instruction stringlengths 31 24.3k |
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In this paper 1 written by Joseph Polchinski, he seems to indicate that all symmetries of nature may not be fundamental:
From more theoretical points of view, string theory appears to allow no exact global symmetries, and in any theory of quantum gravity virtual black holes might be expected to violate all global symm... |
Why Coulomb's Law is only valid for point charges? Is there any reason? Why this law is not valid for other charges rather than point charges?
|
According to Maxwell's equations:
$$ \vec{\nabla}\times\vec{E} = -\frac{\partial B}{\partial t}$$
But if we have an electric field that is dependent upon both the radial distance and angles, we can get a non-zero curl. Does that mean that the rotor of the electric field due to any static configuration of charges, even ... |
I have constructed a thought experiment regarding whether the future is deterministic or not.
It goes like this:
Let’s take an Observer 100 light years away from earth. Now presently, if he looks at earth then he sees the earth as it was 100 years ago. Now I, a scientist, flashes a beam of radiation from earth towards ... |
In all the references/textbooks that I have looked at, the precise definition of spacetime is never really clear. By gathering the hypothesis that we need to make, I get the following definition: $$\text{spacetime is a smooth connected and orientable Lorentzian manifold with or without boundary}.$$
But it seems that we... |
Is there experimental evidence of a single, free massive particle wavefunction can spread in space to macroscopic size?
Thanks for the answers
|
In this excellent article, the author, in sec. 1.4 describes the full capacitance matrix properties.
He writes:
The capacitance matrix is symmetric: $C_{ij} = C_{ji}$. This is related to the fact that in electrostatics, the electric field has zero curl.
Do you know a proof of this fact. I will content myself with a l... |
please note that I am a high school student trying to understand the quantum model of the atom; I have only the most basic understanding of quantum mechanics.
I am trying to comprehend the wave nature of electrons in atoms but I am unsure on a number of things.
what is meant by a probability cloud of electron(s)?
does... |
I serve fresh made coffee in my cup, collecting the grounds in a strainer. Then I move them back to the pot, add milk to "rinse," and strain again.
My strainer collects about three spoonfuls of coffee grounds, and I tap it against the cup's lip to try and make sure all the liquid comes down before discarding.
Still, ev... |
In many biological models, the mass is negligible compared to friction and force. In this friction dominated regime, the equations of motion are therefore
$$
\mu \dot x = -\nabla W(x)
$$
where $\mu$ is the friction coefficient and $W$ is the potential energy.
Is there a canonical name for this equation?
(Gradient flow ... |
I recently had a problem on a quiz for a classical mechanics course that looked something like this:
A bead of mass $m$ is constrained to move on a rod that is tilted at a fixed angle $\theta$ with respect to the $x$-axis. The rod is accelerated along the $y$-axis with constant acceleration $a$, as shown in the diagra... |
in the text book by Altland and Simons (Condensed Matter Fiel Theory) in chapter 4, summation over Matsubara frequencies is explained. The basic idea is to choose an auxiliary function and multiply it to the expression in the sum such that one gets the original function back with the residue theorem. On page 171/172 it... |
We've an isolated system inside which currents and charges reside.
If the Poynting vector on the surface of the system is non zero, then there is energy exchange between the system and the surroundings.
Then is it necessary that our system is radiating?
(To me it is because there is no other form in which energy can be... |
The energy in a current carrying loop is given as
$E_{\mathrm{m}}=\frac{1}{2 \mu_{0}} \int B^{2} d \tau$
If I cut the loop abruptly the current and hence the magnetic field quickly fall to zero and hence the energy goes to zero as well, as is evident from the above equation.
But where does that energy go to?
|
The wikipedia page says that sound waves when reflected at a solid surface show no phase change, but when reflected from a region with lower acoustic impedance, they exhibit a $180^\circ$ phase change.
