Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Do quarks oscillate via Charged Weak Interaction (CKM Matrix)? In the Standard Model, with the introduction of the CKM matrix, we have that quark mixing between different generations is possible via a charged current (W boson).
My question is if this also implies that a given quark can change flavour (oscillate), auto-... | Yes, this type of oscillation is possible. Your specific example is forbidden because there are no charmed baryon states whose masses overlap with the nucleon, so the $u\to c$ diagram you’ve drawn would have to be followed by a second weak loop to get you back to the initial zero-charm state.
However, the simpler virt... | {
"language": "en",
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Explain Heisenberg's uncertainty principle There was one homework question that asks what Heisenberg uncertainty tell us about the energy of an electron in an infinite square well when the length of the well decreases. The correct answer is that the energy decreases when length increases. I know that the energy should ... | The infinite square well is a time-independent solution.
Energy is related to time through the HUP. Position is related to linear momentum.
It means that the infinite square well, with a definite energy, has arbitraryily large uncertainty on when the particle is in the well.
The width of the well is related to the unce... | {
"language": "en",
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Peskin and Schroeder's QFT book page 289 On Peskin and Schroeder's QFT book page 289, the book is trying to derive the functional formalism of $\phi^4$ theory in first three paragraphs. But the book omits many details (I thought), so I have some troubles here.
For the free Klein-Gordon theory to $\phi^4$ theory:
$$ \ma... | User Zack has already answered OP's first part. Concerning the equivalence between the interaction picture (4.31) and the path integral formulation in the Heisenberg picture (9.18), note that P&S presumably assumes no derivative couplings/interactions. For the latter case, see e.g. this Phys.SE post.
| {
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"Lowest yield" atomic weapon possible I would ask that folks be tolerant of my ignorance in this field. When discussing tactical and strategic nuclear weapon yield I wonder about what is the lowest possible fission weapon is possible. A "dirty bomb" (conventional bomb spreading nuclear contamination) is not the questio... | The yield of many weapon designs can be adjusted, typically by changing the firing time of external neutron initiators or the quantity of deuterium-tritium boosting gas injected into the core.
The lowest yield setting on a fielded US nuclear weapon was 10 tons TNT equivalent, on the W54 warhead as used in the Davy Croc... | {
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Change in absolute magnitude caused by a change in apparent magnitude Imagine that we have an object with apparent magnitude $m_1$, later, we observe that the same object appears with an apparent magnitude $m_2 = m_1 + \alpha$, then what we can say about the absolute magnitude M? By the definition I believe we find tha... | The absolute and apparent magnitude are simply related by the distance to the source.
If the distance is fixed and the apparent magnitude changes, then the absolute magnitude must have changed by the same amount.
The absolute magnitude is not called that because it can never change - there are lots of examples of varia... | {
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Low temperature behavior for ferromagnets: theoretical and experimental discrepancies This is in reference to page 326, 327 of introduction to solid state physics, 8th edition by Charles Kittel
The mean field theory does not give a good description of the variation of $M$ at low temperature. For $T<<T_{c}$ the argumen... | For the first question you can rewrite $\tanh$ in terms of exponentials, see e.g. this Math.SE post for details. For the second question, yes, $M(0)$ is the magnetization in the zero temperature limit, where you approximate $\tanh \xi \approx 1$.
| {
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Why does a piece of thread form a straight line when we pull it? Experience tells that if we pull a piece of thread, it forms a straight line, a geodesic in the Euclidean space. If we perform a similar experiment on the surface of a sphere, we will get an arc of a great circle, which is also a geodesic.
How to show thi... | If we pull a piece of thread, it should form a catenary curve (a curve resembling a hyperbolic curve) I guess!
| {
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Clarifying volume symbol notation with a slash through it I am reading Munson's book on Fluid Dynamics. One thing I found confusing was this notation in the image below, where the Volume has a slash or strikethrough through it. I am not clear about the meaning of that notation. Does it have something to do with intensi... | Munson uses a barred, italicized V to distinguish—when the context doesn't make it clear—volume from velocity, which is shown upright and in bold. (Subscripts referring to volume are italicized and in lowercase, as shown in your example.)
The barred V doesn't seem to indicate any special type of volume, as it's used th... | {
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I'm having trouble understanding the intuition behind why $a(x) = v\frac{\mathrm{d}v}{\mathrm{d}x}$ I was shown
\begin{align}
a(x) &= \frac{\mathrm{d}v}{\mathrm{d}t}\\
&= \frac{\mathrm{d}v}{\mathrm{d}x}\underbrace{\frac{\mathrm{d}x}{\mathrm{d}t}}_{v}\\
&= v\frac{\mathrm{d}v}{\mathrm{d}x}
\end{align}
However, this feels... | the kinematic equations are
$$x(t)=f(t)\quad\Rightarrow\\
v(t)=\frac{dx(t)}{dt}=\frac{df(t)}{dt}\\
a(t)=\frac{dv(t)}{dt}= \frac{d^2f(t)}{dt^2}$$
now if you want to obtain the acceleration $~a=a(x)~$ first you eliminate the parameter $~t~$ with the equation $~x=f(t)\quad\Rightarrow~t=g(x)~$ hence
$$a(x)=\frac{d^2f(t)}{d... | {
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Thermal Equilibrium and adiabatic walls - Zemansky In Zemansky's "Heat and Thermodynamics" it is stated that:
A thermodynamic system is in thermal equilibrium with its sorroundings iff it is in mechanical and chemical equilibria with its sorroundings, it is delimited by diathermic walls and its macroscopic coordinates... | For an adiabatic system to be in thermodynamic equilibrium, there can be no spatial variations within the system in temperature, pressure, or chemical potential.
| {
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"source": "stackexchange",
"question_score": "3",
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Standing waves in a resonance tube I am doing an experiment about standing waves in a resonance tube. I use a bucket of water, a waterproof tube (open at both ends), and a frequency generator app. I have two set-ups, A and B:
A. Setting the frequency to be constant and dipping the tube into the bucket of water until I ... | It's hard to comment on a specific experimental setup, but I am not surprised by your result. In B, the machine can control the value of the frequency much more precisely than you can manually submerge the tube into the water to a certain length in A.
One thing to try calculating is, if your length measurement is off ... | {
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How to derive the $vx/c^2$ term from first principles? In Lorentz transforms, the formula for time transformation is
$$t' = \gamma \left( t - \frac{v x}{c^2} \right)$$
I understand that the term $\frac{v x}{c^2}$ represents "time delay" seen by a stationary observer but I don't understand how to derive it from first pr... | I'm not sure there's a meaningful way to derive it apart from the full Lorentz Equations, but one thing reflected in the equation is that a time interval $t'$ for one observer will correspond to partly a time interval $t$ and partly a space interval $x$ for a different observer.
This happens in exactly the same way tha... | {
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Where does energy go? Where does energy go?
Given is the Michelson interferometer. One sends light in
in the form of a plane wave $E_0\exp[i(kx-wt)]$ into the interferometer.
The position of one of the mirrors is adjusted in such a way,
so that at the output of the interterometer
completely destructive interference ta... | The Michelson interferometer produces two beams. One is the usual one typically directed toward a "screen" or photodetector. The other is reflected back toward the source (laser).
