Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Solution to Dirac equation with external source The Dirac equation is:
\begin{equation}
\left[i\gamma^{\mu}(\partial_{\mu}-iA_{\mu})-m\right]\psi=0, \tag{1}
\end{equation}
where $A_\mu$ is a gauge field. The solution to this equation is:
\begin{equation}
\psi=\exp\Big(i\int^xA_{\mu}dx^{\mu}\Big)\psi_0, ... | Neither of your claimed solutions are valid in general. In order for an expressions like
\begin{equation}
\psi(x) =\exp\Big(i\int^xA_{\mu}dx^{\mu}\Big)\psi_0,
\end{equation}
to be a valid function of positionm the integral has to be independent of the path chosen. This is only the case if the $F_{\mu\nu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/710124",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
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What is the instant velocity? The velocity is the variation rate of the position correct? So does it make sense to talk about velocity without time?
| Instantaneous speed is just the speed something has at some instance in time. Time is still involved, but in an infinitesimal fashion.
You are correct in that if you took a picture of a moving object at some time, the picture would be still and you cannot tell anything about the motion of the object from the photo. Onl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/710296",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 7,
"answer_id": 2
} |
Can't understand a statement about motion From the book where I am studying motion, It says
Motion is a combined property of the object under study and the observer. There is no meaning of rest or motion without the viewer.
I know that, for an object, it can be said that 'it is moving' in one frame of reference, and ... | It is just saying that all motion is measured relative to something else that could also be moving since there is no absolute reference for position in the universe. Though I think there was supposed to be something special about the CMB.
So it's just saying that you always need something to measure velocity against (v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/710421",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 5,
"answer_id": 1
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Contradiction in my understanding of wavefunction in finite potential well Most things like to occupy regions of lower potential. So the probability amplitude should be higher in a region of lower potential. I denote the potential by V.
However, we also know that the kinetic energy of a particle is given by E-V - the b... | Imagine a perfectly elastic ball dropped vertically onto a flat surface. The ball heads for the point of lowest potential, ie the ground, but because of conservation of energy it bounces back to its initial position and continues to bounce up and down. It spends most of its time near the top of its bounce, because it i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/710744",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 3,
"answer_id": 2
} |
Renormalization Group Flow I am reading a book on effective field theory where the following "renormalization group equation" is given:
Now a quick search on google shows a bunch of interesting pictures of "renormalization group flows":
My question is: what is the relationship between the RG equation and the RG flow?... | RG time is usually introduced as a dimensionless parameter like e.g. $$\Lambda\equiv\Lambda_0\mathrm{e}^{-t},$$
where in this convention $t=0$ corresponds to the ultra-violet (UV) at the initial momentum scale $\Lambda_0$ (which might be asymptotically large/infinite) and $t\rightarrow\infty$ corresponds to the infra-r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/711150",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
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Eyes shut, can a passenger tell if they’re facing the front or rear of the train? Suppose you’re a passenger sitting in one of the carriages of a train which is travelling at a high, fairly steady speed. Your eyes are shut and you have no recollection of getting on the train or the direction of the train’s acceleration... | Yes, because the train predictably hits bumps/gaps in the track.
As you travel on a train, you hear first one set of wheels then the other then the other going from the front of the train to the back hit these imperfections in the track. If you are facing the direction of travel you hear these coming from in front of y... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/711352",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 9,
"answer_id": 1
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How do experimentalists measure the exciton binding energy? The exciton binding energy in semiconductors is determined theoretically by the energetic difference between the fundamental gap and the optical gap or, in other words, as the energetic difference of the fundamental gap and the first exciton peak in an optical... | One can measure light absorption in a semiconductor. Peaks in absorption could appear corresponding to the photon -> exciton transition. They appear bellow optical gap
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/711604",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What is a "cycle time" in Allan deviation formula for atomic clock instability? And why does having more independent atoms reduce $\sigma_y(\tau)$? The usual formula for clock instability is given as
$\sigma_y(\tau)\approx\frac{\Delta f}{f_0\sqrt{N}}\sqrt{\frac{T_c}{\tau}}$
First off what do each of these symbols reall... | Partial answer: Each atom is an independent measurement of the local oscillator frequency so you get more statistics on your frequency estimate each shot. However, you’re right that if different atoms are frequency shifted relative to each other due to, for example, a non zero velocity distribution or a inhomogeneous z... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/712068",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
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Points where electric field is zero when charges are present at vertices of a regular polygon There is a $n$-sided regular polygon with a charge $q$ at each vertex. I know that there are $n$ points, other the center of the polygon, where the electric field is zero. But why is this so? Is there a general way to prove it... | Consider a line connecting two adjacent charges on your polygon, and then another line which bisects that one, going in the positive x direction through the center of the polygon (at x = 0). To show that your premise is true, you would need to find one (and only one, if (n) is odd) other point (other than at x = 0) on ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/712514",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
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How are these Covariant Derivative Identities found? In David Tong's Gauge Theory notes on page 137 near eq. (3.30) he makes use of the following expressions for the covariant derivative $D_{\mu}$
$$\frac{1}{2}[\gamma^{\mu},\gamma^{\nu}]D_{\mu}D_{\nu}=\frac{1}{4}[\gamma^{\mu},\gamma^{\nu}][D_{\mu},D_{\nu}]\tag{1}$$
and... | Hint for eq. (2):
$$e^{-ik\cdot x} f(D) e^{ik\cdot x}~=~f\left(e^{-ik\cdot x} D e^{ik\cdot x}\right)$$
and
$$\begin{align} e^{-ik\cdot x} D_{\mu} e^{ik\cdot x}~\stackrel{\text{Hadamard}}{=}&~e^{-ik_{\nu} [x^{\nu},\cdot]} D_{\mu}\cr
~=~~~&D_{\mu}+ik_{\nu} [D_{\mu},x^{\nu}]\cr
~=~~~&D_{\mu}+ik_{\mu},\end{align}$$
where... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/712683",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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In Hamilton-Jacobi theory, how is the new coordinate $Q$ time-independent when Hamilton's principal function separates? Following the notation in Goldstein, the solution to the Hamilton-Jacobi equation is the generating function $S$ for a canonical transformation from old variables $(q,p)$ to new variables $(Q,P)$ wher... | I will assume you are only talking about the case of $1$ degree of freedom (or else, your notation is problematic).
Generally, it is always a good reflex to study a specific case when you have two conflicting arguments. Take for example a free particle with $H = \frac{p^2}{2}$, solving the Hamilton-Jacobi equation, you... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/713564",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is the universe made up of particles or fields? QFT describes the electron as an excitation of the electron field. The spin of electrons create magnetic fields. So which came first? How can a particle created from a field then create its own field? Or are some fields not fundamental?
|
QFT describes the electron as an excitation of the electron field.
