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Mathematically viewing, the Aharonov-Bohm experiment shows that the magnetic field creates a connection with a nonzero holonomy on a multiply-connected domain. This means that there isn't a state function that is continuous on that domain. This isn't a problem if we regard the state function as an element of $L^2$, sin... |
A point charge q is moving in a straight line with a velocity $\textbf{v}$. The magnetic field due to it at a point P, whose position with respect to the charge is given by $\textbf{r}$, is usually derived in textbooks using Biot-Savart's law as
$$\textbf{B} = \frac{\mu_oq}{4\pi}\frac{\textbf{v}\times\textbf{r}}{\lVert... |
I am reading about how to generalize the Galilean law of addition of velocities using the Lorentz transformation, but I am confused about one step.
Here, I have the following equations for Lorentz transformation:
$$
\overline{t} = \frac{t}{\sqrt{1-v^2}} - \frac{vx}{\sqrt{1-v^2}}
$$
$$
\overline{x} = \frac{-vt}{\sqrt{1-... |
Suppose in space, there is an electric field. Now we introduce a dielectric medium in space with dielectric constant $K$. Is it necessary that an Electric Field will become $1/K$ times inside a dielectric in all cases, independent of the distribution and shape of the medium?
Is it a general rule that the electric field... |
Is it easier to induce an electric field using a changing magnetic field or the other way around?
The question is from my high school booklet, and I am pretty sure it was to be answered on an observational basis.
However, I was wondering if anyone could help me by providing a direction to think in as I wanted to approa... |
This idea of white noise cancelling other background noises is quite popular these days and I always wonder how it works?
https://www.youtube.com/watch?v=nMfPqeZjc2c
This is a sample of white noise. If I put it on in a noisy place, then I am able to cancel other background noises and sleep well, but without it, it beco... |
In the mathematical treatment of quantum mechanics, we have a wave function ($ψ$) that helps us to know the different information (like position, velocity, energy, etc.). To measure such a quantity we use operators. Let us drive down to the real situation where we are measuring the position of a particle (say electron ... |
While introducing Diffraction, physics textbooks say that this effect (Diffraction) is observed distinctively when the light is passed through a very small opening, the length or diameter of which is comparable with the wavelength of the light. Later, they also end up saying that Diffraction is also observed at sharp e... |
For primary operators we have $$T(z)O(w)=\dfrac{hO(w)}{(z-w)^2} + \dfrac{\partial_wO(w)}{z-w}+\cdots$$
(the ordering problem can be ignored by setting $|z|>|w|$.)
If we apply $\partial_w$, then a $(z-w)^{-3}$ term appears, meaning that $\partial_wO(w)$ is not primary.
However, $\partial_w$ apparently transform like $\p... |
I'm watching a video(ICTP-SAIFR Numerical Relativity by Sascha Husa) where he mentioned that
$$R_{\mu\nu}
=-\frac{1}{2}
g^{\lambda \rho} g_{\mu\nu,\lambda \rho}
+\nabla_{ (\mu }\Gamma_{\nu)}
+\Gamma_{\lambda} {}^\eta {}_\mu g_{\eta \delta} g^{\lambda \rho} \Gamma_{\rho} {}^\delta {}_\nu
+2\Gamma_\delta {}^\lambda {}... |
Is the angular acceleration and the resultant acceleration of tangential and centripetal acceleration the same thing in non-uniform rotational motion? If not, what's the difference?
|
I know there are several questions asking this problem, but I found this problem has not been solved yet to me. I will repeat the problem and state my view.
Consider the statistical mechanics of a system of Hydrogen atoms. By the spirit of Gibbs ensemble theory, one have to calculate the partition function
$$
Z = tre^... |
I understand that complex polarization transformations (e.g., in Mie scattering) can occur without changing the technical degree of polarization (P). I'm interested in the mechanisms that specifically reduce P, leading to a genuine mixture of polarization states or even unpolarized light.
