Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why are the diagonals of the pressure tensor non-negative? I understand that the pressure tensor is simply the momentum flux which makes sense to me (pressure is force per unit area which is momentum change per unit time per unit area). From this, a simple mathematical deduction shows that the flux in any direction of... | From a mechanical perspective, the mechanical pressure $p$ is the magnitude of a momentum density flux, but certainly does not correspond to the entirety of the non-convective momentum density flux in the system.
Recall that the mechanical pressure $p$ is related to the stress tensor $\bar{\bar{\sigma}}$ in the followi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What determines the color of the light emitted in a Tokamak? We see images of Tokamak plasma with all sorts of colours from red to purple. Why do we see any light at all, since the plasma should be so hot to have dissociated all its electrons? It is all from contamination or unwanted cooling?
| In most cases it's a fake: they often use test gasses with the explicit goal of being partially ionized so they give off light and thus allows us to take fancy photographs. The ultimate example of this was the DCX at the 1958 Atoms for Peace where they injected xenon (IIRC) to make a visible glowing ring. Its also poss... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/445571",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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In what context is enthalpy a convenient concept? Internal energy $U$ is clearly an important concept; the first law of thermodynamics states that for an isolated system internal energy is constant $(\Delta U=0)$ and that for a closed system the change in internal energy is the heat absorbed by the system $Q$ and work ... | The quick answer is: flow processes. e.g. fluid flowing into a chemical plant; gas running through a turbine; chemicals reacting at constant pressure. The equation $dU = T dS - p dV$ gives us
$$ dH = T dS + V dp$$
which you can regard as a 'fundamental law' (equivalent to the familiar one for $dU$).
An important appli... | {
"language": "en",
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Compton Scattering Lowest Order Feyman Diagram I have some trouble understanding the lowest order feyman diagrams for compton scattering.
Does two feyman diagrams mean that compton scattering can happen through two processes? What is the specific process in each case?
| Here is a clearer sum of the two lowest order diagrams:
It shows the two geometric ways energy and momentum can be exchanged between the two incoming particles to produce the two outgoing, to first order in a series expansion.
Does two feyman diagrams mean that compton scattering can happen through two processes? Wh... | {
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Is a nucleus a collection of quarks or a collection of neutrons and protons? I do not much about particle physics. But people say that neutron and proton are composed of quarks, and in turn a nucleus is composed of neutrons and protons.
Therefore, the question is, is this hierarchy necessarily well defined? Could we v... |
Could we view a nucleus as a collection of quarks, without the in-between neutrons or protons?
Conceptually this is similar to asking "could we view a building as a collection of bricks cement glass and iron". In some sense, one can, but it would be a funny way of defining a building because there is a hierarchy, an... | {
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Periods of non-circular Schwarzschild orbits I have been thinking about non-circular orbits in the Schwarzschild spacetime. How would you define a period of one orbit? I was thinking, in terms of proper time, for $r$, how long it takes to go from one apogee to another. For $\phi$, again in terms of $\tau$, how long it ... | You actually described two inequivalent definitions of "period," both legitimate. The paper
*
*Geisler and McVittie (1965), "Orbital periods in the Schwarzschild space-time" (http://adsabs.harvard.edu/full/1965AJ.....70...14G)
considers essentially the same two definitions of "period" that you described. One is t... | {
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What is the length of null geodesic? There are many questions about this but none of them adresses my concrete question. If it is indeed true that for light we have $ds^2 = 0$ does that mean that in 4d spacetime total "distance" is zero for light? By distance I mean lenght of a geodesic that light moves on? Describes? ... |
If it is indeed true that for light we have $ds^2=0$ does that mean that in 4d spacetime total "distance" is zero for light?
Yes, but the scare quotes on the word “distance” are exceptionally important. The spacetime interval is not just a distance in spacetime.
In space a distance is always just measured by a ruler... | {
"language": "en",
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Please help identify this physics apparatus!
This was my grandfather’s and have no idea what it is only that it is some piece of physics equipment!
The main black cylinder doesn’t seem like it wants to rotate but not sure if it should?
| It looks like an induction coil with the make and break device at the bottom and a switch right at the bottom. If you connect it up to an accumulator, be very, very careful as the output between the two balls, when separate, could be lethal. Also the electrical insulation elsewhere may be poor and you might get a s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/446618",
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Difference in spectrum of green laser and green LED In an experiment I conducted I used a spectrometer to find the spectrum of green laser and green led.
this is what I found:
LED spectrum:
Laser spectrum:
why is the spectral width of the LED is wide compared with the laser?
| In short, because they produce light using completely different mechanisms. In fact, the light produced in a green laser is actually frequency-doubled infrared light (which is part of why cheap green laser pointers that don't properly filter out the leftover infrared light are dangerous).
| {
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Falling object and the side wind I don't have a big knowledge on Physics so I'm sorry in advance if it doesn't make sense..
If a brick is falling from 100m tall-building when there's the side wind of 30m/s, is there any way I can find how far the brick would have traveled from the origin?
If there's any equation I can... | There's no easy way but it is possible to 'model' what you're asking.
The brick in question has a velocity vector $\vec{v}$ made up of two components, that are completely independent of each other:
*
*A vertical one $v_y$:
For simplicity's sake we'll assume the no significant drag forces act in the $y$ direction.
