See? It's easy!

That was Vogel as he launched into a discussion (that we talked him into) of the relativistic consequences of magnetism. As he put it: Magnetism = Electricity + Relativitly. While my head did hurt at various points throughout the explanation, the concept of time dilation (why it happens) makes more sense to me now than it ever has. In the past it's always been "Well, since you're going so fast the distance seems to be shortening too quickly and the only 'logical' explanation is time dilation." I'm sorry, but that just doesn't cut it for me. However, this magnetism based one does:
Lets say theres a wire carrying a current and some charged particle that will experience a force in the presence of a magnetic and an electic field. Next you put something, lets say a crystal wine glass, nearby. Then you bring a charge of some sort nearby to the other charge. For the sake of argument, we shall suppose that this second charge was created spontaneously and was just 'there' suddenly. Now our first particle experiences a force due to the E field from the new particle. It accelerates away (because both charges are of the same sign, cause I want them to be) and smacks into the wine glass and shatters it. Oh No!! So the outcome of our activities is that the wine glass is broken because of the motion of our first particle. Now part of the theory of Relativity is that no matter what your frame of reference is (in the case I just described the frame was at rest relative to the wine glass and both charges) the outcome remains the same.
The magnetic field due to a moving charge is proportional to the charge times the cross-product (vector a cross vector b = |a|*|b|*sine(angle between them) in a direction perpendicular to both a and b) of the charge's velocity and the unit vector of the radius to the point we're observing all over the distance to that point. Alright, so the physically astute among you may ask "well, the velocity/speed relative to what?" Well, its relative to the observer (that's us)! So that means that if we are moving towards the setup as we watch what's happening, the charge(s) are moving, and thus creating a magnetic field, even though we didn't have one in the first example! Crazy huh?
Now we can't alter the outcome by altering out frame of reference (otherwise we'd create paradoxes in the space/time continuum, and nobody likes those) so no matter where we watch it from, the glass has to break, even though there are now additional forces on it since we're accelerating/moving relative to the charges. This means that if we're moving towards the setup at, say, .2c (2/10 the speed of light), then the particles are moving quite fast and thus the magnetic field is going to be relatively large. Now, it will reduce the net force on the mobile charge (the one that breaks the glass) because the E field is repelling and the M field is attractive. This means that the charge will accelerate at a reduced rate (F=ma, Newton's Second Law and whatnot) and the charge will 'take longer' to break the glass. Wacky, huh?
Now, a note: the E field is also affected by relativity meaning that the E field will always yeild a greater force than the M field, otherwise the particle would move backwards. I guess, theoretically, if you are moving at a v such that v>c, perhaps Mfield could be greater than Efield and the particle would move backwards, but since it requires an infinite amount of energy to accelerate anything with mass upto a velocity of c, that's not something we need to worry about.
Physics is phun! Alternately: Fizzix is fun!
So, right, that was probably the highlight of my day, learning about relativity and it making sense overall. Calc was alright. We're doing differential equations at the moment and while I sorta see why they're useful, I'm not really convinced based on what we've done. I mean, I know that physics/engineering is all about differential equations, I mean F=ma is one, but Brandon hasn't really explained them so much yet. I think partially it's because they're her area of expertise and she gets really excited about them, which is very cool, but she forgets, perhaps, that the rest of us haven't spent years working with them before. Hopefully it starts to make more sense.
Econ was uninspiring as per the usual. We have a test on Friday, and it should be easy, but still, I'm a bit nervous. I feel like I haven't really learned much. I should go to the review session tomorrow night after course center (if I go to that).
Lunch was fun. I ran into Ally and we lunched at Skibo before she had to run off to a test. It took me about 10 minutes but I finally got my e-mail notification on my PDA that I had a package (the thing insists of d/ling hundreds of folders when it checks my e-mail. It also refuses to get the body of the letters. It tells me I have x unread messages, who they're from and the subject and precisely when it was sent, but no body. And since it has to check 100's of folders, it takes forever. I gotta figure that out at some point.) Turns out the drill bits I ordered on ebay like 3 days ago arrived. So now we have a whole range of largish drill bits ( 7/16" all the way up to 7/8"). Goody. We can use them to drill speed holes in our mousetrap car chassis and drill out mounting points for the axle bearings.
I should have gone down to Career services right after MechE to talk about a resume I need to write to try and get a summer internship at somewhere other than Home Depot or Ace Hardware. However, I forgot, which means I shall need to make an appointment soon to go do that; cuz I've never written a resume before.
Anyway, after MechE I procrastinated for a while before buckling down and doing the remants of my Calc HW. After that I worked for a while on my Intro to Math Software HW. The first part of that was alright but the second half was obnoxious. He wanted us to derive Newton's law of gravitation through recursion analysis from a bunch of data he gave us on the planets in the solar system. However, parts of it were given as relative to the Earth (planetary orbital radii were given in AU for example) but the actual gravitational forces were given in terms of Newtons; therefore any meaningful numerical answer was meaningless. Since I knew what I should be getting, I worked backwards and eventually got a straight line that had a slope that, given real units, would have been G. I called it a day on that one and uploaded it to my AFS for printing tomorrow before class.
I then rushed off to the UC for dinner before M&I course center. However, 2/3 of the way there I realized I wasn't hungry and decided to settle for coffee at Skibo and dinner later. I ran into Doug, Grace and Hilda there and I made the executive descision not to go to course center. I hung out there for a while, till about 7:30 when I hit up the U for dinner.
I was feeling fairly melancholy, even while talking to people at Skibo and during dinner at the U. I think it was the weight of what I had to do/accomplish/pull off over the next...2 weeks lets call it. I have this econ test on Friday, physics test Monday (the one that makes people cry, I remind you), Load-in immediately following that till like 3 or 4 in the morning, then physics labs at 8:30 in the morning tuesday morning. Wedensday is the Calc test and Thursday is MechE design review and we open. Then we have another show Friday and two on Saturday followed by 6 hours of strike. And before we can open I have to finish getting all the sound stuff together for the show. I will be glad when the Double shot is over. Not that I don't love both shows, but it's just too much right now. Next year I may have toi stick to doing just one or two shows a year (the musicals, perhaps), at least assuming courseload doesn't somehow go down for next semester. We shall have to see.
Ok, after I got back I dove into the last calc problem that I couldn't get before (Hilda showed me how to do it, it was crazy: U substitution (a fairly convoluted one, at that) followed by partial fractions, all to find out it diverges anyway) and then plowed through the first 5/9 of my physics HW (that isn't due till next Wedensday). I feel pretty accomplished and my spirits brightened as I worked through the physics. I also mananged to get a load of laundry through in the meantime.
Well, it's time for a shower then sleep (so much for turning in 'early' tonight).