If you adjust the mirrors for destructive interference at the output beam, you will have constructive interference at the reflected beam, an... | {
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Is the continuity equation used to **define** the current density? Recall the continuity equation:
$$\frac{\partial}{\partial t}\rho+\boldsymbol{\nabla\cdot J}=0$$
Given $\rho$, there is obviously not a unique solution $\boldsymbol{J}$, but I guess one could choose an additional requirement (e.g. some condition on the ... | The continuity equation is not the definition of the current density.
One way to define the current density $\mathbf J(\mathbf r)$ is via the three components $J_x(\mathbf r), J_y(\mathbf r), J_z(\mathbf r)$ where
\begin{equation}
J_x(\mathbf r) = \lim_{s \to 0} \frac{I_x(\mathbf r, s)}{\pi s^2}
\end{equation}
where th... | {
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Could you feel your weight falling through the a tube drilled through the center of the earth? Suppose you drill a hole through the center of the earth (assume the earth is uniform and no air resistance) and you jump in. Would you be "weightless" throughout the entire fall?
The reason I ask is that if you jump off a cl... |
Suppose you drill a hole through the center of the earth (assume the earth is uniform and no air resistance) and you jump in. Would you be "weightless" throughout the entire fall?
Yes, because you would follow the spacetime geodesics. The case you described has been precise analyzed by Edward Parker in A relativistic... | {
"language": "en",
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Branes in Closed Bosonic String Theory I've seen in these lectures by Freddy Cachazo that type II-A/B superstring theory has to contain D-branes and open strings non-perturbatively, even though it appears to only contain closed strings in the perturbation theory. I've also read here that heterotic superstring theory mi... | I would say that the bosonic string doesn't make sense non-perturbatively so the question of whether it contains non-perturbative objects is meaningless to begin with.
| {
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Does a random number generator have real entropy? In thermodynamics, entropy is defined for gases. Of course, my laptop is not a gas. However, it contains a random number generator and I have seen the word ‘entropy’ being used in this context. Is this the same entropy? How can this entropy be linked to the definitions ... | I am not sure about my expertise. But here is a shot anyway.
The 'random number generator' will keep giving numbers out. And it never ends. So it keeps drawing energy out from your computer. And I doubt you can covert the heat created back to energy which would power your computer.
Of course the random-number-generator... | {
"language": "en",
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If the spin operator is a matrix, why aren't the momentum or position operators a matrix? So my question is to do with the fact that some operators seem to be matrices while others are not. I suspect if the eigenvalues of an operator has continuous eigenvalues then the operator is not a matrix but if it is discrete it ... | *
*If the position operator $\hat{x}$ and the momentum operator $\hat{p}$ were represented by finite-dimensional square matrices, then ${\rm Tr}[\hat{x},\hat{p}]=0$, which would violate the CCR, cf. e.g. this Phys.SE post.
For their infinite-dimensional representations, see instead the theorem of Stone and von Neumann... | {
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Is the resonance of a wine glass and resonance in an electrical circuit the same thing? I am quite a noob at Physics, but I find it quite interesting, and resonance was especially intriguing when I first found out about it, but now that I have done a little bit of research, I either get results of a wine glass (or any ... | Yes, resonance in both these different phenomena is conceptually the same thing: it is when external driving force and velocity of the driven object (electromotive force acting in circuit and electric current in the circuit) oscillate in phase. This can happen only when frequency of the external oscillating force gets ... | {
"language": "en",
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How can I show the following contraction of the electromagnetic field strength and its dual? Given the electromagnetic field strength $F^{\mu\nu}$, and its dual $$\tilde{F}^{\mu\nu} =\dfrac{1}{2}\varepsilon^{\mu\nu\alpha\beta}F_{\alpha\beta},$$
how can I show that
$$\tilde{F}^{\mu\nu}F_{\nu\rho} = -\dfrac{1}{4}\delta^\... | A possible proof can be:
From lorentz invariance you have
$
\tilde{F}^{\mu \nu} F_{\rho \nu}= C \delta_{\rho}^{\mu} , \quad C \in \mathbb{R}
$
now taking the trace both side you obtain $C$
$
\tilde{F}^{\alpha \nu} F_{\alpha \nu}= C \delta_{\alpha}^{\alpha}= 4 C
$
so
$
\tilde{F}^{\mu \nu} F_{\rho \nu}= \frac{1}{4} \delt... | {
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Explain Feynman's explanation why KE + PE = constant I'm reading Feynman's lecture on physics, and I'm having trouble following the logic. In section 14-4 he says:
"Now we have the following two propositions: (1) that the work done by a force is equal to the change in kinetic energy of the particle, but (2) mathematic... | You have the following equations:
$
\begin{align}
& W= \Delta T \quad \text{Work-Energy theorem} \\
& W= -\Delta U \quad \text{only valid in case of conservative force}
\end{align}
$
so
$
\Delta T=-\Delta U
$
by definition you have $\Delta T= T_f-T_i$ and also $ \Delta U= U_f-U_i$, so the last equation became
$
T_f-T_i... | {
"language": "en",
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Why is it possible to neglect higher order terms in the variation of the action? In order to get the Euler-Lagrange equations, we should find the variation of the action $\delta S$ and to neglect higher-order terms:
$$\delta S=\int L(q+\delta q,\,q'+\delta q',\,t)dt-\int L(q ,\,q',\,t)dt+O[(\delta q)^2]$$
I have two qu... | The following is not mathematical rigorous, but a sketch of the central ideas.
To start, let us consider the case of a (differentiable) real scalar function $f: \mathbb R \longrightarrow \mathbb R$. We say that $x$ is a stationary point if and only if $f^\prime(x)=0$. The Taylor expansion of $f$ around a point $x$ is... | {
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How do we prove that the 4-acceleration transforms as a 4-vector in Special Relativity? In order to define the acceleration of a body in its own frame, we need to first prove that the acceleration is a four-vector so that its dot product with itself can then be labeled as acceleration squared in the rest frame. For vel... | In physics, we prove things with experiments. Four-vectors are components of a mathematical model. Does that model pass experimental test? Yes, in many cases. We use it because it passes those tests, not because of any mathematical proof.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Higher Dijkgraaf-Witten Theory I am trying to understand higher-form symmetries in TQFT. In particular the higher-form version of Dijkgraaf-Witten Theory.
It is known that for a 0-form symmetry we can specify the principal G-bundle through homotopy classes of the classifying map
$$ M \rightarrow BG = K(G,1). $$
This is... | Higher-form symmetries are abelian so, with $G$ a discrete abelian group and $p\in\mathbb{Z}_{\geq 0}$ (or $G$ a discrete group, not necessarily abelian, if $p=0$):
$$ [M, K(G,p+1)] \cong \mathrm{H}^{p+1}(M;G) \cong \operatorname{Hom}\left(\pi_{p+1}(M),G\right) $$
and everything works as it should.
