You can interpret that as a lazy "it is numerically equal to 1 in whatever units I chosee", as a "it has become dimensionless and fully equal to 1" or as a notation trick saying "Everything that's dimensionally a power $p$ of action gets implicitly divided by $\hbar^p$ to make the formulae simpler"
@ThomasKlimpel conservation of energy is always meaningful. What Einstein was saying (einsteinpapers.press.princeton.edu/vol6-trans/401) is that there is no magical mysterious method by which the ascending photon loses energy. Instead if I lift you up I do work on you. I add energy to you. So to you it looks like the photon lost energy when it didn't.
@ACuriousMind : and what happens in practice, is that NIST optical clocks go slower when they're lower. Then if you open up one of those clocks, you don't find any thing called time inside them. See the Shapiro Time delay (en.wikipedia.org/w/index.php?title=Shapiro_time_delay): "according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path".
no, but if it's bad I want to get it out of my system instead of slowly realizing it over a few evenings and if it's good I don't want to have to try to work without sleep :P
"A dirty coin doesn't necessarily mean just viruses and bacteria, most of the visible dirtiness you use is caused by dirt or oxidation. When coins are used by people, no matter how well you wash them, they will leave (lipids) oils, dirt, and (amino) acids from your skin that tarnish the metal. In the case of pennies the copper reacts with the oxygen in the air causing copper oxide."
What you're specifically describing is typically known as UV degradation. The color change is due to the oxidation of the polymers that make up the plastic. These chemical reactions are demonstrated in satisfying detail here. Under the section titled "Photodegradation" is where you can find th...
For $N = 2$ in $(1,1)$ dimensions this apparently means, for example $$\Phi(X) = \Phi(X_0(\sigma_1),X_1(\sigma_1);X_1(\sigma_2),X_2(\sigma_2)) = X_0(\sigma_1)^{44} + \frac{2}{3} X_0(\sigma_2)^3 + X_0(\sigma_2) X_1(\sigma_1) + X_1(\sigma_2)^3.$$ Does 3.2 then mean, if $\mathcal{L} = \Phi(X)$, that $$\Pi[X,\sigma_2] = \frac{\partial \mathcal{L}}{\partial X_0(\sigma_2)} = 2 X_0(\sigma_2)^2 + X_1(\sigma_1)?$$
Earlier he writes $P(\tau,\sigma) = \frac{\delta \mathcal{L}}{\delta (\partial X_0/\partial \tau )}$ for the usual first-quantized Polyakov action
The comment below 3.2 about the infinity of times is just super jarring
Sometimes I find a particular concept which I can't find much description about in the books I know. Is it accepted to ask for references in such scenarios?
Guys help me out! What does “positive definite” mean in this context? — “the Green's function for the wave equation in even spatial dimensions is positive-definite inside the light cone, so you can't get destructive interference“
What you're specifically describing is typically known as UV degradation. The color change is due to the oxidation of the polymers that make up the plastic. These chemical reactions are demonstrated in satisfying detail here. Under the section titled "Photodegradation" is where you can find th...
Sometimes I find a particular concept which I can't find much description about in the books I know. Is it accepted to ask for references in such scenarios?
