Physics Highlight of Rainbow Rocks · 10:53pm Nov 22nd, 2014
Apologies for not posting anything last week. I have been busy. I was in the US last week, visiting Fermilab, which was really cool, but I then had a ton of work to catch up on when I got home.
And I had to watch my new Rainbow Rocks DVD.
My verdict: It's awesome. The post-credits ending makes it 200% cooler. I particularly loved the reference to Maxwell's equations.
Did you miss it? It's here:
Look closely, remove the scraps of paper and that reads:
For the benefit of everyone who was napping while Cheerilee was explaining vector calculus, here is a short tutorial. (Yes this entire blog post is all about a small detail in a single frame of a full length movie, and why it’s so awesome).
These equations fix the link between electricity and magnetism. They were put together by the Scottish scientist James Clark Maxwell in the 1860s, and show that light is an electromagnetic wave. The way they’re written here is a bit archaic, using CGS units, but it seems that human scientist Twilight takes a somewhat retro approach to research. She still uses a chart recorder!
First, what do all these symbols mean? Well E is the electric field, and B is the magnetic field. These are both vectors, which means we can measure how big they are (the closer you are to a magnet, the bigger the magnetic field), but also the direction in which they point (as indicated by a compass needle, following a line between the two poles). The upside down triangle is about how the fields vary across space, from one point to another.
The blue equation:
basically means that in any bit of space, the number of magnetic field lines going in, is the same as the number going out. Magnetic fields follow closed loops, from north pole to the south pole, and then through the magnet back to north.
[Actually there are reasons to believe that magnetic monopoles do exist, but no one has ever seen one. Well, probably not. But that's another story.]
Unlike magnetic poles, electrical charge can be isolated. So the red equation:
Relates the divergence of the electric field to the amount of charge lying around. A cloud can build up a large electric charge, giving an electric field between itself and the ground, until the field gets so high that we get electrical discharge—zap—lightning!
Moving on:
This one’s my favourite. This relates the way the electric field curls around a line, to the rate at which the magnetic field changes in that direction. Twang a steel guitar string next to a magnet, and the magnetic field jumps up and down, which makes an electric field gradient, and a voltage which you feed into your amp.
Finally, the yellow equation
This is the reverse of the green one, as it relates a changing electric field to the curl of the magnetic field, with an extra term j for the electric current. This mean if you feed an electric current into a coil, it makes a magnetic field. And when you connect your amp to a coil with a permanent magnet, it will move with the music, and you can feel the beat.
But the really cool thing is when we bring the equations together. A changing magnetic field induces an electric field, and a changing electric field gives a magnetic field, making an electric field… The net effect is a self-sustaining wave – an oscillation in the electric and magnetic field which can ripple across space as LIGHT!
For any math/physics nerds who want the full derivation:
It can’t, however, explain a rainbow double helix, or give you pony ears, wings and a tail. So Twilight correctly concludes that there's something strange going on at that school.
Oh wow, that is really cool.
I don't have the science or math to fully follow where my thinking is leading, but is there anything we could conclude about how equestrian magic works based on that little bit of math?
As a Physics student who has had to learn to do that derivation in my sleep, I have simply two points to make:
Then again, everyone says it's pretty good, so I guess I should just stop worrying about it and get my hands on the DVD.
1) I'm tired and sleepy and I genuinely spent about a minute and a half wondering where ε0 and μ0 were as I skimmed through this post, before realising that, as you pointed out, they've used CGS units. Wow, I'm slow when I'm tired. I didn't even notice you'd pointed it out at first!
2) Now I actually have to watch this film. Like, soon. I'd been trying to put it off and everything, too
Bonus Point 3) I can't believe it took the derviation of the EM wave equations in a vacuum for me to get over my fear of commenting on other people's stuff, even if it is just a blog post.
This is really cool. I'm learning the connection between electricity and magnetism on FimFic.
Man... This is one of about 10⁶ reasons I love this show!
Man... I remember my visit to Fermilab. It really is a very beautiful place! It's not just the science there, but the nature too! Not too many labs can claim to have a herd of buffalo living on site... Which is ALWAYS a good reason to bring Chief Thunderhooves into the discussion! I don't think they've EqGed him though.
I should mention that the end of Rainbow Rocks literally made me squee! Lab coat Twily rocks!
2610612 Magnets... Bucking magnets!
Also, the lack of arrow over the ∂B/∂t term is really upsetting me, now that I've noticed it. I mean, come on, it's a vector. It has to be a vector. Why can't they just draw an arrow and make it clear it's a vector?
2610612
The nature of Equestrian magic remains a mystery. All we can say is it seems to involve a lot of rainbows. We can hope for some more clues in the next film.
2610668
I would never usually use CGS units, especially for electromagnetism - it leads to so much confusion.
Thanks for the comment.
2610677
EqG Thunderhooves - someone should definitely write that story.
2610711 He could be a Native American coworker of EqG world Twilight, living in the on site village on the EqG version of Fermilab's grounds. She could rely on him as a second set of eyes for her work, when she knows she's just missing something, and would do the same for him as well.
Hey, Thunder... You have GOT to see these readings! I can't make heads or tails out of them!
Fortunately, Twilight is TAing.
I enjoyed my physics classes more than any other. Yet I simply don't have the brains for it. Not that economists are slow, but....
I intend to watch Rainbow Rocks over the upcoming weekend. It will be my first serious adventure into the pony world since the very first two episodes of the show I watched perhaps a year ago. Do I need to have seen the previous film first? And is there any pony knowledge it draws on that I might lack?
Yes, but ¿what is this “π” strange symbol? ¿Where is “τ (tau)”?
Last week, I had a NightMare about Dave “AntiScience ProGenocide” Polsky writing the next movie.
2611187
That might be sensible, but is not essential. With a bit of imagination you can figure out the setting.
2611366
Write it out in SI units and you don't need to worry about that. But Twilight is evidently a traditionalist.
I honestly hadn't noticed this until now, but it's always great when they slip in actual equations. I loved it when they did it with relativistic time dilation in "It's About Time," and I loved it here.
I also love how Twilight wrote Maxwell's equations in a rainbow of colors, as if that would make them explain the impossible phenomena.
Your blog posts never fail to fascinate and educate. Bravo on spotting such a small reference and thank you for teaching the rest of us. You manage to make things really approachable. Pity I'm not still in touch with tutor friends as I'm sure they'd love these blogs.
2613770 I'm a tutor and a physicist, and I do find these blogs awesome!
I've always found this really funny: I continuously struggle to fully grasp electromagnetism.
But "if a spacetime is foliable then no closed timelike-curves exist within it," and "gravitational waves are affected by gravitation" make intuitive sense to me. I find curved spacetime easier to envision than electromagnetism for some reason. Maybe it's just because of years of finding it more fascinating