If you took introductory physics, you learned about the “fundamental forces.” It goes something like this: All interactions are the result of one or more of five basic forces: strong nuclear, weak nuclear, gravity, electric, and magnetic. “Doing physics,” then, means identifying the forces in play.
There’s a problem, though, which might not have been mentioned: The forces you observe depend on your vantage point—your “frame of reference.” Look out the window. Trees, houses, lawns—they’re all stationary, right? But look at that same spot from space and it’s moving a thousand miles an hour. It looked still to you before because you were moving with it.
We have this same problem with electric and magnetic fields. Depending on your reference frame, what appears to be a magnetic force from one spot appears to be an electric force from another.
Is your brain melting yet? Just wait—it gets even weirder. To understand what’s going on here, let’s first look at electric and magnetic forces in isolation.
The Electric Force
See all that stuff around you? Everything. It’s all made of just three things: protons, electrons, and neutrons. That’s kind of wild when you think about it. Two of these fundamental particles have an electric charge: the negatively charged electron and the positive proton.
If an object has more electrons than protons, it will have a net negative charge. So, that sock in the dryer that clings to everything? It picked up extra electrons by rubbing against other clothes. If an object loses electrons it has a positive charge.
We can calculate the electrostatic force between two charged objects with Coulomb’s law. This says that the force between them depends on the product of their charges and how far apart they are. To illustrate, I built this high-tech contraption below, which has two little foam blocks hanging on strings. I gave them both a negative charge, which means they’ll repel each other. Check it out:
See? Because of the repulsion force, they aren’t hanging straight down. If they were oppositely charged, they would attract and stick together. That’s the electric force.
The Magnetic Force
OK, so objects with charge experience an electric force. But if the charged objects are moving, they can also create and experience a magnetic force. One way to get moving charges is to run electric current through a wire. (This is literally a stream of electrons.) This will create a magnetic field, and other wires with electric current will experience a magnetic force.
Imagine you have two parallel wires carrying electric current in the same direction. Since wire 1 has moving charges, it creates a magnetic field. Wire 2 is in the presence of this magnetic field, so it experiences a force that pulls it toward wire 1. The reverse is also true, which means that wire 1 is attracted to wire 2. If one wire has a current in the opposite direction, the two wires repel.
We can be really glad about magnetic forces. This is what makes electric motors work, powering everything from electric cars to dishwashers to air conditioners. It’s not just weird repelling wires.
But This Is Weird
To review: Charges experience an electric force, and moving charges experience a magnetic force. We can break this down by saying that electric charges create an electric field (E), and other charges in an electric field experience a force. At the same time, a moving charge makes a magnetic field (B), and other moving charges experience a force in that field.
So let’s say we have a moving charge (with a velocity v and charge q) in a region with both an electric and magnetic field. In that case, the total force on the charge can be calculated with the Lorentz force equation. It looks like this:
Let’s see how this plays out in a couple of situations. First, suppose we have two electrons all by themselves. If these electrons begin at rest and you release them, there will be an electric force pushing them apart. If you could see electrons, here’s what that might look like:
Now say we have another pair of electrons starting the same distance apart. However, these are moving with some velocity v to the right. The electric force also pushes them apart. But since they’re moving, they will produce an attractive magnetic force that partly offsets the electric force. As you can see, in the same amount of time they aren’t as far apart as the first pair. Check it out:
So far so good. Or IS IT? Let’s say the initially stationary (purple) electrons repel and are 1 meter apart in 1 second. (I’m just making up nice round numbers.) For the moving (yellow) electrons, it takes a bit longer to get 1 meter apart—maybe 1.1 seconds. This is actually a problem.
Imagine you’re in a tiny car traveling beside these two moving electrons. From this reference frame, the two electrons are at rest. But since they’re at rest, there is no magnetic force, only an electric force pushing them apart. So if we record the time it takes to get to 1 meter, would it be 1 second (like the stationary electrons) or 1.1 seconds like the moving ones? See the problem?
Albert’s Answer
The answer to this situation uses Einstein’s theory of special relativity. The idea is that the velocity of an object depends on the motion of the observer—“it’s all relative.” If you measure the speed of a train from a moving car you get a different value than a pedestrian would see. Yeah, we get it. It’s fine. However, Einstein also said the time at which events occur and their duration is also relative.
That … doesn’t feel so fine. Let’s go back to the repelling electrons. It turns out that the stationary and moving observers agree that it takes 1 second for their charges to move apart by 1 meter. But from the stationary observer’s perspective, time would seem to slow down for the moving frame.
This is called time dilation. You don’t notice it in the world because the effect is super tiny for normal speeds, but as a moving frame gets closer to the speed of light you get more and more time dilation.
So time dilation reconciles the observations from the two reference frames. But the problem isn’t solved, because it means two observers are seeing two different fundamental forces. Looking at the yellow electrons above, the stationary observer sees a magnetic force in action, while the moving observer sees only an electric force.
Really, this was a big deal in physics. So how did they fix it? By saying that the electric and magnetic forces are essentially the same thing—called the “electromagnetic force.” We now consider this just one type of interaction between objects that have the property of electrical charge.
This is how science goes: You build a model and ride it until it breaks. Then you build a new model. The failure is actually when you learn. So it’s no longer the five fundamental forces—now we have the fundamental-er four!