... | {
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Reason for force in Stern-Gerlach experiment I'm currently working at an assignment, and I'm having some trouble understanding how the magnetic field deflects the silver atoms passing trough it. From what I understood, the atoms are deflected up or down of a specific amount according to their magnetic moment, but I can... | If an atom has a magnetic moment (not momentum), that means it acts like a tiny dipole magnet -- like a tiny bar magnet. A uniform magnetic field will not exert a net force on a dipole magnet, because (thinking of it as a bar magnet) the magnetic field will push on one pole and pull on the other pole with equal but op... | {
"language": "en",
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Can a battleship float in a tiny amount of water? Given a battleship, suppose we construct a tub with exactly the same shape as the hull of the battleship, but 3 cm larger. We fill the tub with just enough water to equal the volume of space between the hull and the tub. Now, we very carefully lower the battleship into ... | Yes it floats. And it has displaced its "own weight of water" in the sense that if you had filled the container with water and only then lowered the ship into the container, nearly all that water would have been dispaced and is now sloshing around on the floor.
| {
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The water analogy seems to imply that power = current. Why is this incorrect? Many people think of the water analogy to try to explain how electromagnetic energy is delivered to a device in a circuit. Using that analogy, in a DC circuit, one could imagine the power-consuming device is like a water wheel being pushed by... | The analogy with water actually holds really nicely if you consider a water wheel, or other hydroelectric system.
But what you're missing is that the power produced does not only depend on the amount of water going past - it also depends on the speed at which it does so. (this makes sense for the hydro system because k... | {
"language": "en",
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Energy dependence on boundary conditions for particle in a box I am taking a course in solid state physics, and I have some trouble with the "hard wall" and the periodic boundary conditions for a particle in a box.
The thing is that we obtain, for a box of length L, $k= n \pi/L$, $n\in \mathbb{N}$ for the hard box, w... | From what I understand of your question, you are treating a quantum problem classically. When you’re dealing with h-bar , you leave behind deterministic-classical physics, and enter the world of probablistic-quantum physics. If you consider your wave-function, with sinusoidal changes within a box, the particle is consi... | {
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Is numerical lattice wavefunction smooth? -- graphene tight binding case I tried to follow exactly Sec. II.K [page 112-113, Hamiltonian after Eq. (113)] of the standard Review of Modern Physics paper on graphene, which is a tight-binding model of a graphene stripe under magnetic field.
It's periodic and hence fourier ... | The interaction in almost all tight-binding models has finite range (e. g. only includes nearest-neighbor or next-nearest-neighbor interactions), and therefore the associated matrix-valued trigonometric polynomial is smooth (even analytic). Hence, Bloch functions and energy band functions are locally smooth away from b... | {
"language": "en",
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Two wheels and a ball problem confusion When I was preparing for a job interview for chemistry, the following question appeared:
Now, my answer was as such:
If the bigger wheel is rotated clockwise, the smaller wheel moves anticlockwise so the ball will move down and fall off the plank.
However, the answer (which wa... | The drawing is not entirely clear, but I'll try...
Assuming that the black dots are bearings with axis normal to the picture, both blue wheels can rotate freely. The rotational motion of the small blue wheel is generated through an horizontal friction force. This force do not causes motion of the green bar since it is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/449118",
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How can two electrons repel if it's impossible for free electrons to absorb or emit energy? There is no acceptable/viable mechanism for a free electron to absorb or emit energy, without violating energy or momentum conservation. So its wavefunction cannot collapse into becoming a particle, right? How do 2 free electron... | To resolve this paradox requires study of time dependent perturbation theory; solving Schrodinger's equation with a time dependent perturbation corresponding to the interaction time of two particles.
If you do this you arrive at the following conclusions:
A single free electron cannot absorb a free photon ( $e + \gamma... | {
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Why Coulomb gauge is a possible gauge choice? In classical field theory we can get, that adding gradient of some scalar field to magnetic vector potential does not change the physics at all. So, we have such a symmetry:
$\boldsymbol{A}\rightarrow\boldsymbol{A}+\nabla f$
Then there is such a thing written almost in ever... |
Why this symmetry allow us to say, that divergence is zero?
Stipulate a vector potential with non-zero divergence
$$\nabla\cdot\mathbf{A}\ne 0$$
'Gauge away' the divergence
$$\nabla\cdot\mathbf{A}'=\nabla\cdot\left(\mathbf{A}+\nabla f \right)=0$$
and it follows that
$$\nabla\cdot\mathbf{A}+\nabla^2f=0\Rightarrow\nabl... | {
"language": "en",
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Completeness of an electron-electron-scattering in the Feynman diagram During an electron-electron-scattering in any case the electrons change their directions and by this undergo accelerations.
Shouldn’t the electrons emit photons in this time, loosing a part of its kinetic energy and slowing down a bit?
|
Shouldn’t the electrons emit photons in this time...?
Yes. They do. Just as in classical physics, an accelerating (or scattering) electron in QFT emits EM radiation. If desired, this radiation can be described in terms of photons, although (as usual) that's not necessarily the most natural description.
To see this, c... | {
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How can we define energy other than the definition that it's a capability to do work? It is actually a property of energy that it can do some work not an actual mean to define it because we cannot define a thing on the basis of what it is doing or what it can do.
| To set up a mathematical model that describes a physical system, one has to define observables, and one has to define "laws", i.e. axioms imposed on the mathematical model so that there is a correspondence of the mathematical solutions to the measured data and also predictions for future behavior.
Here we start with th... | {
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Is gas flow always compressible? From Franz Durst's Fluid Mechanics: An Introduction to the Theory of Fluid Flows:
When a fluid element reacts to pressure changes by adjusting its volume and consequently its density, the fluid is called compressible. When no volume or
density changes occur with pressure or temperatu... | For "normal" gas flows, you can only have a constant density if the fluid pressure is not changing (assuming constant temperature). Unfortunately, fluid flow requires a pressure drop, so as a gas is flowing down a pipe, the pressure is decreasing, the gas volume is increasing, the density is decreasing, and the gas is... | {
"language": "en",
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I have a question regarding the Painlevé-Gullstrand (PG) metric with factor 2 I have a question regarding the Painlevé-Gullstrand (PG) metric.