I am not able to understand the meaning of "phase difference" in waves travelling in opposite directions. As far as my... |
Assuming we have a 2D hexagonal lattice and its reciprocal lattice. The difference between them is that the real lattice and its reciprocal lattice have 30° rotation. So if the following image is its first Brillouin zone, we have a direction $Γk$ in reciprocal lattice, is this direction kept the same in the real lattic... |
This is a doubt from a question I have solved, I will extract only my queries from it.
Case1: let a rod of mass '$m$' lie on a smooth table and impulse $Ft$ is given at one of the ends.
(assume the center of mass moves in a straight line )
*in this case the center of mass will move with a velocity $Ft/m$.
$Ft$=change i... |
Consider a room filled with air and containing a vessel filled with pure liquid A. Now, the vessel is opened and liquid A exerts a partial pressure on the room from the equilibrium of liquid and vapor of A. What I'm wondering is how the partial pressure exerted by A is unaffected by the amount of A in the vessel. What... |
I am stuck in the derivation of $G$ (Einstein tensor) in the condition of weak field ($h$ small) where $g_{\alpha\beta}=\eta_{\alpha\beta}+h_{\alpha\beta}$ and $h^{\alpha\beta}=\bar{h}^{\alpha\beta}-\frac{1}{2}\eta^{\alpha\beta}\bar{h}.$
I calculated the Ricci tensor:
$$R_{\alpha\beta}=\frac{1}{2}\left(\bar{h}{^{\mu}}_... |
I'd like to ask for your recommendation on literature regarding classical electromagnetic scattering at an introductory level.
The aim is understanding the mathematics behind simple scattering problems, namely by a cylindrical perfect electric conductor, which I plan to figure in my Master's Thesis.
|
I was reading the Jackson and suddenly in one line they wrote the electric field as:
$$E(x,t)=E(x)e^{-iwt}$$
why is this valid?
|
When working with discretized QFT one moslty works with the Finite Difference Method (FDM) on the hypercubic lattice, and the fields live on sites, links, faces ... of the lattice. Also QFT can be defined on non-square domain, like honeycomb lattice, which resembles more the Finite Elements Model (FEM).
And I wonder, w... |
Define a pure state to be one that can be expressed in the form $ \rho = | \psi \rangle \langle \psi |$. How can we show that this is equivalent to $ \rho \neq p \sigma_0 + (1-p) \sigma_1 $ for any distinct states $ \sigma_0 \neq \sigma_1 $ and $ 0 < p < 1 $.
Intuitively this statement makes sense to me - I've managed ... |
The general Schrödinger equation in 3d is
$$i\hbar\frac{\partial\psi}{\partial t}(\mathbf r, t)=-\frac{\hbar^2}{2m}\nabla^2\psi(\mathbf r, t)+V(\mathbf r)\psi(\mathbf r, t).$$
Now consider that $$V(x, y, z)=\mathcal V(x)$$ for some univariate function $\mathcal V$. Then can we show that in this 1d potential, the above ... |
If the laws of physics work the same forward and backward in time, why does entropy grow in one direction?
|
The following statement is made when separating the spatial and time components of the field.
But I do not see how Fourier is related.
|
So I was reading about the expansion of the Green function in Spherical coordinates from Classical Electromagnetism by J.D. Jackson and I'm really confused about a subtle step that he makes to go from equations $(3.117)$ and $(3.118)$ to equation $(3.119)$ (the image is attached at the bottom of the question). Summaris... |
I can show that
$$ [\hat L_i,\hat L_j] = i\hbar\epsilon_{ijk} \hat L_k $$
where $\hat L$ is the angular momentum operator.
But I'm struggling to show that
$$[\vec a \cdot \hat L , \vec b \cdot \hat L] = i(\vec a \times \vec b) \cdot \hat L$$
where two vectors $\vec a$ and $\vec b$ commute with each other and with $\... |
I'm trying to learn some physics on my own and I'm having problems understanding waves. I haven't even begun studying electromagnetic waves because I'm stuck with something very elementary, which is trying to understand why particles in the wave medium through which a transverse wave propagates move perpendicularly to ... |
For some cases, like two blocks colliding head-on, it is quite obvious that the normal reaction between the blocks would be impulsive in nature (and the normal force between the blocks and ground is non-impulsive).
