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The object of making the silicon sphere was not to define the kilogram by the mass of sphere, but redefine Avogadro's constant in terms of the number of silicon atoms. Then use the fixed Avogadro's constant to fix the kilogram. Avogadro's constant was defined as the number of atoms in 12 grams of carbon atoms. You can read up on the Avogadro project here ...

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Con: There are 3 naturally occurring isotopes of silicon, so isotopic purification would be required after elemental purification. I'm unsure about how hard it is to maintain pure silicon. Isotopically, beryllium would be better (100% $^9$Be, naturally), but I don't know about its reactivity, either. Carbon has two naturally occurring isotopes, but we know ...

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But light is essential to the theory of relativity. Yes you can measure distance in meters but time in space is not absolute. You could put a person on the start line and person on the finish lines with atomic clocks and they would not agree on when a person when the person started and finished. The person at the finish line would start the clock the ...

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From Roemer and Light Speed: The orbital period of Io is now known to be 1.769 Earth days. The satellite is eclipsed by Jupiter once every orbit, as seen from the Earth. By timing these eclipses over many years, Roemer noticed something peculiar. The time interval between successive eclipses became steadily shorter as the Earth in its orbit moved toward ...

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I've been taught that when you measure the value of an observable for some state of a system described by $|\psi\rangle$ then the state of the sistem "collapses" to the eigenvector associated with the eigenvalue measured. ... Following this logic, when you measure the position of a particle described by $|\psi\rangle$ and you get a value $x_0$ ...

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You can use the vector, just expressing it at a "lower level" is difficult When you say $\langle x| x_0\rangle = \delta(x - x_0)$ you are already succeeding, even if you're a little confused about what the "square root of a $\delta$-function" looks like in terms of a real, honest-to-goodness wavefunction. So for example once you have the above result you ...

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How do you describe a state with a density matrix after measuring position? If you already have a density matrix, you use the Heisenberg picture. In the Heisenberg picture the state never changes. Instead the operators corresponding to observables change in time. So if you measure position at time $t_1$, then density matrix and state does not change, but ...

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The energy shifts of transitions including the s-orbitals of various isotopes of hydrogen are dependent on the proton's charge radius and are a surprisingly sensitive tool for this kind of thing. Recently this has been checked with muonic hydrogen, with surprising results. Paper at http://dx.doi.org/10.1126/science.1230016, and references therein. Related ...

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You seem to think that when you measure one entangled particle, the other is affected even if you have not interacted with it. If that were true, then the result of the measurement on the first particle would determine the result of the measurement on the second. And then if you measure them at the same time, there is a problem of how to determine the tie ...

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Short answer: This is impossible in principle for all states. A bit more elaborate: Given any state, by the postulate of quantum mechanics, it will be projected into the eigenspace of the eigenvalue measured when measuring an observable (this can be extended to quantum instruments). This means that the state will not be altered if and only if it is in the ...

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It depends on the packaging: it's highly variable. But by far the most common one is defined by the Synchronous Digital Hierarchy standard or the almost identical American SONET standard. This is pretty much standard on all optical trunk networking. The data for this answer and your question will almost certainly have passed through an SDH link for the ...

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https://en.wikipedia.org/wiki/Optical_fiber states that a rule of thumb is that the speed of light in an optical fiber is 200,000 kilometers per second. https://en.wikipedia.org/wiki/Fibre_Channel states the fibre channel networks run at 2,4,8 and 16 gigabits per second. ...

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Ever since Einstein formulated relativity we describe spacetime as a manifold equipped with a metric. Then we can use all the machinery of differential geometry to calculate properties of our spacetime. In particular, volume is defined using the volume element, $dV$, and we get volumes by integrating $dV$. For a flat space with Cartesian coordinates the ...

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It is correct if not equivalent in most contexts. For example, if you have a cuboid tank for water, $m^3$ would be the unit used to denote its volume, $m$ the depth of water. Then, when you try to denote the ratio of volume of water to depth with the unit $m^3/m$, you suddenly realize what you are trying to mean is equivalent to its horizontal ...

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$${m^3\over m} = {m^3\over m^1} = m^{3-1}=m^2$$ Units work the same way as algebraic quantities, at least with integer powers. A volume divided by a length will give something with the same dimensions as an area.

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