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30

Which year? The sidereal year? The tropical year? The anomalistic year? The calendar year (and whose calendar)? The sidereal year is the average amount of time it takes the Earth to make one complete orbit about the Sun with respect to the fixed stars. The tropical year is the amount of average amount of time between successive spring equinoxes. The ...


13

If I saw the word "amp" written as such in a paper in my field (astrophysics) it would strike me as a bit informal. I would expect to see the full "ampere" written. That said, it is rare to actually write out the full name of a unit; usually it follows a number and is given its standard abbreviation. When abbreviated to e.g. "$5\ \mathrm{A}$", I would ...


11

Technically, apparently, your teacher is correct. BIPM and NIST In the official brochure from the Bureau international des poids et mesures (BIPM, the keepers of SI units) in §5.1 Unit symbols we find: It is not permissible to use abbreviations for unit symbols or unit names, such as sec (for either s or second), sq. mm (for either mm2 or ...


11

It's c for constant or celeritas, which means speed in Latin. Everyone uses it because it's convention. You could use $\xi$ or $\zeta$ or $\gamma$ or any other symbol you wanted, but then you'd have to explain what it meant, and people would have to go through the trouble to remember this every time they read your papers. Better to go with convention and ...


10

Indeed most examples of unambiguously labeling chiral states fall back on having another pre-labeled chiral object on hand. For a long time it seemed as though "left" and "right" were entirely interchangeable labels. This symmetry is known as parity. However it turns out there is a way to distinguish left from right in a fundamental way; parity is not ...


10

A particle is said to be on-shell if it satisfies the relativistic dispersion relation, $$E^2 = p^2 +m^2$$ in units wherein $c=\hbar=1$. If you graph it, you obtain a parabolic surface for massive particles, and a cone for massless particles, like a photon. This is known as the mass shell, it is quite literally a shell or surface. The momentum of a real ...


10

The no-go results from Algebraic and Constructive QFT you mention deal with related but slightly different matters. (Edit: the previous version of the following paragraph was slightly misleading - Haag's theorem is actually stronger than I stated before; see below for details) Haag's theorem (which actually slightly predates the inception of Algebraic ...


9

The "shift in the meaning" refers to some attempts to reinterpret the terminology that were made by a metrological document, ISO 5725, in 2008. That may be described as a bureaucratic effort by a few officials – really bureaucrats of a sort – and as far as I know, the "shift in the meaning" hasn't penetrated to the community of professionals. The people ...


9

I say "ee-vee per see-squared" or "ee-vee over see-squared." If it's convenient to assume $c=1$, I'll say "ee-vee" or "electron volts." I can't remember ever having said "electron volts over see-squared." For MeV and GeV I'll say "em ee vee" or "gee ee vee." I know people who say "mev" or "jev", to rhyme with the first syllable of "Beverley", but in ...


7

Such an ordering arises from the fact that they are arranged chronologically, i.e., according to the dates they were "discovered". The principle quantum number $n$ entered the picture with Bohr's theory of the Hydrogen atom in 1913.Bohr introduced $n$ in his quantization of angular momentum postulate where $n$ is the allowed orbit. Mathematically, $L = ...


7

Lenses and glass bottles are transparent. As you quoted above, the different has to do with diffusion. Here is an example of an image through a transparent object: Here is an example of a translucent object: This is an example of how diffusion causes translucency: As light passes through a translucent object, it either enters or exists a rough ...


6

Your question is kind of vague but I will try to respond. Acceleration is defined as the time rate of change of velocity. Since velocity has both magnitude and direction, so does acceleration. In other words, acceleration is a vector. The length of the vector is its magnitude. Its direction is the direction of the vector. So the magnitude of ...


6

"Schroedinger equation" unfortunately is a bit ambiguous word. It could refer to $$i\hbar\frac{d \psi(t)}{dt} = H_t\psi(t) \tag{1}$$ but also to a more precise form like this: $$ i\hbar\frac{d \psi(t)}{dt} = \left(-\frac{1}{2m}{\bf P}^2 + V_t\right)\psi(t) \:.$$ The former version does not depend on the quantum physical system you are dealing with. So, in ...


6

The quadrature is a process – any process – of turning something into a "square". "Quadro" in Latin is "make square", "quadrus" is a "square". It comes from "quattors", four, because that's the number of vertices of a square. So integration of a function is also known as "quadrature" because we are calculating the area i.e. looking for a well-known area ...


6

The more common names for what you are talking about are the abbreviated action $$S_0[q] := \int p \mathrm{d}q$$ versus the action $$ S[q] := \int_{t_1}^{t_2}L(q,\dot q,t)\mathrm{d}t$$ Both are used in different formulations of classical mechanics, and deliver a different "flavor" of solutions. On both one can do variations calculus and obtains the ...