If we have the line element in a radial fall we get:
$$d\theta = d\phi = 0$$
$$ds^2 = -dT^2 + \left(dr+\sqrt{\frac{r_s}{r}}dT\right)^2.$$
Writing out the binomial formula we obt... | You can write the line element with this general ansatz:
$ds^2=\begin{bmatrix}
dT & dr \\
\end{bmatrix}
\begin{bmatrix}
g_{00} & g_{01} \\
g_{01} & g_{11} \\
\end{bmatrix}
\begin{bmatrix}
dT \\
dr \\
\end{bmatrix}
\qquad (1)$
The metric $g_{\mu\nu}$ must be symmetric!
from equation (1) we obtain :
... | {
"language": "en",
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Non-Relativistic Limit of Klein-Gordon Probability Density In the lecture notes accompanying an introductory course in relativistic quantum mechanics, the Klein-Gordon probability density and current are defined as:
$$
\begin{eqnarray}
P & = & \dfrac{i\hbar}{2mc^2}\left(\Phi^*\dfrac{\partial\Phi}{\partial t}-\Phi\dfrac... | You can substitute $\Phi = e^{-mc^2t/\hbar} \Psi$ and then neglect the second order time derivative of $\Psi$. Drop the constant $mc^2$ and you will have recovered the Schrödinger equation.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/450076",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Why do we care only about canonical transformations? In Hamiltonian mechanics we search change of coordinates that leaves the Hamilton equation invariant: these are the canonical transformations.
My question is: why we want to leave the equations invariant? I mean: we want to solve a differential equation (the Hamilton... | You're right. Sometimes it can be fine to take a non-canonical transformation and this is often done in practice (though not usually emphasized). I'll explain in an example from quantum mechanics. The analogy to classical mechanics can be seen by replacing the commutator with the Poisson bracket..
Consider a harmonic o... | {
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Potential Difference of a battery - What does it mean? I have studied current electricity for a while now. When I look back at basic concepts, I am quite clear about what current, electron, resistance is. But I cannot imagine about the potential difference or voltage of a battery. Or in a circuit, it is said that poten... | A voltage difference of 1 volt means that you gain 1 joule if you move 1 Coulomb of charge between the electrodes from plus to minus. A resistor exerts friction on charge carriers, so if this charge is moved through a resistor, this energy will appear as heat in the resistor. If you move the charge through vacuum, the ... | {
"language": "en",
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What is ground state useful for? Many textbooks and research are oriented to computing or finding the ground state of a quantum mechanical system. Why is it such a big deal? What can be done once one has the ground state?
| The ground state is often the state of lowest energy, i.e. the state that nature will most probably occupy, and if not, there must be a reason why not, a reason why the system should be excited.
In addition, the ground state is very often the zero-order approximation, e.g. of perturbation theory or mean-field approxima... | {
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It seems that the Euler equation in thermodynamics and The first law of thermodynamics are in contradiction The Euler equation in thermodynamics are as followed:
$U=TS-PV+\mu N$
But The first law of thermodynamics states that
$dU=TdS-PdV+\mu dN$
But I think that The Euler equation can be written by
$dU=TdS+SdT-PdV-VdP+... | The Euler equation is a consequence of the extensive property of energy $U(\lambda S,\lambda V,\lambda N)= \lambda U(S,V,N)$.
\begin{align}U(S,V,N)&=\Big(\frac{\partial{U}}{\partial{S}}\Big)_{N,V}S+\Big(\frac{\partial{U}}{\partial{V}}\Big)_{N,S}V+\Big(\frac{\partial{U}}{\partial{N}}\Big)_{S,V}N\\
&=TS-PV+\mu N\end{al... | {
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Does the inverse-square law apply to linearly polarized light? It's a stupid question but: We did and experiment using linearly polarized microwave radiation generators and receivers. Our teacher asked to check experimentally if the receiver measurements are proportional to the intensity of the radiation I or to the in... | Static electric fields fall off as $1/R^{2}$, but the ${\bf E}$ field associated with a spherical wave does not. The electric field of a radiating spherical wave falls off as $1/R$. In finding the solutions of problems with accelerating charges, the difference in behavior can often be used to separate space into a "q... | {
"language": "en",
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Question about Lagrange method and line element Consider the following line element:
$$ds^{2} = K(x,y,z,t)(-dt^2+dx^2)+M(x,y,z,t)dxdt+dy^2+dz^2$$
Then the lagragian method give to us the lagrangian from line element:
$$\mathcal{L}^2 = K(x,y,z,t)(-\dot{t}^2+\dot{x}^2)+M(x,y,z,t)\dot{x}\dot{t}+\dot{y}^2+\dot{z}^2 \tag{1}... | The Lagrangian is $$ L= \frac{1}{2} g_{\mu\nu}\frac{dx^\mu}{d\lambda}\frac{dx^\nu}{d\lambda}$$
and the Euler/Lagrange eqs. are $$\frac{d}{d\lambda}\frac{\partial L}{\partial(dx^\mu/d\lambda)} = \frac{\partial L}{\partial x^\mu} $$
Now the part in the $t$ component that you considered
$$-\frac{d}{d\lambda}\Big( \frac{\p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/451228",
"timestamp": "2023-03-29T00:00:00",
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Do mass and motion affect space-time differently? Mass is said to create curvatures in space-time thereby creating gravity, yet technically the smallest movements, even on Earth, create gravitational waves. Are there different "types" of disturbances of space-time? How?
| Spacetime curvature is actually caused not by mass but by the density and flow of energy and momentum. These quantities are encapsulated in something called the “energy-momentum-stress tensor”. Even massless particles like photons can cause spacetime to curve because they have energy and momentum even though they don’t... | {
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The reasoning behind doing series expansions and approximating functions in physics It is usual in physics, that when we have a variable that is very small or very large we do a power series expansion of the function of that variable, and eliminate the high order terms, but my question is, why do we usually make the ex... | Consider the function $f(x)$ defined by
$$
f(x)\equiv \int^\infty_{-\infty} ds\ \big(\exp(-s^2-xs^4) - \exp(-s^2)\big).