However for some other cases, like an oblique collision with a particle stationary (or moving) on a plane... |
In the second chapter of string theory book by Green-Schwarz-Witten, the advantages of string theory over others is discussed. It is stated that the higher-dimensional analogs, with the action proportional to the world-volume of a "brane" object, are not perturbatively renormalizable QFTs. Their action is as follows:
$... |
In my city, electric motorbikes are becoming very common and I have noticed a high pitched whine coming from their engines when accelerated. How is this sound produced? Why electric cars are not that noisy?
|
Thank you all for so much help as I work through Zee's QFT book. Here I finally have a question about physics instead of math.
Zee makes several comments that the main thing left to do in QFT is find a way to solve
$$ Z(J)=\int\!D\varphi\,\exp\!\left[ i\int\!d^4x\,\frac{1}{2}\big[ (\partial\varphi)^2-m^2\varphi^2 \b... |
The mass of Universe in kilograms is about 10 power 53.
But how much energy exists in the Universe in form of photons?
And if they would all be converted into mass, how much mass that would make?
Dark matter and dark energy are out of the question.
|
Can a hypothetical elementary particle, at least in theory (according to the current science), have 0 mass and yet also have both spin and electrical charge (at the same time)?
|
In Ref. [1], the authors show how
The geometric (Berry) phase is shown to have its origin in the
nontrivial geometry of the fiber bundle:
Hilbert space --—> space of
states. The nontrivial geometry comes simply from the scalar product
in Hilbert space.
Part of their derivation considers the tangent space of a point o... |
Consider a very long vertical cylinder containing air in thermodynamic equilibrium. Observe that the air column is necessarily bottom heavy. The macrostate is described in part by a pressure gradient that is due to gravity. All corresponding microstates for this particular macrostate will have a matching density distri... |
I see that the harmonic field is sometimes written in exponential form. But sometimes the complex amplitude of this form is just a constant and in others (like when talking about modes) is dependent on the position. Why sometimes is dependent and what does it represent in both cases?
First case $E(\vec{r},t)=he^{-i\ome... |
A tall Styrofoam cup is filled with water. Two holes are punched in the cup near the bottom, and water begins rushing out. If the cup is dropped so it falls freely, will the water continue to flow from the holes? Explain using Bernoulli's Principle.
|
Longer version of the question:
Let's say I'm an immortal being (I could be artificial) going to "party" to IC1101, one of the biggest galaxies of the universe, 1 billion light-years away from us, and that the speed of my space ship is 50% c. ("c" is the speed of light). Later, I’m coming back to the local galaxy group... |
I was wondering about the following question.
In maths/computer science, many optimization problems ask for integer optimizations. A prominent example would be spin-glass (Ising) systems for simulated annealing (which encompasses quadratic unconstrained binary optimisation problems, such as Max-Cut etc.). Here, we have... |
In comparing the electric field in gel electrophoresis to that of a parallel plate capacitor (PPC), what would be the difference between them? What I mean is, PPCs are known for their constant fields. Gel electrophoresis is accomplished by placing two electrodes into a buffer that contains a gel, which contains usually... |
The density of states for tight binding electron, $D(\epsilon)$, with respect to $\epsilon$(electron energy) followed an inverse cosine, a flat region ,and inverse cosine function in 3D.
It was easy to show from the math the two inverse cosine curves. However, I had a hard time to show in math that there's a region whe... |
The electric potential energy stored in a charged capacitor is just equal to the amount of work required to charge it—that is, to separate opposite charges and place them on different conductors. When the capacitor is discharged, this stored energy is recovered as work done by electrical forces... |
While deriving expression for the voltage across capacitor in a discharging RC circuit, I stumbled across whether I should treat the capacitor as an active or a passive component(To properly apply the loop rule).
