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15

Actually there are terminological subtleties when you are talking about that. Particles in the accelerator's tube are gathered in a sequence of little "bunches". For the proton-proton mode there was roughly ~3000 bunches per beam. And each bunch contained roughly $\simeq 10^{11}$ protons. So, at the largest level what you actually have during the ...


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 ...


9

A theory is a collection of concepts, laws, and equations in science that is meant to explain some particular subset of observations. It's also used for theories describing gedanken worlds that differ from ours. There is also a related word "model" that differs by a theory by being really specific while a "theory" may leave some details adjustable, and ...


9

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 ...


8

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 ...


7

People have essentially explained the details, but let me make an attempt to formulate it in a language more familiar to a mathematician. I will ignore subtleties that enter for more general Lie superalgebras. Let $\mathfrak g$ be a Lie superalgebra with the $\mathbb Z_2$ grading $\mathfrak g = \mathfrak g_e\oplus\mathfrak g_o$, where the two factors are ...


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

An ultra-relativistic particle is any particle you observe to have almost all its energy stored in the form of momentum. In other words, we are talking about particles that have only a very tiny fraction of their total energy stored in (rest)mass. The relativistic mass-energy-momentum relationship $$E^2 - c^2 \ p^2 \ = \ c^4 \ m^2 $$ is valid for a ...


6

Lasers typically operate in two regimes: as CW or continuous wave (the radiation leaving the laser cavity or resonator continuously by a partially reflecting mirror, or as you put it, forming an uninterrupted wave) or as a laser pulse (the radiation leaving the cavity during a short time at a repetition rate, that is, as a burst of short pulses very separted ...


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 ...


5

$H$, sometimes called the Hubble "constant" should actually be called properly: the Hubble parameter. It is a function of the scale factor $a(t)$ of the Universe or of the redshift $z=1/a-1$ and depends on the cosmological parameters. It gives the rate of change of the size of the Universe with respect to its size. Through the Friedmann equations it is ...


5

It is a matter of confusing terminology , at the present times when so much differentiation has happened in physics related scientific disciplines. Radiation was a general terminology assigned to transfer of energy radially, to start with with waves: acoustic waves, waves in water. Then came Maxwell's equations and the discovery of electromagnetic waves, ...


5

User twistor59 has addressed the part regarding the "generator" terminology, but let me give a bit more detail on the second part of the question. I'm going to restrict the discussion to matrix Lie groups for simplicity. Some background. Given a Lie group $G$ with Lie algebra $\mathfrak g$, there exist two mappings $\mathrm{Ad}$ and $\mathrm{ad}$, both ...


5

"They" are probably talking about symplectic integrators. Most numerical integrators for (partial) differential equations do not specifically consider the energy of the system; they are generic integrators capable of solving any set of DEs, and not all DE's have a concept like "energy". When these are applied to a classical dynamics problem concerning ...


5

I know we've had this discussion on the Astronomy SE site, but let me try to elaborate on my answer. Dark matter is an altogether different component of the universe from baryonic matter. It does cause the same overall dynamics when it comes to the universe as a whole. What I mean by this is that the hubble parameter: $$ H(a) = H_0 ...


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

The terminological mismatch arises because different physicists use the terms differently in different contexts. For example, here is how Landau and Lifshitz define an adiabatic process in the context of thermodynamics: Let us suppose that a body is thermally isolated, and is subject to external conditions which vary sufficiently slowly. Such a process ...


4

To uplift a solution to the field equations (such as Einstein's equations or their generalizations) or to uplift any other construction or argument means to find a solution of a higher-dimensional theory (or the analogous construction or argument) given the known solution of a lower-dimensional theory. This is possible if the lower-dimensional theory may be ...


4

Yes, Newton was definitely using the term "mass". His Principia were written in Latin but the English translation of his Latin definition of gravity said: Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square ...


4

The neutral current is electrically neutral. To see why, one must first understand what the current is. It is a composite field or (in the quantum theory) an operator, something like $$ J^{\mathrm{(NC)}\mu}(f) = \bar{u}_{f}\gamma^{\mu}\frac{1}{2}\left(g^{f}_{V}-g^{f}_{A}\gamma^{5}\right)u_{f}, $$ where $u_f$ is the Dirac field for the fermion $f$. Note that ...


4

The doppler shift causes a shift in wavelength at the origin of the wave (the frequency of the source never changes). This results in a shift in frequency for the observer. In the link below you can see the emission of the wave for a moving source causes the wavelength to be shorter in front and longer behind. The actual source isn't changing in ...


4

Some examples come to my mind: Fourier's law of heat conduction $\vec{J} = -c\vec{\nabla}T$ in crystalline solids is a good example of a phenomenological law. It is an ampirical law easy to verify in a broad range of materials in various phases and yet, as explained in this presentation, there is no derivation of it from first principles in solids and ...


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

Such an ordering arises from the fact that 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 = n{h ...


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

The term "shell" originally derives from the non-relativistic version of the answer by @JamalS. In a non-relativistic theory, a free particle satisfies the following dispersion relation $$ E = \frac{ {\bf p}^2 }{ 2m } $$ For a fixed energy a particle satisfies $$ {\bf p}_x^2 + {\bf p}_y^2 + {\bf p}_z^2 = 2 m E $$ In momentum space, this is precisely the ...


3

The Hubble-constant gives the rate at which the universe expands at the present. Since the expansion of the universe hasn't been constant this is indeed not the case. So yes, the Hubble-constant is actually a time-depandant value (the name constant dates back to the time people believed the universe was static). The behaviour in time of the hubble constant ...


3

There is no consistent usage of these words among scientists. Usually, when someone says "law" or "principle", they are referring to a general idea that has been found to apply to many different situations, but not always. More speculative ideas are generally called theories, but use of the word "theory" does not always mean that an idea is speculative. ...


3

If you have a basis for the Lie algebra, you can talk of these basis vectors as being "generators for the Lie group". This is true in the sense that, by using the exponential map on linear combinations of them, you generate (at least locally) a copy of the Lie group. So they're sort of "primitive infinitesimal elements" that you can use to build the local ...



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