I'm working with Stokes parame... |
In Example 7.9 (Griffiths Introduction to Electrodynamics), I know how to determine direction of current due to induced electric field (see example in the figure below), but I have trouble understanding why the solution says "E here runs parallel to the axis". Why does the induced electric field have no vertical compon... |
In elementary explanations of lightning, it's generally stated that the clouds are negatively charged, the Earth is positively charged, and lightning is a discharge between the two. E.g. this source says:
As ice crystals high within a thunderstorm flow up and down in the turbulent air, they crash into each other. Smal... |
According to GR, what’s the mechanism for a star to form a wormhole? How is it different from collapsing to a black hole? What’s the energy scale required?
|
We know that light has momentum. Under normal conditions, momentum is given by E/c where E is the energy of the EMW and c is the speed of light in a vacuum.
If say light enters glass, with a certain refractive index, c would go down to v.
As far as I know, frequency doesn't change, nor does the energy of the wave. So i... |
Using Srednicki's notation:
For a massive left-handed spinor $\psi$:
$\mathcal{L}=i\psi^{\dagger}\bar{\sigma}^{\mu}\partial_{\mu}\psi-{1\over 2}m\psi\psi-{1\over 2} m\psi^{\dagger}\psi^{\dagger}$
It can be arranged into a Majorana spinor $\Psi \equiv \begin{pmatrix}\psi_c \\ \psi^{\dagger \dot{c}}\end{pmatrix}$
so that... |
Say we have a thin hollow conducting sphere in empty space. Then an external uniform electric field is suddenly induced.
How can we calculate the time it will take the charge carriers to redistribute themselves until the net internal electric field becomes zero?
|
could someone explain to me how to get the derivation? I do not understand how to get from eq. 8 to 9. Thank you
|
In a longitudinal wave, both particle velocity and wave velocity occur in the same direction. It might seem intuitive to assume that the particle velocity should be identical to the wave velocity, given that both are consequences of particle motion.
To explore this, consider differentiating the equation $A\sin\left(\fr... |
My question is a bit long and chaotic since I haven't learnt group theory systematically.
I am looking at the Banks-Fischler-Shenker-Susskind (BFSS) matrix model. It consists of 9 bosonic matrices $X_I$ and 16 fermionic matrices $\phi_\alpha$,
which transform under an $SO(9)$ $R$-symmetry in the fundamental and spinor ... |
The topic of this question is the collection of radiation from the sun. (renewable energy course) The total radiation flux is $$I_\text{total} = I_\text{direct}+I_\text{diffracted}+I_\text{reflected} .$$
According to the Threlked & Jordan model $$I_\text{diffracted}=d\cdot I_\text{direct}$$ and $$I_\text{reflected}=f(d... |
I would like to find motion equations $m\frac{\text{d}^2}{\text{d}t^2}\vec{x} = -\vec{F}(\vec{x},\dot{\vec{x}},\vec{E},\vec{B})$ or Hamiltonian $\mathcal{H}$ or Lagrange function $\mathcal{L}$ of moving magnetic dipole given by $\vec{m}$ without any charge, e.g. $q=0$, in homogenous magnetic field given by magnetic ind... |
Here is a mock scenario I have to illustrate my confusion,the regular basic assumptions here apply ie smooth floor so there is no friction and air resistance, and a inextensible string . There is a force of 60 N acting on block 2, the tension, however, will be a lot lot lower than 60 N ie the force pulling block 1 wou... |
Consider a quantum system with a hamiltonian $\hat{H}$, which is invariant under the action of a lie group $G$, meaning we have a unitary representation of $G$, $\hat{U}(g)$, in Hilbert space, and $\hat{H}$ commutes with every $\hat{U}(g)$.
As is well known, the generators of the Lie algebra of $G$ give rise to generat... |
From what I have read, bremsstrahlung is caused by electrons loosing kinetic energy when being decelerated by another charged particle. The lost energy being converted into radiation.
So why isn’t bremsstrahlung produced when inducing current in a conductor for example? Is the electron velocity not high enough?
Obvious... |
I am setting up classical ghost imaging. I am trying to reproduce the results by this paper. It mentions that crucial things to get the experiment to work is spatial incoherence and measurement time must be much less than correlation time. The spatial incoherence can be generated by using a rotating ground glass and us... |
We have Work-Energy Theorem as follows:
$$W_c +W_{nc} + W_{ext} = ΔK$$ $-(1)$
, where $W_c$ = work done by conservative forces,
$W_{nc}$ = work done by non-conservative forces, $W_{ext}$ = work done by external forces
Now what my teacher did is that he replaced $W_c$ with $-ΔU$, i.e.,
$$-ΔU +W_{nc} + W_{ext} = ΔK$$ $-(... |
Consider the following simple circuit consisting of an AC generator with voltage $V$ and a resistance $R$. As a result, current $I$ flows. Below the corresponding time-voltage diagram of the generator.
