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bio website motls.blogspot.com
location Czech Republic
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Hi, I am a string theorist and a publicist.


Jan
7
comment Physical meaning of the energy density of an electrostatic field
Quite generally, you are imagining that the energy and work have to be mechanical and the fields are "completely different". But they're not completely different. The energy density $E^2/2$ may be imagined as having a spring, energy like $kx^2/2$, at each point of space (or in a dense lattice): you just call it $E$ instead of $x$, and there are 3 springs per point, $E_x,E_y,E_z$. Then the changing of the energy in the electric field is the same kind of work as stretching a spring. These are words that may be disputed; the formulae express exactly what I mean and what is true.
Jan
7
comment Physical meaning of the energy density of an electrostatic field
Dear Marco, "moving charges" is a mechanical work. But mechanical work is not the only type of work. Just like there's energy in electric field, there's el. work. A transformer is made out of 2 coils inside each other; one of them works to increase the magnetic field in the other which ultimately induces the current in the other coil; and although they're not mechanically connected (and they're not connected by conductors, either), it's possible to transfer energy between them. This energy, coming from the otherwise disconnected 2nd coil, may be later used to lift an elevator or anything else.
Jan
7
answered Why is it concluded that the cosmos is expanding when in fact the observations are for events further back in time?
Jan
7
answered Why is spacetime near a quantum black hole approximately AdS?
Jan
7
comment Differentiation of the action functional
Now I see you fixed you eqn in the subcomment before the deadline. So yes, it's valid for finitely or countably many variables $x_i$, but in the case you started with, functional analysis, there are continuously infinitely many variables $x_i(t)$ that depend on a continuous $t$ and not just discrete $i$, so there has to be the integral over $t$ as well. The integral $\int dt$ has nothing to do with the variation itself - it's a continuous generalization of the summation $\sum_i$.
Jan
7
comment Differentiation of the action functional
Dear Whelp, not quite. The left hand side of your latest equation is "infinitesimal", you know, its size is 0.0000000001, so to say, while the right hand side is finite, comparable to 1, so they're clearly not equal. The symbol $d$ or $\delta$ in front of a variable only represents the "numerator". The valid equation is $\delta I = \sum_i (\delta I / \delta x_i) \delta x_i$. In this case, there are continuously many variables $x$, so $\sum_i$ must become $\int dt$ and $x_i$ becomes $x(t)$. I am confused: I am explaining you the very equation you started with. Why are you trying to damage it?
Jan
7
comment reflection, refraction and diffraction occur in radio waves, which one occurs the most?
Dear David, while I agree that the question isn't totally quantitatively well-defined, I am confident that people who actually understand radio waves would have something to say – whether reflections in the forests may be neglected or not etc.
Jan
7
revised Photon spin projection to arbitrary axis
added 679 characters in body
Jan
7
answered Photon spin projection to arbitrary axis
Jan
7
answered Physical meaning of the energy density of an electrostatic field
Jan
7
answered Differentiation of the action functional
Jan
7
comment Uniqueness of the 5 string theories
Let me just say that at the leading order, the partition sum that has to cancel has relevant open-string-related and unoriented contributions from the cylinder (2 boundaries); Klein Bottle (2 crosscaps); Mobius strip (1 boundary 1 crosscap). Those 3 terms may be written as $(b+c)^2$, formally, where $b$ is an insertion of one boundary and $c$ is the insertion of one cross cap. In this way, one may reduce the cancellation to the cancellation of dilaton tadpoles from a cross cap and from colored boundaries themselves, and this calculation says that the number of half-colors has to be $2^5$.
Jan
7
comment Uniqueness of the 5 string theories
Dear Squark, the anomaly that has to cancel is the "dilaton tadpole", a one-point function of the dilaton vertex operator, see e.g. scholar.google.com/… - It's related to the vacuum energy density in spacetime (partition sum with no insertions). A nonzero value would make the perturbative physics inconsistent, to say the least, because the energy density would blow up as $1/g$ or so and one can't $g$-expand around it.
Jan
7
comment String landscape in different dimensions
A good example of the richness of the vacua even in 7 large dimensions and above. See Triples, Fluxes, and Strings: arxiv.org/abs/hep-th/0103170 - various disconnected components of commuting Wilson lines, dualities between these vacua etc. I think it's a great paper by 7 authors, a substantially undervalued one (with 100 cits or so).
Jan
7
answered Is it possible to create a hologram using X-Rays?
Jan
7
comment Advanced topics in string theory
And one more comment. I still feel that you underestimate the perturbative part of the theory. In the mid 1990s, there's been a huge activity that ultimately clarified many features of the non-perturbative behavior of string theory. But it's still true that most of the phenomena are accessible from one perturbative description or another - dualities are just statements of equivalences (sometimes nonperturbative equivalences) between different descriptions that were known perturbatively. But much of the "explicit" quantitative calculation has to use some expansions.
Jan
7
comment Advanced topics in string theory
Matrix string theory was reviewed in various papers e.g. Susskind-Bigatti and Taylor, see the resource letter by Marolf at the bottom of my 2006 page. Little string theory is extremely special. One should read the original papers and their most important followups. This is a domain intensely studied by a few people in the world so it's obviously not terribly efficient to write "textbooks" of it.
Jan
7
comment Advanced topics in string theory
Otherwise I skipped F-theory, Matrix theory, and little string theory. There are specialized reviews of those because they're really special. To understand F-theory including the applications that give it the "juice", one must understand lots of algebraic geometry, bundles, and so on. A great arena for people who love (advanced) geometry. The physical essence is really simple: it's type IIB where the axion-dilaton $\tau$ is interpreted as the complex structure of a $T^2$ fiber of two new dimensions attached to each point.
Jan
7
comment Advanced topics in string theory
Dear @Squark, thanks for your interest. SFT didn't really "fail". It is a totally consistent and from many viewpoints uniquely useful - "explicitly local, off-shell" - formulation of perturbative open string dynamics and the open-string-related solutions such as D-branes solutions (as tachyon condensation from other D-brane starting points). The most explicit and rigorous framework to discuss tachyon condensation etc. It's very manageable in the bosonic string case. People could have expected some other miraculous things from SFT but there have never been "rational justifications" for them.
Jan
7
comment Advanced topics in string theory
This URL was (for years) on the top of my page, too. ;-)