6

A 'moment' is quite a general term, and its use ranges from electrostatics (e.g. dipole and other multipole moments) to mechanics (moment of force but also moment of inertia) to huge stretches of statistics. The general intuition is that you have some amount of 'stuff' (charge, force, mass, probability) with some distribution function $s(x)$, and the various ...


6

The term 'equation of motion' is somewhat subjective as it depends on the context, but for any given context there is usually one single equation, or set of equations, which can be described as an equation of motion. These are typically differential equations in time, usually of second order, and for simple objects in Newtonian mechanics they do not involve ...


6

$mr^2\dot\theta$ is the angular momentum, which is conserved. The quantity $r^2\dot\theta$ is conserved if $m$ is independent of time, but it doesn't have a name that I know of.


6

Microscopically, i.e. in the quantum theory the scattering with radiation is a collision of particles with photons such as $$ e^- + \gamma \to e^- + \gamma$$ The momentum vectors of the particles above are $$ \vec p_1+\vec p_2= \vec p_3 + \vec p_4$$ where the identity holds due to momentum conservation. But in general $\vec p_1\neq \vec p_3$ and $\vec ...


6

The sort of trick involved in removing the $|P\rangle$ on both sides to get the conjugate imaginary equation $$\langle P|\xi|P\rangle = \langle P|a|P\rangle \tag1 $$ is quite common but it is indeed nontrivial to grasp the first time. In essence, you leverage the fact that in an equation of the form $$ ⟨\psi|\hat A|\phi⟩=⟨\psi|\hat B|\phi⟩\tag2 ...


5

Yes! Any beam that is blocked by an object will basically make a shadow. For example, the IceCube detector can see the moon's cosmic ray shadow.


5

why does it seem improper to add many speeds (or velocities)? Adding speeds is ofttimes inappropriate even in Newtonian mechanics. Suppose Mark is moving 3 m/s eastward with respect to Bob, and John is moving 3 m/s westward with respect to Mark. The relative velocity between Bob and John is zero rather than the 6 m/s suggested by adding speeds. You can ...


5

Your question, as of right now, seems confused to me. An extensive property of a system is one that scales with the system size. An intensive property is independent of the system size. For example, consider a system $A_1$ with $N$ particles in a volume $V$, with density $\rho=\frac{N}{V}$. Now, we consider two of these systems separately, $A_1$ and $A_2$, ...


5

See this article on the history of phase space. Assuming the article is to be trusted, Boltzmann noted that in a 2-D system the trajectories looked like Lissajous figures, and the shape of the Lissajous figure is determined by the relative phase of the two input signals. He then used the work phase to refer to that part of the configuration that was ...


5

In signal processing, the Nyquist–Shannon sampling theorem says you need at least 2 samples of a frequency to be able to perfectly reconstruct it. So in your question, a sampling rate of $200\: \mathrm{MHz}$ means you can perfectly reconstruct frequencies in the range of $0 - 100\: \mathrm{MHz}$. So what happens when frequencies above $100\: \mathrm{MHz}$ ...


4

It started with conservation of quantum numbers, from baryon number when we did not know about quarks, to lepton number, when we discovered the positron.For the neutrino momentum and energy conservation played a role too, since it is only seen as a missing mass. In time the symmetries in the assignments of the quantum numbers became more and more evident ...


4

You have pinpointed an important nuance of quantum information theory. A perfectly entangled state is, in some sense, like a single bit in a one time pad: just two copies of a shared random bit. In fact, the teleportation protocol is perfectly analogous — not the same, but certainly analogous — to transmitting a message securely using a one-time ...


4

The Schrödinger equation you use in non-relativistic quantum mechanics describes the evolution of the wave-function for a single particle, or at least, a fixed number. So you can think of it as being the "wave equation" for a one particle wave-function. Nice, neat interpretation. Also incomplete. But the Schrödinger can also be viewed as the defining ...


4

Refs. 1 and 2 define a canonical transformation (CT) $$\tag{1} (q^i,p_i)~\longrightarrow~ (Q^i,P_i)$$ [together with choices of Hamiltonian $H(q,p,t)$ and Kamiltonian $K(Q,P,t)$] as satisfying $$ \tag{2} (p_i\mathrm{d}q^i-H\mathrm{d}t)-(P_i\mathrm{d}Q^i -K\mathrm{d}t) ~=~\mathrm{d}F$$ for some generating function $F$. On the other hand, Wikipedia (March ...


4

"Equilibrium" means thermal equilibrium. The solid has one well defined temperature, and a constant Fermi energy. The Fermi energy is an energy value against which energy levels are compared to determine how fully occupied (or not) an energy level is. Generally when the Fermi level is constant throughout a solid electrons diffuse equally in all ...



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