@Jacobadtr : maybe I misunderstood what you were saying. Why don't you ask a proper question about Compton scattering? PS: don't pay any attention to Slereah or 0celo.
@BernardMeurer Well...it's basically taking a function (in this case $\zeta(s) = \sum_n \frac{1}{n^s}$) which is only defined for certain values of $s$ ($s\geq 1$ in this case, since the series diverges otherwise) and thinking of it as a function on the complex numbers instead. There are techniques to determine how much you can now "expand" the domain of the function on the complex plane, and it turns out in this case it works for all $s\neq 1$.
@ACuriousMind From a mathematical viewpoint, the difference between vectors and pseudovectors is their degree in the exterior algebra (i.e. $1$-forms vs. $(n-1)$-forms). Does it also make sense to talk about them in the context of representation theory of $O(n)$?
I mean, $O(n)$ is generated by the same infinitesimal generators as $SO(n)$ plus the discrete generator $\mathbf P$ (parity), so if I choose a representation of $SO(n)$ and a rep of $\mathbf P$, I can construct a rep $\rho$ of $O(n)$. For a trivial $\rho(\mathbf P)=\mathbf 1$, we get a pseudo representation (pseudoscalar, pseudovector, "pseudotensor" whatever) and for $\rho(\mathbf P)=-\mathbf 1$ a "normal" rep (scalar, vector, tensor etc). Does that make any sense?
@Bass Yes, that makes sense, but it only works that way for odd $n$. For even $n$ the "pseudovectors" are wedges of odd numbers of vectors and behave like vectors under parity
@ACuriousMind: yes, and a frequency does not have units, other then just a cycle (which could be the same as a length which whill repeat itself right? Just allowing for another definition of frequencies in terms of (an unlimited amount of) lengths)
@Ropstah I'm not sure what you're going for here. The wavelength is the period length of the wave. The frequency tells you how many wavelengths it moves per second, and thus the relation between them is that wavelength times frequency is the velocity.
@ACuriousMind Well, photon energy/wavelength is not Lorentz covariant, so it's difficult to even define "change photon wavelength" for all observers. Maybe one can define it by saying "if its energy change's sign is the same for all observers, then it's really a change", and that would be the case with a black hole.. nvm
@Ropstah You can't define all light to have the same wavelength but different speed in vacuum because it is obvious that all colors have the same speed in vacuum
@Ropstah Otherwise you would see prism-like effects all over the place, not only in special materials. The way a prism functions is precisely by having different speeds for different colors.
@Ropstah Yes, that's how it works. You can understand refraction very well with that if you draw the wavefronts and let them move slower once they enter the prism - if the ray is not incident perpendicularly, then one part of the wavefront will enter the prism first, and since it is moving slower, this will slant the wave towards the side where it entered first
...I'm not sure that made any sense without a picture
The presence of a magnetic charge is also modelled classically like that, but of course you can also just add a magnetic source term to the Maxwell equations and don't care that this destroys the gauge theory
@Ropstah I don't understand the question. It's just that the electromagnetic waves in solids are not well-described by imagining a photon moving through them
@Ropstah Uh, well, the whole solid will behave in a certain fashion, not just the electrons
And I honestly don't know how the exact quantum mechanical description of that works. Maybe you can say there are photons, just like there are phonons? At least it won't be your picture of the light wave being made up out of well-localized photons that just fly in a straight line
@ACuriousMind: I'm assuming that photons interact with electrons in a way that electrons are 'pushed/pulled' by photons rushing by, in turn redirecting/slowing down the photons. << does this make sense?
@Ropstah The fundamental description here is probably not in terms of photons. You don't insist on thinking about sound waves in terms of phonons, do you?
@ACuriousMind, no because the wave is deducted as a result of behavior of multiple particles. However the photon itself has a wave like behavior in it's particle state
@Ropstah Classically, if the angle at which the wave (light) enters the medium (prism) is so low that the wavelength would be infinite inside of the medium, it gets reflected instead of entering it. I think that's the threshold you mean. Best example: look at a water surface, you see what's in the water at high angles, but near the horizon, you just see reflections.
Short answer: It has changed over time, drastically.
Initially (and by that I mean after the conjectured inflationary epoch, which I will not consider here), radiation dominated all other forms of energy by far. However, as the universe expands---as measured by the increase of the ''scale facto...
@Ropstah They have deBroglie wavelengths. But even if they hadn't, I don'T see what's your point. I asked about phonons because I wanted to make the point that the particle description is not always the best
It is not the case that "photons make up electromagnetic waves" in the sense that the photons are "fundamental" and the wave is somehow emergent. It's that the wave is one way to describe what is happening and "a bunch of photons" is another.
@ACuriousMind Because that is i think where I was trying to go, if I am trying to be ignorant and take the photon as a particle, then it doesn't make sense to 'repeat' or 'copy' it using a wave, but rather define it's size and speed.
My point was I never learned any of this, so I figure it out by myself most of the time, which generally leads to badly formed ideas that take a long ass time to get corrected
If your function is "how much money do I have on which day" (accumulation), then you can differentiate it and you get the function "how much money am I getting per day" (rate of change).
If you start with the rate of change, you can integrate it for a specific period (a week) and you get the accumulation.
@BernardMeurer Yes, aka indefinite and definite integral. The second one (definite integral) is the one with a specific "period", like, how much do you earn this week.
The first one (indefinite) is just any function that is an "anti-derivative" of the function you start with. $g=\int f$ means basically that $g'=f$.
@BernardMeurer You can, but you have several possibilities. There is more than one function. For example, if $g$ is such a solution, then if you add a constant $C$ like $g+C$ its still a solution
So you have to set something like a start condition, which basically says with what "amount" or "accumultation"you are starting.
@Danu Usually, "canonical" maps are those induced by universal properties
But they can also be maps coming from adjuctions...let's say that "canonical" is made more precise in category theory, but the word itself is not formalized, afaik
@Danu If it reassures you, I have always been bothered by the word "canonical". It doesn't actually convey any information about the thing that's described as "canonical".
I think the main use of the word is that if it is used consistently for the same map, you can really just say "Take the canonical map" instead of having to define the map.
Reversible implies entropy of a closed loop is zero.
But the pen hasn't completed a full loop, so it will have some change in entropy.
Moreover I understand that heat will be dissipated from the pen as it falls, but the increase in entropy of the surroundings isn't just dQ/T, is it? Because that's only for reversible processes.
Short answer: It has changed over time, drastically.
Initially (and by that I mean after the conjectured inflationary epoch, which I will not consider here), radiation dominated all other forms of energy by far. However, as the universe expands---as measured by the increase of the ''scale facto...