Quantum field theory fields are completely different than the fields of Newtonian gravity and classical electrodynamics. It is a theoretical model that is very successful in fitting existing data and observation of elementary particles, the electron i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/713942",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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"answer_id": 1
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What is the generally expected or more useful form of supersymmetry, on-shell or off-shell? If the on-shell numbers of degrees of freedom of bosons and fermions match we
have on-shell supersymmetry, if the off-shell numbers match we have off-shell
supersymmetry. When LHC people say they are searching for supersymmetry ... | On-shell SUSY means the theory is supersymmetric when taking into account equations of motion. Off-shell means that the action is supersymmetric even before writing equations of motion (obviously off-shell SUSY holds on shell as well). Physically, we are interested in on-shell stuff, because physics is ultimately expre... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why I cannot write the time evolution operator $e^{-i(T+V)t}$ as the product of operators $e^{-iTt}e^{-iVt}$ To calculate the wave equation of a time-independent Hamiltonian we use:
$$
\Psi_{i}(r,t)=e^{-iH^{0}t}\psi_{i}(r,0).
$$
We also know that the time-independent Hamiltonian $H^{0}=T+V$ is given to the sum of kinet... | Let $t$ be a dummy variable to keep track of orders in a series expansion:
$$e^{tA} e^{tB}
=
\Big(1 + tA + \frac{1}{2} A^2 t^2 + \mathcal{O}\left(t^3\right) \Big)
\Big(1 + tB + \frac{1}{2} B^2 t^2 + \mathcal{O}\left(t^3\right) \Big)
= 1 + (A + B)t + \frac{1}{2} (A^2 + 2 AB + B^2) t^2 + \mathcal{O}\left(t^3\right)
\, .
... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/714531",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 0
} |
Infinite conducting plane Let $\pi$ be an infinite conducting plane laying in $z=0$.
the plane is kept in potential of 8 volts, ($\phi(z=0)=8[V]$).
Prove or disprove:
the surface charge density - $\sigma$ is well defined.(there is a single solution to the surface charge density.
What I thought:
You have to solve a Lapl... | Without knowing what happens at any other point, the solution is indeed non-unique. The potential has to obey Laplace's equation below and above the plane, so
$$\phi''(z) = 0,$$
meaning that
$$\phi(z) = \begin{cases}
A_+ z + B_+ & z>0\\[5pt]
A_- z + B_- & z<0
\end{cases}$$
Note that since the system has translational i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/714941",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Issue expanding $\sin \theta$ about $\theta_{eq}$ Quoting a textbook:
$$(m_1 + 2m_2\sin^2\theta)\ddot\theta = m_1\Omega^2\sin\theta\cos\theta - \frac g L (m_1 + m_2)\sin\theta.\tag{10}$$
We can simplify this expression a bit by relating $\frac g L (m_1 + m_2)$ to the equilibrium angle $\theta_{eq}.$
$$(m_1 + 2m_2\bbox... | This is because your $\ddot{\theta}$ is already assumed small.
I think the simplest way to deal with this is to introduce an explicit counter $\epsilon$ which keeps track of the "smallness" of various things.
If you are expanding near $\theta_{eq}$, write
$$
\theta=\theta_{eq}+\epsilon \delta\theta
$$
where $\delta\the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/715750",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
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Is this proof that massless objects cannot be charged? In the realm of pre relativistic physics.
$$\vec{p}=m\vec{v}$$
$$F= \frac{dp}{dt}= m\vec{a}$$
If there exists an electric field in space, the force experienced by it would be $$F= q\vec{E}$$
Applying newtons laws:
$$q\vec{E} = m \vec{a}$$
This an equation stating a... | As described in Michael Seifert's answer, the question requires relativity, not Newtonian mechanics. As explained in the comments by Andrew Steane and Michael Seifert, the question also requires quantum mechanics. So we're in the realm of quantum field theory.
Massless charged particles are problematic in QFT, because ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/715865",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 5,
"answer_id": 4
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How to solve for the trajectory of the center of mass? I'm working on the physics engine component of a game engine I'm building, and I need some guidance with this particular situation.
Consider a square with mass M that is free to translate in the xy plane and free to rotate about any axis perpendicular to the page (... | If $\mathbf J(x(t),y(t))$ is the external force acting on square between times $t_0, t$, then the total impulse is $\int_{t_0}^{t}\mathbf J(x(u),y(u)))du$. So we get $\int_{t_0}^{t}\mathbf J(x(u),y(u)))du=\int_{t_0}^{t}m\frac{d\mathbf v}{du}(u)du=m\mathbf v (t)-m\mathbf v (t_0)=\mathbf p(t)-\mathbf p (t_0)$, where $m$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/715966",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Are two states with the same measurement probabilities necessarily equal up to unitary equivalence? Let $\rho$ and $\rho'$ be $n\times n$ density matrices, and suppose that for every observable $A$ and every $\lambda$ in the spectrum of $A$ we have
$$
\text{tr}(\rho P_{\lambda})=\text{tr}(\rho' P_{\lambda}),
$$
where $... | Let $H$ denote a finite-dimensional complex Hilbert space, $\rho$ and $\rho^\prime$ be two density matrices, i.e. positive semi-definite operators with unit trace and $A$ an arbitrary hermitian operator. Its spectral representation reads
$$ A=\sum\limits_\lambda \lambda(A)\, P_\lambda (A) \quad .$$
If the equality in t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/716096",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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"answer_id": 1
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Number of Independent Components of Levi-Civita Christoffel Symbol Can anybody explain why Levi-Civita Christoffel symbol in general $N$ dimensional space have $\frac{N^2(N+1)}{2}$ independent components?
I have read that in $N$-dimensional space, metric tensor has at most $\frac{N(N+1)}{2}$ independent components and ... | First, let's talk about the metric tensor; it has $\frac{N(N+1)}{2}$ independent components, because it is a symmetric tensor: $g_{ab}=g_{ba}$. Writing this out in a matrix format:
\begin{align}
[g]&=
\begin{pmatrix}
g_{11}&\dots& g_{1N}\\
\vdots &\ddots&\vdots\\
g_{N1}&\dots & g_{NN}.
\end{pmatrix}
\end{align}
In this... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/716251",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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The value of $g$ in free fall motion on earth When we release a heavy body from a height to earth. We get the value of $g=9.8 \ ms^{-2}$. Now, I'm confused about what it means. For example, does it mean that the body's speed increases to $9.8$ every second? Or, does it mean that the speed of the body is $9.8 \ m/s$?
| It means the speed increases by $9.8$ m/s every second.
At the beginning (when you release the body) its speed is $0$.
