On Losing Your Marbles

There is, perhaps, nothing scarier to a physicist or mathematician than losing the ability to perceive reality objectively. We rely critically on our abilities to discern when something makes logical sense or not, and experiencing a reality that is individual to us and not shared is a horribly isolating thought. I know this from experience; having spent a significant amount of my childhood around older family members suffering from varied forms of dementia, I am perennially sobered by the statistical likelihood that I will, like them, retreat into a private screening room of the world, a personal universe where what I see and do only makes sense to myself and appears as irrational nonsense to everyone else. However, the universe has decided to play a mean prank on those of us who fear lack of objectivity, and I’ll try to show you in this entry just how bad this goof is (and how a very common physical phenomena is a result of it).

Imagine a rocket, traveling to Mars very close to the speed of light, zooming past you over the horizon. Strangely enough, you see that the rocket has a very strange asymmetrical shape as it flies by, and this doesn’t make sense to you because you’ve been on this rocket to Mars before and saw it as perfectly rocket-shaped back then. You then try to look at it when it docks back on Earth and there it is, stationed in the hangar, looking exactly the same as it was when you were on it; normal and symmetrical. “That’s strange” you may say, and dismiss your previous observation as some trick of your mind; until you see this strange lopsided rocket over the horizon again on its next trip! Having been prepared, you take a picture, and show it to the permanent inhabitants of the rocket as proof. They will say without hesitation that they have never seen this rocket change shape; and to prove it to you, present on-board camera footage that shows the rocket has never altered its form! They would then probably accuse you of doctoring your photograph, quietly assess you as a lunatic, and send you off amidst scattered chuckles.

The root of the problem here is that the universe will alter your perspective of things that are moving quickly relative to you. In fact, since all the universe cares about is relative speed, the people on the rocket would have seen you in a similarly strange asymmetric shape too if they had windows!

Rockets 2

These “hallucinations” are not just visual either; if the rocket had an electrical charge, you would detect an electric field that’s compressed in the direction of motion. This is strange because someone on the rocket would also get a completely different measurement of the electric field, and would call you insane and your equipment defective just like in the example above. The only difference between a “normal” hallucination and this specific type of hallucination is that, since they affect our equipment as well, we can document them consistently, make predictions about them, and subsequently generate a set of physical laws governing this movement-induced psychosis called special relativity.*

*It is an interesting and unfortunate historical coincidence that Einstein, who created special relativity, had a son who suffered from schizophrenia.

Getting to the meat of this entry, I’m going to give you a slightly deeper look at how special relativity gunks up our understanding of the universe. Picture a positively charged particle next to a very long wire with an equally distributed amount of positive and negative charges. Since the charges in the wire are equally distributed, the net charge of the wire is zero, and the single particle doesn’t feel any push or pull towards it.

Current 4

Now consider what happens from the particle’s point of view if I make all the positive charges, both itself and the charges in the wire, move to the right at the same speed. The positive particles don’t change since they don’t move relative to the particle; but the negative ones appear as if they’re moving to the left, and become compressed horizontally like the electric field from the rocket. What’s astounding about this is that the deformation causes the negative charges to be more densely packed than the positives from the particle’s point of view, and so the particle feels a wire with a slightly negative net charge! And, since opposite charges attract in electricity, the particle would also move toward the wire as it moves to the right.

Current 3

Now let’s see what happens if I try to move the individual charge and the positive charges in the wire in opposite directions. The negative charges would still appear deformed like in the example above, but the positive particles in the wire will be even more deformed/tightly packed because they’re traveling twice as fast to the left as their negative counterparts! Consequently, the particle feels a net positive charge on the wire, and would travel away from the wire as it moves forward.

Current 5

Now, these are all things that only the moving particle is perceiving. If we were sitting down in a lab and accelerated the particle while a current was running through the wire, we wouldn’t feel the wire suddenly gain or lose a net charge; we’d only see the particle moving forward and then somehow start drifting towards/away from the wire for no reason! From our point of view, our particle is hallucinating the existence of some net charge in the wire, and is reacting as the laws of electricity dictate it should in that situation. Describing how special relativity warps the perception of charges directly is a little complex; luckily for us, we can avoid this by interpreting these strange behaviors in charged particles as due to another physical phenomenon called magnetism.

Voilà! Now you know why currents running in the same directions attract, while currents running in opposite directions repel. You now also know why people say “electromagnetism” (other than it sounding cool), since the laws of magnetism are just the laws of electricity in a different frame of reference. Sadly, this doesn’t intuitively explain the most common source of magnetism to humans, which are the bar magnets you see everywhere; these don’t have an electric current, so how do they generate these magnetic effects? A simplified answer is that the electrons in the atoms of these magnets are all spinning around in a synchronized way; this is, for the purposes of external charges, equivalent to a very large electrical current running along the surface of the magnet, and this “current” is what triggers the magnetic effects.

I’ll finish off by answering a question I once had regarding how special relativity distorts the laws of physics; “If that happens to electricity, doesn’t some kind of magnetic analogue exist for gravity too?” And the answer is yes, there absolutely are effects in gravitational physics that pop up thanks to the movement of mass. The only reason we don’t really talk about them much is because 1) the laws of gravity already involve special relativity directly (hence our name for them) and 2) these effects are much weaker than their electromagnetic counterparts.

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