\tag{1}
$$
When $x=0$, we get $f(0)=0$. What if we want to know the value of $f(x)$ when $x$ is a very small positive number? We don't know how to evaluate this integral exactly and explicitly, and ju... | {
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"source": "stackexchange",
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Will it be complicated to use Gauss's Law in this problem?
The electric field strength depends only on the $x$ and $y$ coordinates according to the law $\vec{E}=a(x\hat{i}+y\hat{j})/(x^2+y^2)$ where $a$ is a constant.
Find the flux of the vector$\vec{E}$ through the closed surface $x^4+y^4+z^4=81$.
I used integral ... |
Hint :
The surface is as in the picture. Accidentally the electric field is that produced by the infinite $z-$axis with uniform linear charge density $\lambda$. So, it would be interesting to compare your result with that applying Gauss's Law for the charge on the $z-$axis from $z=-3$ to $z=+3$. Note that it's not ne... | {
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What would happen if antiprotons were studied under the conditions of particle deceleration that they are collected under? I have not had a very clear understanding of how antiprotons are collected, but I do know that when they collide with matter they explode in a puff of energy. Or so I have been told. If the curre... |
I do know that when they collide with matter they explode in a puff
of energy. Or so I have been told.
Don't trust whoever told that. They told nonsense. There is nothing
like "a puff of energy". Energy is not a substance, it's a physical
quantity particles may have in variable amounts.
Collision of an antiproton w... | {
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"timestamp": "2023-03-29T00:00:00",
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Computing a matrix element with the Wigner-Eckart-theorem I learned about the Wigner-Eckart theorem and want to apply it to the following matrix element
\begin{equation}
\langle j \, m | r_kr_l | j' \, m'\rangle.
\end{equation}
I know this can be done by writing the involved tensor operator as a sum of irreducible tens... | I am assuming here that with $r_i$ you mean the Cartesian components of the position operator.
In general the decomposition of $u_i \, v_j$, with $\vec{u}$ and $\vec{v}$ vectors, includes an additional antisymetric component $\frac{1}{2} \left(u_i \, v_j - u_j \, v_i\right)$ with 3 additional DOFs. In this case we don'... | {
"language": "en",
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"source": "stackexchange",
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Are Maxwell's equations "physical"? The canonical Maxwell's equations are derivable from the Lagrangian
$${\cal L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} $$
by solving the Euler-Lagrange equations.
However: The Lagrangian above is invariant under the gauge transformation
$$A_\mu \to A_\mu - \partial_\mu \Lambda(x) $$
fo... | *
*You are correct that there are gauge degrees of freedom in the solution for $A_\mu$ - precisely the ordinary gauge transformations. But $A$ is not physical, the electromagnetic field strength $F$ is. There are no gauge degrees of freedom in $F$, and as an equation for $F$ Maxwell's equations are physical.
*The pol... | {
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If the universe is flat, does that imply that the Big Bang produced an infinite amount of energy? Too much density and the universe is closed, analogous to a sphere in four dimensions: you travel in a straight line and you end up where you started. Too little and you have a saddle: not sure about the destination if yo... | What you calculated above ($\infty$, for a flat space universe) is just the proper mass-energy of matter. It doesn't take into account the - negative - energy of the gravitational "field" itself, which cannot be localised in General Relativity. The "total energy" of the universe could be 0, but there's no way we coul... | {
"language": "en",
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are there changing magnetic and electric fields that are not EM radiation? Let us consider these two Maxwell equations:
$$\frac{\partial \vec{B}}{\partial t}=-\vec{\nabla}\times \vec{E}$$ and
$$\frac{\partial \vec{E}}{\partial t}=\frac{1}{\epsilon_0}\left(-\vec{J}+\frac{1}{\mu_0}\vec{\nabla}\times \vec{B}\right).$$
Whe... | An electric or magnetic field always obeys a wave equation this can be proven by eliminating one or the other from the two equations that you display. In order to qualify as radiation the wave should transport energy, that is, propagate. Evanescent fields exist only near the current or charge, see https://en.wikipedia.... | {
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Stone skipping does spinning help? I have tried to hurl a stone with some added rotation and it performed slightly better but I have great difficulty replicating this feat for consistency, my question is should I add angular momentum to my throw or it was just a waste of energy?
| There are two tricks to a good skipping stone.
Lydéric Bocquet published some meaningful work on this subject.
Firstly, the spin makes sure the stone maintains its orientation just as a spinning top does.
Secondly, the orientation you want to impart to the stone should cause its trailing edge to hit the water first so ... | {
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Interpretation of the Boltzmann factor and partition function $$p_i = \frac{ \exp\left(-\frac{\epsilon _i}{k_BT} \right)}{Z} $$
$$ Z= \sum_{i} \exp\left(-\frac{\epsilon _i}{k_BT} \right)$$
A) Is $p_i$ the probability of the system having an energy equal to $\epsilon_i$? (Probability to be in any of the many microstates... | To the first question, the answer is B: $p_i$ is the probability of being in the $i$-th microstate, which happens to have an energy $\varepsilon_i$. However, microstates other than the $i$-th one may also have an energy $\varepsilon_i$.
