Cap'n Refsmmat

The NASA budget has been increased, not cut, and there's an increase in science spending on the new budget. http://www.newscientist.com/article/mg20527462.700-obama-abandons-moon-shot-but-invests-in-science.html

I'm curious; you suggest that there is no motional emf, yet you are unwinding the wire, which should induce a motional emf. (After all, the wire has to move.) Now, the situation you describe is complicated enough that I may be mistaken, but whatever... With the Faraday disk example, it's apparent that misinterpreting Faraday's law and complaining when you get the wrong answer doesn't work. Faraday's Law does work in that situation. The "physicality" of the law is unimportant, anyway -- look at Maxwell's equations, for example. They're not actually Maxwell's, because Maxwell's original equations were horrendously complicated and had a few dozen unknowns. Oliver Heaviside used vector calculus (a mathematical formulation) to create a new formulation that described electromagnetism in just four equations, which became known as Maxwell's equations. But the modern Maxwell's equations are a result of complicated mathematical manipulation, not a direct physical principle.

The emf generated by a Faraday disk can be computed using Faraday's law as follows, for a disk of radius r with an angular frequency of [math]\omega[/math]: The arc length s = r θ and the area A = r s can be approximated to be a triangle of height r and base s, so [math]A = \frac{1}{2} r s = \frac{1}{2} r^2 \theta = \frac{1}{2} r^2 \omega t[/math] and [math]\varepsilon = -\frac{d\Phi}{dt} = IR[/math] [math]|I|R = \frac{d\Phi}{dt}[/math] [math]|I| = \frac{1}{R}\frac{d\Phi}{dt} = \frac{B}{R} \frac{dA}{dt}[/math] [math]= \frac{B}{R} \left( \frac{1}{2}r^2 \omega\right) = \frac{B r^2 \omega}{2R}[/math] as given by the solution manual for my homework problem from a week or two ago. It works!

This is not strictly true. My textbook's definition of Faraday's law has two separate wordings: That is, in the Faraday's disk case, we can measure the flux a path on the disk sweeps through in each unit of time, and use that to determine the emf. The book then defines the version of Faraday's Law for a closed loop, which agrees with your version: However, any closed loop in the disk would necessarily have a zero potential difference, because in a closed loop, the start point and the end point are the same point. (They can't be different points if it's a closed loop.) The law gives the correct result -- the voltage difference across a point is 0 -- but it's not useful at all, since it's not what we're looking for. Physics for Engineers and Scientists, 3rd. ed., Ohanian and Markert.

Could you provide some specific examples of situations where Faraday's Law is improper or fails? You're using different terminology than I used when I learned Faraday's Law. (You're also not using SI units, but that's another story...)

Take a few sine waves of different frequencies and add them together, and see the sort of graph you get. (It looks rather goofy.) That's what the graph of the displacement of the string at one particular point would look like with several different frequencies playing at once.

I'll agree that discussions feel more personal when you actually know who you're talking to, but I'll also point out that SFN predates Second Life by a year. It'd be nice if more people chose to be less anonymous on SFN, but that's hard to encourage. Many people are afraid of what will happen if they put their personal information on the Internet. But anyway, hi, I'm Alex.

Funnier than some of the segments I see on the Daily Show, at least.

Intelligence is also an evolved trait, so our intelligence overriding other traits (like being too stupid to successfully catch animals) isn't too surprising. Also, wearing condoms isn't an inherited trait, so evolving to not use condoms isn't very plausible.

Never fear, I'm not a sea captain either. And I've never used a refsmmat.

Also, why can't the First Cause be some principle of physics rather than any special Prime Mover?

Obama's money has changed quite a bit in the past few years. http://blogs.suntimes.com/sweet/2010/04/obama_income_for_2009_is_55054.html Book sales are great, apparently...

Yeah, I've heard of this happening on other vB sites as well. I don't recall a solution, but I can look around.

Good grief, everyone. This thread just goes to show how a movement like the Tea Party can anger and split apart otherwise normal, rational people. The tone here has gotten far too personal, condescending and insulting for my tastes. Please, when you're angry about how people behave, don't descend to their level while doing so.

Please keep your personal hypothesis to its own thread for now. We try to avoid answering questions about mainstream science with nonstandard speculative hypotheses.

Sure. And you could do a similar mass-time diagram showing the mass of the object over time. The space-time diagram doesn't say the object exists at all time (although that could be true depending on how you interpret time). It just describes where it was at each time. Agreed?

Nope. What I'm saying is that the lines represent object throughout time. The moving dot makes sense if you want to show what the world looked like from one perspective, but there's a time axis on the graph for a reason. Or, more pointedly, what's the point of a time axis on a graph if you insist on only showing the object at one time? The time axis is there to show what the object did in the past.

What you are saying is that its mass has existed throughout time. A space-time diagram shows the object at different points in time. Now, if you want a diagram that only shows what you can perceive at this instant, it's wrong, but that's not its purpose.

Why does there have to be duplicated mass? All the chart says is that at time t, there was a given mass in existence. That is true, because at that time we could have measured it and found that mass. At any other point in time, we can also measure the mass and record it. If you mark the mass as existing at only one point in time, than someone reading the graph will go "I wonder what the mass was back at t=0.5", look, and find nothing, concluding that there was no object at all at that time. But there was. You don't have to interpret it to mean "that mass still exists in the past", whatever the hell that's supposed to mean. You interpret it to mean "at time t, there was mass." Suppose I graph an object's velocity over time. I don't say that at t=1, the object still has a velocity, even though that time's in the past -- so it's moving while frozen in time. I say that the object had that velocity at that time.

http://www.bit-tech.net/news/gaming/2010/04/15/gamestation-we-own-your-soul/1

Why does there need to be mass on a space-time diagram? You could add a third dimension of mass and make the bars thick, but they'll be uniformly thick throughout unless there's some sort of nuclear reaction occurring. The space-time diagram is no more complicated than, say, this graph: where the x-axis is time (pretend that's not negative) and the y-axis is height, and saying "this represents a ball I threw up in the air."

Just wanted to point this out: http://arxiv.org/abs/0801.1734 Written by my TA from E&M class.

No, stress is related to the internal forces in the object. Check out the Wikipedia on it: http://en.wikipedia.org/wiki/Stress_%28physics%29

Very true. Especially if you get the dream woman naked in the room with him. You could tell her it's for national security purposes. As stated in post #6, "there are no harmful side effects. No long-term damage. Just pleasure." So no withdrawal symptoms.

That's because you're only testing the row number, not the cell. I'd do: Image[Table[if[PrimeQ[x*800 + y], 1, 0], {x, 0, 799}, {y, 0, 799}]] I think that gives the right result. edit: err, wait, that might go vertically instead of horizontally. But you get the idea.