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3h
comment Does a set of eigenvalues in QM correspond to a random variable in statistics?
But ValterMoretti is talking about measurements of two observables (which as I understand don't commute in QM in general). That is not what I'm asking about. My question is much simpler and only concerns the measurement of a single observable.
4h
comment Does a set of eigenvalues in QM correspond to a random variable in statistics?
The term "eigenvalue" does not appear in the answer of ValterMoretti you link to, so I think my question is different.
Feb
1
comment Is what statisticians call a “random variable” what physicists call an “observable” in QM?
Terence Tao seems to share my view "...and quantum mechanics (with physical observables taking the role of random variables, and their expected value on a given quantum state being the expectation)" (terrytao.wordpress.com/2010/02/10/245a-notes-5-free-probability)
Feb
1
comment Is what statisticians call a “random variable” what physicists call an “observable” in QM?
That is interesting. Can you put your statement about four tuples of binary random variables into a mathematical form?
Jan
29
comment What is the point of complex fields in classical field theory?
@Numrok But isn't a set of two real scalars a vector? The two scalars also have the same units and it is often said, that complex numbers can be represented as vectors.
Jan
29
comment What is the point of complex fields in classical field theory?
@Numrok I'm not sure about that point, too. The idea is that a complex number is by definition a en.wikipedia.org/wiki/Scalar_(physics) quantity, so invariant under coordinate transformation. But a vector of two real quantities is not a scalar. So it is not invariant under coordinate transformations.
Jan
22
comment Why don't antiparticles have antispin?
@ACuriousMind: Wouldn't a change in P (=parity?) imply spinning backwards?
Jan
14
comment Why is the Fourier transform more useful than the Hartley transform in physics?
@Daniel Sank: Thank you. Actually I was expecting somebody to say something along the line that a optical lens performs a Fourier transformation and not(?) a Hartley transformation, and that is why Fourier is more "physical". But your edit is very interesting, too.
Jan
12
comment Why is the Fourier transform more useful than the Hartley transform in physics?
I would love if someone could address this part of the question: "Are their any properties that make the Fourier transformation more "physical"?" .
Jan
12
comment Why is the Fourier transform more useful than the Hartley transform in physics?
@DanielSank I know that hermitian means, that the operator has real eigenvalues. What confuses me is that an operator involving the imaginary unit like $i (d/dt)$ can in fact have real eigenvalues. But maybe this leads to far away from the original question. Maybe I ask another question about this. Thank you.
Jan
11
comment Why is the Fourier transform more useful than the Hartley transform in physics?
@DanielSank Isn't the eigenvector of $(d/dt)$ simply the real exponential function $e^{x}$ ? Why is the exponential function with a complex argument be used for the Fourier transformation?
Jan
9
comment Why is the Fourier transform more useful than the Hartley transform in physics?
I think it is interesting to note that when looking at second derivatives both kernels show again the same behaviour: $(d^2/dt^2) \text{cas}(\omega t) = -\omega^2 \text{cas}(\omega t)$ and $(d^2/dt^2)\exp(i\omega t) = - \omega^2 \exp(i \omega t)$
Sep
2
comment Is the universe a Turing machine?
Do you have a reference that shows, that classical mechanics is non-computable?
Mar
17
comment What was the amount of energy released in the 9/11 terrorist attacks?
I see what you want to say: en.wikipedia.org/wiki/Orders_of_magnitude_%28energy%29 .
Mar
7
comment Why is the imaginary unit conventionally put on the right hand side of commutation relations?
I believe this question is more than just about convention. It touches also the question whether a "pure" commutator $[a,b]$ is actually a physical meaningful quantity or not. I believe it is not, because it is a complex quantity and not an observable. But I could be wrong, there might be other important reasons why relations between complex quantities like commutator relations are still of interest in QM and that is why I asked the question.
Mar
2
comment How can it be that the beginning universe had a high temperature and a low entropy at the same time?
Unfortunately the link to the paper is dead. Is this the article you are talking about : Davies, Cosmological dissipative structure, International Journal of Theoretical Physics September 1989, Volume 28, Issue 9, pp 1051-1066 ?
Jan
27
comment Good book on the history of Quantum Mechanics?
I believe this is the correct reference for D. J. Candlin: On sums over trajectories for systems with Fermi statistics: Il Nuovo Cimento, 1956, Volume 4, Number 2, Page 231 (DOI: 10.1007/BF02745446)
Aug
15
comment Is thermodynamic free energy and potential energy the same thing?
Can one say that thermodynamic free energy is the same as potential energy in the limit when the number of particles N -> 1?
Jul
20
comment Homemade salad dressing separates into layers after it sits for a while. Why doesn't this violate the 2nd law of thermodynamics?
I think this could also happen without friction. The selfgravity of the balls would make them clump together , if their initial speed is not too high (see en.wikipedia.org/wiki/Jeans_instability). Does that mean that for a selfgravitating system a clumped/ordered state can be the one with the highest entropy?
Apr
16
comment Can nowadays spin be described using path integrals?
Google books allows to see the relevant pages online: books.google.de/…