After $1$ second the speed is $9.8$ m/s, after $2$ seconds the speed is $19.6$ m/s, and so on.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/716376",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 0
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Solving 3D Kepler Problem substitution goes wrong I'm trying to arrive at the effective potential equation in Kepler Problem using Routh reduction method. We can procede in two ways, either using polar coordinates in the plane where the orbit happens or using spherical coordinates. I'm having trouble with this last one... | *
*The underlying reason for OP's flawed argument is, that a premature use of EOMs in the stationary action principle
$$\begin{align} S~=~-&\int\!dt ~R(r,\dot{r};\theta,\dot{\theta}), \cr
-R(r,\dot{r};\theta,\dot{\theta})~=~&\frac{1}{2}m(\dot{r}^2 +r^2\dot{\theta}^2) -\frac{p_{\phi}^2}{2mr^2\sin^2\theta} -V(r),
\end... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/716481",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is there a version of the Einstein field equations that uses the Riemann curvature tensor instead of the Ricci curvature tensor? I understand that the Einstein field equation uses the Ricci curvature tensor, Ricci curvature scalar, and stress-energy momentum tensor. But is there a way to form an equation that uses the ... | Here is the Lichnerowicz' form of Einstein's equations:
\begin{eqnarray}
R^μ{}_{νρσ;μ}=J_{νρσ},\\
R_{μνρσ;α}+R_{μναρ;σ}+R_{μνσα;ρ}=0,\\
\end{eqnarray}
where the “current” tensor is
$$J_{νρσ}=\left(T_{νσ;ρ}-\frac12 g_{νσ}T_{;ρ}\right)-\left(T_{νρ;σ}-\frac12 g_{νρ}T_{;σ}\right) .$$
The second equation is just (differenti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/716623",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
"answer_id": 2
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Double slit experiment: Are electrons interacting with other electrons to create a wave? Assume a double slit experiment with electrons and no observer (light source). Can the wave-like behavior and resulting interference pattern be explained by the single electron that is being shot, doesn't really travel to the detec... | Let me first point out that the double-slit experiment is a Gedankenexperiment, designed to illustrate quantum mechanics - not some puzzling observation requiring explanation. What happens in this experiment is a consequence of the wave-like nature of electrons when described by Schrödinger's equation - the math is nea... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/716763",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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When is it admissible to neglect the pressure term to use the Burgers' equation instead of the Navier-Stokes equation? The Burgers equation can be understood as a simplification of the Navier-Stokes equations when the pressure term is neglected:
$$
\frac{\partial u_i}{\partial t}+\ u_j\frac{\partial u_i}{\partial x_j}=... | Two relevant examples, the decay of an initially linearly increasing wind and a source of water spreading out in a circular symmetric pattern, are illustrated here. As for neglecting the pressure gradient, one may think it as a toy model of the barotropic NS equations where pressure is a function of density alone , $p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/716953",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 3,
"answer_id": 1
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How can we know the maximum of a scalar field after Lorentz transforamtion? Support that we have a field $\phi(x)$. we do the Lorentz transformation for it, namely,
$$
\phi(x) \to \phi'(x)= \phi(\Lambda^{-1}x).
$$
If the field $\phi(x)$ takes the maximum at point $x=a$, where does the field $\phi'(x)$ take the maximum ... | Obviously the transformation $x^{\mu}=\Lambda^{\mu}_{\nu} x^{\nu}$ considering you are transforming four vector from one frame to another. Then the field's mode coordinates will be changed but the field itself will be invariant since proper time are connected by Lorentz transformations.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/717249",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
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Breaking down of 2nd law of thermodynamics Do you know a scenario where the second law of thermodynamics breaks down?
| There is a really cool example I heard of that was published a few years ago, an instance of it actually being violated in practice, not just in theory.
Very roughly, what they did was construct a thermodynamic analogue to an RLC circuit, where energy oscillates back and forth, instead of entropy uniformly increasing b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/717412",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
"answer_id": 0
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Why do we need Legendre transformation for thermodynamic potentials? I get the idea that thermodynamic potentials are introduced because it is not always easy to describe a system's energy as a function of variables like $S,V,N$ as we normally do with internal energy $U=U(S,V,N)$. For example, temperature is much easie... | Something that hopefully adds to Salvatore Manfredi D's answer: the goal isn't just to change variables, it's also to build a function that is minimized when equilibrium is reached after a specific process completes.
Start with $U$:
$$dU=T\,dS-P\,dV$$
You can read two things in this equation:
*
*$U$ is a function of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/717564",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 3,
"answer_id": 2
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Minus sign in Feynman's The reason for antiparticles I was going through Feynman's lecture on "The reason for antiparticles", which can be found here, and I got a little confused early on. His statement of Eq. 3 seems clear to me, from which Eq. 5 follows directly. But then he says that from that an Eq. 8 one can deriv... | The probability of being in some state or another at the end of the interactions is $1$. Equation (5) gives the probability of being in the state $\phi_0$ after the two interactions. Then equation (8) gives the probability of being either in state $\phi_0$ or another state, which is $p$. So equation (8) there is
$$
\te... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/717654",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How can quantum tunneling happen conceptually? I have read in Griffiths' Quantum Mechanics that there is a phenomenon called tunneling, where a particle has some nonzero probability of passing through a potential even if $E < V(x)_{max}$.
What I don't understand about this is how to conceptualize how this can happen. I... | From the viewpoint of the Schrödinger equation, the key relation is
$$\hbar k = \sqrt{2m(E - V)},$$
where $k$ is the wave number ($\psi \propto e^{ikx}$). This holds locally in a spatially varying potential $V$ under the semiclassical WKB approximation. In the classically allowed region, $E > V$ and $k$ is real, i.e., ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/717902",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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Will quantum events ever occur on a macro-scale rather than a vacuum? Michio kaku says there's a chance we'll wake up on Mars tomorrow https://www.theatlantic.com/science/archive/2018/10/beyond-weird-decoherence-quantum-weirdness-schrodingers-cat/573448/
In this post, it is shown that quantum decoherence in the macro w... | The rate of a tunneling event in which an object of your mass (or any human's mass) moves from Earth to Mars is not zero, but so small that by the time it has a reasonable chance to occur, you, Mars, the solar system, the galaxy, all visible light and known structures in the observable Universe, and the black holes tho... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why magnetic field doesn't do any work on moving charge? As we know the Lorentz force $F=qv\times B$ never does work on the particle with charge $q$. But it does work on a dipole.
My question is, doesn't a moving charge behaves like a dipole? I mean an electron moving around nucleus behaves like magnetic dipole then wh... | In a particle accelerator, the charges are deflected sideways by magnets and thus forced into a circular path. What happens in the process?
Firstly, permanent magnets could be used for this and they would not lose their magnetic field nor would it weaken. Secondly, the particles emit electromagnetic radiation in a narr... | {
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Moment of Inertia Tensor and Center of Mass Can the Moment of Inertia Tensor be diagonal in a reference frame where the Center of Mass of the system is not on some of the axes?
| Given the general inertia tensor about the center of mass as
$$ {\rm I}_C = \begin{bmatrix}
I_{xx} & I_{xy} & I_{xz} \\
I_{xy} & I_{yy} & I_{yz} \\
I_{xz} & I_{yz} & I_{zz} \end{bmatrix} $$
and the parallel axis theorem in 3D given the center of mass at a position $(x,y,z)$ from the reference frame origin, the MMOI abo... | {
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Assume a photon has a wave function, what can be said about its Hamiltonian and eigenvalues? I understand a photon does not have an associated wave function, but what if we assumed a photon does in fact have a wave function. How would this look and how could its Hamiltonian be determined?
| In classical mechanics, a particle with 0 mass is not so clear, and this extends to quantum mechanics as well.
In relativity, however, light has a rigorous framework. In relativity, $E \neq \frac{p^2}{2m}$ for a free particle. It's instead:
$$E^2 = (mc^2)^2+(pc)^2$$
and so for light, which has 0 mass:
$$E^2=(pc)^2 \imp... | {
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If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it? I have read that water (or any other liquid) cannot be compressed like gases and it is nearly as elastic as solid. So why isn’t the impact of diving into water equivalent to that of diving on hard concrete?
|
So why isn't the impact of diving into water equivalent to that of diving on hard concrete?
