Recent content by berlinspeed

Ahh okay thanks.

What's the meaning of the "bar" on the basis set of W at bottom right corner?

No I thought it was the product of ##\alpha## and ##\beta## but it's not, which wouldn't make much sense.

Thanks for the explanation however my question was simply regarding the notation of ##\mathcal {g_{\mu\nu,\alpha\beta}(P_{0})}\neq0## -- does the ##,\alpha\beta## signify ##\partial_{\alpha}\partial_{\beta}## or ##\partial_{(\alpha\beta)}##, now it seems to be the former..

So if ##P_{0}## is an event, and I have ##\mathcal {g_{\mu\nu}(P_{0})}=0## and ##\mathcal {g_{\mu\nu,\alpha\beta}(P_{0})}\neq0##, does this notation mean ##\partial\alpha\partial\beta## or simply ##\partial(\alpha\beta)##? And what is the significance of it? Why can't it be zero in curved spacetime?

Thanks so much! Gonna grind on that for a while now..

I don't own any SR books, which ones would you recommend?

Anyone know how to derive ##u^0=\frac {dt} {d\tau}=\frac {1} {\sqrt {1-\mathbf {v}^2}}## and ##u^j=\frac {dx^j} {d\tau}=\frac {v^j} {\sqrt {1-\mathbf{v}^2}}##?

Oh yes

Anyone know what the "conv" stands for in ##x^0=t=ct_{conv}##?

But why is light speed the same for all observer? I would think about Maxwell's equations give speed of light as the speed that the EM fields are propagating, but nowhere it gives satisfactory answer there..

Okay I see now with the help of Minkowski diagram, what I'm seeing is that when a particle is at rest in the primed frame, its ##\Delta t## is exactly the line segment in the unprimed frame given by the Pythagorean theorem ##\Delta x^2 + \Delta t^2## however scaled differently in the primed...

Hi do you mind showing me the special cases where the distances come out right? I'm still wrapping my head around it..

I failed to show it graphically..

Yes but why? Can you derive it?