Any help will be appreciated....
|
On axial members connected to a rotating rigid element,
we have the following relationship
$$\frac{-\delta_1}{a}=\frac{\delta_2}{b},$$
which is based on the concept of similar triangles.
In the relationship, what is $a$ and $b$?
|
The questions:
Our Prof wrote the following expression that confused me,
\begin{align}
\Lambda^0_{\,\,\,i}&=\eta^{00}\eta_{ij}\Lambda_{0}^{\,\,\,j}\\
&=-\eta_{ij}\Lambda_{0}^{\,\,\,j}\\
&=v_i\gamma
\end{align}
Now, as far as I understand, this could only be true, if
$$\Lambda_0^{\,\,\,j}=-\Lambda^j_{\,\,\,0}$$
because ... |
Chiral vortical effect is a generation of an axial current in the presence of the rotation.
On the one hand, the expression for the $\mathbf{CVE}$ has the following form:
$$
\vec{J}^{5} = \vec \Omega \left( \frac{\mu^2}{4 \pi^2} + \frac{T^2}{12} \right)
$$
where $\vec \Omega$ is the angular velocity, and $\mu$ is the... |
I came up with this argument: it’s possible that in the right circumstance helium would weigh more than the empty bottle. If I were to fill empty bottle full of helium can it lift the bottle in the air?
Any idea would be greatly appreciated.
|
(I am not a cosmologist and instead currently working on a master thesis about Feynman integrals, so sorry if I'm missing something obvious. This question is merely out of interest.)
I was wondering whether there are people working on Higgs cosmology and if they are not, then why are they not? Is there some clear predi... |
I read about a technique called $b$-tagging in which one can check if a $b$ meson was produced in a collision by looking for a jet which has a secondary vertex within it. The reason is that b mesons are long lived, so that meson would travel a bit before decaying, hence the secondary vertex. Why are $b$ meson long live... |
Generally in the literature on quantum critical phenomena (as opposed to ordinary critical phenomena in statistical mechanics), there is the idea that quantum fluctuations can prevent ordering of a phase. My very basic question is: formally speaking, what does it mean for a phase to be unstable (or melted) due to quant... |
In Sean Caroll's Spacetime and Geometry Textbook, at page 183 (discussing scalar-tensor theories) Carroll defines a conformal metric by performing a conformal transformation as:
$\tilde{g}_{\mu\nu} = 16\pi\tilde{G} f(\lambda) g_{\mu\nu}$
where $\lambda$ is some scalar field and f is a function of $\lambda$.
On the way... |
Very simple question but I came across a website discussing sources of infrared radiation and it used an example to illustrate which objects emit more infrared than others. It said 'a candle flame emits more infrared radiation than a cat'. Is this true? A candle flame is much hotter but the mass difference between a ca... |
Assume we have an object moving along a path $p_W(t)$ that is described in some fixed reference frame $W$. If we now have a second reference frame $B$ which differs from $W$ by some time varying rotation $R_{BW}(t)$ we can describe the objects path in the reference frame of $B$ then as $p_B(t)=R_{BW}(t)p_W(t)$. If I no... |
I am a high school student and i am little confused between superposition of Simple harmonic motions{SHM's}, suppose a spring of spring constant $k_1$ has time period $T_1$ and another spring of spring constant $k_2$ and time period $T_2$ when connected with a block separately, if both are now connected in parallel or ... |
The Dirac wavefunction $\psi(x)$, a four component spinor, transforms under Lorentz transformations according to
$$\psi'(x')=S\psi(x)$$
where $S$ is the transformation matrix.
In Ashok Das' QFT book, pg 77, he says that the product $S^\dagger S$ is a non negative matrix, i.e. all the matrix elements are positive. Why i... |
There is a claim in this cookware infomercial that a "traditional" (aluminum) non-stick pan, placed on a burner set to 400 degrees F, will reach a surface temperature of about 700 degrees F (while, by contrast, the pan being advertised remains around 400 degrees F). "A pan that is made mostly of aluminum is just going ... |
While I was reading materials, the author mentioned that Monte Carlo converges slowly due to shell effect while filling the single particle states, but using a twisted boundary will make it go much faster.