Water is rather incompressible, but it is not very hard. It deforms rapidly under shear stress, unlike concrete. This greatly prolongs the duration of the deceleration and therefore reduces the impact.
| {
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Obtaining the conjugated momentum operator after coordinate transformation I am mostly uncertain if my definition of the momentum operator and the resulting commutator is correct after a simple coordinate transformation. Lets say we have in our first coordinate system the following definitions,
$$
H = -\frac{\hbar^2}{2... | The comments and the preliminary answer from User Feynman_00 helped me to see where I went wrong. My error was assuming that the new momentum operator is the same as old one expressed in the new coordinates.
$$\hat p_y \neq \hat p_x=-i\hbar \frac{d}{dx}=-i\hbar \frac{dy}{dx}\frac{d}{dy} = -i\hbar m^{1/2}\frac{d}{dy}=\h... | {
"language": "en",
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How does a decelerating universe agree with this version of the Friedmann-Robertson-Walker formula? I was watching a video discussing dark matter, and he presented the following simplified version of the Friedmann-Robertson-Walker equation:
$$ \left(\frac{\dot{a}(t)}{a(t)}\right)^2 = \frac{8\pi G}{3} \rho(t) -\frac{k}{... | There are two Friedmann equations, and they are usually written as:
$$ \frac{\dot{a}^2 + kc^2}{a^2} = \frac{8\pi G \rho + \Lambda c^2}{3} \tag{1}$$
$$ \frac{\ddot{a}}{a} = \frac{-4\pi G}{3}\left(\rho + \frac{3p}{c^2}\right) + \frac{\Lambda c^2}{3} \tag{2} $$
The equation you cite is obtained from equation (1) by assumi... | {
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In the twin paradox or twins paradox what do the clocks of the twin and the distant star he visits show when he's at the star? In the twins paradox of relativity one twin stays on earth while the other travels to a star ten light years away, and then immediately flies back. Because his rocket travels at just under the ... | This is an example of the relativity of simultaneity. Let's suppose the distances and speeds are such that the journey takes exactly 10 years in the Earth frame and 12 hours in the ship frame.
When the twin arrives at the star, the clock on the star will read 10 years, while the clock on the spaceship with show 12 hour... | {
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Bernoulli's equations on a falling (not freefall) bucket of water If a bucket of water with a tiny spout at the bottom (allowing the water to jet out) is falling (not at freefall due to a pulley system), will the air pressure above the water level in the bucket be equal to the water pressure at the spout (that is, atmo... | The air pressure above and external to the spout do not change. But, if the bucket is accelerating downwards, the water in the bucket experiences a (fictitious) upward force that counters gravity and lowers the pressure at the bottom, hence lowering the flow rate out the spout. (In free fall the pressure at the botto... | {
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On average, how often does any given hydrogen nucleus run into another hydrogen nucleus in the Sun? I think there is a misprint in an article. I will include the link if you don't mind and cut paste the sentence that I think is a misprint. Here is the link
https://www.abc.net.au/science/articles/2012/04/17/3478276.htm#... | If “run into” means takes part in a fusion reaction then this is correct as an order of magnitude approximation. Wikipedia says:
... each proton (on average) takes around 9 billion years to fuse with one another using the PP chain
As noted in comments, if the average lifetime of a lone proton were very much shorter t... | {
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Normal ordered exponential of one-body operators Let $\{a_i\}_{i=1}^N$ be a set of annihilation operators (they are either all bosons, or all fermions) satisfying the canonical commutation or anti-commutation relation. In the book Quantum Theory of Finite Systems by Blaizot and Ripka, Problem 1.6 claims that (summation... | Let us prove OP's claim for a single bosonic mode:
Proposition:
$$ e^{ta^{\dagger}a}~=~:e^{(e^t-1)a^{\dagger}a}: \qquad t~\in~\mathbb{C}.\tag{A}$$
Sketched proof of eq. (A): Let's call the LHS for $U(t)$ and the RHS for $V(t)$. Both sides can be written as a function of the operator $n=a^{\dagger}a$ without the use o... | {
"language": "en",
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How conservation of energy looks like in the moving frame? It is obvious that a car accelerates by converting its chemical energy in the fuel to produce kinetic energy to accelerate itself.
If the energy is lost into friction and heat, the car will slow down.
But from the point of view of the car, it always appears to ... | Energy is not invariant across reference frames. From the car's frame you would correctly calculate the car's kinetic energy to be 0. The earth, on the other hand, would have massive kinetic energy.
The fuel does work against the pistons in the engine. The energy is lost in the same places as before.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/720630",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can a mass on a spring oscillate when it is in contact with a heat bath? I am reading statistical mechanics from Concepts in Thermal Physics, the author states the following after deriving the equipartition theorem.
A mass on a spring has energy $E$ which is given as the sum of two quadratic terms:
$$E = \frac{1}{2}mu^... | Short answer is: Mass will oscillate with an amplitude given by the following expression:
| {
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What is virtual photon concept in classical electrodynamics? If we observe a charged particle like an electron passing us at some high speed $u$, then as $u \to c$ the field we observe looks like a superposition of plane waves normal to the trajectory of the electron. The field can be Fourier transformed, and the modes... | After searching lots of sources i haven't found a direct answer. But my suggestion is yes. It may not be entirely correct. But when
$r→0$
We need to find a impact parameters which can't be zero because integral contain $1/x$ term that convert $\log(x)$ and $x=0$ is quite annoying. Therefore the lower limit definitio... | {
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What is the meaning of a thermal equilibrium between matter and radiation? I understand that the thermal equilibrium between two bodies means that the two bodies attain the Same temperature. Therefore,there is no flow of a thermal energy between them. However, I don't know how i should understand the meaning of it when... | A "Stationary radiation field" means that the intensity and spectrum of the radiation is not changing with time. For the matter and radiation to also be in thermal equilibrium, requires that the radiation has reached an equilibrium state with the matter that both absorbs and emits it. For every photon that is absorbed,... | {
"language": "en",
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$(a - a^t)e^{\frac{1}{2} a^ta^t} | 0 \rangle = 0$ When talking about the limits of squeezed states, we reach the conclusion that $e^{\frac{1}{2} a^ta^t} | 0 \rangle$ must be an eigenstate for momentum since the uncertainty in momentum becomes zero.
As such I would expect that $(a - a^t)e^{\frac{1}{2} a^ta^t} | 0 \rangl... | If I may suggest another approach:
Defining $\left|-1\right\rangle$ as the zero vector,$$\begin{align}(a-a^\dagger)e^{\tfrac12a^ta^t}\left|0\right\rangle&=(a-a^\dagger)\sum_{n\ge0}\frac{\sqrt{(2n)!}}{n!2^n}\left|2n\right\rangle\\&=\sum_{n\ge0}\left(\frac{\sqrt{(2n)!}}{n!2^n}\sqrt{2n}\left|2n-1\right\rangle-\frac{\sqrt{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/722516",
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Producing cherenkov radiation using radioactive source I want to produce cherenkov radiation by transpering $\beta$ particles through a dialectric media. To do this , I will use a radioactive decay as a source for the $\beta$ particles, The thing that bother me is that the radiation (the visible spectrum) will be too... | Use the Frank-Tamm formula, which describes the energy emitted ($E$) per unit frequency ($\omega$) per unit length ($x$):
$$ \frac{\partial^2E}{\partial x\,\partial \omega}=
\frac{q^2}{4\pi}\mu(\omega)\omega\Big[1-
\frac{c^2}{v^2n^2({\omega})}
\Big],$$
where $\mu(\omega)$ and $n(\omega)$ are the frequency dependent per... | {
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Did electric charge not exist in the early universe? I ask this question based on something Don Lincoln said in a video about leptogenesis over at the Fermilab Youtube channel. Video for reference: https://www.youtube.com/watch?v=PsqEcGMjEfo
Here is his exact quote:
... during a time in the universe very shortly after... | In the earliest part of the big bang, the electromagnetic force had not yet split out from the unification of all the forces because it was still too hot for this to happen. At that point in the process, there were fractionally-charged quarks in existence but they didn't "talk" to one another electromagnetically. Thing... | {
"language": "en",
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"source": "stackexchange",
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Besides traveling at the speed of light, how can we be sure that it is possible to have energy and momentum without mass? How can we be sure that it is possible to have energy and momentum without mass? If something were to continually lose energy, would it not also lose a corresponding amount of mass? I understand tha... | You cannot separate the idea of having energy and momentum without mass from the idea of moving at the speed of light. I.e. there is no "besides". The basic equation that relates energy, momentum, and mass is: $$m^2 c^2 = E^2/c^2 -p^2$$ From this equation, in the special case that $p=0$ we get the famous $E=mc^2$. And ... | {
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Can speed be entangled? When reading about quantum entanglement, I see that all variables that are discussed (spin for instance) have discrete states.
