# Special Relativity and Magnetism

In 1830 Hans Christian Oersted demonstrated that when a current passes through a wire, there is a magnetic field around that wire. The reason is an everyday example of the effects of special relativity. Here is a video that explains the relationship between electricity and magnetism:

How Special Relativity Makes Magnets Work

This is an excellent video. However, if you think about it a bit, it leaves a burning question. At 1:57, Derek says that when the cat moves with the electrons, she sees the positive charges moving in the opposite direction. So far, so good. Seeing the positive charges moving, they are length-contracted from the cat's frame of reference due to special relativity. Therefore, the positive charges appear more densely packed than the electrons, and the positively-charged cat is repelled from the wire. However, go back to 1:29, and Derek shows the electrons moving, but they are not length contracted, and there is no net charge. Why are the moving electrons not length contracted? The answer is that the moving electrons are length contracted, and there should be a net charge. However, Derek is apparently blowing this off to avoid explaining a tricky concept, but one you should understand.

To consider this, let's imagine playing a round of golf. At a particular green, you putt out and move on. Here's a picture of the green.

Golf green on day 1.

The next day you play another round. When you get to that same green, you find that the hole has been moved to another part of the green (as is commonly done). You putt out to the relocated hole and move on thinking nothing of it. Here's the green on that day.

Golf green on day 2.

However, if you think about it, what really happened? Did the hole really move? Of course not. The groundskeeper cut a new hole and moved the grass and dirt from the new hole to the location of the old hole. The hole didn't move. The dirt and grass did. But it sure looks like the hole moved. And it appeared to move in the opposite direction as the grass and dirt.

Each positive charge in Derek's wire is a place where there should be an electron but is vacant. Physicists call these vacant slots holes. As the electrons move, they briefly occupy these holes and then move on. This looks like the groundskeeper moving the plug of grass and dirt from one location to the other. When the electrons move in one direction, the positive charges appear to move in the opposite direction. So, when you or the positively-charged cat are stationary, and the electrons are moving, you see the electrons length-contracted, and they appear to be closer together than when they are not moving. However, you also see the positive charges moving in the opposite direction, appearing to be equally length contracted. You and the cat see no net charge on the wire.

When the cat moves with the electrons, the cat sees the electrons as unmoving and, therefore, not length contracted. However, the positive charges appear to be moving twice as fast as before, so they are double-length-contracted and appear more concentrated. The positively-charged cat then sees the net positive charge and is repelled by the wire.

I explain this in the following video. However, I take much longer to explain electricity, magnetism, and special relativity than Derek. I'm talking to engineering and technology students who need to understand this more thoroughly than the average person. I don't have the luxury of ignoring the movement of the positive charges.

Electricity, Magnetism and Special Relativity

Errata for the above video:

04:56 Faraday and Henry had galvanometers and didn't use a spark gap to detect induction.
24:19 Galilean relativity. not general relativity

 Holes in metals The word hole is used in physics, electronics, and chemistry to mean a place in an atom or crystal structure where an electron could exist but doesn't. For example, one type of hole exists in p-type semiconductors. This is where an impurity atom in a crystal has too few electrons to fill the crystal matrix (see Semiconductors in Solid State Devices). Another type of hole exists when an electron is removed from its place in a particular atom. This type of hole may form when an electron disassociates from its atom in a metallic bond. For example, in a mass of copper, the atoms form metallic bonds. These bonds release one electron from each copper atom, leaving a hole in the electron cloud that surrounds the atom. This results in a positive ion in the matrix where each copper atom resides. Many say holes don't exist in metals because the structure of a hole in a p-type semiconductor does not occur in metals. Regardless of the mechanism that forms holes in p-type semiconductors, scientists use the term "hole" to describe the entity left behind when an electron is removed from an atom. The many web pages that say metals do not have holes notwithstanding, scientific literature referring to holes in metals is common as in the following article — Spin transport of electrons and holes in a metal and in a semiconductor.