I am wondering why is shell effect causing this issue, I have never done computation physics but intrigued by this... |
If the light meets behind the mirror, without really meeting, how is it even supposed to be interpreted.
If two light rays never meet because they are diverging but they meet behind the mirror-which it doesn't actually do, because it doesn't exist, what is happening?
Does wave theory provide a deeper and meaningful exp... |
I have been introduced to momentum in fluid flow recently and was covering a jet striking a plate (stationary, inclined and moving away/toards the jet). In each of these cases the resource I was working through mentioned that the normal velocity to the plate = 0, however, they didn't say why (presumably because it is o... |
If both choices explain the same experimental observations, then the latter seems more reasonable. In the former case, the frame of reference of a photon would look like everything in the universe, including time, squeezed together with events landing on top of each other. Why do we choose to accept such a thing in the... |
In my physics class our teacher taught us about this canoe-man problem, where a man walks across a canoe and due to the "law of momentum conservation", the canoe attains a constant $v$ velocity, and the man attains constant $u$ velocity. Is this possible because, each step he exerts a force on the canoe and that gives ... |
Derive rules of selection between matrix elements of eigkets $|{l,m}\rangle$ and $|{l',m'}\rangle$ for the operator $\hat{X}$ and $\hat{P}$. Use only parity arguments.
I now that that the elements of the operators $\hat{X}$ and $\hat{P}$ between states of defined parity is only different from zero if the states have ... |
It is a well know question, be the function space $L_{2}(-\infty,\infty)$, evidently the eigenfunctions of $$i\frac{d}{dx}, X$$ are $$f = Ae^{-i \lambda x}, g=B \delta (x-\lambda)$$ respectively.
Evidently again, it is not normalized in such function space. In order to orthonormalize both, we can do it:
$$\int f^{*}_{\... |
I am currently doing Linear Algebra in hopes of one day tackling QM, and I need some motivation now to continue in this pursuit. The University I attend set this as a pre-requisite for QM. Now I have gone as far as Projections Onto Subspaces in LA but I just can't wrap my head around why I might be asked to do the thin... |
I would like to explain in physical terms, why the pressure in the uterus falls, if volume (amniotic fluid) is removed.
So far as I understand, p in spheres is inversely proportional to the radius, according to the Law of Laplace P = 2T/R.
However, this is obviously not the correct explanation, since the pressure falls... |
A man running at a speed 5m/s is viewed in the side mirror of radius of curvature R=2m of a stationary car. Calculate the speed of image when the man is at a distance of 9m from the mirror.
|
The off-diagonal term of the 1-D Bose-Hubbard model is :
$K=\sum_l a_l^\dagger a_{l+1}+a_{l+1}^\dagger a_l$.
We can diagonalize it by introducing the Fourier transformation:$a_l=\frac {1}{\sqrt{N}}\sum_k e^{ikl}a_k$.
Then the Hamiltonian can be written as: $K=2\sum_k a_k^\dagger a_k \cos k$, which means the eigenenergi... |
How to show that $\sum |c_{n}|^{2} = 1$ ?
Where, $\psi = \sum <c_{n}|e_{n}>$ (completeness)
and $e_{n}$ are the eigenvectors of the general operator $Q$ (with discrete spectra)
I started as below:
$c_{n} = <e_{n}|\psi>$, so $c^{2} = <e_{n}|\psi><e_{n}|\psi>$, but not sure how to go on here...
|
Griffiths says that if a incident sinusoidal wave on a string gets reflected, it's form will be sinusoidal as well.
Why is it so? Does it hold for all wave forms in any medium?
|
Osmosis creates pressure on the side of the membrane with higher concentration. But where does the energy for this come from?
|
I am a theoretical physicist and I have a reasonable understanding of the early universe, inflation, FLRW metric, leptogenesis, baryogenesis, perturbations, the works (mainly in the style of the classic Kolb & Turner "The Early Universe"). However, I would like to improve my understanding of the evolution of the univer... |
I am wondering whether the following set-up can be used to generate an induced EMF.