Can a continuous variable such as speed be entangled? In the case of annihilation for instance with two particles moving at a certain speed - by measuring the speed of o... | Yes, speed can - and almost always is, if you pick a random particle in the universe - entangled. As are most variables. The corresponding operator for speed is just the magnitude of total momentum operator divided by mass. Positions can be entangled, momenta can be entangled... all it takes for a state to be entangled... | {
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Is the equal sign in "$0 ^\circ \mathrm{C} = 273.15\, \mathrm{K}$" fair? I'm in doubt whether the equal sign in an expression like "$0 ^\circ \mathrm{C} = 273.15 \,\mathrm{K}$" is fair because, normally, if $A=B$, then, say, $2A=2B$, which is hardly applicable to "$0 ^\circ \mathrm{C} = 273.15 \,\mathrm{K}$".
So is it ... | The equal sign is fair, the multiplication is not.
$^\circ C$ does not have a meaningful meaning of multiplication, for any value. One requirement for multiplication to be meaningful, you basically need a zero that has a philosophical meaning of zero (i.e., that there is no quantity of something). The Kelvin scale sa... | {
"language": "en",
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Wave Function Collapse and the Dirac Delta Function When the wave function of a quantum system collapses, the probability of finding it at some specific point is given depends on $||\Psi||^2$:
$$
\int_{\mathbb{R}^3}{d^3 \mathbf x \; ||\Psi||^2} = 1
$$
Could this modulus square, the instant you measure, be thought as t... | I read this question as to be simple and precisely asked. Without knowing what a collapse of the wave function could be like, it understand: there is no longer a wave function when the object represented by the wave function is "measured".
But then the object exists, so it is just "there". It is all about "what actuall... | {
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What causes light passing through a hole to change direction? On diagrams showing light passing through a hole, the wave of light appears to change direction when it emerges from the hole.
What causes that change of direction? Is it maybe the walls of the hole imparting a pulling force or the sudden absence of light ne... | It might be useful to first ask a different question. Namely, why does light not scatter (change direction) when passing through a bulk medium such as glass (assuming no impurities, etc.)? One answer is the Ewald-Oseen extinction theorem which gives a rigorous mathematical account of how light propagates through matter... | {
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How can the energy-momentum tensor influence the metric outside an energy-momentum distribution? The elements in the energy-momentum tensor are determined by the mass-energy-impuls distribution as viewed from an inertial frame.
So, if you see a collection of masses with different momenta you can fill in their values in... | The absence of energy-momentum ma only requires the space to be Ricci flat. In other words it requires $R_{\mu\nu}\equiv {R^{\lambda}}_{\mu \lambda\nu}=0$ and not that ${R^\mu}_{\nu\sigma\tau}=0$.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How could proper distance today be infinity in a curvature only Universe when the age is finite? So for a curvature only universe, the Friedmann equation becomes
and we get the solution $a(t) = t/to$, and $to = 1/Ho$.
If we calculate the proper distance today we will get
As $z-> infinity$, the proper distance today a... | When $a(t) = t/t_0$ and $κ=-1/t_0^2$, the FLRW metric
$$ds^2 = dt^2 - a(t)^2 \left( \frac{dr^2}{1-κr^2} + r^2 dΩ^2 \right)$$
with the coordinate substitution
$$\begin{eqnarray} T &=& t\sqrt{1-kr^2} \\ R &=& r\,a(t) \end{eqnarray}$$
becomes
$$ds^2 = dT^2 - dR^2 - R^2 dΩ^2$$
which shows that it's just Minkowski space in ... | {
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Why does the opposing force differ in when falling on concrete vs on water in spite of Newton's third law? If a person jumps from the first floor of a building and lands on a concrete surface, they will suffer serious injury because of Newton's third law.
If the same person jumps the same distance and lands in swimming... | Newtons third law says that the $F = ma$, where the acceleration $a$ is the change of velocity per time $\Delta v/ \Delta t$. At the instant you hit the ground, $\Delta v$ is very high if you are falling fast, resulting in a high force. When you fall on the water, $\Delta v$ is less, since you do not totally stop. The ... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If Aristoteles was right and heavier objects falled faster towards the ground how would be Newton's Laws of Motion described? It seems like it would be like:
a(m)=km
and may be a(m1,m2)=K(m1-m2)
Am I doing any sense?
Btw I'm no negationist, nor I'm trying to create a negationist movement here, I just wonder how physics... | If acceleration due to gravity depended on mass then you have the following conceptual obstacle (first pointed out by either Galileo or Newton, I think).
Two objects each of mass $m$ will fall with a certain acceleration. If you join them together into an object of mass $2m$ then they fall with a different acceleration... | {
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How does pilot wave theory explain "identical particle" interference? Pilot wave theory says that there exist waves in 3D space which carry particles. This explains, say, the double slit experiment.
But this does not explain the behavior of identical particles. According to standard QM, a system of two identical partic... | The pilot wave theory is mostly a strategy for denying the implications of quantum theory. The pilot wave theory takes the wavefunction and adds particles on top of it. Pilot wave theorists then have two options. (1) They can deny that the wavefunction is real, in which case it makes no sense that the particles are inf... | {
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What frame of refernce to select in statistical mechanics? Suppose we have a solid particle suspended inside a fluid such as an ideal gas, as shown in the following picture:
Our system is the solid particle and the environment is the gas (which acts as a heat bath). Our frame of reference is attached on the edge of th... | $V_{cm}=0$ in the box frame. What makes you think the gas is macroscopically moving in the box?
| {
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"timestamp": "2023-03-29T00:00:00",
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Dispersion equation with variable wavenumber The wave equation
$$u_{tt}=c^2 u_{xx}$$ is known to have a simple wave solution $u(x,t)=Ae^{i(kx-\omega t)}$ where the dispersion equation is simply $c=\omega/k$. Yet, let the wavenumber be a function in $x$, then the independent variable $x$ will appear in the dispersion so... | From a mathematical point of view your idea does not make sense. Remember that plane waves do not exist, they are just a tool that physicists introduce to build up a mental representation. Ask a mathematician; he will tell you that to get a dispersion relation, you just need to take the Fourier transform of your wave e... | {
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Current loop and the associated magnetic field under mirror reflection Let a circular current loop in the $xy$ plane carries a current in the counterclockwise sense. Therefore, it produces a magnetic field in the $+z$ direction (think of it as an arrow parallel to the $+z$-axis). Now consider reflecting this by placing... | Some physical quantities that most of us treat as vectors, they are indeed pseudovectors, whose nature can be appreciated when you do reflections as a transformation of coordinates.
