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I think I have came up with the answer, which I hope is correct. Although, neither internal nor the gauge symmetry operations affect the space-time coordinates, there is a big difference: Internal symmetry is an actual symmetry of the system (field): two physically distinct field configurations (or in QM, two physically distinct states in Hilbert space) ...


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I don't remember having seen the specific expression of the proposed "signed arc length" either (anywhere but related to the OP question), nor anything resembling (1) the more abstract expression for determining the sought resemblance. For naming this proposed functional from the set of curves (or rather, arcs) into the set of real numbers (incl. $\mathbb ...


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I don't really like summaries like that cause there's too many short-cuts taken in the summary - but that's my personal take, you don't have to share that opinion. I like this one better, as it has pictures: http://abyss.uoregon.edu/~js/cosmo/lectures/lec22.html The first sentence you quoted - as pointed out, is incorrect, or, at least, said badly. "As ...


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baryons are a superclass of protons and neutrons. More broadly, they would be considered to be any particles made up of three quarks. They will interact via both the strong and electroweak forces Leptons are spin 1/2 particles that interact via the electroweak force but not the strong force. photons are neither leptons nor baryons (which are both ...


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Assuming the interpretation I suggested in the comments is correct. Consider the normal support force. It is an expression of the solidity of the surface that won't allow interpenetration. In order for penetration to not happen, there must be a force to prevent the supported object from accelerating toward the surface. Ultimately the origin of this ...


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The "signed arc-length" is not used in relativity and I give reasons why. You are free to call and denote it in any way you like. $s$ and $\ell$ are interchangeably used to denote arc-length of space-like paths $g(\gamma',\gamma')>0$ in relativity and $\tau[\gamma]$ is used for "proper time" of $g(\gamma',\gamma')<0$ time-like paths but the notation ...


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To give an answer we have to remember the historical facts. While making a light source point like and for better visible results nearly monochromatic one can see behind an edge an intensity pattern (fringes) right and left from the geometric line of the shadow. Hence the intensity pattern are something equal to water waves light has to have wave ...


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I have never seen that second definition before. The first definition is standard. For a Riemannian manifold the metric tensor is positive definite, that is $$g(u,u)>0\quad\forall u\ne0$$ We have the standard relation (tensor product omitted) $$\mathrm{d}s^2=g_{ij}\mathrm{d}x^i \mathrm{d}x^j$$ Let $t\in\mathbb{R}$ be a curve parameter and ...


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Electromagnetic waves are called waves because there are waves (propagating disturbances), waves in the electromagnetic field. These electromagnetic waves, like material waves, transport energy. According to the Wikipedia article "Wave" In physics, a wave is disturbance or oscillation (of a physical quantity), that travels through matter or space, ...


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In addition to the other answers, back in the olden days they were thought of as oscillations in the ether. As a result of the Michelson-Morley experiment back in 1887, physicists began to think that there was no ether. But the term didn't change.


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The electromagnetic waves satisfy the Maxwell equations for waves. They don't need a medium for propagating, because these waves are their own energy-carriers, the photons. By that, they differ from water waves whose energy is propagated by the intermediation of the water molecules, or sound waves whose energy is propagated through the molecules of the ...


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The definition of a wave is not that it is the oscillation of a medium. Waves are called waves because they are solutions to a wave equation, which is, for a generic "excitation" $A(t,x)$ depending on the time $t$ and some spatial coordinate $x\in\mathbb{R}^n$, of the general form $$ \frac{\partial^2 A}{\partial t^2} = c^2\Delta A$$ where $\Delta$ is the ...


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By the one who's exerting the force. It depends. When a system exerts some force on some other system, it does work on it and loses its energy. The lost energy is transferred to the second object, which in turn does work against the frictional force and loses its energy which is transferred into the molecules or atoms of the surface as heat.. There are a lot ...


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Mutually commutative means that every operator in the set commutes with every other one. This implies that, if the operators in question are observables, they can all be measured simultaneously. A complete set of mutually commuting observables is a set of observable, hermitian operators that commute - therefore their eigenvalues can be used to label a ...


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For your case work is done by the one who applies force and displaces an object in any direction. You take this example "if an object falls from a height then the work is done by gravity (look who is applying force here )" I hope u understood it . Work cannot be done by a body who does not have it's own energy source like an hammer can never do work.


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For your case work is done by the one who applies force and displaces an object in any direction. You take this example "if an object falls from a height then the work is done by gravity (look who is applying force here )" I hope u understood it .


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A Non-Newtonian fluid acts like anything that isn't a Newtonian fluid, so it's a pretty broad category. In the specific case of oobleck, the type of Non-Newtonian fluid that you can walk on, the resistive force it exerts is proportional to the velocity. So it acts like a dampener in regular mechanics. Push real hard and you will displace faster, but the ...


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In YM theory, you generally don't take the constant transformations to be gauge transformations, since the constant transformations are generated by the charge operator. If the charge operator generated gauge transformations, it would act trivially on all physical states, which would mean that you couldn't have charges.


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There are such things are large gauge transformations, which I think are related to your question. For example, consider general relativity where the gauge invariance is diffeomorphism invariance. Typically gauge transformations are considered that leave the boundary invariant, but there are also large gauge transformations that for example rescale the ...


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Strictly speaking, if a body is moved from a point to another by some force, it is said that the force does some work on the body.


