Recent content by speeding electron

Can someone tell me the key differences between a frame in free-fall and one at rest in a gravitational field. For example: if monochromatic light is sent radially outward in the field described by the Schwarzschild metric, how will the observed frequency differ between an observer higher up at...

Thank you mathwonk - very interesting

I'm beginning to get this. My main difficulty was in working out the analogy between the notion of different observers in space and that in space-time. In space it seems that where the observer is does not affect their metric. In space-time the metric is different for different observers and...

Is there a general method whereby one can proove that a general solution one has obtained to a D.E. is unique?

So what is signficant about the observer's position - is this considered a transformation. This is different from SR, where the metric was an invariant under transformations? When you transform to a frame in free fall, what happens to the matric? Will it become minkowskian from the equivalence...

Nice work there pmb phy! Thanks.

I believe this is usually stated by saying that the path along which you integrate must all be within simply connected region in which the vector function is continuous with continuous first derivatives. A region is simply connected if any loop you can form in it can be 'capped' by a plane...

I've been trying to work out the meaning of the metric in General relativity. I have a few ideas, but nothing's really come together. These are what I think is right, from SR: the space-time distance is a quantity which is agreed upon by all observers, a fundamental property of the interval...

What do you mean by a 'potential per unit length'? Length of the line/rod? This changes according to where this unit length is. Thanks - please clarify.

If you want to calculate the electric field at a distance r from a line of infinite length and uniform charge density you could one of three things: 1. Employ symmetry and Gauss' law. 2. Use superposition and integrate from minus to plus infinity along the rod. 3. Integrate to find the...

Check again - I'm pretty sure the scalar potential propagates at a finite speed.

Are there names for the Lorentz invariant norm of the four-potential and four-current? I assume that they are invariant under the transformations. Also, is it true that any physical quantities which form a four-vector have an invariant quantity associated with them (i.e. the norm of the...

The value of the electric and magnetic fields are determined by the value of the respective potentials, and vice versa. Therefore the fields must propagate at the same speed as the fields. This is pretty much by definition, and if the potentials traveled say faster than the fields, you would...

Could you explain your problem a little more? The vector r goes from the co-ordinates of the point charge to the the point (x,y,z) where you want to find the electric field. It has magnitude |r| = \sqrt{\left( x - x_0 \right) + \left( y - y_0 \right) + \left( z - z_0 \right)} . So if we divide...

singleton: It seems that 'Calculus for The Practical Man' was the name of Feynmann's calculus scrapbook, and that he learned the essentials from 'Calculus Made Easy'.