Luboš Motl

Czech Republic

motls.blogspot.com

Age: 41

Hi, I am a string theorist and a publicist.

6h
comment Is there a spacelike curve connection two events in Minkowski space?
Dear @Richard, what is exactly the "problem" you are referring to? What you described, with the $ct$ as the time component, is the most widespread description of a timelike curve. That's exactly what a timelike curve is - a trajectory $\vec x(t)$ which is moving at a speed $v\lt c$ at each moment. Spacelike curves indeed correspond to propagation by $v\gt c$ in your parameterization, which is prohibited for massive objects.
6h
revised Is there a spacelike curve connection two events in Minkowski space?
added 217 characters in body
6h
answered Is there a spacelike curve connection two events in Minkowski space?
23h
comment Did NASA mistakenly create a warp field?
Dear Kyle, I am not sure. This article was posted on Sputnik News, a rather major Russian information source that was previously running the news of RIA (try en.ria.ru), and it cites posts on a NASA forum. This is in fact a rather typical example of the flow of information through the media - similar sources are being used, and similar news outlets are key in spreading them. The result in no way guarantees that the "hot news" inside is right. There are both tons of false positives and false negatives, big events that don't get reported and bogus events that do get reported.
1d
comment Why is there zero point energy at absolute zero temperature?
Because energy is something else than entropy. The lowest (zero) entropy occurs if there is the minimum number of microstates that have approximately the same macroscopic appearance, namely one such state. So it's an isolated state of the lowest entropy. But such a state, by the laws of quantum mechanics, especially the uncertainty principle, has to balance the kinetic and potential energy, so both of them (and their sum) are nonzero. To have an exactly zero energy for a harmonic oscillator (and similar other systems) would mean to have $x=0,p=0$ exactly which is forbidden.
1d
answered Are electrons just incompletely evaporated black holes?
1d
comment Did NASA mistakenly create a warp field?
Zero. Warp drive is prohibited by relativity, energy conditions, and other laws of Nature, see e.g. quora.com/… Sorry, Kyle and his upvoter, but the laws of Nature are a vastly more accurate guide than what the media write or not write.
1d
comment The integral is zero! $\int \frac{\mathrm{d}^d k}{(2\pi)^d} = 0$
Dear Marcel, when doing physics and related forms of calculus, the sum isn't interpreted as a limit of partial sums but in a more general, natural, and physical way, and it is often literally written to be equal to the constant for a very good reason. Divergent sums and integrals appear everywhere in quantum field theory (physics) but that doesn't mean that one can assign them with any value he wants. They have to be regularized, renormalized, and the final result may depend on some parameters. In $\sum n$ the dependence goes away and the finite part of the sum is always equal to $-1/12$.
Apr
23
comment Does the path integral measure have dimension?
In principle, one can imagine the logarithm of dimensionful things as well - but they produce things like bizarre additive log(meter) terms. But in quantum mechanics, there is a reason why you are right: one computes the path integral over a spacetime with a thermal circle. And the Euler character of $A\times B$ is $\chi_A\times \chi_B$, and because $\chi$ of a (thermal or other) circle $S^1$ is zero, $\chi=0$. In classical statistical physics, one must be more careful about the normalization factors in front of $Z$ when going in the continuum limit.
Apr
23
answered Does the path integral measure have dimension?
Apr
18
comment Double slit experiment in the Heisenberg picture
Try to read > motls.blogspot.com/2015/04/… for my treatment of the double slit experiment in the Heisenberg picture.
Apr
18
comment 273 + degree Celsius = Kelvin. Why 273?
Particle physicists do, and they usually express energy - and therefore also temperature - in electronvolts and its power-of-ten multiples. Room temperature is about 0.025 electronvolts: wolframalpha.com/input/…
Apr
16
comment What are the alternatives to the Periodic Table of the Elements?
No, getting closed as a duplicate means that the questions are merged as duplicates.
Apr
16
comment Making a bright beam of artificial white light
@fffred, fair enough. But you're asking people to solve a very technical engineering problem. Physics is really about the individual mechanisms that may make something work. One may discuss the useful components - small holes, strong sources, lenses, mirrors, reduction of size of the source of light etc. It's pretty clear that there is no miraculous way to make ordinary light laser-like without combining the things above. Why don't you buy a laser? They are cheap. You may combine several colors of laser beam, too.
Apr
16
awarded Editor
Apr
16
comment Organisation in Periodic table
I don't think that this is really a duplicate of that previous question - at least people react nervously over there that mine is not an answer. Anyway, it is an answer to this question, see: chemistry.stackexchange.com/questions/901/…
Apr
16
revised What are the alternatives to the Periodic Table of the Elements?
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Apr
16
comment What are the alternatives to the Periodic Table of the Elements?
This is an answer to another question that was labeled a duplicate and closed. It's not my mistake if it was labeled a duplicate even though it is not.
Apr
16
comment Making a bright beam of artificial white light
Dear @fffred, you mentioned my name but I think that you have ignored 100% of my comment. I was talking about a parabolic mirror in the flashlight, not a pair of holes.
Apr
16
comment Light clocks measure conformal time - detailed argument
Sorry, this equation is completely wrong. If you have $r$ as a function of $\tau$, the correct formula is still $r(\tau)=r(\tau(t))$, i.e. $r=r$. There is no $dt/d\tau$ here. The latter factor only appears if you express the derivative $r'$ - $dr/dt$ and $dr/d\tau$ differ by this factor.
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