Recent content by nuclearhead

Why does that matter? You might say sin(x) is the equivalent class of all series definitions of sin(x). As long as one series converges you don't need to use the rest of them.

δ(x) = limε→0 1/√ε exp(-x2/ε) ∫δ(x-a)δ(x-b)dx = limε→0 1/ε ∫exp(-(x-a)2/ε-(x-b)2/ε) dx = limε→0 1/ε ∫exp(-2x2/ε+2(a+b)x/ε-a2/ε-b2/ε)dx = limε→0 1/√ε exp(-(a-b)2/ε + O(ε) ) = δ(a-b)

I've thought of some more. If you cut out a toroidal knot, and create a fibration of the knot with circles (e.g. decompose the torus into circles) then you can identify opposite points in these circles. The circles will loop N times around the major circle and M times around the minor circle so...

I know the solution for R2. That is a for an infinite plane you can have one of 2 things (from the classification of 2D surfaces): 1) cross cap (cut a circle out of the plane and identify opposite points). 2) a oriented handle (cut two circles out and identify points on one with reflected...

That's what I mean. If you stretch the image so they are both circles, the orange line is no longer perpendicular. Isn't that strange? I mean shouldn't contact force be the same if you stretched the image? Where has my logic gone wrong?

But aren't the Newton's laws invariant under scaling of a coordinate axis?

If you zoom into a billiard ball it won't look very smooth at all. It will look very lumpy. Also you will find that it is not as solid as it appears. So when it is resting on a surface (which will be equally lumpy) zoomed up close it would look more like a sponge resting on another sponge. There...

I have a paradox here. Look at this diagram of colliding ellipses (they might be elliptical prisms in 3D). Now if you stretch the image (for example looking at the image from an angle) it becomes two colliding circles. Therefore you would expect by that argument that the colliding force would...

That's kind of my point. If we can't rule out superstring theory, why do we need M-Theory?

But supposing we set all the parameters of string theory, that will presumably model some sort of Universe. But like classical physics doesn't explain radioactivity, is there something that superstring theory fails to predict? I'm looking for an answer like "Superstring theory can't contain...

If superstring theory works, has no infinities, etc. Then what is wrong with it? It must describe some Universe unless there is a contradiction in it somewhere? If it predicts all particles and gravity what is missing from it? Is it not compatible with cosmology for instance? Is Superstring...

I have been reading about M-Theory and LQG, and from what I read they are actually very similar. It seems that just a a string-world sheet is the same as a sum of an infinite number of Feynman diagrams, a membrane would be the sum of an infinite number of graphs or networks. Or as Susskind...

Thanks for being honest. Well you can assume that the sources contain neutrons (or anti-neutrons) which decay into protons and electrons for example. I think maybe the paradox is similar to the statement that "if you removed the sun, the Earth would continue on it's orbit for a further 8...

I think you could be right. I have a feeling that the Feynman propagator is a mathematical simplification that is only applicable if each end of the propagator can take on any value of time (and space?). Hence why in scattering processes we assume the particles have "come in from infinity". For...

The queries relate to the fact that the Feynman propagator for a virtual particle DF(x-y) is non-zero for space-like separations. I want to understand how using this in the calculations results in solutions where causality is preserved. If you can answer this question then please go ahead...