New answers tagged measurement
1
Yes. Not only is it possible, the solution is not unique and there exists a solution that is independent of $\rho$.
So for $p_k$ being probabilities with $\sum_k p_k = 1$, you can say $E_k = p_k \mathbf{1}$, where $\mathbf{1} = \sum_j |j\rangle \langle j|$ (ie the identity matrix). Then $Tr[ E_k \rho] = p_k Tr[\rho] = p_k$. This works for all $\rho$.
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0
If you count the number of variables that you want to find you get 18 (=9+9, 2 hermitian operators, the third is fixed by the others), but you impose only four conditions on these variables (=2x2, the trace may be complex, the third trace is already counted), therefore I think it's impossible.
2
Well, in essence, they're equivalent. But you're probably comparing apples to oranges here – depending on your detector.
The error in your measurement will almost certainly be determined by statistical noise. Depending on the size of your detector (and its orientation), you might get 10 muons in far less than 10 minutes, meaning you could improve your ...
1
It depends a lot on the precision that you want to achieve on your measurement. As standard, it is considered that with 10 times that you run the operation it should be enough. But to know clearly the times that you need to run the operation, just check the standard deviation. With a few times, say 5, it is large but it goes down as you add more runs to the ...
2
Jinawee and dmckee have already given answers describing the bounds from the spherical capacitor technique.
A different, and more model-dependent, approach is to build and test empirically a theory in which the photon has nonzero mass. There are some theoretical difficulties involved, e.g., local gauge invariance is broken, and it's not trivial to show that ...
5
Quoting from my copy of the 2nd edition of Jackson's book on Classical Electrodynamics, section 1.2:
Assume that the force varies as $1/r^{2+\epsilon}$ and quote a value or limit for $\epsilon$. [...] The original experiment with concentric spheres by Cavendish in 1772 gave an upper limit on $\epsilon$ of $\left| \epsilon \right| \le 0.02$.
followed a ...
0
I know that the inverse square law has been verified at least 1 part in $10^{16}$.
Feynman Lectures said something about that.
2
The easiest method is to put a magnetic compass on one of the magnet's axes of symmetry, and orient the compass and magnet such that the magnet's field is perpendicular to the earth's. Then the tangent of the deflection angle is equal to the ratio of the fields.
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Here is the home page for the GUFM model website. It also includes a link to a freely available pdf of the modern reference. Also of interest is the NOAA WEBSITE.
GUFM MODEL HOMEPAGE
NOAA PAGE
Note that this model is based upon catalogs of geomagnetic field measurements, these did exist prior to 1800 - although as you would expect their quality and ...
1
Apologies for the hasty questioning. I found the reference in the File Description of the wikipedia image description page. The model is apparently called the GUFM model, for which a good reference is
Four centuries of geomagnetic secular variation from historical records. A Jackson, A R T Jonkers and M R Walker. Phil. Trans. R. Soc. Lond. A 358 no. 1768 ...
3
Take its differential form :
$$\mathrm{d} \rho = \frac{1}{4/3 \pi r^3} \mathrm{d}m - \frac{m}{4\pi r^4}\mathrm{d}r$$
The greatest variation in $\rho$ will be achieved when all the terms add positively
$$\delta \rho =\frac{1}{4/3 \pi r^3} \delta m + \frac{m}{4\pi r^4}\delta r$$
Factor of $-3$ appears as matter of integration. Which you can recast into
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How about the [Feigenbaum constants?],1 I'm not sure if they have been proven irrational though. Anyone know btw?
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One of the directions to look at goes under the name of "commensurability". Imagine electrons that can travel on a two-dimensional lattice and suppose there is a constant magnetic field perpendicular to the lattice. Making a discrete loop on the lattice will add to the electron-wavefunction an Aharonov-Bohm phase propotrional to the area coverd by the loop. ...
1
This answer is kind of parallel to Brandon's, because I want to emphasise the point underlying these types of observations.
We will never be able to observe a black hole, because for external observers the formation of an event horizon takes an infinite time. This may seem a bit pedantic, but it's an important point because our aim is not to directly ...
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There are so many ways we can either directly or indirectly detect black holes that this answer will be necessarily incomplete.
Although no light can escape a black hole, the effects of black holes on the space, matter, and activity around them is often very dramatic. One of the most common ways is via an accretion disk of matter spiraling around the ...
2
I think the best physical references would be at the high end, such as the maximum volume of undistorted sound around 194 dB. There are several other examples of sound pressure level including one on Wikipedia. I don't know enough to know if a thermoacoustic device would meet your requirements, but that's another possibility, anyway.
As an added note, I ...
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For the purpose of solving problems in physics class, uncertainties are not that important, as the solution will usually be stated to 2,3, or 4 significant figures. However, it is important to understand the concept of uncertainty to be able to do lab work, and to understand if your data are reasonable or not. Uncertainty is usually mentioned in the ...
0
The simplest device to measure magnetic fields (and not integrated magnetic flux) is an electron. The spin-up/-down energy splitting in a magnetic field is $g_S\mu_B B$ where $g_S \mu_B \sim 2.8~\mbox{MHz/G}$. This can be measured in a beam machine. The next simplest is the Zeeman splitting of atomic energy levels. The latter forms the basis of some of the ...
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