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Jul
8
comment How does one determine an inertial frame?
I like this related list.
Jul
8
comment How does one determine an inertial frame?
Yes, that's right. But it doesn't follow that one needs general relativity, just because the latter is a theory that doesn't exhibit this unnice circularity. One needs that particular alternative IF what? Maybe you mean if you want to describe gravity without inertial frames? You could just drop the obligation and state that the research relevant theory of general relativity doesn't make use of those frames.
Jul
8
comment How does one determine an inertial frame?
+1, the "really, on can't" was not yet stated like this in the answer section. (But I'm not sure what "one needs General Relativity, since..." really means, though - Newton didn't seem to need it either. When it comes to pure understanding of things, I think it's always unfinished business: The question what the right energy tensor for a physical situation should be is open enough to claim, I think, that the problem is just moved.)
Jun
29
comment Why can't the Navier Stokes equations be derived from first principle physics?
But probably one can't properly talk without making statements susceptible to semantic criticism like that. Where's the "let's take this to the chat" button here, actually?
Jun
29
comment Why can't the Navier Stokes equations be derived from first principle physics?
@CuriousOne: I don't understand how the second sentence about trusting principles is an "instance" elaborating on the "elements that are used by theory" in the first sentence. I also don't quite grasp what you mean by "do physics" here, if it's something I can only do when I have trust in a meta-principle. If you advice a Bachelor student to do an experiment, is he not doing physics? He doesn't need to have faith, he can work like an automaton and report back once something doesn't work.
Jun
29
comment Why can't the Navier Stokes equations be derived from first principle physics?
@CuriousOne: I'm skeptical that experiments can be first principles. An experiment is formulated with reference to a theory - for example they might be done by humans that have a notion of "particle", "mass", "location" which are theoretical physical concept which are more of less hard to define and not necessary. Maybe it works if "an experiment" is nothing than a sheet of numbers to you. As soon as you imply "this is a sheet with distances, measured in time intervals of five clock ticks", you're deep in theory land, speaking in context of a bunch of notions that people made up.
Jun
24
comment Why does hot oil explode when pouring water on it?
@babou: "debt". I feel honestly saddened you didn't listen to me at all.
Jun
24
comment Why do we must initially assume that the wavefunction is complex?
@ValterMoretti: I read your answer without reading the comments and was also confused at first. "End of 1900" should be the end of the year 1900, while you mean the end of the 20'th century. I see people discuss an associated issue here.
Jun
22
answered Hamiltonian related to Riemann zeta function
Jun
19
comment Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$
@smiley06: Ah, here's another factoid: The sum was exploding as $\frac{1}{(1-z)^2}$, and the finite limit emerges after subtracting $\frac{1}{\log(z)^2}$. More broadly, $$\dfrac{1}{\log(z)^n}=\dfrac{1}{(z-1)^n} \left(1+ \frac{n}{2} (z-1)+ \frac{n}{2} \frac{3n-5}{12} (z-1)^2+\frac{n}{2}\frac{(n-2)(n-3)}{24}(z-1)^3+\dots\right)$$ and use may use this to produce limits for high powers too. Above, for $n=2$, you got $-\frac{2}{2}\frac{3\cdot 2-5}{12}=-\frac{1}{12}$. Or plug in $n=1$ and you find $-\frac{1}{2}$.
Jun
19
revised Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$
added 24 characters in body
Jun
19
revised Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$
added 263 characters in body
Jun
18
comment Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$
@smiley06: In that light, it's not so surprising that it pops in connection to the Riemann zeta function, which has the integral representation $\zeta(s) =\frac{1}{\Gamma(s)}\int_0^\infty\frac{x^{s}}{e^x-1}\frac{{\mathrm d}x}{x}$. And now take another look at Planck's law $B_\nu(\nu, T) = \frac{ 2 h \nu^3}{c^2} \frac{1}{e^\frac{h\nu}{k_\mathrm{B}T} - 1}$. I can go on..
Jun
18
comment Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$
@smiley06: Or say you want to compare the difference $\Delta_h f(x)=f(x+h)-f(x)$ with it's first order approximation $f'(x)\,h$. You'll find $$\dfrac{f'(x)\,h}{\Delta_h f(x)}=1-\dfrac{f''(x)}{2!}\left(\dfrac{h}{f'(x)}\right)+\left(\dfrac{f''(x)\,f''‌​(x)}{2!\,2!}-\dfrac{f'(x)\,f'''(x)}{1!\,3!}\right)\left(\dfrac{h}{f'(x)}\right)^2‌​+{\mathcal O}(h^3).$$ Note that $\frac{1}{2!\,2!}-\frac{1}{1!\,3!}=\frac{1}{1!\,2!\,3!}(3-2)=\frac{1}{12}$! :)
Jun
18
comment Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$
@smiley06: I have a bunch of other perspectives too. It's interesting to point out that the $\frac{1}{12}$ here is "the same" as the one in Baker–Campbell–Hausdorff formula or the Todd class.
Jun
18
revised Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$
edited body
Jun
18
revised Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$
edited body
Jun
18
comment Why does hot oil explode when pouring water on it?
@babou: If you actually read his main work, you'll find that Gods are by far not the only Master figures. Start with the first page here, it's written in an entertaining way, too.
Jun
18
comment Why does hot oil explode when pouring water on it?
@babou: What do you mean by the Masters line here?
Jun
18
comment Why does hot oil explode when pouring water on it?
@babou: I don't understand what you say here. The s at the end is also not part of his name, did you even look at the linked page?