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Probably not the correct way to think about it but this is my reasoning if you applied force on the body you had to spend the energy to do that work therefore you did the work the body gained the energy in some form say you lifted it of the ground the body has gained potential energy while you lost some bio-mechanical energy.


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If you exert a force on a body and it becomes displaced, then it is said that work is done by you or, by the force on that body.


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The difference is typically the diffusion coefficient: \begin{align} \frac{\partial \psi}{\partial t}&=\nabla\cdot\left(\kappa\nabla\psi\right)\tag{diffusion}\\ \frac{\partial \psi}{\partial t}&=\kappa\nabla^2\psi\tag{heat} \end{align} Under the diffusion equation, we typically take $\kappa$ to be a spatially-dependent variable whereas in the heat ...


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Probe brane means that the brane is not backreacting on the geometry. It's very similar to the idea of a test particle in GR. A test particle follows geodesics of the spacetime. In reality, of course the particle will backreact on the geometry, but for small objects it's a good approximation to neglect this backreaction. In the context of AdS/CFT, this ...


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Under common assumptions and ignoring potential energy, static pressure is the expression of the fluid's temperature (internal energy) and dynamic pressure is the expression off the fluid's velocity, so if the fluid is brought to a rest adiabatically, their sum is equal to the stagnation pressure. The stagnation pressure represents the total energy of the ...


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To fluid dynamicists, Bernoulli's equation is better known as the 'Energy Equation' since it does indeed account for the energy changes that occur along a fluid path. The energy equation says that the energy is constant along any given streamline. Static or stagnation pressure can exist in the absence of fluid velocity creating a potential energy component. ...


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The quantity $\frac{1}{2}\rho v^2$ is called dynamic pressure for two reasons: because it arises from the motion of the fluid, and because it has the dimensions of a pressure. It is not really a pressure at all: it is simply a convenient name for the quantity (half the density times the velocity squared), which represents the decrease in the pressure due ...


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Special relativity says that how things happen can look different to people in different places or moving at difference speeds--except for things involving the speed of light in a vacuum. Things moving at the speed of light always move at the speed of light compared to you, no matter how fast you're moving. General relativity says that space and time are ...


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For a transistor, you need to consider the biasing conditions of both the emitter-base and base-collector junctions. In forward active operation, the emitter-base is forward biased to inject majority carriers from the emitter into the base. These transit the base (now as minority carriers with the chance of making it modulated by the base current). The ...


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Usually this is called "hysteresis" - a bit of "memory" of the last state (definition from Google): the phenomenon in which the value of a physical property lags behind changes in the effect causing it, as for instance when magnetic induction lags behind the magnetizing force. It can also (in the case of mechanical instruments) be known as "backlash". ...


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According to this source, (and this one), it's the "wobble" one can detect in nearby stars if they have an orbiting exoplanet - either detected directly or via Doppler shift of the star's spectrum.


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Coordinates and momenta of the system are called variables by convention. Time is sometimes called variable, after all its nature is to keep changing. But to distinguish time from coordinates and momenta, people call it parameter in some cases. Parameter is a word used instead of variable when the quantity is a different kind of argument of a function. ...


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The symbol $s_{NN}$ is in OP's context of RHIC the Mandelstam $s$-variable in a Nucleus+Nucleus collision. The $s$-variable is also known as the square of the center-of-mass energy.


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In mechanics, "kinematics" means describing the motion mathematically, so, for example, if the acceleration is known I can integrate to find the velocity and position. "Dynamics" means analyzing motion due to the influence of forces. The two are related through Newton's second law: F = ma (dynamics version) is the same as a = F/m (useful for kinematics). ...


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I think diffusivity of momentum is actually a pretty good way of describing kinematic viscosity. After all viscosity acts to transfer momentum from one region of a flow to another. This is analogous to other diffusivities and has the same dimensions $L^2T^{-1}$. Another way of describing kinematic viscosity is molecular diffusivity, or diffusion of ...


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Heat is a type of energy transfer from one system to another, rather than an internal energy of any given system ('thermal energy' might be a good term for what you're thinking of). In An Introduction to Thermal Physics by Daniel Schroeder, p. 18 says: Heat is defined as any spontaneous flow of energy from one object to another caused by a difference in ...


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As the other answer states, objects don't posses heat. Heat is the actual amount of energy transferred from an object to another. The typical case is when you have two objects $A,B$ at different temperature in contact, $T_A>T_B$. Then, it means as you say that the average energy of $A$ is bigger than the average energy of $B$. This induces some of the ...


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Object don't posses heat. They posses internal energy. Heat, like work, is a transfer of energy and is a property of a process or interaction not of an object.


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In stellar pulsations, multi-periodicity literally just means that there is more than one period present. In the cases of the classical pulsators (usually Cepheids and RR Lyraes), this is noteworthy purely because some stars oscillate at multiple frequencies and some don't. Typically we see the fundamental radial mode, and sometimes harmonics thereof. How ...


1

I know that the question specifically refers to classical electrodynamics, but I think it is helpful to look at this from a QED perspective. The term $-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$ is the kinetic term, i.e. from it we obtain the propagator. In a course on QFT, you probably derived the general relation $$Z[J]=\int\mathcal{D}\Psi\,\exp\left(i\int ...



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