See e.g. the Wikiped... | {
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How do non-holonomic constraints work in Hamiltonian formalism? In Lagrangian formalism, if $(M, g)$ is our configuration manifold, equipped with a Riemannian metric $g\in Hom(TM\bigotimes TM, \mathbb{R})$, Lagrangian function $\mathcal{L} : M\times TM\times [0, 1]\rightarrow \mathbb{R}$ is defined as $$\mathcal{L}(x(t... | It depends on whether the first principle for the Lagrangian formulation is
*
*a variational principle [i.e. the stationary action principle (SAP)],
*or not,
cf. e.g. this & this related Phys.SE posts.
*
*In the 1st case, one can in principle find a Hamiltonian formulation via a singular Legendre transformation, ... | {
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The uncertainty principle for angular momentum and angular position For $$L_{z}=xp_{y}-yp_{x}$$ we see that angular position in the $x-y$ plane is canonically conjugate,
$$\theta_{x-y}=\mathrm{tan}^{-1}\left(\frac{y}{x}\right)$$
that is,
$$\{\theta_{x-y},L_{z}\}=1$$
where $\{\}$ represent Poisson brackets. Applying can... | You don't even need the uncertainty principle for a contradiction here: $\widehat{L}_z$ is hermitian ($\widehat{L}_z^\dagger=\widehat{L}_z$) and therefore by applying $\cdot^\dagger$ to your last equation, we get $\langle m|\widehat{L}_z=m\hbar\langle m|$, which directly results in the contradiction:
$$i\hbar
=i\hbar\l... | {
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Newton's Second Law and External Forces I was reading about Newton's Second Law, and I saw that only external forces can move a body. However, when animals and people walk, when rockets launch, and cars drive, isn't it an internal force that causes a change? How do these things fit into Newton's Second Law?
| One has to be careful how to define what is the system under consideration so as to know what is internal and external. When animals and people walk, they are acted on by an external force - the friction between their feet and the ground. With rockets, hot gases are forced out the back. They exert an equal and opposite... | {
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Definition of momentum We say that momentum is the measure of how a body is moving or the quantity of movement inside a body
But what this definition really mean?
This terms are very vague
$p=mv$,why the movement inside the body depend on it's mass?
| An object's momentum is the product of its mass and its velocity.
$$\vec P = m \vec v$$
Nothing vague about it.
Why is this referred to as the "quantity of motion"? That's more of a history os science question.
| {
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Are thermodynamic quantities based on frame of reference The Kinetic Energy $mv^2/2$ does depend on the FoR, and hence maybe the internal energy?
I've also seen temperature being defined as "a measure of the average kinetic energy of the particles".
Are thermodynamic quantities based on frame of reference? Is there a d... | For simplicity and convenience, we often conduct thermodynamics using a frame of reference in which the system of interest is motionless, but this is not essential. I quote at length from Callen's Thermodynamics and an Introduction to Thermostatics:
In accepting the existence of a conserved macroscopic energy function... | {
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Momentum: How can a rolling wheeled vehicle turn 180 degrees without stopping? "In Newtonian mechanics momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. An object will stay still or keep moving at the same speed and in a straight line, unless... |
How can a rolling wheeled vehicle turn 180 degrees without stopping ?
The answer is in the last sentence of the passage you quote:
An object will stay still or keep moving at the same speed and in a straight line, unless it is acted upon by an external force
The external force that acts on a coasting car to change ... | {
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Size of metal domain needed to reflect light ; are small graphene sheets shiny? I remembered that shininess of a material is because of reflection, ie surface current responding to light. Mathematically, one can solve Maxwell equations under a relevant boundary condition, with plane waves ansatz. This math only corresp... | We say something is shiny when the reflection from it is specular i.e. the angle of reflection is equal to the angle of incidence. Note that it doesn't matter whether the substrate is a metal (i.e. conducting) or not as insulating plastics can also be shiny.
The problem is that objects of around the wavelength of light... | {
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Non- Local operators and Entanglement Given a separable state, $|\psi\rangle$ = $|a\rangle\otimes|b\rangle$, operating on this state with a local operator of the form, $A\otimes B$ will not lead to an entangled state. Is the converse true? i.e., given that I know that action of an operator on a separable state is a sep... | No.
The swap operator will never entangle any product state, yet it is not a local operator.
(Note, however, that it will create entanglement if it acts on part of a larger system.)
| {
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Does Proca's hypothesis make sense of giving mass to the photon in reference to special relativity? The Romanian physicist Proca formulated his famous Lagrangian to describe a hypothetical massive photon. From it we derive, as equations of motion, the relations that the electric and magnetic fields must obey (the analo... | In this scenario, $c$ would still be the maximum possible velocity at which information can propagate locally, i.e. in a piece of spacetime small enough to be considered Minkowskian, even if no information would actually travel with that speed.
The parameter $c$'s existence does not require light in Einstein's massless... | {
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Velocity in power calculations in different inertial frames In calculating power using the formula $\underline{F}\cdot\underline{v}$, what is the correct velocity to use? Does one use the velocity of the body on which the force is acting, or the velocity of the body providing the force? I always thought it was the form... | Given a reference frame, the total power of a force field acting on a system is the sum of the dot product of each force and the velocity of the point where the force is acting
$\displaystyle P = \sum_i \mathbf{F}_i \cdot \mathbf{v}_i$,
being $\mathbf{F}_i$ lumped forces. If you deal with continuous distribution of for... | {
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Why is the mass of small elements taken as $∆m$ in center of mass of a continuous body? A continuous body has continuous distribution of mass. Doesn't $\Delta m$ mean $m_f - m_i$? But, is the mass Changing? If yes, how is the mass varying? Why is the mass of the small elements in a body taken as $\Delta m$? Why isn't i... | You are right: it is a confusing notation. Usually it is used to "construct integrals", where it represents a finite-sized small chunk of the body, which is later assumed to go to zero size when a limit is taken. I prefer to use something like $m_n$ for these "chunk masses", and reserve the $\Delta$-notation for coord... | {
"language": "en",
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Connection between parameter space and configuration space I am just wondering what is the connection between parameter space and configuration space (or phase space)? I know the connection between configuration space and phase space but it seems like any paper/source I see uses one of "parameter space" or "configurati... | My understanding is that "parameter space" is a generic name that could apply for both configuration and phase space (or really any other kind), while configuration space exclusively refers to the space of the genealised coordinates. It might be the case that authors tend to avoid refering to phase space as "parameter ... | {
"language": "en",
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Does free molecular flow have a newtonian force in between 2 chambers? If a vacuum chamber is in free molecular flow pressure say $10^{-7}$ Pascal, and another container is added to it that is at $10^{-9}$ Pascal, will they reach pressure equilibrium eventually? At higher pressures, say between $101$ kPa (1 atm) and $5... | Like the continuum flow case, the two connected chambers will eventually reach equilibrium and there will be a net force pushing gas from the high pressure chamber to the low pressure chamber until that occurs.