Since the electric field between the parallel-plates is in such a direction that the positive charge accumulate at the upper end and negative charge accumulate at the lower end, thus creating a potential difference between them and so ... |
So I was in the process to find the Killing vectors for the Minkowsky Metric and I stumbbled into a material that does a different procedure at the very end of the process, in comparisson to usual books and articles I've seen. The resoning goes as follows:
For example, suppose we have found the Killing vector
$$
K=x \f... |
I am trying to follow Weinberg's derivation (in the book Gravitation and Cosmology) of the Lorentz transformation or boost along arbitrary direction. I am having trouble deriving the $\Lambda^i_{\,j}$ components. Here's how I am trying,
\begin{align}
\eta_{0i}=0&=\eta_{\alpha\beta}\Lambda^\alpha_{\,0}\Lambda^\beta_... |
In my class I have learned that the cross-product of two vectors are perpendicular to those two vectors. Teacher says it has something to do with torque. If it is, then 'if we have to open a door it should be easy to open it by exerting force on top of the hinge', but we know it is not. Is there any scientific reasonin... |
Why is the combination of two light waves (red, yellow) percieved as the same color as the arithmetic mean of their frequencies (orange) while we percieve two musical notes at the same time as just those two waves stacked on top, and not the mean of those frequencies?
|
I get that $(1 - \Omega) = \Omega_k$.
What I used to know, but have forgotten and cannot find is
what is the equation relating $R_{curv}$ (radius of curvature) and $\Omega_k$?
I have found the answer to this question before, but now that I want to work with it again, I seem to have misplaced it, and I am unable to fin... |
As the title says, I'm trying to prove that if a system is translation invariant, then its propagator depends only on the difference of coordinates. That is to say
$$K(\boldsymbol{x},\boldsymbol{x}';t - t_0) = K(\boldsymbol{x} - \boldsymbol{x}';t-t_0)$$
where
$$K(\boldsymbol{x},\boldsymbol{x}';t - t_0) = \langle \bolds... |
Context:
Consider a Bogoliubov-de Gennes Hamiltonian,
\begin{align}
\hat{H}_{BdG} = \sum_{j,k} \hat{\Psi}_j^{\dagger}H_{jk}\hat{\Psi}_k,
\end{align}
where $\hat{\Psi}$ is a $2n$-dimensional vector of fermionic creation operators and its annihilation counterparts, and $H$ is a $2n\times2n$ Hermitian matrix that obeys pa... |
When reading about the Big Bang you’ll commonly hear that the universe began “cooling down” soon after. However, if we assume the universe is a closed system, would that thermal energy not continue to exist? If quarks couldn’t bond during the initial phases of the Big Bang, that energy would have to go somewhere. Was i... |
Let's assume that a standing still black hole attractor can have a star orbiting it in an orbit if the star was somehow a result of the same past proccesses as the black hole.So the star must be on a given point with right velocity and direction to be in an elliptical orbit around the BH.If the star was approaching fro... |
Example: If a football game between the Pittsburgh Steelers @ Tennessee Titans will happen in 3 days Sunday 10/25/2020 at 1pm, why can't light leave today 10/22/2020 and go to where the Earth will be on Sunday and transmit that information back to an observer prior to them arriving at the location on Sunday?
This is an... |
So I'm curious to know why, so very naturally, I have been poking my thick straw at the center of the seal of Boba cup. Why not the side, nearer to the brim where the plastic is not so stretchy? Intuitively, the center appears to be where most force from me will be efficiently translated (in other cases too; be it punc... |
Take a wire that doesn't form a closed loop, moving at velocity $v$ perpendicular to a constant magnetic field. In the frame of reference to a stationary person the induced emf caused by the magnetic force
is the emf just the non closed line integral of ($v \times \vec B$) still? I guess so.