The reason you never see the multiplicity in the partition function is because you... | {
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Why is a temperature gradient set up in a heated rod? Suppose a cylindrical rod is maintained at 100 degree Celsius and the other at 0 degree Celsius. My book says that after reaching "Steady State" the rod will have developed a constant temperature gradient all throughout the rod.
Why does the rod reach a steady state... | You can use your same argument for the $0$ degrees Celsius.
In other words, you state:
... shouldn't the rod keep absorbing heat until it reaches 100 degrees?
But you could just as easily say "Shouldn't the rod keep 'losing heat' until it reaches $0$ degrees?" You might find this statement subjectively a little more... | {
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On Planets orbiting binary stars Several years ago a discovery was made of planet orbiting a star of a binary system (two stars orbiting each other). Since binary star systems are plentiful in our galaxy, I presume we will be discovering even more such planets.
However, as far as I know, no planet has been discovered ... | 1
Generally speaking, binaries cannot have shared planets orbiting at close distances. Neither dynamics nor kinematics holds.
If a binary has a common planet, the planet must be far enough, that is, the radius of the circle is large enough to be far greater than the distance between the two stars. This approximates two... | {
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Voltmeter has high resistance If voltage remains constant in parallel combination then why doesn't the voltmeter with low resistance give correct reading if there is only one resistor?
If there are two resistors then the one on which we are calculating voltage would be less but if there is only one resistor in the cir... | Voltage in a parallel combination is same across all device in the combination.
If the voltmeter has low resistance it will act like a "load"
It will draw current itself leading to a change in current passing through resistance .
Let me explain mathematically,
In a parallel combination current passing through each comp... | {
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How do we measure the age of the universe? How do we measure the age of the universe if time is relative to the observer? What is the reference frame we use to measure the age of the universe?
| Cosmologists use the “comoving frame”, which is the unique reference frame at each point in which the universe appears isotropic. For example, if you measure the temperature of the cosmic microwave background to be 2.725 K in every direction, you are in a comoving frame. Observers moving relative to this frame see a ho... | {
"language": "en",
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Why air spacing for high power beam splitters? Ordinary glass cube beam splitters are constructed with a dielectric or hybrid coating on the hypotenuse of a right angle prism which is then cemented to another right angle prism. These fail in high energy applications because the cement absorbs enough energy to cause ... | There's a really good answer in another thread. Basically its FTIR that's causing the one part of the beam, and evanescent waves that couple to the second prism for the second beam. That way there's no coating to burn off.
The air is not important, just the spacing of the gap, which controls how much of the beam goes w... | {
"language": "en",
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Why is the composite fermion not included in the anyon contents of FQH topological orders? For example, both the $\nu=1/3$ Laughlin state and the Moore-Read state has a simple interpretation in terms of composite fermions, which are bound states of an electron and two fluxes.
Both the Laughlin states and the Moore-Read... | Just some comments on your reply to Jainendra. (I cannot directly comment under your reply because I am a new user.) As both Wen and Jain have mentioned, the anyons are the excitations of FQH states which have fractional braiding statistics and can be described by excited CF wave functions. On the other hand, if you at... | {
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Why does diode built-in voltage persist when current begins flowing?
When P and N type semiconductors are connected together, some of the electrons drift from the N type into the P type to recombine with holes. This leaves positive ions on the N type and negative ions on the P type. Therefore an electric field exists ... | The built-in field comes from diffusion of charge carriers, from a region of high concentration into a region of lower concentration. While an applied forward current DOES change those concentrations, the numbers (for silicon diodes at least) do not indicate a zero-thickness depletion/space-charge region at any feasi... | {
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Still Confused about Linear Momentum in a Circle
A point mass with mass $m$, distance $r$ from circle and constant tangential velocity and constant angular velocity is swung around a circle. ($p$ is linear momentum)
Angular momentum is radius x linear momentum. It is conserved.
If $r$ is increased, linear momentum... | "Linear momentum is conserved when there is no force acting on the system". So far so good. As the mass is moving in a circle, there is a force acting on it and linear momentum is not conserved. If the force vanishes, the bass will move on a straight line and both linear and angular momentum are conserved.
| {
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Varying a scalar field Lagrangian density I was varying a scalar field density and I look at this term $${\cal L}~=~-\frac{1}{2}\partial _\mu\phi\partial^\mu\phi.$$
The result that I need to come is $$-\frac{1}{2}\delta(\partial _\mu\phi\partial^\mu\phi)=\nabla_\mu\nabla^\mu\phi\delta\phi.$$
But I can't find a way to d... | It is the through the 4d-version of the 3d vector identity
$$
\nabla\cdot (\delta \phi \nabla \phi)=(\nabla \delta \phi) \cdot (\nabla\phi)+\delta \phi \nabla^2 \phi
$$
together with an integration by parts that gives
$$
\delta\left\{\frac 12 \int (\nabla\phi)\cdot (\nabla\phi) d^3x\right\}
$$
$$ =
\int (\nabla... | {
"language": "en",
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Why did Planck took frequency from a wave and incorporated it to explain particle behavior of light? Well if we assume anything to be a particle then it can never be a wave right??
But when planck developed his idea then he incorporated the frequency into the formula E = hv
but frequency is a character of waves, not pa... | Planck was trying to explain experimentally measured spectra of thermal EM radiation within electromagnetic theory, where radiation is a collection of waves. The formula
$$
\Delta E = hf
$$
was for quantum of energy by which energy of an oscillator can change, it does not in any way require that there be particles of l... | {
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Explanation of Lenz's Law phenomena If we drop a magnet through a copper pipe (without it touching any of the sides), it would fall slower than it would if there were no pipe.