Let's consider flow from one chamber to another. The momentum carried by an average individual molecule* is
$... | {
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How can we say that work done by carnot engine in a cycle equals net heat released into it even when it is operated b/w 2 bodies and not 2 reservoir? When a carnot engine is operated between 2 reservoir then after each cycle it return to its initial state so change in internal energy is zero and so work done by it equa... | The process you are describing is not a cycle. So depending on where you start your process, the final internal energy of the working fluid (ideal gas) may not be equal to the starting internal energy of the working fluid, and the working fluid will have done a different amount of work than the amount of heat it recei... | {
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Why does a small thermocol ball fall slower than a metal ball of the same volume and surface area (air resistance equal)? Suppose a thermocol ball and a metal ball of same volume and surface area (but different masses, obviously) are dropped from the same height from rest. The acceleration due to gravity is 'g' and the... | I offer a nearly-zero-mathmatics answer:
The acceleration due to gravity is $g$
Here is your misconception. $g$ is the acceleration due to gravity in free fall. When there is air resistance or other forces involved, you don't have perfect free fall, in fact you may have nothing like free fall, for example if the obje... | {
"language": "en",
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Lorentz contraction using odometers? In principle, would cars moving between a pair of points at different speeds show different odometer readings due to Length contraction? When we use odometers to measure length between two points, what can we say of length contraction?
| You ask what can be said in principle about the measured distance in that situation, and the answer to that is "nothing". The principle of relativity only says that Lorentz-boosting the whole system can't change the physics. Lorentz-boosting a system consisting of a car driving on a road at 100 km/h gets you another sy... | {
"language": "en",
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What is the correct gravitational potential energy of a single particle in an $N$-body system? I am aware that the total gravitational potential energy of a system of $N$ particles is given by pairwise interactions, i.e., you start with a single particle in the system, and then calculate the work done (negative for an ... | Equation (1) is relevant if you're studying the evolution of the whole system. For example, you can use it to construct the conserved energy or the Lagrangian.
Equation (2) is relevant if you're studying the kinematics of the subject particle over a short time period (so you neglect motion of the rest of the system). F... | {
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Why the closest to the nucleus electron has lower energy (contrary to Heisenberg)? According to shell theory the lowest energy electrons are on the $s$ level and are closest to the nucleus. This means they are localized in a smaller volume then other outer shell electrons and according to Heisenberg uncertainty relatio... |
Why the closest to the nucleus electron has lower energy (contrary to Heisenberg)?
The first has nothing at all to do with the second. The energy content of the electron is determined by the energy absorption at a photon absorption or the energy release at a photon emission. Empirically it was determined that the ele... | {
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Derivation of the braking torque induced by Eddy current in a rotating disc This question was cross-posted here, but I didn't receive an answer. So, I thought that, maybe, there was a missing physics assumption, which makes me post the same question here.
In the article On Eddy Currents in a Rotating Disk, the function... | First off, to make things more simple, I would integrate by parts in $r$:
$$
T = \frac{\Phi}{\pi a^2}\left(\int_{-\theta_1}^{\theta_1}d\theta [Ur^2]_{c-a}^{c+a}-\int_{c-a}^{c+a}dr 2r \int_{-\theta_1}^{\theta_1}d\theta U \right)
$$
so you just need to perform at fixed $r$ the integral:
$$
\int_{-\theta_1}^{\theta_1}d\th... | {
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What is the difference between mechanics and analog? What is the difference and the relationship between mechanics and analog/analogue? I have noticed that mechanical things are often considered analog.
Note: The difference between digital and analog is clear to me.
| "Mechanical" refers to the physical technology; "analog" refers to the nature of the processed signal.
As @John-Doty says in his answer, analog signals/data have continuous values, digital signals/data have descrete values. Both analog and digital computers can be (in whole or in part) electronic, mechanical, optical,
... | {
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How to derive that total kinetic energy is conserved during the collision?
*
*How to derive the below equation from scratch?
*What law support this equation?
*What is the name for it?
*Does it refer to the conservation of kinetic energy?
Like law of conservation of momentum derived from newton's 3rd law.
$\frac... | Suppose that $m_1$ and $m_2$ are interacting with each other via some conservative force with a potential of the form $\phi(|x_2-x_1|)$. Then the Lagrangian is $$\mathcal{L}= \frac{1}{2}m_1 \dot x_1^2 + \frac{1}{2} m_2 \dot x_2^2 -\phi(|x_2-x_1|)$$
Since $\mathcal{L}$ does not depend explicitly on time then per Noether... | {
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How is thermal energy split between kinetic energy and potential energy? Internal ("thermal") energy must be some combination of kinetic energy and potential energy, although most discussions of internal energy mention only the kinetic energy. However you also have potential energy -- as particles collide, they reach ... | In thermal equilibrium, the energy is equally distributed among different types. More precisely, any quadratic term in the energy per particle has average energy of $kT/2$ where $T$ is the temperature of the system and $k$ is the Boltzmann constant. This is the so-called equipartition theorem.
A diatomic molecule that ... | {
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Why is the internal energy discontinuous in a first-order phase transition? Using the Ehernfest classification where first order phase transitions are those where the 1st derivative of the free energy has a discontinuity, I can follow why the entropy and volume are discontinuous $S=-\frac{\partial G}{\partial T}$ & ${V... | Once we have a closed thermodynamic system having a discontinuity of the first derivatives of the Gibbs free energy $G$ as a function of temperature and pressure, the discontinuity of the internal energy $U$ as a function of the same variables is a trivial consequence of the relation between $G$ and $U$:
$$
U(T,p)=G(T,... | {
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Hydrogen wave function for electron orbitals I am a little confused about the quantum mechanics wave function. Hydrogen has a single electron in the first shell n=1, in the first subshell 1s with positive spin. In the attachment the wave function is represented for each unique quantum number n,l,m where n is the respec... | When the one electron is in the $n=1$ shell the atom is said to be in the ground (lowers energy) state.
That one electron can be in one of the other shells and you would then have an excited atom.
So the one electron could occupy any one of the shells and the diagrams show the probability of the electron being at a par... | {
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Is Hubbles law due to Gravity? Hubble's law states that Distance is proportional to Velocity. A ScienceDirect article states that Classical Hubble expansion is characterized by a proportional increase in the rate of expansion groups based on the distance from the main center of gravity
So is it due to gravity?
| Hubble's law describes the expansion of the universe. Is it due to gravity? Well gravity is the interaction by which space time responds to energy soruces (and therefore does anything at all), so yes. But you can't just say that any hypothetical universe containing gravity will therefore automatically obey Hubble's law... | {
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Why the derivative of the coordinate of a volume control is not zero? When deducing the Navier-Stokes equation, for conservation of momentum, in an Eulerian frame (a control volume)
the derivative of fluid velocity $U_{(t)}$ is calculated
$$\frac{\mathrm{dU} }{\mathrm{d} t}=\frac{\partial U}{\partial t}+\frac{\partial... | Given a (scalar) quantity $\varphi(\mathbf x,\,t)$ that exists in a continuum and has a macroscopic velocity represented by the vector field $\mathbf{u}(\mathbf{x},\,t)$. Then via the chain rule,
$$\frac{\mathrm{d}\varphi}{\mathrm{d}t}=\frac{\partial\varphi}{\partial t}+\dot{\mathbf{x}}\cdot\nabla\varphi.$$
Here, $\dot... | {
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Converting the weight into thermal energy Can we convert the weight into thermal energy? For example we would have a device like scale that if we stand on it, our weight can be converted into the thermal energy. Is this possible?
| There is no way to convert your weight into heat, unless you were made of plutonium and fashioned into a bomb. when you blew up, a fraction of your mass (not weight) would be converted into heat.