Examples of pseudovectors are angular velocity $\omega$, force moment and torque $M$, angular momentum $\Gamma$, and the magnetic field $b... | {
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Einsteins gravity theory, but for static objects https://www.youtube.com/watch?v=XRr1kaXKBsU this is a good video to explain Einsteins gravity.
The video claims that objects always move in a straight line, with an absence of a force of gravity, rather that space is curved, so that the straight line becomes curved.
It d... | The geodesic equation of general relativity reduces to Newton's Law of Gravity, to a very high approximation, in such a case. Therefore, there is no contradiction. In the language of GR, the object is moving uniformly along a geodesic in spactime and, in the language of Newton, it is accelerating in space. It is simpl... | {
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What is the current going into a resistor-capacitor parallel circuit and the current coming out of it? I'm looking at the circuit below and know that I1 = I2. Can someone explain why those 2 currents are the same?
| It might appear that because there is a charge storing device, the capacitor, the two current can be different and a difference in the currents results in the charge stored in the capacitor to change.
However the fact is that the net charge on the capacitor is zero in that a change in positive charge on one plate is al... | {
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Diagonalising the Hamilton operator, why does this magic work? Let the Hamilton operator $H= \omega_1 a_1^\dagger a_1 + \omega_2 a_2^\dagger a_2 + \frac{J}{2} (a_1^\dagger a_2 + a_1 a_2^\dagger)$ be given, of course $a_j$ and $a_j^\dagger$ are the creation and annihilation operators, respectively. This operator can be ... | We are dealing here essentially with a one-particle Hamiltonian - more precisely, a Hamiltonian for many non-interacting particles. The Hamiltonian in question is simply the second quantized version of
$$
H=\omega_1 |1\rangle\langle 1|+ \omega_2 |2\rangle\langle 2| +
\frac{J}{2}\left(|2\rangle\langle 1| + |1\rangle\lan... | {
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Andy Weir's Project Hail Mary - Does the travel time to Tau Ceti make sense? I'm an English teacher with a modest science background teaching Science Through Science Fiction this fall, and I need some help with the physics in Andy Weir's Project Hail Mary. Here's one question I have. (Light spoilers for the book.)
The ... | The book clearly states
1.5g acceleration outbound from Earth, &
1.5g deceleration approaching Tau Ceti.
| {
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What is the matrix representation of a function of an quantum operator? If we know the matrix representation of a quantum operator, say $J$, will the matrix representation of any function of the operator i.e$f(J)$, same as acting the function on the matrix of the operator?
| It's not clear what you mean by "the function acting on the matrix of the operator."
If you mean
$$f\left(\begin{pmatrix}a & b\\ c & d\end{pmatrix}\right) = \begin{pmatrix}f(a) & f(b) \\ f(c) & f(d)\end{pmatrix}$$
then the answer is no, that is not what it usually means in physics.
The typical meaning is this: if a fun... | {
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Do Neutrons Have a Charge Radius? The radius of a proton is described as a "charge radius", about 0.84 fm. The neutron is about the same size, 0.8 fm, but has no measureable charge. Is this a contradiction? Are the two radii measured in the same way?
| Netrons have no net charge the same way a neutral hydrogen atom has no net charge. I don't know what the electric charge profile of a neutron looks like, but it's going to be rather complicated. See the parton distribution for hadrons - it describes how much each particle type contributes at each length scale.
At a gue... | {
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„Orbital“ of an quark Inspired by the idea of the electron orbitals ( probability of finding an electron in an atom) i was wondering what that would look like inside a proton or neutron for quarks. For simplicity consider a meson where we know the location of one quark. What is the orbital - or probability of finding t... | Unlike atomic electrons, the spin-orbit coupling in the strong interation is always non-negligible. If you know the spin and parity $J^P$ for a meson, you can figure out the allowed values for $L$. But in general, even a wavefunction which consists only of valence quarks will allow multiple values of $L$ to end up with... | {
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Which direction will the beam of electrons be deflected?
For D.C. sources like the one shown, do we apply Fleming's right hand rule or left hand rule? I derived my answer using Fleming's left hand rule in this case. If I am not mistaken, we use Fleming's right hand rule for A.C. motors only. I got C but the answer is ... | D.C. source connected to solenoid will produce constant current, generating constant magnetic field (directed up in the solenoid and down outside the solenoid). The right direction of electron velocity equals left orientated current of positively charged particles, so if the current goes to the left anf field points do... | {
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What work does a microwave oven do? I learned that when energy is transfered it either produces work or it becomes thermal energy (heat).
Work implies a force that acts on an object producing changes in its position.
I'm learning these concepts from Khan Academy, and in this article they say:
A hot cup of coffee has a... |
Work implies a force that acts on an object producing changes in its position.
Not necessarily. It is possible to do work on an object and only change its internal energy, not its position. Heating coffee in a microwave is one example; heating a wire by passing a current through it is another; compressing a spring is... | {
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Lagrangian Mechanics: semi-holonomic constraints By switching to a different set of coordinates, can you make problem with semi holonomic constraints into a problem with holonomic constraints? If so, then when can you do this? I wold like to know if this is possible for all semi-holonomic problems, some semi-holonomic ... | *
*A non-holonomic$^1$ constraint is by definition a constraint that is not holonomic,
e.g. on the form $f(q,\dot{q},t)=0$ or an inequality.
*A semi-holonomic constraint
$$ \omega~\equiv~\sum_{j=1}^na_j(q,t)~\mathrm{d}q^j+a_0(q,t)\mathrm{d}t~=~0 $$
is equivalent to a holonomic constraint iff there exist an integrati... | {
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Synthetic aperture for visible light camera It seems to me a camera array for visible light could be constructed to synthesize a large effective aperture to achieve high angular resolution just as a synthetic aperture radar does. This could be used for example on a satellite with several small cameras mounted on extend... | Short answer: Yes... and also no...
Longer answer as to why "yes" and how to turn it into a "no" below:
For wavelengths of visible light our sensors can only collect intensity (amplitude) but the phase information is lost. So just attching several cameras spread out is not an option with current technology.
But there i... | {
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Property of reciprocal lattice I came across the following property of the reciprocal lattices.
Let be $\Lambda$ a Bravais lattice and $\Lambda^*$ its reciprocal lattice; let be $\vec{G} \in \Lambda^*$ and $\vec{G}_0$ the shortest vector in $ \Lambda^*$ that is parallel to $\vec{G}$. Then, the relation between the two... | Suppose $n$ is not an integer. Denote by $[n]$ the integral part of $n$, and $\{n\}=n-[n]$, so $0<\{n\}<1$. Consider $\vec{G}-[n]\vec{G}_0=\{n\}\vec{G}_0$, which is still parallel to $\vec{G}$, and belongs to $\Lambda^*$. But the length of $\{n\}\vec{G}_0$ is strictly smaller than $\vec{G}_0$, so a contradiction.
| {
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Why only harmonics allowed in the Casimir effect? My question is really a request for an intuitive explanation as to why only harmonic frequencies of photons allowed between two conduction plates.
