usually presented, but unfortunately, it doesn’t point out that this shows that electricity and magnetism are two sides to the same coin. It does state that Maxwell showed this and presents his equations in del notation. (In school, we called that a “clearly”, as in some amazingly non-obvious conclusion “clearly” followed from the assumptions.)
Thanks again,
Rob
Well, first I suppose I should expand on what the Faraday tensor is. Instead of assigning a 3-dimensional vector to each point of spacetime (getting three functions for the three components) we use a 4-dimensional antisymmetric matrix. That is, something that looks like
( 0 E_x E_y E_z)
(-E_x 0 B_z -B_y)
(-E_y -B_z 0 B_x)
(-E_z B_y -B_x 0 )
“antisymmetry” means that if you reflect this matrix along its diagonal you get its negative. In particular, this means that there are only six independent components, which are the six components of the electric and magnetic vector fields before. Any observer will thus find six functions describing the electromagnetic field.
But different observers will see different matrices. Thus they will see different electric and magnetic fields. However, the matrices that two observers see are related to each other in terms of how the observers are moving relative to each other. It’s like if you and I are looking at an eye chart, but I’m standing on my head. The letters look rotated around by 180 degrees to me – what you call “left” I call “right”, and similarly for “up” and “down”. But you can predict exactly what I’ll see once you know how our viewpoints differ, because there really is some objective thing out there we’re both observing. It’s just how we describe that one thing that differs.
So here there’s one Faraday field, and different observers measure different collections of six independent components. The electroweak unification is similar, except instead of considering transformations like rotating our perspective in space, or moving at a steady pace, we consider some other sort of transformation. It’s not a physical, macroscopic variable we’re looking at here, so I can’t point to some sort of rotation and say “that’s it”. All I can do is say that the math works out the same as for rotations. Except instead of rotating up, down, forward, backward, left, and right among each other, it rotates the photon and the three weakons among each other.
But why do you need high energy for electromagnatism and the weak force to be unified or in other words, why are they not unified with the particles just sitting around?
Though the thread is asking how E & M can be the same thing, I want to take this opportunity to ask in what way they are different. What is properly called “electric force” and what is properly called “magnetic force”?
-FrL-
Electric force is the Coulomb force a static charge (or, more generally, an electric field, such as for instance the one created by a static charge) exerts on another; magnetic force, thus, is the force a magnetic field exerts on a moving charge or a magnetic dipole.
Both are equivalent to the so-called Lorentz force, which is the same as the Coulomb force in the absence of a magnetic field, and conversely a purely magnetic force in the absence of an electric field.
Of course, you don’t really catch either on their own in nature – the Coulomb force is only correct in a purely static system; once it takes effect, whatever charge you have will start moving, which means you’ll have to deal with a magnetic field as well, and conversely, the assumption of a purely magnetic field is only correct in a magnetostatic case, where you in principle deal with ‘stationary currents’ (flows of charge).
The fancy answer is “spontaneous symmetry breaking”. But here’s a rough sketch.
Imagine you’ve got a spherical bowl. You can rotate it, and it looks the same. That’s symmetry. Now if you drop a marble in it settles at the bottom. It’s still symmetric. This corresponds to the “vacuum state”. If you jiggle the ball (and forget about friction) it’ll move around but never go higher than a certain level. This corresponds to a particle moving around in a “potential well”, where the bowl describes the potential energy curve. The more energy the ball has, the higher it can move up the bowl. Still, the whole situation is symmetric, because any realistic path, when rotated, is still a realistic path.
Now add a bump in the bottom of the bowl, like the punt in a wine bottle. If you place the ball exactly at the top of the bump, it’ll stay there, but that’s an unstable equilibrium. The slightest nudge and it’ll fall down in some random direction. Once it settles at the bottom, the situation is no longer symmetric. The symmetry has been “spontaneously broken”. Now jiggling the ball a little we still get little vibrations, and the situation is still not symmetric. But if you jiggle it a lot, then the ball can manage to go up above the level of the bump, and at this point there is enough energy for the whole picture to be symmetric again. Essentially, the bump is down below us, so we can move up and over it without trouble, and so it doesn’t break our symmetry.
See my later explanation (at 02:37) of the Faraday field. You’ve got a matrix instead of a vector, but there are only six independent components that correspond clearly to the electric and magnetic fields.
If I made a bunch of bar magnets shaped just right so they could be stacked to form a hollow sphere, with the north poles on the inside and the south poles on the outside, how would the lines of force emanating from the inside surface get to the outside surface? The bars are tapered and shaped so that there are no spaces between them. It is a completely solid spherical shell.
You’re assuming you can form them into a solid shell like that. They’ll push each other apart.
Suppose there was a world with magnetic monopoles but no electric monopoles. Would it be like our workd. Is it like matter vs antimatter?
But couldn’t you then say there was a magnetic photon field and an electric photon field, and the two kinds of photons get mixed together differently depending on how you are moving?