Here is the closest you can come to this goal without using plutonium:
You climb a ladder to the top. at the bottom is a buc... | {
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Given a magnetic field how to find its vector potential? Is there an "inverse" curl operator? For a certain (divergenceless) $\vec{B}$ find $\vec{A} $ such that $\vec{B}= \nabla \times \vec{A} $.
Is there a general procedure to "invert" $\vec{B}= \nabla \times \vec{A} $? An inverse curl?
(I was thinking of taking the ... | You were very close in taking the curl and looking for a Laplace (actually Poisson) equation for $\mathbf{A}$.
You are allowed to assume that $\boldsymbol{\nabla} \cdot \mathbf{A} = 0$ (Coulomb gauge, as mentioned in doublefelix's answer). Then, using your triple cross product identity, you get $\boldsymbol{\nabla} \ti... | {
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Linear velocity is cross product of angular velocity and position
Why is linear velocity is cross product of angular velocity and position?
| If you take $\bf d\theta$ to be the (infinitesimal) angle swept about the rotation axis (about axial vector $\bf\omega$ in diagram) after a small displacement $d\bf r_j'$ then looking at the diagram, you can form the cross product $$\tag 1d\bf r_j'=d\theta\times r_j'$$
If this displacement occurs in a time interval giv... | {
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Why doesn't a double slit act like a single slit? Well, a single slit can be considered a continuous array of sources, and thus its spectrum is different than that of a double slit. But why is a double slit so different from a single slit if it is just 2 single slits. Also, if the waves coming from the slits of the dou... | The double slit is missing the waves coming from the blockage between the slits. So yes, it's an array of sources, but it's not the same array.
| {
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What would a standing wave of light look like? I want to know what a standing wave of light would like and what properties it might have that are interesting.
| The light in a laser cavity is standing wave. If we measure the intensity of light, we will get an image like this:
This picture is from Chang H C, Kioseoglou G, Lee E H, et al. Lasing modes in equilateral-triangular laser cavities[J]. Physical Review A, 2000, 62(1): 013816.
But if we observe the cavity with eyes, in ... | {
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Why isn't amplitude modulation used more often in magnetic resonance technologies? Optically pumped magnetometers utilize a visible light carrier wave which is amplitude modulated down to a Larmor frequency of ~1000 Hz. This is in contrast to the vast majority of magnetic resonance implementations where the carrier fre... | Because AM needs a strong carrier and whose modulation rate is much less than the carrier frequency. In NMR, as mentioned in the answer of @AadhavVenkatesan, the "carrier" is actually a constant bias field. So the closest to AM one can have with that kind of background is a pulsed or On/OFF keying type modulation, and ... | {
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When two gas molecules collide, can they send out an IR photon? When a ball bounces on the ground, each bounce is smaller than the previous one because of friction in the system, i.e. the collision between the ball and the ground is not completely elastic. We are taught that the kinetic energy lost in an inelastic coll... | Yes, it is common for colliding molecules to emit IR and microwaves.
When molecules collide some of the kinetic energy may go into rotational and vibrational excitations, so that after the collision one or both of the molecules are in an excited state. Then the molecules decay by emitting a photon. Typically the decay ... | {
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Why can infinite quantities not be shown in an experiment or observed in physics? To modern physicists knowledge, there are no truly infinite quantities that can be shown with an experiment or observation. Time is not infinite, it had a beginning. Matter and energy is finite (otherwise there would be a giant black hole... |
Why can we never observe infinite quantities?
All physical measuring/observing devices (including our own senses) are constructed from a finite number of parts with a finite number of states and carry out a finite number of processes in a finite amount of time. Therefore it is impossible to design or construct a devi... | {
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Why $F = m(v_f - v_0)/2$? Force is directly proportional to mass and velocity and inversely proportional to time so why don't we write $F=1/t+m+v-v_0$ where $m$ is mass, $v$ is final velocity, and $v_0$ is initial velocity?
| By Newton's second law force is defined as mass times acceleration. Acceleration is defined as the time derivative of velocity, and velocity is defined as the time derivative of position. Force, acceleration, velocity, and position are vectors.
| {
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Different radiation intensities from a black body I am a high school student and was wondering about the radiation curve of a black body. Why do the emitted wavelengths from a black body have different intensities? What happens at the atomic level that makes some wavelengths stronger than others resulting in a radiatio... | TL;DR: The density of electromagnetic modes increasing with frequency, while the number of photons contained in each mode drops with frequency.
According to the Planck's law, the spectral radiance is given by
$$
B(\nu, T)=\frac{2\nu^2}{c^2}\frac{h\nu}{\exp\left(\frac{h\nu}{k_B T}\right)-1}$$
The factor $\nu^2$ originat... | {
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How to define the inverse of Dirac Gamma Matrices in QFT? The Dirac gamma matrices are a set defined by the 16 following matrices:
$$\Gamma^{(a)}=\{I_{4x4},\gamma^\mu,\sigma^{\mu\nu},\gamma_5\gamma^\mu,\gamma_5\}.\tag{2.122}$$
Now, I wish to determine the inverse set of gamma matrices, $\Gamma_a$.
According to Ashok Da... | Yes, Ashok Das should strictly speaking not call (2.124) the "inverse set of matrices"; they are only proportional$^1$ to the inverse. Rather (2.124) is (2.122) where the upper collective index $(a)$ of the 16 matrices (2.122) has been lowered by a metric $g_{(a)(b)}$. The (inverse) metric is here defined as
$$g^{(a)(b... | {
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Why are generators of the Lorentz group antisymmetric, while boost matrices are symmetric? We know that a Lorentz boost can be written as
$$
\begin{aligned}
x_0^{\prime} &=\gamma\left(x_0-\beta x\right) \\
x^{\prime} &=\gamma\left(x-\beta x_0\right) \\
y^{\prime} &=y \\
z^{\prime} &= z,
\end{aligned}
$$
symme... | It's in the funny Minkowski metric. In point of fact, as a matrix, for a boost,
$$
\omega^\mu_{~~\nu} = \omega^\nu_{~~\mu},
$$
so it is symmetric, unlike the antisymmetric covariant object,
$$
\eta_{\mu\kappa} \omega^\kappa_{~~\nu} ~~~~~~~~\leadsto \\
\omega_{\mu\nu}= - \omega_{\nu\mu},
$$
as the lowering of the space-... | {
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Does the formula for time period of a simple pendulum hold up for larger angles? When calculating the time period of a simple pendulum as an experiment in junior classes we used the formula
$$T = 2\pi\sqrt{\frac{l}{g}}$$
But recently seeing the derivation of the formula using Simple Harmonic Motion, I can't understand ... | If you want to have an idea how far the result deviates from its small-angle approximation…
The pendulum's total energy is:
$$E=K+V=\frac{1}{2}m(l\dot{\theta})^2-mgl\cos(\theta)$$
Let's assume that the pendulum starts from an angle $\theta_0$ with no velocity. Conservation of energy yields:
$$\dot{\theta}^2=2\frac{g}{l... | {
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Energy of compound harmonic oscillator Consider two harmonic oscillators of masses $m_1,m_2$ and spring constants $k_1,k_2$ respectively. Their motions are described by equations $$u_1=A_1\sin(\omega t+\varphi_1),\qquad u_2=A_2\sin(\omega t+\varphi_2).$$
Total mechanical energies of these two are given by $$E_1=\frac12... | If you mean just the mathematical addition
$u1+u2=A(sin(\omega t+\phi_1)+sin(\omega t+\phi_2)=B*(sin(\omega t+\phi_3)$ you have $B=A*\sqrt{((sin(\phi_1)+sin(phi_2)^2+(cos(\phi_1)+cos(\phi_2))^2))}$
and $\phi_3=\arctan(\frac{sin(\phi_1)+sin(phi_2)}{cos(\phi_1)+cos(\phi_2)}$ so the energie is not added, bu the system is ... | {
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Second Law of Thermodynamics Restatement with usable energy instead of entropy Is it technically accurate to state the Second Law of Thermodynamics as:
"The total amount of usable energy only decreases in a closed system"
I ask because it doesn't evoke the term "entropy", which usually only confuses the average perso... |
Is it technically accurate to state the Second Law of Thermodynamics as: "The total amount of usable energy only decreases in a closed (actually, isolated) system"
Yes, we can give the following qualitative interpretation of the above statement without explicitly mentioning entropy or exergy.