Having the pipe otherwise accelerate the magnet would be in violation of Lenz's law and conservation of energy. I agree that, if there is any in... | It looks like what we call Lenz's Law can actually be explained by the Lorentz force and Biot-Savart Law.
Suppose in the classic example of dropping a magnet down a conducting pipe (not touching the walls), the north pole is facing downwards while the south faces up. The relative motion of the magnet and pipe will indu... | {
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Water mixture at different temperatures Let's say that we mix homegeneously and instantly cold water at $t^\circ $ C and hot water at $T^\circ$ C (like in a water tap) in ratio $p:1$. My question is the following: What is the instant temperature of this mixture? Is there a law in that sense?
I am a mathematician, not ... | The above answers are correct at normal pressure, where all is linear. At high pressure and temperature the heat capacity of water strongly depends on temperature and simple averaging no longer works.
| {
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How does measuring the location of one entangled photon affect its pair? If you have two entangled photons that are moving in opposite directions and you measure the location of one of them, what happens to the wave function of the location of the other photon?
| For two entangled particles there is only one wave function, the wave function of the entangled system. It is not the case that each entangled particle has its own wave function. If you want to say there is such a thing as the collapse of the wave function, then when you measure one of the particles, the wave function ... | {
"language": "en",
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Do real electrons solve the Thomson Problem? The question of how $N$ electrons (seen as point charges) on a conducting sphere will arrange themselves in the electrostatic final state was first posed by J.J. Thomson in 1904--hence, aka the Thomson Problem. If these abstract point charge electrons are initially placed ra... | If the sphere is a good conductor then the electrons will be all over the sphere. If it is an insulator then they will remain where you put them.
| {
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Why are my interference patterns completely out of phase? DIY physics enthusiast here doing a double slit eraser experiment at home with a laser pointer, double slit diaphragm, and few linear polarizers (horizontal at one slit, vertical at the other, +/-45 degrees for the eraser).
When I angle the eraser polarizer at -... | The +45° polarised light has positive amplitude for both being vertically polarised and horizontally polarised, on the other hand -45° polarised light has positive amplitude for being vertically polarised and negative amplitude for being horizontally polarised, this difference makes the interference pattern on the scre... | {
"language": "en",
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Why are Spin 1/2 particles invariant to $4\pi$ rotation loops while Spin 1 particles are invariant to $2\pi$ loops? Why do Spin 1/2 particles when turning them by 360 deg get a phase factor of -1 and a loop of 720 deg leads to the identity while for spin 1 particles a loop of 360 deg gives already the identity?
| You ask for "why". Well the reason is that the rotation operator in matrix form does that.
For a spinor $\left( \begin{array}{} a \\ b \end{array} \right)$, you find that the rotation operator about an axis defined by the unit vector $\hat{n}$ along an angle $\theta$ is:
$$U(\theta)=cos\left(\frac{\theta}{2}\right)\mat... | {
"language": "en",
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Height of water fountain due to pressure difference This was a question on a fluid dynamics exam: the pressure $p_A$ on a plane is lower than the atmospheric pressure. We fill a water bottle with a straw on the ground and open it in the plane. Water will come out due to the pressure difference. Calculate the maximum he... | In my judgment, it is invalid to apply the Bernoulli equation to this problem because the Bernoulli equation applies only to steady state flows (or to flows that are nearly steady state), and this problem involves neither. However, water is very nearly incompressible, particularly for a change in pressure that is rela... | {
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3D perfectly elastic collision between two points There is a high probability, I think, that this question is a duplicate of some other question ... but to may knowledge, it hasn't been posed in this exact manner:
Assume we have 2 points, $P_1$ and $P_2$, of mass $m_1$ and $m_2$ in a world coordinate system $(O, \vec{i... | You must know the direction for at least one of the masses after the collision. Then, for an elastic collision, you can use the fact that the speeds relative to the center of mass are reversed during the collision.
| {
"language": "en",
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Van der Waals equation of state plot limitations When I plot the van der Waals equation of state in terms of Pressure (bar) versus density (mol/L) for propane at 400 K,
$$P=\frac{RT}{\big(V_m-b\big)}-\frac{a}{V_m^2}$$
in terms of density,
$$P=\frac{RT}{\big(\frac{1}{\rho}-b\big)}-\frac{a}{\big(\frac{1}{\rho}\big)^2}... | The Van der Waals equation is a model. It's popular because it gives physically realistic predictions without too much work, but it's rarely used in serious modelling because it doesn't describe real substances with especially good accuracy. Overall: it is not surprising that the model doesn't model propane correctly a... | {
"language": "en",
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Why we neglect the $\hbar ω/2$ in the Hamiltonian of the the Electromagnetic Field? After the quantization of the electric and the magnetic field, we get the Hamiltonian of the electromagnetic field:
$$H= \hbar ω(a^{\dagger}a +1/2) .$$
with $\hbar$ the planck constant and $a^{\dagger}$ the creation operator.
Why can w... | Because the vacuum-energy (lowest energy that's being neglected) doesn't affect the anaylsis that you want to do if you're using the Rabi Hamiltonian.
| {
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What does it mean for a plane wave to be an eigenstate of a 3D vector?
Show that $$ \phi_p(r) = \left(\frac{1}{2\pi\hbar}\right)^{3/2}e^{ip\cdot r/\hbar}$$
is an eigenstate of p, where p and r are 3D vectors.
