@ACuriousMind : no, charge doesn't run. Charge is conserved. I know the NIST page says the effective charge varies, but the effect of the charge varies. The charge doesn't. Remember what anna v said: virtual particles only exist in the mathematics of the model.
Apparently there is no general solution of the Mathieu equation
"The equation obviously possesses a solution which for large real values of the variable becomes exponentially infinite, i.e., a so called unstable solution."
@0celo7 : "but aren't wormholes woo?" Yes. Because they permit time travel. And time travel is woo. It's easy to understand why when you look into it. See for example this answer to is time an illusion? The answer is no, but it isn't something you can travel through. Sadly however, people just love their woo. They have a habit of clinging to woo like a baby to a teat.
@TanMath : yes. If you're my twin and you go on a fast out-and-back trip, you get time dilated. You come back younger than me. But I can watch you every step of the way through my telescope, and you don't end up living in the middle of last week. You never depart the present. You don't "travel to the future". You merely suffer less local motion than me. Your local motion plus your macroscopic motion cannot exceed c. It's all down to the wave nature of matter.
@Ghost : people love their woo. In times gone by they lapped up the tales of heaven and hell and sweet baby Jesus. Now it's branes and SUSY and the Goldilocks multiverse. Meh, same old same old.
@TanMath : cling on tight, Tanmath. If you want to believe that there's some way you can move such that everything else in the universe not only moved back to where it was, but never moved at all, well, there's nothing I can ever say to convince you otherwise. Just as I can never convince some starry-eyed sucker that there ain't no heaven. Hallelujah!
@TanMath : I can't prove that wormholes don't exist. And nor can I prove that fairies don't exist either. Or unicorns. Or heaven and hell and sweet baby Jesus.
@0celo7 : you shedding your anonymity for starters. I would recommend that everybody uses their real name in discussions. It tends to keeps things nice.
Suppose we have an equation
$$
\tag 1 y'' + (A -2q\cos(2t))y = 0,
$$
called Mathieu equation. How does it provide instabilities for small $q << 1, A > q$? I don't understand this because as the result of adiabaticity Eq. $(1)$ admits WKB solution
$$
y = \sum_{\pm}c_{\pm}\frac{\text{exp}\left(\pm...
I am currently confronted with a physical equation that, after a fair amount of reworking, can be recast in the form of the modified Mathieu equation :
\begin{equation}
y(x)'' - (a - 2q \cosh(2x)) y(x) = 0
\end{equation}
In this case, the parameters $a$ and $q$ are somewhat arbitrary real numb...
@0celo7: I recommend you use it. Honestly. Look around, the regular guys do. Anyway, I have to go I'm afraid. Follow those references, do your own research, and think for yourself. Oh, and having just seen the above, take care who you hang around with.
I guess the difference is between $ds^2 = (c+a\cos(\theta))^2d\phi^2 + a^2 d\theta^2$ and $ds^2 = d\phi^2 + d\theta^2$
"This metric of the square flat torus can also be realised by specific embeddings of the familiar 2-torus into Euclidean 4-space or higher dimensions."
Weird
Apparently you can't have a flat torus in 3D
"In 3 dimensions one can bend a flat sheet of paper into a cylinder without stretching the paper, but you cannot then bend this cylinder into a torus without stretching the paper (unless you give up some regularity and differentiability conditions, see below)."
does anyone know if I set up remote access from my laptop to a Linux terminal in work, can my home computer be accessed from that system by someone else using it?
I am currently confronted with a physical equation that, after a fair amount of reworking, can be recast in the form of the modified Mathieu equation :
\begin{equation}
y(x)'' - (a - 2q \cosh(2x)) y(x) = 0
\end{equation}
In this case, the parameters $a$ and $q$ are somewhat arbitrary real numb...