Question: aren't the directions (voltage and current) marked in the circuit correct only half of the time (i.e. duri... |
I've found a solution for how fast you have to slap a chicken to cook it.
For example:
½m1v1² = cm2Δt
m1 = hand's mass (5 kg)
m2 = chicken's mass (2 kg)
c = 4185 J/kgK
Δt = 50 K
v1 = ± 409 m/s
But I know collisions can be either elastic or inelastic. And the situation when both colliding bodies would come to a ... |
Electric current is the rate of flow of charges (electrons) or the rate of flow of positive charge. Okay, I get it. But here's my question. The electron flows in the wire and then the current flows in the opposite direction of it. What is that thing that is flowing in the opposite direction of the electrons? Protons do... |
I am trying to learn properly about scattering. For this I was pointed to Wave Propagation and Scattering in Random Media by Ishimaru.
I got a bit stuck in section 2-2 General properties of the Cross section.
In general I don't understand the extinction paradox and even if I've watched some youtube videos and read othe... |
I was solving nuclear physics today.I used the binding energy formula on hydrogen.I found that B=0.But,B is also,as mentioned in my textbook,13.6eV. How?
|
For decades since my physics master's I daydreamed about machines that work on a quantum level unitarily. The reason I found it interesting was because I knew that unitaries map pure states to pure states and hence don't increase "entropy": $tr( \rho ln(\rho))$.
I have never read up on this, but I did recently. I fou... |
What if there was a robot that got sent to the other side of the Milky Way by just traveling with a fusion engine and started orbiting a planet that has around Earth's gravity in order to avoid any time dialation problem, and then started scanning the CMB and the universe from there and then the robot traveled that dis... |
I am stuck on equation 3.124 on p.65 in Peskin and Schroeder quantum field theory book.
There they are claiming that:
$$P\psi(x)P=\displaystyle\int\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_{\bf p}}}\sum_s\eta_aa^{s}_{-{\bf p}}u^s(p)e^{-ipx} + \text{similar terms}.\tag{3.124}$$
where $P$ is the parity operator. From what I... |
I am given hydrogen that is put into some pressure and high temperature conditions. After this it was found out that mass has decreased. It was also found that energy was released.
Can someone, please, explain why energy was actually released? And if I would be given initial and result mass, how to find the amount ene... |
I was wondering if anyone could point me towards the analytical solution for the probability distribution for the momentum of a quantum harmonic oscillator in the canonical ensemble. I've come across the position distribution which one can obtain by taking the diagonal of the thermal density matrix in the position repr... |
If a have a arrangement like-( Where r is radius of hollow conducting sphere with centre C and Q is point charge)
Then what is potential at any point between P and C?
I think first we need to find Potential at P-
$$V_P=\frac{Kq_{in}}{r}+\frac{KQ}{3r}$$ where $q_{in}$ is induced charge on the sphere surface. Now as we ... |
Consider an inertial frame of reference $S$. Now take a second frame $S'$, defined as follows: If a point $P$ has coordinates $$(t,x_1,x_2,x_3)$$ in $S$, then it has coordinates $$(t,2x_1,2x_2,2x_3)$$ in $S'$. Now my question is: is $S'$ an inertial frame of reference?
I get contradicting results by using the definitio... |
I'm studying Shankar's Quantum Field Theory and Condensed Matter and got stuck in the issue related to changing measure in Majorana path integral.
In section 9.4, the Euclidean action for the continuum Majorana theory of the 2D Ising model is given by
$$S = \frac 12 \int dx\, d\tau\, \Psi^T (x,\tau) \begin{pmatrix} -\p... |
This may be a peculiar way of asking but given the image below:
Flemings left-hand rule
How does the wire experience a force upwards rather than being attracted directly to the magnet? If a current in a wire creates a magnetic effect, what makes the wire jump upwards rather than towards the magnet? I understand Flemin... |
What do physicists typically say gives gravity the ability to act on a pair of objects?
I am not asking for a description of gravity as a scalar field, but rather what the current accepted theory is on how objects thousands of light years away from each other can exert force on each other?
