/sci/ - Science & Math

>>5778299
>everything is energy - even matter.
>that's what einstein's infamous E=mc^2 is about
Uh, no it's not. Energy is an abstract quantity - it doesn't make up anything. E=mc^2 tells us that mass is a form of energy, nothing else.

http://www.colorado.edu/physics/phys1110/phys1110_fa10/Feynman_energy.pdf

Everyone needs to read that at least once.

Because it holds for any z. I.e. you have a circle at z=0, a circle at z=1, a circle at z=100000, a circle at z=pi, etc. You have an infinite number of circles stacked on top of each other, which is of course a cylinder.

>please use the laws of physics to explain what would happen in this scenario which violates the laws of physics

>>5774290
You're right, I read his chicken-scratch wrong.

Or, if you don't want to use the squeeze theorem, you can taylor expand cos(x) and simplify. But that, of course, requires prior knowledge of the cos(x) taylor expansion, which you may or may not have learned yet. Basically:

<div class="math">cosx=1-\frac{x^2}{2}+\frac{x^4}{4!}-\frac{x^6}{6!}+...</div>
So the limit becomes:

<div class="math">\lim_{x \to 0} \frac{x - (1 - x^2/2 + \mathcal{O} (x^4))}{x} = \lim_{x \to 0} ~ 1-x^{-1} + \mathcal{O} (x) = 1 - \lim_{x \to 0} x^{-1} = D.N.E.</div>

Intentionally skewing or falsifying data is complete academic suicide.

The logarithmic integral function is a good upper bound:

http://www.wolframalpha.com/input/?i=plot+li%28x%29+and+pi%28x%29

The Alcubierre Drive *IS* gravity.

In the limit the n->infinity the binomial distribution becomes a continuous normal distribution.

What's wrong with 2001's artificial gravity? Centrifugal force works fine.

Engineering classes tend to work with both SI units and English units, because a lot of oldfag engineers still use the English system. Intro physics classes pretty much exclusively use SI units, and more advanced classes use Planck units or geometric units.

>>5763789
>unlike relativity and quantum
Well it's a good thing your computer doesn't rely on either, or your post would be pretty ironic... oh wait.

What's with the Deutsche Physik in vier Bänden lately? This is the second thread I've seen today. It's crackpot nonsense.

The guy was an antisemitic crackpot. Why would you want to read anything of his?

>>5758389
I don't know if "generated" is the right word. The distance between points in space is simply increasing.

In General Relativity the fundamental object is called the "metric," which determines distances between points in space.

Say you label each point on an elastic band with a coordinate "x." (I.e. we draw a bunch number of points on the band and give them numbers). If the band is being held constant, the distance "ds" between two points infinitesimally close together "dx" is given as:

<div class="math">ds=k|dx|</div>
where "k" is some constant. If instead the band is being stretched or compressed over time, the distance in relation to the coordinate separation with vary as a function of time:

<div class="math">ds=f(t)|dx|</div>
This is pretty much exactly what's happening in GR. The exact form of the function f(t) is determined by the Einstein Field Equations, and is related to the energy density in space.

>>5758378
No, by definition. A meter is a meter is a meter. But the number of meters between two points in space isn't fixed.

>>5758361
Expansion has to do with the space itself. Two objects in an expanding universe aren't being accelerated away from each other; the distance between them is simply increasing. They aren't moving *through* space, rather they are sitting still in a non-static space. It's a bit like drawing two dots on an elastic band, then stretching it. The dots aren't moving through the band - the band itself is changing.

>>5758328
Obviously, but it isn't. Not by a very large order of magnitude. Ordinary attractive gravity is many orders of magnitude weaker than EM, and expansion only becomes significant at inter-galactic scales. So the notion that expansion would be significant at the atomic level is far beyond the patently absurd.

>>5758259
Have you? You don't feel acceleration when you're falling, only when you're standing on the ground. I.e. if you carry an accelerometer on the surface of the Earth, it will measure ~9.8 m/s^2. In free-fall it measures zero.

>>5758125
This is the most accurate answer. Objects in an expanding universe don't "feel" expansion in the same way you don't feel acceleration when you're in free-fall. It's because you're not really accelerating at all.

>>5758201
Also, this anon has an interesting point about tidal forces. So again, you don't experience tidal forces due to expansion in much the same way that you don't feel like you're being "stretched" while in free-fall near the Earth's surface; it simply isn't significant enough.

<div class="math">L = \int_{t_1}^{t_2} \sqrt{\left (\frac{dx}{dt} \right )^2+\left ( \frac{dy}{dt} \right )^2}dt</div>
What part are you having trouble with? Remember, you don't need to actually evaluate the integral for x in order to take its derivative.

>>5757287
Because they're in free-fall. I.e. they're in geodesic motion, i.e. an accelerometer measures no acceleration.

>>5755788
I'm not sure how figure that. It's a bit like saying Newton postulated that the Schrodinger equation would be Galilean-invariant. Newton had absolutely no knowledge of QM, and Tesla had absolutely no knowledge of QFT.