I'm unclear on what the final equation I'm trying to get to should look like. I thought that the final resu... | It's almost certain that you're misreading the text, or that it got mangled in some other way, and that it should really read
Show that $$ \phi_{\vec p}(\vec r) =\left(\frac{1}{2\pi\hbar}\right)^{3/2}e^{i\vec p\cdot \vec r/\hbar}$$
is an eigenstate of $\hat{\vec p}$, where $\vec p$ and $\vec r$ are 3D vectors,
and ... | {
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$\hbar \approx 0$ and the spread of QM wave function Is there a direct mathematical method to show that if a quantum wave funtion is initially sharply localized, then it will stay sharply localized if $\hbar \approx 0$? In that case the Ehrenfest theorem implies the transition from quantum mechanics to classical mechan... | The problem with trying to understand the spread of the wavefunction in the classical limit by taking $\hbar\approx 0$ or taking the limit $\hbar\to 0$ is that in reality $\hbar\neq 0$. Taking the real non-zero value of $\hbar$ there are cases of perfectly ordinary objects for which Ehrenfest's theorem doesn't imply an... | {
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Equation for: How does Thickness of Aluminum Pipe affect the velocity of the magnet falling through? I need help in finding the equation for how the velocity of a magnet dropped through an aluminum foil pipe is affected when the thickness of the pipe is changed. Thank You.
| An exact equation would require an exact description of the shape, strength, orientation of the magnet. But generally, we can say the thicker the walls, the slower the fall. This is because the electrical resistance of the walls is less, the thicker they are.
| {
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Being Frictionless, surface of contact I frequently hear references to a smooth surface, or frictionless pulley.
Can being frictionless be obtained if only one of the 2 surfaces has 0 coefficient of friction?
Or is it for the contact of those 2 surfaces (in friction due to material roughness)?
What in the cause of fric... | I realize this is not an answer. But frankly, I don’t think there is a simple answer. The very good, in my opinion, comments posted thus far confirm that friction is a complex topic. Although we try to use some simple models, one can always find examples where the model we use do not apply.
If we were faced with actua... | {
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How does the negative energy solution to the Dirac equation predict the antielectron? Please, can someone explain how the negative energy solution can be used to predict the existence of the antielectron?
| It was not a prediction, it was a conjecture, in what was Dirac's hole theory:
The negative E solutions to the equation are problematic, for it was assumed that the particle has a positive energy. Mathematically speaking, however, there seems to be no reason for us to reject the negative-energy solutions.
....
any ... | {
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Derivation of the work-energy theorem We state the following version of work-energy theorem :
$$ K_2-K_1=Fd=W $$
Where acceleration is assumed to be constant, so is the force $F$.
Then the physicists proceed by writing
$K_2-K_1=F[x(t_2)-x(t_1)]$
$$=F(x_2-x_1)$$
Notice, $x(t)$ was a polynomial of time $t$ with highest... | The crucial point lies in the equation itself
Then they write $K_2-K_1=F \left. x \right|_{x_1}^{x_2}=
F \displaystyle \int_{x_1}^{x_2} \, dx $
We can take out of the $F$ from the integral only and only if $F$ is not a function of $x$.
For example, $F=10N$ is a constant force. It does not depend on time or the posi... | {
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If mass can be converted to energy than how is it said that energy can't be created? From the mass-energy equivalence E=m(c*c), it can be seen that energy can be created and it is not converted from one form of energy.
Or am I wrong ?
Can you explain?
| Mass and energy are equivalent terms. From the $E=mc^2$ equation,the change in mass corresponds to change in the mass. For better understanding, consider a collision between two bodies A and B of equal mass $m_0$ and moving with opposite velocities to each other in a inertial frame of reference. Let us consider a colli... | {
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Why does sound behave differently in water than in air? I noticed in some experiments at home that sound does not behave the same in water than in air. Is there a good scientific explanation to this?
I noticed that the sound sounded distorted in water but not in air.
I also used a software that I could use to hear the... | You can think of waves in matter, whether light waves or sounds waves, as acting on tiny tuning forks.
Light is scattered, reflected, etc, by being re-radiated by atoms. Like with a tuning fork, There's a characteristic frequency, the Natural Frequency, at which the electron in an atom will oscillate ideally leading t... | {
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Conceptual understanding of operators in QM Do operators in QM represent in some fashion the action of the measurement apparatus on a state being measured? Usually operators in QM are introduced as abstract transformations whose eigenvectors/eigenvalues are axiomatically the possible results of measurement, with an exp... | Quantum observables, i. e. hermitian/selfadjoint operators are mathematical representations of measurable quantities. The spectrum of the operator, namely the set
\begin{align*}
\sigma(F) = \bigl \{ z \in \mathbb{C} \; \; \vert \; \; F - z \; \, \mbox{not invertible} \bigr \}
\end{align*}
of complex numbers where F - ... | {
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Why does a SUSY Lagrangian only contain $F$ and $D$-terms? I'm reading a book on AdS/CFT by Ammon and Erdmenger and chapter 3 covers supersymmetry. This isn't my first look at SUSY but it's my first in depth look to really try to understand it, and when they talk about constructing a Lagrangian for $\mathcal{N}=1$ chir... | This answer should help https://physics.stackexchange.com/a/403388/221660 .
Also, you may check Section 95 of "Quantum Field Theory" by Srednicki or Section 4 and 5 of "Supersymmetry and Supergravity " by Wess and Baggar.
I wanted to write this as a comment but I can't due to the low reputation. XD
| {
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What happens to the spin when photon is absorbed by an electron? Photon is spin 1 and electron is spin 1/2, so when a photon is absorbed by an electron it is destroyed and the electron becomes excited by that amount of energy. The next moment the electron will go back to it's ground state and emits a photon with the sa... | As has been indicated above, it is not the electron which will gain some
internal angular momentum (spin) from the photon, but it is the atom which absorbs the energy as well as the angular momentum of the photon (1 hbar).
