July 10th, 2014

We all know that special relativity has many odd implications that are, to say the least, counterintuitive. The way space gets squashed and time slows down in moving frames of reference is weird, weird, weird. But some implications have recently occurred to me that I have never seen discussed in any books.

Magnetism

One of the most stunning realizations of my undergraduate studies was that magnetic fields are a relativistic effect of electric fields. The basic logic is pretty simple. Imagine that there are two wires parallel to each other, with a current flowing in the same direction in both. The electrons are moving through each of the wires. Imagine yourself as one of the electrons. When you look at the other wire, you see other electrons just like you in the other wire, stationary in your frame of reference. But the protons in the other wire are, in your frame of reference, moving en masse — and that motion causes their space to contract: their meter stick is shorter than yours. Therefore, the protons in the other wire appear to be crowded together in a smaller space, which means that, when you look at the other wire, you see it as positively charged, and you are therefore attracted to it. This is a magnetic field.

This suggests that magnetic fields are not a fundamental force, but rather a derivative of electric fields. But if that were true, then how can we assign a magnetic spin to a fundamental particle? What’s moving? Worse, what about light? It’s an oscillating wave of electric and magnetic fields. But if magnetic fields are just a relativistic effect of electric fields, then where does the magnetic field in a photon come from?

Time, Entropy, and Time Dilation

We also know that relativistic motion creates discrepancies between time as measured in moving frames of reference. When an observer watches a clock in a frame of reference that is moving relative to him, he sees that clock moving more slowly. Indeed, the equations of relativity show space and time mixing together: time is not quite independent of space. But how does this comport with the relationship between time and entropy as specified by the Second Law of Thermodynamics? The relationship between time and entropy has a bit of a chicken-and-egg aspect: how can we be sure that the increase of entropy is driven by time rather than the other way around: the increase in entropy is what we use to measure the passage of time.