What they seek to describe is a way to group the forces of nature into one compact unit. So far we've been able to find gauge theories for EM, Weak, and Strong forces. But the math involved in Einstein's general relativity currently makes it more problematic to make gravity into a gauge theory that's compatible with the other forces. What pops out of these gauge theories when you plug away at the math are the masses of the interacting particles as well as what level do the strengths of the forces become equal.kurokotetsu said:Do you understand de Yang-Mills theorems and hypothesis? Can you explain them to me? (As some one into Math, that theoretical physics question rises my eyebrow)
The shyguy answered it pretty well. It's something that's used in mathematics for hypothetical or theoretical cases.Can you please explain how does Dirac's Delta Zero work? How can a function be 0 almost everywhere, infinity in one point an the integral still be one? Is that related to Lebesgue integrals?
Time dependent solutions are pretty common in both homework and in the lab. The wave functions that are solutions to the equation aren't measured. What's measured is the wavefunction times its complex conjugate, which is the probability distribution. A good example of a time dependent solution is a wave packet of an electron that's moving through space. At the quantum scale, electrons are described by their probability distributions, which appear like waves.DO you know of any time dependent solutions to the Schrödinger equation? What implications do those have?
Aside: The complex conjugate of a number like 1 + 3i, where i is sqrt(-1), is 1 - 3i. And (1+3i)(1-3i) = 1 + 9 = 10.
His math is based on the idea that space and time are intertwined. To do this in a compact manner, we like to assign what are called tensors. And these tensors are 4x4 matrices. They're made that way because they include time as a dimension. What these tensors contain is the way the local space-time is bent due to gravity. If you were to put in the parameters a spherical mass into those tensors under spherical coordinates, you can reduce the tensors down to Newton's Law of Gravitation.Can you explain to me a little a about the math behind Einstein's Equations of relativity?
Other things that can be done with them are what the local gravity might be like around a pulsar. And they can even answer why the Earth revolves around the Sun one way and not the other! Which is really wild.
I hope that answers some of your questions.