If the answer involves gravit... |
General comment: despite the longish historical introduction this question is not about the history of physics but rather about a specific conceptual problem in physics.
Following Bridgman in the famous publication, "On the Irreversible Production of Entropy", see in Section 19 Tolman & Fine derive the standard Thomson... |
Huygens principle
The Huygens principle states that every point on a wavefront of a spherical wave
$$
A(\vec{r},t) = \frac{A_0}{r}e^{i(kr-\omega t)}
$$
can be seen as the source of a spherical wavelet. I tried to understand this quantitatively, by deriving the amplitude $B_0$ of the secondary waves.
My Derivation
.
Sup... |
Let $\psi(x)$ and $\phi(x)$ be wavefunctions. I usually see the inner product defined as
$$\int dx\, \overline{\psi(x)} \, \phi(x)$$
and interpreted, I think, as "the amplitude that state $\phi$ will fluctuate to state $\psi$".
Here dx could be a line element in a 1-dimensional problem, or replace it with $d^3 x$ a vol... |
What mathematical term actually shows a "singularity" in a black hole and why is this so special compared to other singularities? It seems super hard to find any concrete formulas about the black hole theories.
I mean, Newtonian central forces have a mathematical singularity at $r=0$ as well (e.g. gravitation and elect... |
I am interested in classifying all the possible equilibrium configurations for an arrangement of $l$ equal point particles $P_1, P_2, . . . , P_l$ $(l > 2)$ on a circle of radius $R$ and centre $O$. The costraint is smooth and the $P_i$ is attracted to $P_{i−1}, P_{i+1}$ with an elastic force ($P_0= P_l$).
I have chose... |
Could you please assist an absolute beginner in understanding the core aspects of this problem and the relevant topics necessary for solving it, as well as specific of electric-car that should be used in the problem?
The problem begins with the statement that there is an electric car and when the gas pedal was released... |
Sorry if this has been asked before in some manner, but I'm just a bit confused about the distinction between a state $\alpha$ and its ket $|\alpha\rangle$. I was recently told that a state $\alpha$ is an element of the Hilbert space $\mathcal{H}$, and a ket can be interpreted as a linear map $\mathbb{C} \rightarrow \m... |
I've found online that the formula for the effective focal length of 2 lenses separated by a distance is:
$$
\frac 1f=\frac 1{f_1}+\frac 1{f_2}-\frac d{f_1f_2}.
$$
However, I'd like to know how this formula is actually derived. Also most places don't really define where f is measured from but I was able to find that i... |
In General Relativity, gravity is described as the curvature of spacetime caused by mass. This curvature is often visualized as a straight path bending due to a warped surface. My question is: If, hypothetically, spacetime had a linear instead of a radial curvature (think of a constant pull in one direction), would an ... |
I am a high school student and I am a little confused about how the pulley system works here
Here in this example below, we always only shown tension on points A and B as acting upwards and then we say that the same force is being applied on the block "m" but as it's assumed that the rope is massless, the tension on th... |
Intrinsic parities of various particles we know are $\pm 1$. My question is, can it be a more general phase?
It seems it's sometimes argued (like page 140 in "Introduction to elementary particles" by Griffiths) that because $P^2=I$, the eigenvalues has to be $\pm 1$. As far as I can go, by definition $P^2$ commutes wit... |
The heat conduction equation is usually written as
$$\frac{\partial T}{\partial t} = \alpha \vec \nabla^2 T$$
But what if a moving air parcel is considered? The standard derivation of the equation above is to consider the energy balance of a small control volume, hereby considering heat flow through the boundaries due ... |
The typical way to arrive at Hamiltonian mechanics is through Lagrangian mechanics, defining canonical momentum and the hamiltonian itself in reference to the Lagrangian and its derivatives, but I'm interested in whether there's any way to formulate it directly from Newtonian mechanics without any Lagrangian.
My though... |
How to prove that a tight binding Hamiltonian of spinless fermions with imaginary nearest neighbor hopping is invariant under time reversal?
$H=\sum_{j=1}^Lit\; c_j^\dagger c_{j+1}+h.c.$
where $t$ is real number.
