Anyone subscribed to SciAm?
My subscription expired months ago and I can't afford to renew it at least until next week. I want to read this article
How Quantum Effects Could Create Black Stars, Not Holes: Scientific American
If someone has it, scan it or something for me please D:
Check your PMs.
Thanks, you're awesome.
It's nice to request something and actually get it. I know this guy (I'll keep his identity secret, so let's just call him "Rizango") who has The God Particle documentary but still hasn't sent it to me a link to it or anything yet D:
I don't think they called it the God Particle in that article. This was the cover of that issue:
http://www.scientificamerican.com/me...er_2005-07.jpg
Also, Miz, I don't want you to go through the trouble of burning and mailing them. I thought it was small enough for you to upload to rapidshare or megavideo or something.
Nothing also happens when you're an undergraduate eitherI've also been really busy at work (where I usually read sciencey news), so I have not had the time to browse around. One interesting thing, is we start Quantum Mechanics (Specifically the Schrodinger equation) the week after next in my Modern Physics class.
Schrodinger equation is like my favorite equation (well, that and Maxwell's). Modern physics was so much more fun after learning that for the first time (I don't know if you've learned it before, but if you haven't, your inner math nerd is going to love it). After you learn it, you're actually able to mathematically derive a lot of the stuff you hear about in books and on the science channel (like quantum tunneling, for example). And in simple or ideal cases, it's fun to solve, though in more realistic scenarios, the schrodinger equation is a huge pain (but then again, this is true of virtually every equation when you try to solve it for real life scenarios. See, this is why I like theoretical math and physics more than applied).
Unfortunately, a modern physics course by itself doesn't even get to the most fun aspects of quantum theory. Once you get to graduate level quantum theory, the postulates are reformulated in terms of linear algebra and functional analysis (two courses that most people taking modern haven't learned yet). In modern physics, they're basically going to say "This is the equation. Why? Because we said so. This is how it's solved. Why? Because we said so. This is the difference between bosons and fermions. Why? Because we said so". You do still get to learn some very important stuff, like the solution to the schrodinger equation for the situation where the potential energy is the same as a harmonic oscillator. But you wont get a true conceptual understanding of it until you learn everything in terms of operators, commutators, and hilbert space vectors (and when I say "conceptual understanding", I mean about as conceptual as QM gets. QM is never going to make as much sense as electricity or fluid dynamics or whatever, but if you're mathematical, you're already used to thinking abstractly anyways).
There is a guy in my vector analysis class who is also currently taking the first semester of E&M. We calculated the gradient of 1/r (or a form of potential), and then the gradient squared turned out to be zero. He said in the E&M class they just kind of hand-waved that calculation, and expected him to realize why that was, and he was completely lost. My math professor actually explained the physics to us lol.
Reactor kinetics equations are always fun, real or ideal. True facts.
http://www.aethernavale.net/Media/images/1rke.PNG
How could that possibly not be fun? Not even that difficult to derive, honestly.
LoL. I wonder if I could get away with making that f into a p.
Neutron Generation Lifetime * (Rate of change of power density of fission with respect to time) = [reactivity - average delayed neutron fraction](power density of fission)+[summation of the six delayed neutron precursor decay groups (fission equivalent concentration * decay constant)]+(fission equivalent source neutron strength).
That help? Clear as mud? lol
Yeah, this equation you're refering to is known as Laplace's Equation. This is typically something studied in a course on Partial Differential Equations. But physics majors typically don't take Partial Differential Equations (at least not as an undergrad, though they should). It's a shame though because other than Maxwell's equations, Laplace's equation is probably one of the most important equations on E&M (well, part of the reason it's so important is because it applies to MANY other fields other than just E&M. I used it a little bit in my research when I was studying heat conduction in carbon nanotubes).
The same thing happens in Mechanics. Lagrange's equations is by far the most important thing you'll learn there, even more important than Newtons formulation (well I guess Hamiltonian's formulation is more important than Lagrange's, but you can't learn that until you understand Lagrange's formulation) , but it's based on a form of math called calculus of variations, which physics undergrads never take. So instead, you're going to just get some weak introduction to Calculus of variations. It will leave you unsatisfied and you'll probably be looking for a math professor to explain it in more detail.
The same thing occurs in QM when the momentum vectors all turn out to be fourier transforms of position vectors. In fact, the whole sturm-louville theory in mathematics would be very useful to know before an undergrad course in QM and as a matter of fact, it's used in modern physics too. Your book is basically going to say "This equation is too hard for the scope of this book. So to simplify it, we're just going to tell you that the answers are Bessel functions/Hermite Polynomials/etc", depending on what you're studying. How the hell do they expect a freakin sophmore to know what a Bessel function is? And instead of proving that they're equation works, they'll probably ask you to verify it yourself, as if someone taking modern physics would know how to differentiate a spherical bessel function. Then they're really confused when they tell you that you can write any function ever as the sum of an infinite amount of bessel functions (or sines, or cosines, or any other solution of the Sturm Louville equation, which of course someone taking your class usually haven't studied yet).
I mean, I can kinda see why they teach the physics way before the math. If you took everything in order, it would take like 8 years to graduate because you couldn't take most of your physics courses until a three or four years of math (actually this isn't true. A book on mathematical methods of physics will give you everything an undergraduate needs and can be taught in just one year. Then you'd literally be ready for graduate courses already, except for QM, which also requires a bit of functional analysis). But still, the way it's set up now causes physics teachers to have to teach material that their students can't really appreciate. So then, when you go to take the higher level version of the courses, you're starting not starting from where you left off on the previous course. You're starting from scratch, which makes you wonder what the point of the previous course was. If your math background is strong enough, you could just completely skip the undergraduate level stuff. I skipped undergraduate level QM. Skipping undergrad Mechanics and E&M should be even easier.
But does the equation still look like this when you're actually using it or do you end up using an approximation of an approximated approximation which is still too complex to be solved analytically so you have to approximate that on a computer?