A non-equilibrium system... | {
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Using displacement field vs. electric field to calculate curl of magnetic field So let's say we have a medium with polarization $\vec{P} = \gamma \nabla \times E$, with no free currents or charges.
So we know that $H = \frac{1}{\mu_0} B - M$ , $D = \epsilon_0 E+P$ and $\nabla \ \times H =\mu_0 J_{free}+\frac{\partial D... | Of course there is current due to changes in polarization. For polarization to change, charged particles have to change positions, and this motion means there is electric current.
In a dielectric with no magnetization, total current can be expressed as
$$
\mathbf J = \frac{\partial \mathbf P}{\partial t}.
$$
In a magne... | {
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Can I still use the table of Clebsh-Gordan coefficients if isospin isn't conserved, to calculate the branching ratio? the title is basically everything. For example, the interaction $\Lambda^0 \rightarrow \Sigma^+ + \pi^-$ or $\Lambda^0 \rightarrow \Sigma^0 + \pi^0$. Isospin isn't conserved but the interaction is still... | The Λ has mass ~ 1.116 GeV, so below threshold for the
Σ(1.189) and π(0.140) system to decay to.
By contrast, the isosinglet Λ(1.405) is above that threshold and can and does decay to Σπ, strongly, 100% of the time. Isospin 1⊗1 of the products can, indeed, combine to an isosinglet, so isospin 0 is conserved. You can, ... | {
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Can water at 0 degrees Celcius and 1 atm have a range of different cooling abilities? Imagine we have two 1L containers of water, both at 1 atm, both at 0 degrees C. However, container 1 is at point (b) in the heating/cooling curve below, while container 2 is at point (c) in the heating curve below.
Then when mixing ... | Point B corresponds to a 1 kg chunk of ice at 0C, and point C corresponds to 1 kg of liquid water at 0 C. It takes 333 kJ of heat to melt the ice and move from point B to point C. What temperature do you think mixing 1 kg of liquid water at 0 C with 1 kg of liquid water at 50 C would end up at. Do you think that mix... | {
"language": "en",
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Why does water feel hotter at larger volume? Why does a 104°F pool/tub feel boiling hot, whereas a pot/cup of water at the same temperature does not feel hot at all.
(Normally a pot/cup of water won't be hot enough to cause one to immediately remove ones finger from the water till it's around 165-175°F).
Probably same ... | The difference in temperature perception between a 104°F pool/tub and a pot/cup of water at the same temperature is likely due to physical phenomenon like thermal mass, convection, heat transfer rate and sensing area (finger vs whole body).
The larger volume of water in a pool or tub means a higher thermal mass that he... | {
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The definition of "total curvature" for a scalar field In Modern Electrodynamics, Zangwill remarks that the total curvature vanishes at every point where $\nabla^2 \varphi = 0$.
Now my question(s): how is "total curvature" defined for a scalar field (is it, perhaps, the "function" of $\hat{\bf{n}}$ for every unit vecto... | I think Zangwill is just being heuristic with the terminology here, and is using “curvature” to mean “second (partial) derivatives of the function”. He is interpreting each of the quantities $\frac{\partial^2\phi}{\partial x^2}, \frac{\partial^2\phi}{\partial y^2} , \frac{\partial^2\phi}{\partial z^2} $ as representing... | {
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What is the Laplacian in the Pauli Equation? The Pauli Equation is given by
$$\left[\frac{1}{2m}\left[({\bf\hat{p}}-q {\bf A})^2-q\hbar{\bf\sigma}\cdot {\bf B}]+q\phi\right]\right]|\psi\rangle=i\hbar\frac{\partial}{\partial t}|\psi\rangle.$$
This contains a component ${\bf\hat{p}}^2 |\psi\rangle$.
However, according to... | As mentioned in the comments, it is understood that $p^2$ stands for $p^2 \otimes \mathbb{I}$. Since $p^2 = - \hbar^2 \nabla^2$, this means you just apply $p^2$ to each component of the spinor separately. In other words, the Laplacian is just applied to each entry separately.
Furthermore, don't forget that each compone... | {
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How to find the corresponding energy given the wave function? So I was struggling doing the following question:
Given the wave function $\psi(x) = A\, \mathrm{e}^{-ax^2} $ with potential $V = \frac12 kx^2$, find the corresponding total energy in terms of $k$ and $m$.
I did the calculation for $\left<x^2\right>$ and $\l... | If you're told that $\psi(x)$ is an energy eigenstate, then it must be the case that
$$
- \frac{\hbar^2}{2m} \frac{d^2 \psi}{d x^2} + \frac{1}{2} k x^2 \psi = E \psi
$$
for some value of $E$. But if you actually take the derivatives on the left-hand side, you'll find that there is one particular value of $a$ for which... | {
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Atmospheric pressure in non-nertial frame? Any object kept in an accelerating container of water feels different pressure than unaccelerated. Because if we go into the frame of water the g effective changes. Since air is also a fluid, a container of liquid accelerating upwards should experience more atmospheric pressur... | This question may be based on an expression for pressure in a column in hydrostatic equilibrium, like $P = \rho g h$ (or its integral generalisation for variable density $P = \int_{z_0}^{\infty} \rho g dz$). It's important to bear in mind the assumptions underlying these expressions. Your equation for pressure would ho... | {
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Why is Astatine-210 (At-210) the longest-lived isotope of astatine despite possessing an odd number of neutrons? I am guessing that isotopes with an even number of neutrons more readily release an alpha particle... When and if At-210 does that, it still has the problem of being 'odd/odd'...
But this begs the question..... | Leaving aside the questions of why only certain decay options are observed, lets just compare the known decays of At-210 and your proposed neutron emission.