And what is a minimal non-interacting Hamiltonian of spinless fermions without time reversal symmetry?
|
A massless particle state with the standard momentum $k^\mu=(\kappa,0,0,\kappa)$ and helicity $\sigma$ is denoted by $\Psi_{k,\sigma}$, Weinberg defines the parity phase $\eta_\sigma$ for the parity operator $P$
\begin{align}
U(R_2^{-1}) P \Psi_{k,\sigma} = \eta_\sigma \Psi_{k,-\sigma}
\end{align}
where $R_2$ is the r... |
What is definition of weight? Does weight of an object change under water, or the weight remains the same, but the: 'apparent weight' = 'weight' - 'buoyant force' ?
Same question for object submerged in air, or object in free fall?
|
Suppose I have a simple machine that has a Mechanical Advantage of 2, ideally.
That would mean its Velocity Ratio is 2, as well.
But practically speaking, it is in very bad condition and has an efficiency of 10%, making its M.A. 0.2.
Would the machine still be considered a force multiplier (although effort = 5 * load)... |
I recently came across this topic in electrostatics and saw derivations using Gauß's law of how the electric field on the surface of a uniformly charged shell is:
$$|\vec E|=\frac1{4\pi\varepsilon_0}\frac q{r^2}$$
This was mentioned in many sources including my school textbook. However, upon digging deeper, I found thi... |
I am working though some questions for my QFT/ QED exam and i am having trouble with the following question:
Explain why the following terms cannot be part of the Lagrangian of QED:
$-g(\bar{\psi}\psi)^2$
$\frac{1}{2}m^2A_\mu A^\mu$
$-\frac{1}{4}F_{\mu \nu}\Box F^{\mu \nu}$
My Answers:
I have no idea. An interaction... |
The Second law of Thermodynamics can be stated as heat always flows from hot to cold.
Consider the following system described in the image, where we have two parts A and B, at some time $t = 0$ we assume that both systems have equal temperature. That would imply no heat flow would occur. However, let us take an example... |
In the context of a zinc-copper electrochemical cell, zinc atoms at the anode are oxidized, releasing electrons and forming zinc ions that dissolve into the solution ($Zn(\text{s}) \rightarrow Zn^{2+}(\text{aq}) + 2e^-$). This process leaves electrons behind on the electrode. Given the high reactivity of electrons, it'... |
I have two questions with regards to unitarity:
To which extent it has been verified experimentally that quantum systems evolve in a unitary way when dealing with unbounded Hamiltonians?
Let us define an operator $\mathcal{\hat{N}}(t,\,t_{0})\,\equiv\,\sqrt{\hat{U}^{\dagger}(t,\,t_{0})\,\hat{U}(t,\,t_{0})}$ where $\h... |
U is a state function.So, ∆U should be same if we carry out an isochoric process from state A to State B or through any other process for real gas. And as ∆U=Qv for real gas in isochoric process, so,∆U=nCv∆T. Taking system from state A to B by any process, let's say P, ∆U should be same. Then, Can't I write it again as... |
Where did 0 come in the first string?
Also, I just wanted to know if my understanding is correct when it comes to identifying the strings... I highlighted the ones that I believe are the sets of inextensible strings acting.
|
Let $ x^\mu(\lambda) $ be a curve in Minkowski spacetime parametrized by some parameter $ \lambda\in \mathbb R $.
For $ x^\mu(\lambda) $ to represent a physically acceptable motion we usually require
that $ x^0(\lambda_1) < x^0(\lambda_2) $ for any $ \lambda_1 < \lambda_2 $;
that $ U^\mu(\lambda)U_\mu(\lambda)\leqq 0 ... |
A mass of object M = 100 g is attached to the end of a string of length R = 20 cm. A person swings the mass overhead such that his hand moves in a circle with radius r = 10 cm with angular velocity ω = 18 rad/s, ahead of the mass M by 90°. Find the force of air resistance on the object. How do I solve this? I guessed... |
I am studying Schrodinger equation with a potential of hyberpolic functions.
$$ H \psi = - \psi''(x) + \Big[1-\frac{12}{1+b \cosh{(2x)}} + \frac{15\,(1-b^2)}{[1+b \cosh{(2x)}]^2}\Big]\psi(x) $$
The first excited state is known $ \psi(x) = \sinh{(2x)}\,[1+b \cosh{(2x)}]^{-3/2} $ and can be seen to have eigenvalue $ E = ... |
I have been trying to reproduce classical ghost imaging(for reference, see this). You can check the setup that I have done
The light beam from the collimator has beam radius of about 0.8 mm.