Why do the plates have to be conductive?
And can real photons with unmatching frequencies exist between the two plates in t... | Plates do not have to be conducting. Various dielectric materials can be used, and the Casimir force on the plates will depend on the characteristics of those materials such as dielectric constants.
But perfectly conducting plates are the simplest toy model, because perfect conductor means electric field is zero in and... | {
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What is the difference between the state $| \psi \rangle$ of quantum mechanics and the microscopic state $St(q,p)$ of statistical mechanics? In terms of physical quantities, the $|\psi \rangle$ of quantum mechanics and the microstate $St(q,p)$ of statistical mechanics are both a vector, and the microstate of statistica... |
What is the difference between the state $| \psi \rangle$ of quantum mechanics and the microscopic state $St(q,p)$ of statistical mechanics?
Apples and oranges.
The $| \psi \rangle$ of quantum mechanics and the $St(q,p)$ of statistical mechanics use mathematics, vectors , tensors and even complicated functions of s... | {
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If reference frames are equally valid, then why do teachers say the geocentric view is wrong? If all reference frames are valid, then why is the geocentric model taught as "wrong" in schools?
I've checked many websites but none of them clear the issue. Wiki says that in relativity, any object could be regarded as the c... | "Geocentric model" is a loaded term. It's not just referring to the the sun rotating around the Earth. If you are only concerned with whether the sun orbits the Earth or whether the Earth orbits the sun it's a wash. It is referring to the model as whole which must explain all the observed phenomena seen. This includes ... | {
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I'm having trouble understanding exactly what $δ$ represents in thermodynamics I know that $δ$ sometimes represents the Dirac delta function but in my book it states "Suppose that equilibrium has been established Then a slight change in the position of the piston should not change the free energy since it is at a minim... | That $\delta$ is not a Dirac delta, but the symbol for indicating a differential form that is an inexact differential, i.e. a differential whose integration depends on the path of integration,
$\displaystyle \int_{\ell^1_{A\rightarrow B}} \delta f \ne \displaystyle \int_{\ell^2_{A\rightarrow B}} \delta f \qquad$ in gen... | {
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Relativistic invariants of a classical field in 4D fashion: why the relation between the components of the current density holds? I'm trying to understand how is justified the following relation between the first component of the current density integrated over the volume and the scalar product of the 4-vector current ... | The definition of $dS^i$ (Landau §6) is that it is a four-vector equal in magnitude and normal to the hypersurface element; in other words, $dS^i$ is the projection of the hypersurface element, respectively, onto the hyperplanes $x^0=$ const, $x^1=$ const, $x^2=$ const and $x^3=$ const.
By definition, the integral
$\in... | {
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Solution of Einstein's field equation for local energy density If there is a uniform positive energy density present in a patch of space-time, what would be the metric describing the patch? a de-Sitter patch? What would be the gravitational potential felt by a mass in that region?
| Under the approximation of spherical symmetry, the FLRW metric describes any homogeneous patch. Note that in general such a patch would not remain static for the same reason that the universe should not be static. The Friedmann equations precisely describe how the patch would evolve.
The gravitational potential is a Ne... | {
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Why does particle leave circular motion after string slacks? If a particle is attached to a string and made to move in a vertical circle with initial velocity of $\sqrt{4gl}$ $m/s$ where l is the length of string, at some angle (approx $131°$ with the initial position), the string slacks and the particle leaves the cir... | Following is not a full answer but a comment to help OP figure out the answer on their own.
Gravity does not provide centripetal acceleration to the particle. This is because centripetal acceleration always points towards a definite point while gravity always points towards a fixed direction.
| {
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Does a solar panel encased in glass give off less power? The speed of light in glass is about 2/3 c. If we encase a solar panel in glass, does it give off less power because of this reduced speed of light? (and ignoring other things like the reflectivity of glass, etc.)
| No, there would be no change in the amount of generated power.
The situation you describe would not change the rate that photons are arriving at the surface of the solar cell. Assuming we aren't worried about angular dependence or changes in reflection, photons would be converted into usable power at the same rate.
| {
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Is the normal force the reaction force? There is a box on the surface of earth. The earth exerts a force to the box (black arrow). The box exerts a reaction force to the earth(brown arrow). But this reaction force is exerted to the earth not the box, so where is the normal force? If the reaction is the normal force the... | There are two different third-law force pairs. One pair is the downward gravitational force on the box and the upward gravitational force on the earth. The other is the upward normal force on the box and the downward normal force on the earth.
In equilibrium, the gravitational and normal force are equal and opposite to... | {
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Does the quantum mechanical wave function work as a charge distribution? The quantum mechanical wave function is traditionally interpreted as a probability distribution of the particles position. It is possible to interact with an electron in a conductor, without collapsing the wave function, which can be distributed o... | Schrödinger initially believed that the wave function is related to actual charge distribution density, rather than to probability density. Some objections were raised to such interpretation. One of the objections is based on wave packet dispersion. I offered some modification of the interpretation (Entropy 2022, 24(2)... | {
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Can a Matrix Have EigenBras? I only need a yes or no, but I cannot find anything online. I know a matrix $A$ can have eigenkets found by using.
$$A\psi=\lambda\psi.$$
However, I was wondering if my matrix $A$ was Hermitian, could I just apply the Hermitian conjugate to the equation and find eigenbras for the system too... | Look for left eigenvectors in linear algebra,
$v^H A = \lambda v^H$.
If the matrix is Hermitian, left and right eigenvectors are the same (just evaluate the conjugate transpose of the expression above to get $A^H v = \lambda^* v$; then you can prove that $\lambda$ is real as well).
Then ket goes to Right-eigenvectors, ... | {
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Two solutions for a collision which satisfy both conservation of momentum and energy. Which is correct? For the following problem, there are two sets of solution which appear to be equally valid:
v_car = 15.7 m/s, v_truck = 12.9 m/s and v_car = 12.3 m/s, v_truck = 15.2 m/s. How can I know which set of solutions is corr... | To approach a more general form of this problem, let's skip the first step of your problem and just suppose you have already calculated:
Total momentum
$P' = m_1 v'_1 + m_2 v'_2$
Total energy
$E' = (1/2) m_1 v_1^{'2} + (1/2) m_2 v_2^{'2}$
Let $f = m_1/m_2$, and let's do our work in the center of mass frame where P=0. A... | {
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Why do we observe particles, not quantum fields? My understanding is that, in the context of quantum field theory, particles arise as a computational tool. We perform an expansion in the path integral in some parameter. The terms in these expansions correspond to Feynman diagrams which can be interpreted as interaction... | The theorists have mathematical rationalizations, but the reality (as Bohr pointed out) is that if your experiment senses fields you observe fields, while if it senses particles, you observe particles. Every radio detects the electromagnetic field, not photons. Waves in any field may be observed to diffract so long as ... | {
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Torus shaped event horizon Is there a solution to GR field equations for a rotating black hole that has a torus shaped event horizon? If so, when a craft flies through the torus, it can pass through a ring singularity while remaining outside of the event horizon. Would it enter a strange region of repulsive gravity and... | There is a result in four-dimensional General Relativity that forbids such situations. Namely, the Hawking's Theorem on the Topology of Black Holes. It is given, e.g., on the classic book by Hawking and Ellis, The Large Scale Structure of Space-Time, which I quote:
Proposition 9.3.2
Each connected component in $J^+(\m... | {
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Do theoretical particle physicists really believe the particles they work on do not exist? Inspired by this article in The Guardian.
