Q:Currently taking electromagnetism, it makes my brain hurt. I'm not physics minded at all but I think physics is really cool. Do you have recommendations on specific sites or textbooks that really lay out electromagnetism well? I watch some khanacademy but I don't know much else. Thanks!
My first recommendation, for all levels of physics, is hyperphysics. There you’ll find lots of small explanations and examples of physics concepts. Wikipedia is also a great place to quickly gloss over topics, and always check the bottom of the page for their citations.
khanacademy, while good, I find to be extremely boring. Still nice as an additional source.
As far as textbooks, Griffiths Intro to Electrodynamics is as good as you can get for entry-level courses. I’m assuming that you’re taking a calculus-based course, because you’ll need that for Griffiths, or nearly any E&M textbook.
I hope that was helpful. Feel free to ask specific questions!
Well crap, people are showing interest. I guess I better start writing more posts.
WARNING: MATH AHEAD
Have you ever seen a magnetic charge? No? Well if you do, let some physicists know. There’s a Nobel Prize coming your way.
We’re all pretty familiar with the idea of electric charges - protons are positively charged, electrons are negative, and things like neutrons and neutrinos have zero charge. These charges are sources for electric fields. Let’s say you’re familiar with three-dimensional calculus. Draw a surface around a charge density (spheres are usually pretty easy to work with, so use that) and integrate the field over the surface. Since you have a source, the flux will be nonzero.
The problem with magnetic charges is that we have yet to find any single particle, or system for that matter, that can be enclosed by a surface so that the flux is nonzero. So, as far as many people are concerned, magnetic charges don’t exist.
One mistake many physics teachers make in the wake of this information is that they say magnetic charges don’t exist, but they certainly can! Maxwell’s equations, four fundamental equations of the universe, are usually written as follows for the microscopic world:
As per the mathy stuff earlier, the divergence of the electric field is equal to the charge density causing the field. Since there’s no magnetic charges, the divergence of the magnetic field is written as zero. But these equations still hold if we throw in factors that represent magnetic charge and magnetic “current density”*:
Setting both these new values to zero recovers the old form of Maxwell’s equations - we’ve really changed nothing. Monopoles can indeed exist, and absolutely nothing about our current understanding of classical electromagnetism would change at all.
Why all the bother about this, you may ask? No one has detected a magnetic charge, so why care? Paul Dirac, one of the forerunners of quantum mechanics and quantum electrodynamics, attempted to work out a theory of relativistic quantum electromagnetism - a fancy way of saying tiny charged particles that move really damn fast. From his work, he found that a magnetic charge naturally arises when considering Maxwell’s equations in quantum mechanics. He further theorized that if a magnetic monopole exists somewhere in the universe, then all electric charges must be quantized. As of the present day, all electric charges are quantized, which points to a magnetic charge existing somewhere.
So keep an eye out for magnetic charges. We have good reason to think there’s at least one somewhere in the universe, so throw some magnets at distant galaxies and see if they blow up or something. Or ask an expert in quantum electrodynamics what to look for. They probably know what’s up.
*I’ve used the convention where magnetic charge has units of webers. Some people define magnetic charge as having units of ampere-meters, but they’re heathens and probably don’t like bacon. Let’s be honest, who doesn’t like bacon? Exactly.
Common Misconceptions: The Big Bang
The Idea: The Big Bang was some sort of explosion that released matter or something, that apparently came from nowhere and happened at the beginning of time.
How it works: This is probably one of the most difficult-to-grasp subjects in physics, mostly because a fairly enormous background in mathematics and physics is required. Because of this, I will disregard that barrier to entry because I break the rules, damnit.
First, we need to shatter a big part of this idea: the Big Bang was not an explosion. The Big Bang itself was a rapid expansion of space itself. Think of it like this - it’s as if you were holding a ruler, measuring a pencil, when very quickly the ruler got really long. “Well, crap,” you might say, “how can I measure this pencil?” Fear not, young physicist, because the pencil expanded too. So did you. The separation between the fundamental particles of the universe increased. (I’ll get to the math reasons for this later.)
You may be thinking, ”But super-smart physics man, isn’t that just semantics? Does it matter if we call it an explosion or an expansion?” In fact, it does. An explosion implies that there was something to explode into! Currently, we don’t know anything about what our universe is “in”, what surrounds it. All we know for sure is the spacetime inside it, and it got bigger. It’s expanding right now! Galaxies move away from each other constantly, but we can observe them all moving away from us. Are we at the center of the universe? No, because we’re also getting further from all other galaxies! We can only move away because the thing we move in, space, is getting “longer”.
“Okay, smart guy,” you may think to yourself, “what about all that matter? The universe is huge and the stuff before the Big Bang is supposed to be small!” You would have a good point, except for a lot of not-so-good holes in your point! One thing to consider is the size of fundamental particles relative to the building blocks of the current universe, atoms. Atoms themselves are approximately 99.99999999% empty space, and that’s even considering the nucleons as three-dimensional objects (since leptons, such as electrons and muons, are usually considered points). Packing all the mass in the universe close together, at high enough temperature to make forces comparatively weak, is not unfathomable.
The math: The Friedmann-Lemaître-Robertson-Walker (known as FLRW or FRW) model of the universe has a very simple metric, given by the following relation (with units where the speed of light and Newton’s gravitational constant are equal to unity):
where dΣ is the spacial elements in any coordinate system. Generally, reduced-circumference polar coordinates or hyperspherical coordinates are used.
This is analogous to the Pythagorean theorem, as this simply measures the interval between two points. (I’ll explain why the time element is negative in a further post, but it is necessary to either have the time component or all of the space components negated.) The function a(t) is a time-dependent scale factor that changes the “spacing” of the spacial components of this interval. Depending on its derivatives, space can expand or contract. Current measurements have calculated the ratio of the time derivative of a(t) to a(t) itself to be approximately (72 km/s)/Mpc - strange units, to be sure, but it means that for every megaparsec the universe expands, its expansion speed increases by 72 km/s. This value is known as the Hubble parameter.
As long as the second time derivative of a(t) is positive, the universe is expanding. There’s many constraints on how this scale factor can evolve, depending on what energies dominate the universe - matter, radiation, and vacuum energy all have distinct relations to the density of the universe itself, with the vacuum energy solution remaining constant throughout all time and matter/radiation decreasing over time. This means, eventually, vacuum energy will dominate and the universe will expand forever.
So there you have it. The Big Bang was an expansion of spacetime itself, all the currently-existing matter (and energy!) was in that Big Bang, and the universe is expanding.
We’re pretty sure about this one. Next time we’ll explore something science is a little less sure about: magnetic charge.