Going to the latest Atomic Mass Evaluation (2020 version, part II with the tables of masses) one can look up the masses of various nuclei as well as their decay pr... | {
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Why does Bragg's law consider only specular scattering for constructive interference? My textbook only considers two-dimensional scattering, so I will stick to that. When explaining Bragg's law, it states that the incidence angle and the scattering angle must be equal so that all trajectories from different atoms (from... | If you have a uniformly spaced linear array of $M$ identical omni-directional emitters such that they have equal amplitudes say $1$ but the phases are in an arithmetic series, that is the $m^{th}$ has phase $m\alpha$ then the sum of all at a large distance such that $R>>Md$ and in direction $\theta$, will be ($\kappa =... | {
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Why is $( \alpha_i r_i) (\alpha_j r_j ) = \frac{1}{2} \{ \alpha_i , \alpha_j\}r_i r_j$? Where $\alpha_i= \left(
\begin{matrix}
0 & \sigma_i \\
\sigma_i & 0
\end{matrix}
\right)$.
To me it should just be $( \alpha_i r_i) (\alpha_j r_j ) = \alpha_i \alpha_j r_i r_j$, but it is not. Why the difference?
| Without loss of generality,
$$
\alpha_i \alpha_j = \frac{1}{2} \left( [\alpha_i, \alpha_j] + \{\alpha_i, \alpha_j\}\right)
$$
Note the first term is antisymmetric under interchange of $i$ and $j$, and the second term is symmetric.
Second, note that $r_i r_j$ is symmetric under interchange of $i$ and $j$. Therefore, $[... | {
"language": "en",
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Distinction between "types of heat" in thermal efficiency The definition of thermal efficiency I see in several sources is "total work" divided by "heat input".
Wikipedia, for example, says: "For a heat engine, thermal efficiency is the ratio of the net work output to the heat input".
I don't understand this definition... | First of all, $\oint pdV$ is the net work only if $p$ equals the external pressure. If the process is not reversible then the internal pressure is not equal the external pressure. So assume that the process is reversible.
In that case, in an arbitrary reversible cycle during which the transported entropy between the sy... | {
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Why is the common envelope ejected in some accretor-donor systems? As an example, let us consider a binary system of a neutron star and an evolved star (e.g. red giant) that has expanded, filled its roche lobe, and started the mass transfer onto the neutron star.
Under certain conditions such mass transfer can become a... | The envelope of the larger star may be rather weakly bound. Roughly speaking, the gravitational binding energy of the envelope is $-GMm/r$, where $M$ is the mass interior to the envelope, $m$ is the mass of the envelope and $r$ is its characteristic radius.
When material is accreted onto the neutron star, then a fracti... | {
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Is it possible to statically generate lift with the difference in pressure like wings? If I understood it correctly, the shape of the wings and/or propellers generates lift/thrust with the difference in pressure in both sides of the wings/propellers; where the lower side has higher pressure airflow and the uper side ha... | Wait, you want to move something upward against the pull of gravity by differentially lowering the pressure on its upper surface?
Uh, have you considered sticking a straw in a milkshake and sucking the shake into your mouth?
| {
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Equilibrium of Electromagnetic Force Between Two Moving Charges Please refer to the 2015 discussion titled "Magnetic Force Between Two Charged Particles", where a couple of the commenters present the generally-accepted equation for the magnetic force between moving charged particles. Magnetic force between two charged ... |
As a result, the combined electric and magnetic forces on the system do not appear to conserve momentum.
That is correct. The EM force does not conserve momentum of the interacting charged particles. The EM field itself contains momentum which must be accounted for to get the conservation of momentum of the total sys... | {
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Is effective mass used in calculating kinetic energy of electron in semiconductor? Is effective mass used in calculating kinetic energy of electron in semiconductor? I recall it was just used to take into account the internal forces so that expression of force fits well. But why
$E_k= \frac{\hbar^2k^2}{2m_e^*}$ uses $m... | Effective mass is not the real mass of electrons. For a free electron we don't need to consider effective mass, here electron's real mass can easily describe things.
But for electrons in solids (such as in semiconductor), it is easier to work with effective mass, because it enables one to proceed as if the electron was... | {
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Does $\exp(-i \theta \sigma_m \otimes \sigma_n)$ represent a rotation operator? It is well known that $\exp(-i \sigma_k \theta)$ where $\sigma_k$ $(k=x,y,z)$ is a Pauli matrix, represents the rotation operator about $k$-th axis. What physical interpretation does $\exp(-i \theta \sigma_m \otimes \sigma_n)$ have, where $... | As emerged from comments on your question, the rotation is better to be intended as a geometrical concept, rather than physical.
The word itself, rotation, helps to understand a geometrical concept when this is isomorphic to a 3D space. But when it is not such a case, its meaning is preserved, even if you lose the abil... | {
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Past and Future I'm new to physics
we've had and argument in our class about:
we know that present (and/or past) can and will affect future.
But how do we know if the future can affect past or present?
Is that even possible? What principles are in effect here?
for example: if I throw a piece of paper in trash can, how... | When you study special relativity, there's a concept called "causality". It explains how different events can be related with each other. This is, of course, due to the speed of light being constant and only achievable with electromagenitc waves.
Moreover, we have to consider the light cone (see figure below). It arise... | {
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Why is the current the same after passing through a resistor even when the drift velocity goes down? A resistor converts some of the electrical energy into heat energy, implying that the energy goes down, implying that the force with which an electron moves, and consequently, the drift velocity goes down.
Now, I=naeV w... |
A resistor converts some of the electrical energy into heat energy,
implying that the energy goes down,
Energy of the charge does not go down in the resistor. That's because electrons alternatively gain kinetic energy from the source of the electric field, while simultaneously giving up an equal amount of kinetic ene... | {
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How did we get the formula $d U = nCvdT$? Our teacher taught us that for any thermodynamic process, dU=nCvdT where Cv is molar specific heat capacity at constant volume and dU is change in internal energy. How did we get this formula and why is it valid for all processes
| It is not valid for all process. In case of single uniform system, it is valid for constant volume processes. It is also always valid in case of ideal gases (even for processes which change volume).
Heat capacity at constant volume is the amount of heat that needs to be added to the system to increase its temperature b... | {
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Why does ice on my car's windshield melt when it's below zero degrees Fahrenheit? This morning I looked outside at my car and windows were covered in ice. The temperature this morning was -7F. A couple of hours later now the temperature is 0F, yet everything on the car is shiny and clear.
What happened to the ice? It j... | If the car was in the sun, the paint, glass and metal of the car will absorb energy from the sunlight and warm up slightly. the frost will then melt, but only on the sunny side of the car.
| {
"language": "en",
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Is the rate with which an object gains speed when it is dropped dependent? Is the rate with which an object gains speed when it is dropped dependent or independent of the object's weight?
(gravitational force)
| It is usually independent of the object's weight.
Weight is given by $W = mg$, while Newton's second law says $F = ma$. Equating the two, the mass cancels out, and $a = g$. So the acceleration is usually independent of the object's weight.