In private, many physicists admit they do not believe the particles they are paid to search for exist – they do it because their colleagues are doing it
This makes no sense to me - ther... | She is referring to particles in speculative theories like Garrett Lisi's E8, various string theories, GUT, and SUSY, etc. The experimental physicists and engineers sometimes have theories but mostly they are testing others weird ideas. Sabine makes good arguments that it's probably a waste of money and resources. It's... | {
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How high and when the bead will be on a spinning parabolically bent wire? Imagine a wire, bend it parabolically with equation $ 4ay = x^2 $, and the vertex as usually at the origin. It is now rotated with angular velocity, $\omega$, on an axis, passing in its plane through the vertex. A bead, of mass $m$, inserted in t... | Your equations are correct and it can only mean that at certain $\omega^2=g/2a$ the body can be stabilized for any x on the wire and for any $\omega^2\neq g/2a$ the solution will not be stable and probably bead will fall to the center for $\omega^2<g/2a$ and will fly away for the $\omega^2>g/2a$
| {
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Finding width of a slit in diffraction $500nm$ light is illuminating an aperture of width
$$d_1=0.2mm$$ The diffracted light from this first aperture then illuminates a second aperture $1m$ away. What is the smallest width, $d_2$, of the second aperture that will allow most of the diffracted light cone to pass through ... | The sketches in your solution do not match the text of the problem. The way I understood the text, it is describing what is known as Fraunhofer diffraction. Check the corresponding wikipedia article. Especially look at the first example: https://en.wikipedia.org/wiki/Fraunhofer_diffraction#Examples . It has the solutio... | {
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Since water can evaporate at any temperature above absolute 0, would the water cycle still be possible even without the Sun? Since water can evaporate at any temperature (or even sublimate at less than 0°C, although at a very low rate: Why does water not evaporate in below 0 degrees?), could there be a water cycle if t... | To have a water cycle you need water to evaporate and condense on the surface of the water at different rates. Without an outside source of energy it would reach equilibrium and there wouldn't be excess humidity condensing into clouds readily.
| {
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At which electric field or voltage does field emission occur? Imagine our environment is a vacuum. At which value of electric field or voltage, does field emission occur? I just want to know what is the maximum electric field we are allowed, to place between two electrodes, without field emission phenomenon. So, you ca... | Well, I am a new master circuit student and I do know so much about physics.
The definition of work function is here:
In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the vacuum immediatel... | {
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Complex Grassmann Dirac Functional - How do we integrate over it? I'm following the Book of Brian Hatfield (Quantum Field Theory of point particles and Strings), p.192 here: For real Grassmann numbers (and Functionals thereof):
If $\Phi[\psi]$ is a functional, and $\psi(x)$ is a Grassmann-valued function, we demand tha... | *
*Be aware that integration over a complex Grassmann-odd variable $\psi$ has 2 different notations in the literature:
$\int \!\mathrm{d}^2\psi$ and $\int\! \mathrm{d}\psi~\mathrm{d}\psi^{\ast} $. This is similar to the standard notations for a Grassmann-even complex integration.
*Similarly, a complex Grassmann-odd ... | {
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Understanding page 141 of Blundell’s Concepts in thermal physics On this page (in the second edition), there is a figure containing two states A and B of a system:
There are two paths between A and B: one is an irreversible change, and the other is a reversible change. However, on the same page it says that entropy st... |
on the same page it says that entropy stays the same for a reversible change,
yes, it says that
and that entropy increases for an irreversible change
yes, it says that
and the latter seems to imply that the entropy of B is larger than the entropy of A.
No, this does not follow from what the authors say.
They say ... | {
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Equivalence between small distance and high energy I see in a lot of particle physics literature statements along the lines of: 'This is valid for high energies (small distances)'. Exactly what do we mean by small distances in this case? From QFT, QM and other physics courses, the connection between small distance and ... | In HEP, where (in units of c=1) momenta are much larger than masses, so they are tantamount to energies, the fundamental scale relation of QM, $[x,p]=i\hbar$, comes to bear. The de Broglie relation ${\lambda\over 2\pi}= \hbar/p$ of the particles/waves involved relates distances to momenta/energies inversely.
Consequent... | {
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Electromagnetic radiation reflected normally causing interference to itself Is it possible to have a body reflect almost perfectly any radiation falling normally with the insident ray so that the reflected ray interferes with the incident and hopefully reduce or cancel it out ?
| High-quality optical lenses are often coated to reduce reflections. A thin film of a transparent material with a different index of refraction is coated onto the lens, with a thickness of a quarter of the wavelength of the light of interest. Incoming light passes through the coating and bounces off the other side, retu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/732282",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Calculating heat removed by cooling system using output fluid temperature I am trying to calculate the amount of energy removed by a cooling system for some medical research. I'm a little out of my depth with the physics calculations.
I have fluid flowing through a variable temperature object (an organ being heated) at... | The heat that is transferred from the organ to the water can be calculated as the difference between the enthalapy of the inlet and outlet water. Within time $dt$ this heat is
$$
dQ = \dot M C_p (T_\text{out} - T_\text{in}) dt
$$
where $\dot M$ is the flow rate of the cooling water and $C_P$ is its heat capacity. We... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/732679",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Thermodynamics : an empty container surrounded by an atmospheric gas I have a small exercices of thermodynamics if anyone can help me :
We start with an empty container of volume $V$. The walls of this container are adiabatic and will not change over time surrounded by a gas of pressure $P_0$ and of temperature $T_0$.
... | Since the container is empty, the pressure inside the container is 0. There is no material/mass inside the system whose thermodynamical quantities can be considered. Please check the question again.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/732997",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Dimensional Analysis, How to determine the right order for the power relation? I came across this question in Solved Problems in Classical Mechanics by O.L. de Lange and J. Pierrus. Question 2.12 is as follows:
Use dimensional analysis to determine the dependence of the period $T$ of a simple
pendulum on its mass $m$... | There's no way to know, since you're starting with four parameters and only 3 equations to solve them. Thus, both $\gamma$ and $\delta$ can be thought as undetermined numbers.
Nevertheless, the results you'll obtain will be identical with any of those two choices, since from a dimensional point of view you have powers ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/733081",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Center of Gravity derivation question I need a sanity check, please.
When determining the center-of-gravity of a lamina described by $f(x)$, we know that by definition,
$\bar{x} M = \sum_{i=1}^{N} m_i \tilde{x_i}$
where $\tilde{x_i}$ is the location of the centroid of strip located at $x_i$
Assuming uniform density and... | to obtain the center of mass use those equations
$$y_{CM}=\frac{\iint\,y\,dx\,dy}{A}\\
y_{CM}=\frac{1}{A}\int_{x_1}^{x_2}\left(\int_0^{f(x)}y\,dy\right)\,dx$$
$$x_{CM}=\frac{\iint\,y\,dx\,dy}{A}\\
x_{CM}=\frac{1}{A}\int_{x_1}^{x_2}\left(\int_0^{f(x)}dy\right)\,x\,dx$$
where $~A~$ is the area under the curve $~f(x)~$
$$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/733288",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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