@Slereah You have to fix that Lorentzian means one negative eigenvalue. That there is an equivalence to metrics with one positive eigenvalue is irrelevant.
@0celo7 I think I basically get his answer, but I'm wondering about some things. First, the indices seem wrong. On the LHS he has the indices $\mu\nu$, on the RHS they're just dummy summation indices. Second, I don't understand what he means by You can admit the penultimate equality.
@0celo7 : That has everything to do with your question. You asked if light waves follow null geodesic paths in General Relativity, and I said No. The null geodesic maps the path of the light wave through space, but light doesn't follow this path. Instead light curves because "the speed of light is spatially variable". And Einstein said "Eine Krümmung der Lichtstrahlen kann nämlich nur dann eintreten, wenn die Ausbreitungsgeschwindigkeit des Lichtes mit dem Orte variiert".
@0celo7 : I told you the answer is no and explained why. But you didn't like my answer, you were happy it got deleted, and you didn't follow up on my references. Since you got no other answers, might I suggest you move on?
The large amounts of whitespace and Arial for everything -- it's currently like a middle school essay that's struggling to meet the minimum length while trying to not be taken too seriously.
@ACuriousMind The thing that is not free but just has the relations that preserve the "homomorphism of directed system" property (to be used to solve the SVK mapping problem)?
@Danu Uhhhhh...the thing that appears in the Seifert-van Kampen theorem. I have no idea what a "homomorphism of directed system" property is, but I guess it's a weird way of saying the amalgamated product is the pushout in the category of groups.
A directed system in this sense is $(G_\alpha)_{\alpha\in A}$ where $(A,\prec)$ is partially ordered and $\alpha\prec \alpha'\implies \exists \varphi_{\alpha'\alpha}:G_\alpha\to G_{\alpha'}$ (a homomorphism)
@0celo7 Accepted your answer. The crucial part is just one line in it, the $\delta \,tr\log\tilde M=tr\,\delta\log\tilde M=tr\,\tilde M^{-1}\delta\tilde M$ part, and the one thing I didn't understand was that the trace commutes with the derivative. Now everything's clear, thanks.
But the thing we called the "generalized amalgamated product" does the job, by construction, because you just add the relations $\varphi_{\alpha'\alpha}(g_\alpha)g_\alpha^{-1}$
So... is this the thing you called the free am. prod?
@Danu Well, admittedly, one uses "pushout" usually for the case where you only have 2 $G_i$, but it's just another name (and the categorically/algebraically more common one) for this.
So the pushout in a more general sense (can vary the category) is: The object so that the every homom. of the dir. sys. (to be defined in every category in a (slightly) different way) factors through the inclusions into it?
@Danu Yes. They can fail to be injective if the subgroup you have to divide out is large enough.
@Danu Because, at least for most algebraic objects like groups, they descend from the inclusions into the free product (which is categorially the coproduct in the category of groups), since you compute the amalgamated product as a quotient of the free product.
@0celo7 Yes I know. I don't understand why you're asking about absolute value, even number of minuses and signature of the matrix. But never mind, I got the answer I was looking for.
^ this is probably self-explanatory about what it does
of course this is the end time and therefore controls how long it takes:
endtime = 100
here is the result for time of 2000 fs or 2 ps:
with the following specs:
#OK - lets try evolving the system over time and getting the number you want out ...
starttime = 0 # this is effectively just a label - `mesolve` alwasys starts from `rho0` - it's just saying what we're going to call the time at t0
endtime = 2000 # Arbitrary - this solves with the options above (max 1 million iterations to converge - tolerance 1e-10)
num_intermediate_state = 1000
and same options...
I have noticed this looks like the site 2 population without trapping and loss.
i wonder why, especially since the trapping is accounted for in the hamiltonian...
While checking out some of the user profiles on Physics I have noticed some of the high ranking users with over 20k rep have asked no questions. Why?
