92,051 reputation
7121246
bio website motls.blogspot.com
location Czech Republic
age 40
visits member for 3 years, 3 months
seen 14 hours ago

Hi, I am a string theorist and a publicist.


Apr
4
comment Klein factors and Conformal Field Theory
Dear Costa, the right prefactor (normalization) is clearly needed for the right normalization of the commutator, but that's it. The essence of the operator is the same, however. It's like if you used $X=x(a/L)^n$ instead of $x$, then the commutator $[X,p]$ will be $(a/L)^n \cdot i\hbar$ instead of $i\hbar$. But the special point about the exponential operators is that only the (divergent) overall normalization is affected by the normal-ordering effects. At least I hope so.
Mar
29
comment If the earth left the solar system for interstellar space. How long would it take for atmosphere to freeze
You're right, thanks.
Mar
28
comment Selection Rules in electron spectroscopy
Dear Laurent, this is really the general situation. The orbital angular momentum does not commute with the full Hamiltonian, and neither does the spin, so they are not "good quantum numbers". It's still possible to diagonalize the Hamiltonian. In a calculation method, we may diagonalize the Hamiltonian without the L.S interaction, and that part commutes with L and S separately. If we can't find a useful "bulk" of the Hamiltonian that commutes with L,S separately, then L,S eigenstates are useless in any search for the H eigenstates, but H still has eigenstates and they may be found otherwise.
Mar
19
comment What's the $\ell$ in the Bicep2 paper mean?
The local peak from the primordial gravitational waves is normally expected around $\ell=90$. The spherical harmonic $Y_{90,90}$, for example, has the $J_z$ aligned "maximally vertically, so it is spinning maximally vertically among the $Y_{90,m}$ harmonics, and on this one, you see that the angular dependence contains $\exp(90 i\phi)$ which contains 90 maxima around the circle. So the "wavelength" of the component spans 360/90=4 degrees on the sky. The resolution has to be a bit better to actually "see" the shape of these waves.
Mar
17
comment What was the major discovery on gravitational waves made March 17th, 2014, in the BICEP2 experiment?
A more advanced essay on what the discovery means, by Prof Liam McAllister of Cornell: motls.blogspot.com/2014/03/…
Mar
13
comment Heisenberg's uncertainty principle - Planck's (reduced) constant divided by two or not?
Well, in these formulae, $\Delta x$ means the standard deviation $\sigma_x$ or whatever is your preferred other notation.
Mar
11
comment Isometries and Kaluza Klein theories
Not really. If you pick an "irrational" combination of two natural generators, $t_a+K t_b$ where $K$ is irrational, the group that this combined generator generates is isomorphic to $R^+$ and not $U(1)$ because you will never return quite to the same place - the periodicity disappears. But it's always possible to choose a Cartan (maximal commuting) subalgebra of commuting and compact generators isomorphic to $U(1)^\ell$. Any generator of a compact group may be written as a combination of some generators in some $U(1)^\ell$ subalgebra.
Mar
5
comment Does limit $\hbar \rightarrow 0$ in Quantum Mechanics mean anything?
Raskolnikov, you meant $c\to\infty$, not $c\to 0$.
Feb
19
comment How can a photon have no mass and still travel at the speed of light?
Dear @clicky-hacky-clicky-hacky, sorry for using a transliterated version of your name via Czech (orig: klikyháky, klikykáky). :-) I don't have the right keyboard to write your name and copy-and-paste would be mindless and disrespectful... If individual claims in a set of claims in physics imply each other so that you may find a loop that you call "circular reasoning", it surely doesn't mean that any of the claims is wrong. Instead, everything I write and everything I have written in my life, more or less, is true. In physics, some claims have to be assumed/extracted from observations.
Feb
18
comment How can a photon have no mass and still travel at the speed of light?
Dear @clicky-hacky-clicky-hacky, I wasn't trying to claim that one may derive the identity out of "nothing". Some formulae or principles always have to be assumed - and defended by a successful comparison of the results with the experiments. That's why criticisms of "circularity" in physics completely miss the epistemical status of natural sciences in general.
Feb
18
comment Why can't photons have a mass
Because the strong force is confining, so only color-neutral ("uncharged") particles are allowed to exist in isolation. Correspondingly, the force among such neutral particles decreases quickly with the distance. In fact, the decreases is faster than the power law because the gluons self-interact so they are confined, too. The mass of colored objects is a subtle thing - it depends on the RG scale and the masslessness is only relevant at very short distances, much shorter than the proton radius (QCD scale) where the confinement starts to matter.
Feb
17
comment Why some particles interact with the Higgs field and others don't?
Hi, in a quantum field theory, it is an undetermined parameter - perhaps constrained by some inequalities (at each scale, due to RG running). In string theory, more precisely in each string vacuum, the Yukawa couplings are calculable. In the leading order, they may arise from various intersection numbers between branes and other geometric quantities. We may reverse-engineering determine the Yukawa couplings from the fermion masses.
Feb
15
comment Boosts are non-unitary!
Hi, they're hard to type on keyboards but most web pages etc. run on Unicode system to encode the characters which allows all of the alphabets etc. of the world! There are ways to type characters on English keyboard, too. Alt with 0161 pressed, release alt, could work on your keyboard (0160 is capital s-caron) although it types something else on mine LOL.
Feb
15
comment Boosts are non-unitary!
Try copy-paste. Yes, in Czechia, we have a Czech keyboard where "š" appears instead of "3" which is obtained as shift-3 and # is elsewhere, or with right alt, and so on. In tex, it is "backslash v space {s}", $\v s$, for some reason, it isn't allowed here. You can add a Czech keyboard in MS Windows. I am myself using a modified Czech American Lumo keyboard, downloadable from motls.blogspot.com/2011/09/… - it's as American as you can get, gives Czech characters more or less at usual Czech places, and allows 100 other characters by easy combos
Feb
13
comment Boosts are non-unitary!
It's related but this question is about the relativistic case but the older debate - both question and answer - is fully about the non-relativistic Galilean case so it's not quite the same problem.
Feb
13
comment Source Theory - Alternative to QFT
It was a pleasure, and good luck becoming a source theory expert - it may be sort of cool if you can do it.
Feb
12
comment Source Theory - Alternative to QFT
I hope so because Schwinger himself is one of the fathers of renormalization theory. But I haven't really learned renormalization in that way.
Feb
11
comment Ambiguity in number of basis vectors
possible duplicate of Hilbert space of harmonic oscillator: Countable vs uncountable? - it is really a mega-duplicate, see also physics.stackexchange.com/questions/87476/… physics.stackexchange.com/questions/65457/… physics.stackexchange.com/questions/98455/…
Feb
11
comment Why do people look different in a photo and in a mirror?
I was mostly joking, but I was also trying to point out that one has more freedom to fool himself when he looks at himself. The 2D/3D difference may make an impact, and so can the fact that one is moving in the mirror – the cuteness of one's motion may make many people more attractive. Mirrors sometimes have too little lightning - which is better for less physically perfect kinds of skin, and so on. But none of these things may be fully quantified up to the moment when you define what you really mean by beauty which is why 3 people have voted this question to be opinion-based.
Feb
11
comment Why do people look different in a photo and in a mirror?
It's due to a special optical effect that is taking place in the mirrors, see kb5.cz/wp-content/uploads/2013/03/…