http://physics.stackexchange.com/questions/83105/explain-reflection-laws-at-the-atomic-level
https://en.wikipedia.org/wiki/Laser#Laser_physics

So basically, using what you said above, since the consituents that made up the moon's surface are not all hopping between well defined states at some characteristic frequency, therefore when a photon scatters from it (and follows the path of least action as it is the only path that does not suffer from much destructive interference) they will end up with different phases that are pretty much depends on which constituet it scatters from. Thus the li…

When reading that xkcd, I intially thought that I could use the lens to tune the phase of the light such that they all end up with the same phase at least for a small (but not point like) area and a small moment of time, so that at leats for that short moment
the energy can be focused onto that region due to how all the photons there will interfere constructively to give a large amplitude of the electromagnetic field there that might be strong enough to start heating or ionising stuff in that region

@ACuriousMind
https://www.physicsforums.com/threads/constructive-interference-energy-non-conservation.420462/

Hmm, so given that the moonlit surface is only ~100 C, that means the maximum power I could get would be just that corresponds to that even if I can somehow superimpose all the waves at one spot

A laser does not have this problem (and theoretically can get to arbitrary high power outputs) because the energy that is used to pump the laser is external to the system (the electricity supply)

Based on what I have learnt from my school, my uni and also extensively though this chat in the past month and feymann lectures, quantum mechanics MAY be a bunch of Hausdorff dimension 2 fractal paths that (for some reason) has a phase hence they can interfere like waves and the outcome we get is the probability for some observables (be it its location, or its various physical quantities like angular momentum to be measured.

There underlying princple is that they are linear "stuff" and thus superposition and to them every obstacle is just a potential, thus empty space

https://en.wikipedia.org/wiki/Quantum_decoherence
https://en.wikipedia.org/wiki/Quantum_entanglement

So I guess, the really fundemantal thing about quantum is that:
1. Why on earth do paths have a phase
2. What is the exact mechanism of making two states coherent (the maths just says, get them to have the same phase, but it is more probable to gain some arbitrary phase factor form interacting with something else than the same phase factor as the state of interest (as quantum states tend to decohere by interact with the envrinoment, so what makes that quite easy to do)

Some random algebra doodling:
Consider the set $$A=\left\{\begin{pmatrix}r \\ \theta\end{pmatrix}:r,\theta\in \mathbb{R}\right\}$$
with binary operator $\cdot$ to form a $\langle$insert name$\rangle$

$$(A,\cdot)$$

Define
$$\begin{pmatrix}r_1 \\ \theta_1\end{pmatrix}\cdot \begin{pmatrix}r_2 \\ \theta_2\end{pmatrix}=\begin{pmatrix}r_1r_2 \\ \theta_1+\theta_2\end{pmatrix}$$
where $+$ and multiplication is as defined in $\mathbb{R}$
Then the identity is
$$\mathbf{1}=\begin{pmatrix}1 \\ 0\end{pmatrix}$$ since $$\begin{pmatrix}1 \\ 0\end{pmatrix}\cdot \begin{pmatrix}r \\ \theta\end{pmatrix}=\be…