# Tag Info

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The speed of light is constant. The reason the observed speed of light seems to slow down as it passes through a medium is because the photons interact with the particles of the medium. The photons never actually slow down, we just perceive their interaction with the medium.

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It's called isochoric process. For thermodynamical systems, work done is always associated with change in volume. When change in volume is 0, I.e. process is isochoric, no work is done

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That is a naming scheme of National Electrostatic Corp. (NEC), and is likely trademarked. The number has to do indirectly with the maximum terminal potential. Their website (pelletron.com) has more info. Not employed by NEC, long time user of their machines (and many others).

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I would guess that given that the book was designed to teach amateur astronomers that most of the book refers to measurements made with reference to earth. Now, you can measure the component of velocity along the distance line between the star and the earth by using the doppler effect and the adsorption lines for particular elements(measuring the adsorption ...

2

It's pretty natural to think that a star can have velocity - there's no reason a star shouldn't be able to move. The first thing you need to know is "velocity relative to what?" Stars in our galaxy are all in some kind of orbit around the galaxy, so you can talk about velocity in galactic coordinates. Binary stars orbit each other, so you can talk about ...

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Good answer by udrv. The importance of perturbative approach was also studied by Aitchison, McManus and Snyder. I think this work is one of the best that deals with Heisenberg's 'magical' paper. As far as I can understand, there have been classical solutions for anharmonic oscillator by Born and Jordan. I don't know how Kramers is involved. The solution ...

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Apparently Heisenberg referenced the perturbative approach to the quartic oscillator because his advisor and mentor, Max Born, was trying hard to use it in an attempt to push quantum theory past the Bohr model. Born actually invited Heisenberg to work on this problem in his group, and this is where Heisenberg had his breakthrough insight on the need for an ...

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Superposition involves linking multiple particles via a single dimensional thread of wave energy. In contrast, entanglement involves the separation of space-time; i.e. a single point in space split into more than one location.

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If the first measurement yields the value $A_1$ with certainty, this means the initial state has collapsed into $u_1$ after the first observation. In particular one has, inverting the above back: $$|u_1\rangle =\frac{\sqrt{3}}{2}|v_1\rangle + \frac{1}{2}|v_2\rangle.$$ Now a measurement of the observable $B$ must be performed and then one more measurement ...

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It's just polarization. Inductive charging requires at least three objects two of which must be conductive. The two conductive objects can be charged by induction by first inducing a difference in charge between them with the third object. This is only possible if charges can flow between the two conductive objects. Then the conductive path between those ...

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He is saying that for both the coupled harmonic oscillators and the electron in the chain of atoms: if you start an irregularity in one place, the irregularity will propagate as a wave along the line That's basically just what it means to be coupled. If one starts doing something weird its neighbor will be affected so it will start doing something ...

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I'm not sure what might be confusing you. Assume, as in most cases with the Golden rule, that the transition rate is constant, $\Gamma$. So, for small times, the cumulative transition probability is $W=\Gamma t$. Think of the transition as leakage from a vessel. At $t=0$, no water has been lost, but with a constant rate of leakage, $\Gamma$, the longer ...

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As you understand from the term itself it has to do with the penetration of heat into a material. Suppose you have a sufficiently thick material (size $D$) of uniform temperature ($T_0$), where you apply a constant (different) temperature ($T_1$) at one side. Eventually, your whole material will be at this new temperature $T_1$. But before this happens, ...

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In an unbound fluid it is sufficient to presume the adiabatic behavior (i.e. no heat transfer and "conservation of enthropy"). BUT! When we examine the flow in the nearby of walls and other real solid boundaries there is a significant energy dissipation due to viscosity, friction etc. etc. connected with thermoacoustical effects. E.g. if we have a duct wide ...

1

For linear operators, the support usually denotes the space which is orthogonal to the kernel (equivalently, the space spanned by the columns of the matrix). Density operators are linear operators, and thus it is used in this sense in the papers you cite. See also this question at math.se or this book from a google search "support of a linear map"

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I am a professor of theoretical physics (although with a doctorate in applied mathematics), and I had never heard of "approximative reduction" until just now. Following the links in the question, I could get a vague idea of what it meant, but it is not something that I have ever studied or discussed with other scientists. I would conclude that this topic ...

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I've often encountered the $\ll$ sign in contexts like: Given $A \ll B$, a certain property $P$ holds - not approximately or as a limit, but exactly. This is then the opposite to that $P$ would be true for $\gtrsim$ or $\gtrapprox$ (depending on style). I don't remember specifific cases, but I've seen the latter in studies of dynamic systems, chaos etc. ...

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I think the answer is no. It generally precedes some approximation method with a bounded error, but there are so many approximations methods in physics -- some rigorous, some nonrigorous -- that it's way too presumptuous to give it a rigorous definition. Generally, it means one of several things: If $a\ll b$, expanding in powers of $\frac{a}{b}$ is ...

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There is a consistent definition, but it involves a couple of arbitrary thresholds, so I doubt you'd consider it rigorous. The construction $X \gg Y$ means that the ratio $\frac{Y}{X}$ is small enough that subleading terms in the series expansion for $f\bigl(\frac{Y}{X}\bigr) - f(0)$ can be neglected, where $f$ is some relevant function involved in the ...

4

It is a symbol and an idea used in mathematics too. But the important part is just that $B$ is 'ignorable' relative to $A$. This depends on the level of precision that is being used experimentally. If you're working to a precision of 1 part in 100, then $B$ should not effect the answer to that level of precision. If you're working to 1 part in a million, ...

1

I think there is a rigorous definition of "$\ll$" sign which is opposite to what you are asking but equally useful notion. You should read this "$\ll$" as is negligible compared to. For example, $f(x) \ll g(x)$ near $x=x_0$ (in a more general context) iff $\frac{f(x)}{g(x)}\to 0$ as $x\to x_0$.

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So there are different kinds of damping on simple harmonic oscillators, but the most common type is a force linearly proportional to velocity acting in the direction opposite to the direction of motion of the oscillator. This works for a vertically oriented spring with an object hanging at the end, since that single damping force is drag, which is a type of ...

1

I don't think that my terminology is suitable, because the term hidden realm carries the connotation of hidden variable theories, which is something else. I don't see them as very different. A hidden variable theory could take as the hidden variable the spinor or the wavefunction as a hidden variable. Many do. Events in the measurable realm ...

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There are classical and quantum descriptions of the world. One of the differences of quantum description is paying attention to the process of measurement and how it affects the measured system. Description of measurements is an integral part of quantum description. Splitting this is into "realms" doesn't make much sense.

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They are very different concept. There are observables that are continous and observables that are quantized. A quantized quantity can take only discrete values. On the other hand, all measures are performed only with finite precision. So each observable can be measured only with finite precision, indipendently of its continuous or quantized character. Let ...

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I think the term "discretisation" in numerical analysis is completely different from "quantisation". In the first case the quantity is actually continuous(e.g. a function of space) but we divide into small parts just to get an practical result. Given enough time and ample computational strength the parts can be as small as one wishes. Whereas, ...

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Quantisation does not imply discreteness. If a system has been quantised, we just mean we have taken the set of states, and replaced it by a vector space of states. In other words, one can add states in quantum mechanics, allowing a system to be in two states "at once". Observable quantities become certain operators acting on this vector space of states. As ...

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The Hilbert space formulation, sometimes with the explanatory add-on: "where observables are represented by linear operators acting on Hilbert space". Both the wave and matrix sub-formulations are basically shadow-double formalisms for the very same structure.

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