Recent content by resaypi

Homework Statement I am studying inflation theory for a scalar field \phi in curved spacetime. I want to obtain Euler-Lagrange equations for the action: I\left[\phi\right] = \int \left[\frac{1}{2}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi + V\left(\phi\right) \right]\sqrt{-g} d^4x Homework...

Why?? The metric is much more natural than the Lorentz transformation, it describes the geometry of spacetime more effectively and intuitively. Solving equations is not physics, like solivng the lorentz transformation, and in this case the metric provides a much better comprehension of relativity.

T is the time for the Earth frame t is the time in Earth frame and x is the length in Earth frame T^2 = t^2 - x^2 /c^2 is a direct consequence of the lorentz transformation. Sorry for the lack of explanation before...

Conservation of angular momentum.

You can subsitute cos(2a) = (1-sin^2(2a))^0.5 and square the equation to get a quadratic equation. Solve for sin(2a).

Why don't you use the metric, it is much simpler. dT^2 = dt^2 - dx^2 / c^2 and dT^2 / dt^2 = 1 - v^2 / c^2

try the cross product of the position and the velocity vectors

try 2sin(a)cos(a) = sin(2a) and cos(2a) = 2cos(a)^2 - 1

why should part b and part c have different answers, can you briefly explain that. what I think about it is since reference frames are the same, they should have the same answer. and using the metric T^2 = t^2 - x^2 / c^2 where T is the time for the...

you can try building your own with some wire and a magnet and dc source

suppose f(a) = 0/0 as x goes to a lim f(x) can yield any real number, so it would not be wise to define 0/0 some real number

What is who? What is what? What is when? What is where? What is how? What is why?

So, when you plunge into a rotating black hole, according to penrose diagram one could travel to different universes, but at the same time black holes emit particles by hawking radiation. So what happens to an object inside the black hole? Do I make an error in reasoning somewhere?

Newtonian gravity accounts for a flat euclidean space. Provided that a particle is far away from a strong gravitational attraction and moving slowly GR provides the same results with Newtonian gravity. They are after all approximations of what really happens. GR is a better approximation than...

In 4 dimensional spacetime intervals of constant length are hyperbolas. Also it is sometimes easier to work with hyperbolic functions tanh(\theta) = v/c The addition of velocities is reduced to adding hyperbolic functions.