98,434 reputation
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bio website motls.blogspot.com
location Czech Republic
age 40
visits member for 3 years, 6 months
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Hi, I am a string theorist and a publicist.


Oct
24
answered If electric charges accelerate towards lower potential energies, why do opposite charges attract?
Oct
24
answered What is the fundamental probabilistic interpretation of Quantum Fields?
Oct
24
answered Spin decomposition in general
Oct
23
revised Speed of a particle in quantum mechanics: phase velocity vs. group velocity
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Oct
23
answered Speed of a particle in quantum mechanics: phase velocity vs. group velocity
Oct
22
comment What are quarks made of?
Well, you may imagine that strings are made out of string bits, a construction popular with Charles Thorn who promoted it. Like beads in a chain, you may design their interactions so that their bound states will be physically equivalent to strings when you're finished. At any rate, the question isn't exactly deep. It's not always true that things are made out of something more fundamental and it's clear that when we get to the Planck (fundamental) scale (or before that), any further "compositeness out of new things" has to end because there can't be things smaller than the Planck scale.
Oct
22
comment What are quarks made of?
You may also check what squarks, the superpartners of quarks, are made of: images.google.cz/…
Oct
22
comment Why the Principle of Least Action?
A philosophical answer but a good one. ;-)
Oct
22
comment Why the Principle of Least Action?
A fresh article trying to answer such questions: motls.blogspot.com/2011/10/…
Oct
22
comment Non-unitarity of wave function collapse
The "calculation" you wrote is completely nonsensical, Jonathan. $\delta(x)$ is still a function of one variable – or, in your completely needlessly nitpicking terminology (it's the point of such distributions that one CAN treat them as functions), a distribution acting on the space of functions of a single variable. You are confusing $[\delta(x)]^2$ which I proved is something else than $\delta(x)$ and ill-behaved even though both are functions/distributions of one variable that vanish outside $x=0$ with $\delta^{(2)}(x,y)=\delta(x)\delta(y)$ which waits to be integrated over two variables.
Oct
21
comment Air flow coming out of a fan feels much stronger than air flow coming in. Why?
All dissipating processes such as friction and viscosity break the time-reversal symmetry of the effective laws of physics.
Oct
21
comment Air flow coming out of a fan feels much stronger than air flow coming in. Why?
Well, right. When the air goes out of the fan, it's directed, so the air molecules are hitting your hand. On the other hand, when the air goes into a fan, it may go from any direction to fill the pressure gap and the solid angle is therefore much greater, reducing the velocity. I think that your intuition about a "natural symmetry" is a good one and if there were no turbulence, I believe that the velocities would be symmetric and had the same absolute values. So the symmetry violation is a consequence of complicated turbulent phenomena.
Oct
21
comment Non-unitarity of wave function collapse
Dear @Jonathan, your claim is obviously incorrect. $\delta^2(x)$ is much greater than $\delta(x)$. For example, you may write $\delta(x)=1/2\epsilon$ in the interval $(-\epsilon,+\epsilon)$. Its square is then $1/4\epsilon^2$ in the same interval and it doesn't integrate to one but to $1/2\epsilon$. That's no coincidence: $\int_{-\infty}^\infty dx\,f(x)\delta(x) = f(0)$, so if you substitute $f(x)=\delta(x)$ to integrate $\delta^2$, you get $\delta(0)$ on the right hand side which is definitely not one as it should be for the integral of $\delta(x)$ but a divergent constant.
Oct
21
revised Why higher frequencies in Fourier series are more suppressed than lower frequencies?
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Oct
21
revised Why higher frequencies in Fourier series are more suppressed than lower frequencies?
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Oct
21
revised Why higher frequencies in Fourier series are more suppressed than lower frequencies?
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Oct
21
answered Why higher frequencies in Fourier series are more suppressed than lower frequencies?
Oct
20
answered Why does charge conservation due to gauge symmetry only hold on-shell?
Oct
19
comment Modern avatar of Englert's solution?
I see, thanks for the clarrified connections etc., @José.
Oct
19
comment Non-unitarity of wave function collapse
Dear @Jonathan, in some modest sense, you may be able to "define" the square root of the delta-function but you won't be able to calculate with it. For example, you won't know what it evolves to. It's easy to see why. An ordinary delta-function evolves to the well-known nonzero functions at time $t$, calculable from the Green's functions. However, the square root of the delta-functions is proportional to delta-function but infinitely times smaller. So it will evolve into "zero" and unitarity will be violated, anyway. This is just not how the calcuations may be done.