Of course, there are possible subtle effects (like air resistance) that can chan... | {
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Landau vibration of molecules angular momentum I'm going through Landau's Mechanics, and I'm a bit confused as to how he's eliminating the total angular momentum. First of all, why can't we simply let
$$\textbf{M}=\sum m_a\textbf{r}_a\times\textbf{v}_a=const$$
which is how I think he eliminated the translational motio... | This is done in order to solve the problem using a method analogously to requiring the centre of motion to be on the origin. Just as with the centre of motion, the mathematical conclusion goes as far as to say that it is constant, but it is more convenient to let it equal zero.
| {
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Short circuit doubt Short circuits occur when a live wire comes in contact with a neutral wire due to poor insulation and stuff, and the main gist of this word short circuit is the fact that the wire gets heated up so fast it might burn. So if im getting this right then that would only mean that a very high current flo... | In the case of AC current, the concept of difference of potential is not quite appropriate for that extreme cases. If we could measure 2 nearby points of the (short circuited) circuit, including along the windings inside the transformer next to your home, a voltmeter would show zero, if the resistance between points is... | {
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Why is the flat spacetime of special relativity not a linear vector space? Why is the flat spacetime of special relativity, not a real linear vector space? It seems to satisfy all the axioms for a set to form a vector space. I mean adding to spacetime points $(t_1,\vec{r}_1)$ and $(t_2,\vec{r}_2)$, is yet another space... | Flat spacetime is more naturally described as an affine space, not a vector space. An affine space is basically a vector space without an origin. There is no unique natural event in flat spacetime which is naturally distinguished as "the" origin.
If we neglect curvature and take two events in spacetime say A is the sup... | {
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Why can't I use $\tan()$ to find the force of tension within a rope that forms a triangle? Apologies if this is too simple, but my teachers could not give me an answer. The following is a question from my grade 12 physics homework:
Now, the solution for $T_2$ is simple:
$T_{1_x} =T_{2_x}$
$96 cos(60) = T_2cos(30)$
$T_... | Your intuition is correct, but you are using the wrong angle.
$$\tan(30°) = \frac{T_2}{96\ \mbox{N}} \Rightarrow T_2 \simeq 55\ \mbox{N}$$
Or, alternatively, you are using the wrong definition of tangent:
$$\tan(60°) = \frac{96\ \mbox{N}}{T_2} \Rightarrow T_2 \simeq 55\ \mbox{N}$$
I was too quick in my previous answer... | {
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What portion of the universe is black holes? What portion of the universe is black holes? Is it possible to estimate the percent of all mass that is in the black holes?
| The cosmic inventory of the mass of various types of object is discussed in a well-known review by Fukugita & Peebles (2004).
They estimate that the fraction of the total matter in the universe that is made up of stellar-mass black holes (the final states of massive stars) is about 0.00025 with about a 30% uncertainty.... | {
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How does the magnetic field strength (in Teslas) change when two cylindrical magnets are pulled appart? I have two cylindrical magnets aligned such that the opposite poles are facing each other (N-S N-S).
I am trying to find a mathematical relationship that models the change in the magnetic field strength (B - measured... | The B field changes as the magnets pull apart. All the answers below are approximate'
*
*When they are still close together they behave like infinite charged planes, so B does not change with distance.
*As they move further apart, the near end of each magnet looks like a point charge, with the far ends of the magnet... | {
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Commutator of two Lorentz charges/angular momenta In Barton Zwieback's book "A first course in string theory" page 261, we calculated a Lorentz charge/angular momentum $M^{-I}$ of the open bosonic string in the light-cone formulation to be;
$$
M^{-I} = x_{0}^{-}p^{I} - \frac{1}{4\alpha^{'}p^+}\left(x_{0}^I\left(L_{0}^\... | Briefly speaking Ref. 2 argues on general grounds an ansatz (2.3.24) for the angular momentum commutator, and then sandwiches$^1$ the commutator between a bra and ket vacuum state to simplify the calculation of the coefficients (2.3.35) in the ansatz.
References:
*
*B. Zwiebach, A first course in String Theory, 2nd e... | {
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Why does magnetic force only act on moving charges? I don't understand why the magnetic force only acts on moving charges. When I have a permanent magnet and place another magnet inside its field, they clearly act as forces onto one another with them both being stationary. Also, I am clearly misunderstanding something.... | At an effective classical level, the atoms in permanent magnets do contain moving electric charges at the microscopic level: the orbiting electrons. These moving charges correspond to microscopic electric currents, and the magnetic fields act on these microscopic currents.
This picture is certainly a simplification of ... | {
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On Bohr's response to EPR If I understand correctly, the EPR paper (1935) points out that quantum mechanics is incomplete theory if it describes individual particles and measurements. This is true by the mathematical formalism. But already in 1926 quantum mechanics had its statistical interpretation, and in 1930 Heisen... | It is possible that Bohr didn't say quantum mechanics is a statistical theory because that claim is false. The square amplitudes of quantum states don't always obey the rules of probability, e.g. - during quantum interference experiments in general break those rules, see Section 2 of
https://arxiv.org/abs/math/9911150
... | {
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Relationship Between Velocity at Lowest Position and Gravitational Acceleration in Pendulum Motion To my knowledge there are two methods of finding this relationship. One with the centripetal force and the other with conservation of energy. I've left my work in the image below.
The problem here is that both of them gi... | Sorry, initially I did not understand what you were trying to do. The issue is that $T$ is not a constant. So $T$ is increasing as well, it increases with $g$ by more than the $-mg$ decreases, leading to a net increase under the radical and overall. If you think about it, this makes sense because $T$ includes both grav... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/751915",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Is there anything truly "stationary" in the universe? Ok, so I read this question and it got me thinking about something. Is there anything genuinely stationary in our universe? What does it mean to be stationary or devoid of any motion? If there isn't anything stationary, can there be a time when a thing is stationar... | Your question is like asking whether there is a particular point that is the centre of the surface of the Earth. The answer is that the surface of a sphere has no unique centre, so it is meaningless to speculate about where it might be. At any point on its surface, you can consider yourself to be centred on a sphere in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/752328",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 1
} |
Why the long lived Kaon can not decay into two pions? The short-lived and long-lived states of kaon $|K_1>$ and $|K_2>$ respectively have the following compositions if they are the eigen states of CP parity:
$|K_1> = \frac{|K^0>\:-\:|\bar{K^0}>}{\sqrt2}$
$|K_2> = \frac{|K^0>\:+\:|\bar{K^0}>}{\sqrt2}$
In the book "Intro... |
But wouldn't it be possible to use the same argument as three pions case for two pions with right combination of orbital angular momenta,
The argument is not about orbital angular momentum, but of the angular momentum any two particles have by definition of angular momentum as
The angular momentum of a particle of m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/752454",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Horizontal force of swinging beam In the diagram, a weighted beam is hinged to a vertical wall and is swinging downward.
As shown in the picture, when the beam is perpendicular to the wall, the horizontal force by the hinge is to the left acting as a centripetal force.
I am curious about the direction and magnitude of ... | You are right that the force is to the right at first. The center of mass starts at the wall. As the beam starts to fall, it starts to rotate. The center of mass starts to move down and away from the wall.
The total horizontal force is the horizontal component of the reaction force that keeps the end of the beam still.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/753832",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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