\begin{equation}
GI(x,y) = \sum_i^n (I_{img}(x,y) - \langle I_{img}(x,y)\rangle)(I_{Obj} -\langle I_{Obj}\rangle )
\end{equation}... |
I am prepping for my QFT2 exam tomorrow, and in one of the mock exams I found the following question (and I'm not quite sure how to go about this). Given the following Lagrangian:
$$
L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} - (D_{\mu}\phi*)D^{\mu}\phi - m^2\phi\phi*
$$
where
$$F_{\mu\nu} = \partial_{\mu}A_{\nu} - \partial_... |
Most introductory textbooks introduce electron bands when discussing metal properties which gives the impression that electron bands are strictly affiliated with delocalized electrons.
However, bands are also discussed in the context of covalent solids as well as ionic solids, where electrons are local to a bond or to ... |
i'm studying Classical mechanics from Analytical mechanics textbook , and i'm encounter with transverse acceleration in Chapter five The term $\omega \times r'$ is called the transverse acceleration, because it is perpendicular to the position vector r'. It appears as a result of any angular acceleration of the rotatin... |
While the nuclide $^{148}\mathrm{Gd}$ is only known to undergo $\alpha$ decay, with a half-life of $86.9$ years, I noticed that it has higher energy than its isobar $^{148}\mathrm{Eu}$: $m_{^{148}\mathrm{Gd}}=147.9181214(16)\,\mathrm{amu}$, $m_{^{148}\mathrm{Eu}}=147.918086(11)\,\mathrm{amu}$, which means that
$$
^{148... |
In QM and QE effects an entangled particle pair is called also a singlet with some properties of the two particles like spin, non-locally correlated. However, there is no transfer of information possible (i.e. non-communication theorem) therefore SR is not violated by this quantum effect. This is instantaneous-action-a... |
So, fermions all interact with the gravitational force and the weak force. All fermion species.
Now, if you eliminate from that list, the particles that don't interact with electromagnetism, you remove the neutrionos, the least massive fermions in any given generation, and are left with two groups of more massive fermi... |
In QM we deal with the Schrödinger equation:1
$$i\frac{\partial}{\partial t}\psi = H \psi$$
the wave function $\psi(x)$ is the main object of interest: it can be interpreted as a scalar field, in the sense that it links every point in space with a scalar value, and the really neat thing is that the scalar value in ques... |
As explained in Axiom 2.3 on page 7 of https://arxiv.org/abs/1609.09523, the independence of the stress tensor $$T(y)=\sum_{n}\frac{L_n}{(y-z)^{n+2}}$$ on the choice of expansion point $z$ leads to the following relation:
$$ \frac{\partial L_n}{\partial z} = -(n+1)L_{n-1}$$
Now consider a primary field for which $L_0$ ... |
According to the Wikipedia page about the Poincaré group, we get 10 conservation laws using Noethers theorem.
10 generators (in four spacetime dimensions) associated with the Poincaré symmetry, by Noether's theorem, imply 10 conservation laws:
1 for the energy – associated with translations through time
3 for the mo... |
I found the derivation of Blasius-Equations here: A free stream velocity hits a flat plate and the goal is to derive boundary layer behavior.
Everything in this tutorial is clear - but the most interesting point has not been answered:
How do I get an idea about how the similarity parameter shall be chosen? And why is t... |
I can think of two distinct notions of symmetry. One in which I start with a system in state $\mathcal{S}_0$ and perform some transformation on it to get another system in state $\mathcal{S}_0'$. Now, I evolve these two systems for some time $t$, to get $\mathcal{S}_t$ and $\mathcal{S}_t'$ respectively. If undoing the ... |
I guess as a result of the energy-momentum tensor $T_{\mu\nu}$ coupling to a flat Minkowski metric, $\eta_{\mu\nu}$, the flat metric can become that of a curved spacetime, $g_{\mu\nu}$. How can one describe this process mathematically?
|
Some gas with initial mass $m_{1}$ was put in a container under high pressure and temperature. After some time its mass became a bit smaller ($m_2$). Additionally, some energy was released and it was accumulated.