But in the reference frame ... |
I am trying to read Weinberg's book Gravitation and Cosmology. In which he derives the Lorentz transformation matrix for boost along arbitrary direction, (equations 2.1.20 and 2.1.21):
$$\Lambda^i_{\,\,j}=\delta_{ij}+v_i v_j\frac{\gamma-1}{\mathbf{v\cdot v}}$$
$$\Lambda^0_{\,\,j}=\gamma v_j$$
Immediately after that the... |
By constants, I'm talking about constants like a mass of electron or proton or gravitational constant $G$. If there are some examples, Please put it.
Thanks already.
|
I have seen several questions on the site about this, but most of them get bogged down into new complex interpretations of quantum mechanics. For reference, I am a high school student just starting to learn quantum mechanics and thus sticking strictly to the copenhagen Interpretation.
If I understand the experiment cor... |
I am trying to analyze in general simple one dimensional QM problems.
To be more specific let's consider this kind of Hamiltonian:
$$H=\frac{\hat{p}^2}{2m}+V(\hat{x})$$
From this one we can derive the following:
$$\frac{\partial^2\psi(x)}{\partial x^2}=\frac{2m}{\hbar ^2}(V(x)-E)\psi(x) \ \ \ \ \ \ (1)$$
Where of cours... |
Anyone can help me proving the following
If x'=sx where s is a constant then
(d/dx') = (1/s)(d/dx)
|
I recently asked a (yet-unanswered) question about the relationship between state-dependence and violations of realism. The more I read on the subject, the more I find myself digging deeper in a rabbit hole where these concepts are poorly distinguished (in terms of logical relations).
Can someone disentangle and contex... |
A liquid drop with radius $R$, with a uniform charge $Q$, divides in two, with equal radius and charges, that move away until they are very far from each other. What is the variation of electric potential energy?
Answer is probably $\Delta U = (1−2^{2/3}) \left[\frac{(3Q^2/5)}{4\pi\epsilon_0 R}\right]$.
I tried conside... |
Inspired by this answer, I want to ask what is going to limit the speed of the tip of a whip in a vacuum?
From my understanding, on Earth the tip reaches speeds only several times bigger than the speed of sound in the air, because as the velocity increases, so does the resistance of the air, dissipating the energy insi... |
I've been reading the paper Bifluxon: Fluxon-Parity-Protected Superconducting Qubit by Kalashnikov et al. which deals with a novel type of superconducting qubit. Without going into too much of the details, it is a qubit consisting of a superconducting island, Josephson junctions, and a highly inductive loop. It forms a... |
If the cations are held together by the sea of electrons (metallic bonding), and if we apply electrostatic induction then what happens to the region of atoms that have a deficit of electrons? Are their bonds weaker? How about the region with an excess of electrons - are their bonds stronger?
Either the above ideology i... |
I understand intuitively that the resistor heats up when electrical energy travels through it and mathematically that the capacitor stores more charge when we fill the space between the conductive plates with a dielectric. However, I cannot see a microscopic explanation for these phenomena. Why is this, at the atom lev... |
Today, I had to do an exercise that talked about conformal geometry and after spending a ridiculous amount time searching for it in General Relativity books I couldn't find it. In books like Ray D'Inverno, Schutz and Sean Carroll they state the theorems, but never prove them, so I am asking if you could recommend any b... |
Why does the jet always come out perpendicular to the plane of the accretion disc around a black hole?
|
Using the Gaussian (path)-integral
$$
\int \mathcal{D}\eta e^{i\int_{t_i}^{t_f} dt \eta(t) O(t) \eta(t)} = N [\operatorname{det} O(t)]^{-1/2}
$$
my book claims that we can compute the following integral as
$$
N e^{\frac{i}{\hbar}S[x_{cl}]}\int \mathcal{D} \eta \exp\left(\frac{i}{2\hbar} \int \int dt_1 dt_2 \eta(t_1)\fr... |
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