Recent content by MrBillyShears

Alright, I'm rather new to General Relativity, and I'm getting confused with four momentum. Back in SR, p^α=mU^α, but, this relationship doesn't hold in curved space, does it? Because, now I'm seeing that four momentum is somehow a covector in GR, and p_0=-E, so the time component of the...

What is the relationship between the differentiable manifold that is space-time and the physical space around us? How does one relate the three seemingly Cartesian coordinates around us, those which we can measure out with a ruler, to the coordinates of the Lorentzian manifold? If i say, measure...

Let me say from the beginning I'm not talking about the non-coordinate unit vectors for polar coordinates. I'm talking about basis vectors. Let me just ask it as boldly as possible: how does one use these basis vectors in order to describe a vector? I know they are different at every point, so...

Ok, thanks. It's becoming much clearer to me now.

I'm trying to figure this out on my own. Perhaps no one understands what I'm asking. I'm asking if the metric tensor I listed above is valid to use in the dot product of two different vectors. Because the basis vectors are different at different points, \vec{e}_{a'}=\Lambda^b{}_{a'}\vec{e}_{b}...

Alright, so I was reading up on tensors and such with non-Cartesian coordinate systems all day but now I'm a bit tired an confused so you'll have to forgive me if it's a stupid question. So to express the dot product in some coordinate system, it's: g(\vec{A}\,,\vec{B})=A^aB^bg_{ab} And, if...

I'm getting myself all confused with complex logarithms. I'll try to explain why. One identity with complex logarithms is ln(z^c)=cln(z)+2πik, with k an integer. This is, of course, a more general case of ln(e^c)=c+2πik, but it doesn't always work the same! Let's say we are evaluating ln(e^i)...

Never mind, my mistake. Don't know how to delete it.

Ok, I'm driving myself mad, so if someone could settle this for me, that would be helpful. So, I'm imagining something like a hockey puck going across ice and coming to a stop. I'm trying to account for the initial energy, Ei, and the final energy, Ef. So this hockey puck starts with a velocity...

Thanks guys, I get it now.

There is several things I am confused about with gravitational potential energy. So, first of all, shouldn't U=mgh always be written ΔU=mgΔh, because isn't that equation only dealing with differences of potential energies when close to the surface of earth? Second, with the equation U=-GMm/r...

In the Galilean formula u=u'+v, the velocities are bold so we know they're vectors, so for instance if u'=(a,b), and v=(c,d), we say that u=(a+c,b+d). But, in SR u=(u'+v)/(1+vu'/c2), none of the velocities are shown in bold, at least not not the way I saw it written. So, if we used the same two...

Ok, thanks I get it now.

So for finding the magnitude of a vector, velocity for example, we use v=√(vx2+vy2+vz2), but in special relativity, velocities can not exceed c. Is their a different formula for magnitude in SR, or could a velocity like(in natural units) v=(.9,.9,.9) not exist, since the magnitude comes out to...