That's incorrect, though. They appear naturally in a geometric context. Suppose you have a black hole of a given circumference C. How far away do you need to stay from its center?
It seems clear to me that that question should have a precise answer (C/2pi), even if measurement error means...
When you say "good for learning," what do you mean? Is it something I, as an undergraduate, would learn from--or would it just be way over my head? I haven't even had multivariable calculus officially yet (though I've used a bit in physics), let alone abstract algebra or complex analysis. We've...
I'm signing up for the Society of Physics Students, which gets me a free 1-year membership in the American Physical Society and a subscription to one of the following journals:
Physical Review Letters
Physical Review A-E
Review of Modern Physics
For a second-year undergraduate, which of...
A simple way to understand voltage is just to look at its units.
1 Volt = 1 Joule / 1 Coulomb.
This means that if there is 1 Volt of potential, that means each Coulumb of charge has 1 Joule of potential energy. So you can think of voltage as telling you each charged particle has a certain...
Instead of doing it with a single example, you can prove that for all integrable functions, the constant of integration doesn't matter for definite integrals.
\int f(x)\,dx = F(x) + C implies that \int^b_a f(x)\,dx = ( F(b) + C) - ( F(a) + C ) = F(b) - F(a) + C - C = F(b) - F(a).
This means...
In America you might have a university, within which are contained several colleges. You might have the College of Engineering, the College of Letters and Science, and the Law School--or you could have what Harvard does: within Harvard University is Harvard College, where all undergraduates go...
Because that's how much energy you get out of each bit of mass. So if you convert 1 kg of mass (= 2.2 lbs) to energy... you'll get
1 kg * c^2 of energy.
That's 1 kg * (3.0*10^8 m/s)^2 = 9 * 10^16 J of energy, or 9000 TJ. Compare that with those bombs.
To put that into perspective: most...
I think that the purposes of this poll would be better served if we could distinguish among the different types of studier who all put in from zero to two hours a day. There's a big difference between someone who studies not at all and someone who studies an hour a day, and between someone who...
But we do know that space seems to behave as if it's curved according to the general theory of relativity. That's why the curved-space view gets airtime, even though the gtr isn't completely in agreement with all our other physics.
Even if space always behaved exactly as if it were curved, we...
Light wouldn't be hitting any objects outside the event horizon, since light can't even get out of the black hole.
Imagine being in a completely dark room. Inside that room, on a table, is a strong box. Nothing can get out of that box. Not even light.
Someone turns on a light inside that box...
This may help.
http://www.math.wisc.edu/~nagel/Math275Assignments.html
Part of 4, all of 5-7. Textbook exercises are from Tom M. Apostol's Calculus, volume 1. Not all of them are from the text, though.
No matter how big any "outward pressure" would be, it still wouldn't be able to push anything out. This is because once something is inside the event horizon of the black hole, it can never get further from the hole. Your question can be converted to this one: why can't anything inside the event...