Assume that the above is a possible process. There is no additional information on exactly what kind of pro... |
I have a problem trying to understand the procedure for using self-similar solution of the second kind. More specifically, I was reading about an equation of this form,
$$\partial_t{d} + \frac{1}{r} \partial_r \left(\left(1+d\right)^3 \left(\partial^{2}_{r}d - \frac{1}{r}\partial_r d \right)\right) = 0$$
which is deriv... |
In the zero energy universe model, the gravitational field has negative energy, and this negative gravitational energy of all the distant mass exactly balances and cancels the positive mass-energy in the universe.
Why do we think they exactly balance? If the universe is expanding, the total gravitational potential incr... |
I often read something like "the Feynman propagator is the Green's function of the Klein-Gordon equation", so I try to write it as a sum over eigenfunctions, as should be possible for any Green's function. The eigenvalue problem is $$(\square + m^2)\psi(x) = -\lambda \psi(x),$$ which can be solved easily by writing $$\... |
I've been scouring the web for explanations of Stimulated emission, and have seen questions Like this one on directions and frequencies, this one on energy conservation, this one one lasers and stimulated emission, and this question on explaining what stimulated emission is. I have found a lot of these unsatisfactory... |
For a bosonic closed string, the field describing the string coordinates $X^\mu(\sigma,\tau)$ can be written as: (ethernal thanks to @ACuriousmind for writing it in an answer to another question)
$$X_\pm^\mu(\tau\pm\sigma) = \underbrace{\frac{x^\mu + c^\mu}{2}}_{\text{initial position}} + \underbrace{\frac{\pi\alpha'}{... |
It is well known that one reason quantum mechanics started to being developed, was because scientist wanted a model to explain electron orbits in atoms.
Borh interpreted that the for orbits to exist they would need to be quantized. Using the Schrödinger equation, this quantization arise from the bound state of the elec... |
This is actually biased on a Meme: Floppy Hammer Know Your Meme
But I was curious if we can actually prove if a floppy hammer applies more force/energy to a nail, than a regular straight hammer? (or prove it does not)
My first thought was that it could be possible because of how a bow and arrow can store and release ki... |
In the hard/soft vs white/black experiment from David Alberts book, used in Allan Adams MIT YouTube vid,
the removal of the barrier enables 100 percent measurement of the conjugate variable but "barrier in" gives
random measurement percentages of the conjugate variable.
If the experiment legs were of unlimited length, ... |
Please clear up this confusion for me:
I just watched the video on khan academy @7:30 where the guy explains newton's 3rd law. He explains that for a box on a table, the forces equal out so it's at rest. I also understand that $F=ma$ so an object with less mass may have more acceleration for an equal force.
But then he... |
If gravity determines the speed of free falling objects, but stellar core collapses happen much faster than the speed of free falling objects, wouldn't that indicate that stellar core collapses are caused by something other than, or in addition to, gravity? Sorry, I'd like to amend question to ask if the speed at which... |
I had a homework problem where I had to find the coefficients for the angular momentum raising and lowering operators. I know the answer is supposed to be $\sqrt{l(l+1)-m(m\pm1)}$. I have figured out how to get to the fact that the magnitude of the coefficients squared is $l(l+1)-m(m\pm1)$. However, I do not know how t... |
Answer key:
[Note: (Please verify this in your comments) The answer key for ii is wrong,right? It has to be non-uniform as the direction of the acceleration is everchanging.]
now , for iii,
I believe that centrifugal force should not be the answer because centrifugal force acts on the body undergoing the circular mot... |
This is a bit of childish question.
When a bus goes around a corner, does the person sitting at the back travel further distance than the person sitting at the front?
My thought is no because the bus is connected and every point moves along the same trajectory.
My friend thinks yes because the trajectory of two endpoin... |
Consider a quantum field theory in flat 1+1D spacetime for simplicity. Let $T_{\mu\nu}$ be the conserved symmetric stress tensor. One writes operators by integrating the tensor over the whole space, such as the Hamiltonian
$$
H = \int_{-\infty}^{\infty} T_{00} (x)dx
$$
which I believe are self-adjoint operators (I don'... |
Reading on the Hong-Ou-Mandel (HOM) effect, I came to wonder how exactly we can be certain that interference that occurs in apparatuses such as a Michelson interferometer and Mach-Zehnder interferometer is truly an occurrence of single-photon interference rather than two-photon interference as seen in the HOM effect. ... |
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