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I agree with your definition of locality (probably not surprising :)). Causality I would say is the statement that an event in the future should not affect an event in the past. We can formulate this in classical physics terms. Causality is necessary in order for there to be a well defined initial value problem: I should be able to choose an initial time ...


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It isn't necessary to introduce the effective potential in orbital mechanics but it is really useful. Let's say we have a particle moving in a central gravitational potential. Newton's laws give you a vector equation of motion \begin{equation} m \ddot{\vec{x}} = - \nabla U \end{equation} where $U = - G M m /r$. In a general coordinate system this is a ...


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The term "preliminary" does not refer to the runs. It refers to the status of results and figures that have not been properly reviewed and/or approved for publication yet.


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I know this is an old thread, but I had to figure this out for a problem on my physics homework. What helped me to understand this is to think about 2 objects on a spinning disk, one being close to the center of the disk and one being close to the outside of the disk. Angular (rotation) speed deals strictly with the angle. How long does each object take to ...


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Notation: I will write a Poincaré transformation as ${x'}^\mu = {\Lambda^\mu}_\nu x^\nu + a^\mu$, the operator representing this transformation on the Hilbert space is $U(\Lambda, a)$. An infinitesimal transformation with ${\Lambda^\mu}_\nu = \delta^\mu_\nu + {\omega^\mu}_\nu$ and $a^\mu = \epsilon^\mu$ can be expanded as $$ U(\delta + \omega, \epsilon) = 1 ...


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Elementary particle physics is an outgrowth of what was high energy physics, historically at the time. X-rays were high energy physics when first discovered, they are part of the tools of solid state physics now. Alpha particles and gamma rays were high energy physics at their time, they are nuclear physics now. Mesons discovered in cosmic rays started ...


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As an alternative to Anna's nice historical discourse a heuristic that covers modern uses of the phrase would be that energies are "high" when the QCD can be treated as perturbative. That regime sets in considerably above the nucleon mass scale, say 10s of GeV. So LHC physics is in, JLAB physics is out (even with the 12 GeV upgrade).


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The terminology "continuous variable system" is non-standard, but likely refers to the fact that any canonical quantization of a classical Hamiltonian system (i.e. a system described by a continuous phase space) must have an infinite-dimensional Hilbert space since the canonical commutation relation $$ [x,p] = \mathrm{i}\mathbf{1}$$ cannot be realized on ...


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Yes, escape velocity should really be escape speed. The Wikipedia article on escape velocity states this explicitly. I doubt there is any logical reason for using the term escape velocity and I suspect it is an accident of history. You might want to ask on the History of Science SE how the term originated - a quick Google failed to retrieve any information ...


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The graph shows a constant speed, which is positive, so we know that the velocity is not changing sign. Depending on the context of the graph (is it dealing with 1D motion or curvilinear motion) we could tell a lot. Technically, on a traditional velocity vs time graph, one is plotting a component of velocity, complete with signs. I don't think the plot is ...


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The simple answer is that displacement, in this context, is distance. There are other uses, such as the weight of a ship, but that is not germane. Consider that the area under the line is x times y. In this case the x axis has the units of seconds, and the y axis has the units of meters per second. So when multiplying them out, $$sec\times\frac{meters}{sec} ...


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A current-current diagram is a diagram in the diagrammatic expansion of a current-current amplitude. For the latter, see. e.g., equation (1.1) in Keith Hamilton, The Standard Model Part II: Charged Current weak interactions I, http://www.hep.ucl.ac.uk/~campanel/Post_Grads/2013-2014/SM-CC-Weak-Interactions-I.pdf


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A representation of the Lorentz group implies a set of matrices $(S_{\mu\nu})_a{}^b$ (one for each $\mu,\nu$) that satisfy the Lorentz algebra, i.e. satisfies a relation of the form (I am not keeping track of signs) $$ [S_{\mu\nu} , S_{\rho\sigma} ] = i ( \eta_{\mu\rho} S_{\nu\sigma} + \cdots ) $$ What this means is that there is a vector space, with vectors ...


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As you've seen, the word quadrature is overladen with many, none-too-precise meanings. Here the "quadratures" loosely refer to the position and momentum observables: $$\hat{x} = \frac{1}{\sqrt{2}}(a + a^\dagger)$$ $$\hat{p} = \frac{i}{\sqrt{2}}\,(a - a^\dagger)$$ where $a,\,a^\dagger$ are the lowering/ raising operators and I've normalized the two ...


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Causality means that if something happens before in one reference frame of your choice, it happens before in any other existing reference frame in the universe. Locality means that if two events are space-like separated then it exists at least one reference frame where they happen at the same time; if two events are time-like separated, then it exists at ...


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Traditionally wavenumber is used in molecule spectrums such as infrared spectrums in organic chemistry where it is given in the incoherent SI-unit $\textrm{cm}^{-1}$. Mostly because one obtains convenient numbers on the axis. Also in most of the wave equations it is used, because again you can make the convenient substitution $k \equiv \frac{2\pi}{\lambda} = ...


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I don't think there's much to say beyond the obvious: You should use whatever terminology is most helpful in communicating the information that you want to communicate. That has to do with the audience you're talking to. Just like how you use °F when talking to Americans and °C when talking to non-Americans ... similarly it's often wise to use cm^-1 when ...


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Wavelength and wavenumber are redundant terms, as it sounds like you know. Their use is a matter of convention, which in my experience changes from field to field which you won't know until you've been around. So...if you know which one people use, go with the flow. Otherwise, use which one you know, and be confident; for questions of order-of-magnitude ...


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When it is saying the light rays converge, it means that they intersect. THe light rays intersect because the lens bends them so they all point at the same spot. I will explain more. When a point source emits light, it emits in all directions. This is why if you are in a dark room and you put a candle in front of a sheet of paper, you will see a diffuse ...



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