Electromagnetic and Gravitational Fields

May my electromag teachers forgive me, but I put forth the butchered version of their wonderful classes for those who need a brushing up on electric and magnetic fields. If you want to skip past this part, go ahead.

Electricity and magnetism 101

I'm sure you're familiar with electricity---little electrons zipping here and there through metal wires---and charges---which arise due to the distribution of differently charged particles in something. There are two types or alignments of charge: positive and negative. Magnetism is that thing that happens with magnets and compasses and the earth. There are two alignments of magnetism: north and south poles. The cool thing is that the two things are linked. Say you've got this wire, and there's a current going through it, which means there are lots of electrons streaming through it in a certain direction. That wire also generates a magnetic field which looks like a collection of rings surrounding the wire at a certain distance. Makes household electrical wiring a pain, but it's still pretty neat.

What is the magnetic field, anyway? That's tricky. The field, be it electric or magnetic, is this invisible thing that happens when you have electrons moving from one place to another. There are equations that describe the field, and laws the field obeys. Should you put certain particles (say, electrons) in the field, you could use those equations to predict what those electrons would do. The earth itself has a magnetic field; so does the sun. They're physically large by our standards. The earth's magnetic field streams out from one pole, curves across the length of the planet in a high arc that looks very much like a curved handle, and streams back into the other pole. The earth's magnetic field is actually kinda weak compared to the fields that we can generate.

Oh, I forgot to tell you what an electric field is, didn't I? An electric field is pretty much the same idea as a magnetic one, this invisible thing that does stuff to electrons. There is a difference in how ya generate one, though. To make an electric field, you have to take an object---anything---and pump it full of electrons (or rip away lots of electrons). Now that object is charged and it's radiating this electric field. Should you put something into this field, there are equations and laws that you could use to predict what would happen.

Congratulations, you've suffered through my crash course on electromagnetic fields. Oh, since there are both electric fields and magnetic fields, why do I keep calling 'em electromagnetic fields. It's to honor the fact that we know that one thing can generate the other.

The similarity I'm trying to make is that both electromagnetism and gravity have a stationary form of their effects in a field. The causes are completely different, really. Electromag fields are caused by various arrangements of atoms and electrons, and gravity is caused by the existence of mass or energy in one place. At second glance they don't really seem too similar. Still, they are both this invisible thing called a field that we can predict with equations and laws. Heh, well, mostly predict---the extremes are usually exceptions, but we don't deal with extreme charges or gravity on a daily basis.

Electromagnetic and Gravitational Waves

Okay, so there is a similarity in that they both have stationary fields. What about the really neat stuff, the travelling waves? How are they similar? Well, what's an electromagnetic wave do after all? (Yes, you can skip down past this part, too) See, it took me a while to figure this one out. I've always heard people say that a light ray, and electromagnetic wave, is an oscillating electric field perpendicular to an oscillating magnetic field, but that didn't make sense. How could they be perpendicular? This ties back into the electric and magnetic fields part. When I said that an electric current generated a magnetic field, I was sneaky and didn't tell you what that field really looked like.

Among engineers and physicists there is this love of something called the 'right hand rule.' There's one for every situation; meaning there are skads of different right hand rules. This particular rule tells you how to figure out which way the magnetic field is going, and, thus, what it looks like (the two being one and the same, really). Say you've got this current flowing through a wire, happy as can be. Take your right hand and point your thumb in the direction of the current. Now curl your fingers around, slightly. The direction your fingers are curling in---that's the magnetic field generated by the current in the wire. You notice something? That magnetic field is perpendicular to the current. Aha! Now you know what I mean by perpendicular. Back to the light ray.

Now, say you have this light ray. What really happens is that it generates an electric field in one direction (let's say the x-axis of a traditional coordinate plane), which generates a magnetic field perpendicular to that electric field, which in this case would be along the y-axis of that coordinate plane. Confusing, I know. Perhaps it is simpler to say that the wave has an electric component and a magnetic component. The eletric component pushes electrons in one direction, while the magnetic component pushes the electrons in another direction that is perpendicular to the direction the electric component is pushing them. Both of these components are in synch: when the electric component is at its strongest, so is the magnetic component.

Although light rays travel in all sorts of directions and with the electric component point every which way, there are basically two orientations of electromag rays. This is very tricky, and I'm not quite sure if I've got it right, so bear with me. Say there is this light ray that happens to be oriented (for my convenience) with its electric component pointing straight up. It'll make electrons bounce around in that direction. Now, the magnetic field is pointing to the right. That is one orientation of an electromag ray. The other is in effect inverting everything so that where something electric was happening, now there is none, and where there was nothing doing, now there is this electric field pushing around electrons. In a more visual description, just take the electric component arrow that used to be pointing up and turn it 90° to the right or the left. That is the second orientation. Told you it was tricky.

One final note: these fields the ray generates are detectable in the plane that is perpendicular to the direction in which the wave travels. Simply put, stick a fork upright in a sheet of jello---the fork represents the direction of the wave, the jello represents the plane in which the electric and magnetic components are pushing the electrons around.

Right, so what does that have to do with gravitational waves? They behave in the same perpendicular way that light rays do, except they do something slightly different. The effects of the wave are still detectable in the perpendicular plane to the direction of the wave---the fork in the sheet of jello is still the direction in which the wave travels and the jello sheet is still the plane of oscillation. How the wave actually oscillates is much trickier. I admit, earlier, I gave a run through of what the wave does, but I didn't explain it. Now is the time for the tricky details.

Just like the electromag wave has two directions of oscillation (the electric and the perpendicular magnetic), so does the gravitational wave. However, instead of being 90° apart (perpendicular), they are 45° apart---which is related to the type of particle that carries the wave, but that's for further down. Okay, that's nice, but what happens with the oscillations?! I called it earlier 'left and right and up and down.' That's...well, it's not quite accurate. Let's take 'em one at a time.

Left and right: straight forward, this one. When it strikes an object, this wave initially compresses it horizontally and stretches it vertically. Then it reverses the treatment and stretches horizontally and compresses vertically. It alternately stretches and compresses in perpendicular directions. Nothing happens along the two diagonal directions. This is traditionally called the plus polarization.

Up and down: this is the tricky one. I really lied to you by saying that it's up and down but it's easier to say quickly. When this one strikes an object, it does the same alternating compression-perpendicular-to-expansion just like the other one, but the direction of compressing and stretching is along diagonal lines 45° off axis. Huh?? Take the xy axis and tilt it 45°---this oscillation affects stuff along the new x and y axes and changes nothing along the old x and y axes. If I were to be accurate each time I described the wave, I'd have to say 'diagonal with a negative slope and diagonal with a positive slope' every single time---which is really confusing. Food for thought: electromag waves oscillate with electromag fields; so, if the analogy to a gravitational wave held, that would mean that the gravitational wave oscillates with fields of stronger and weaker gravity. Hmmm. This diagonal axis oscillation is traditionally called the cross polarization.

So, you see, the two waves are similar in that they both affect stuff perpendicular to the direction in which the wave is going. They are also similar in that the electric and magnetic fields are perpendicular to one another, just as the compression and expansion are also perpendicular to one another.

Electromagnetic and Gravitational Particles

I am cheating on this section because I'm only going to introduce the fundamental particle of the gravitational wave. I need to take a few more classes before I can explain any more.

What particle is associated with the gravitational wave? The graviton. It has spin 2 (for what that's worth since I cannot do the explanation of spin justice). It has no mass and can therefore travel at the speed of light. This is important---it means that gravitational waves propagate at the speed of light. Gravitons can be measured at a range of frequencies that correspond to the source of the wave---ah, but that's for the section on sources!

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