This will result in an increase of the orbital angular momentum exectly by
1 hbar (l=l+1) plus an... | {
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Can you jump higher if you run? If so, why? (High jumping) I have often wondered why high jumpers can jump higher if you run. The way I see it is that you only build up horizontal speed, and since you're running on a plane, I cannot see how this speed can be used to increase the vertical speed.
I cannot say that I hav... | You don't. Velocity is a vector, and the speed you are accounting is in the x-coord which is perpendicular from y-coord. To illustrate this think on the time it takes a bullet to touch the ground when shot (without air)... it will take the same amount of time as if you drop it without shooting, so it does't account for... | {
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Friction acting as an internal force I was solving this problem in my assignment:
Assuming a frictional force F acts on the block of mass m, a force -F will act on plank of mass M. Hence, the net work done by frictional force should be zero, as friction is an internal force , but option D is given incorrect. What's t... | The inner actions have a zero resultant but the associated power can be non-zero when there is slipping.
We have in general $\overrightarrow{{{F}_{1\to 2}}}=-\overrightarrow{{{F}_{2\to 1}}}$ but $P=\overrightarrow{{{F}_{1\to 2}}}\centerdot \overrightarrow{{{v}_{2}}}+\overrightarrow{{{F}_{2\to 1}}}\centerdot \overrighta... | {
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Different expressions for distance & displacement : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$ I came across these expressions in my book. And the book says that all these are different from each other.
The expressions are : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r... | Looks like an integral over radial distance.
| {
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Why is the far point of human eye infinite? In my exams, the presence of this question, which unfortunately I couldn't answer, made me wonder why is the far point of an eye infinite?
First thing that came into my mind was that how come we can see till infinity?
Far point of eye is sometimes described as the farthest po... | I think you are confusing the optical definition of infinity with the literal definition of it. In an optical system, including your eyes, infinity is that distance at which light entering the optical system is considered parallel. This site gives the defnition as:
In optics, it is the region from which a point on an... | {
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Calculation of Gravitational Potential at the centre of the cube
I came across this problem in a test and have been able to come up with a solution however I am unsure if it is correct.
I started by building a cube of twice the initial dimensions to bring point P to the centre of a larger cube. This was to bring an el... | Each cube in the top layer has a matching cube in the bottom layer exactly opposite it:
Top layer:
t1 t2
t3 t4
Bottom Layer
b1 b2
b3 b4
t1 is pulling the center with the same force but in exactly the opposite direction as b4, so the net force is 0. The applies to t2/b3, t3/b2 and t4/b1. All of these have a ... | {
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How can I recreate the greenhouse effect in my car? I am trying to preheat my car during winter mornings using the greenhouse effect. I understand the greenhouse effect in cars works by visible light passing through the glass, with most UV and infrared being blocked by the glass. The visible light is either absorbed by... | 500W is the power input, not the light output. Halogen bulbs have a Luminous efficiency of less than 5%. So if your windshield blocks IR, you're probably getting less than 20W of that power into the car. It's going to be difficult to measure the effect of that.
Full sunlight on a windshield could be more than 1500W.... | {
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Does the resistance of the voltmeter affect the behavior of this circuit? I have this setup.
It consists of a battery of no internal resistance with voltage $V$ and a resistor with resistance $R$. It also consists of a voltmeter of some (not so large) resistance as good ones should have.
Now my question is, will th... | You are right that a low resistance in the voltmeter will not affect its measurement. The rule that a voltmeter resistance should be high compared with all resistors in the circuit is so that you can use the voltmeter in series resistance/impedance circuits without have to ask your question.
I would modify your claim ... | {
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Why and how fast does lightning propagate? While looking at this youtube video of lightning in 1000 fps I was somewhat surprised that such a frame rate is enough to capture the propagation of lightning.
I have no clue about photography or physics, but the naive questions I want to ask are:
*
*How "quickly" does ligh... | There are two processes going on in a lightning strike. There are stepped leaders, searching for the path of least resistance, and there is the lightning strike when that path is found. See youtube.com/watch?v=XWuZqw3LopE. Each process has its own speed, and the stepped leader process may not proceed at a constant spee... | {
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Can we know whether it’s a $1D$ or a $2D$ motion just by looking at the position-time relation? How do I know whether it is a $2D$ or a $1D$ motion, just by looking at position-time, or velocity-time, or acceleration-time equations?
Maybe the question is not very clear, I’m not sure I’m getting it across properly, so ... | In general the position vectors you are looking at take the form $$\mathbf x=f(t)\hat i+g(t)\hat j$$
Now, let's think about what is first taught when learning about lines. In the x-y plane, a line can be described by
$$y=mx+b$$
Now, you can probably convince yourself that our vector components $\langle i,j\rangle$ can ... | {
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Why magnetic field starts from north pole and ends in south pole? In magnets such as bar magnets the magnetic field lines are starting from North pole and ends in south pole..but I don't know what is the reason for it..why this happens.
| In the question are some misunderstandings about magnetic fields.
In a permanent magnet the magnetic field is the result of the alignment of subatomic particles, mostly of electrons. In detail, subatomic particles have an intrinsic magnetic dipole and in permanent magnets these dipoles are aligned (frozen).
Any magneti... | {
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How can there will be current in purely inductive circuit? In a purely inductive circiut there are two emf's one is applied and other is induced
applied emf and induced emf are equal and opposite, then how can there will be current in a purely inductive circuit.
induced emf is not a potential drop and it produce curre... | Going along a path around the circuit, the potential differences must be given by
$$V_s+V_L=0$$
where $V_s$ is the potential of the source and $V_L$ is the potential across the inductor.
But we know for the inductor
$$V_L=-L\frac{\text d I}{\text d t}$$
So we have
$$V_s=L\frac{\text d I}{\text d t}$$
If the source has... | {
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Length Contraction Scenario Suppose a space ship is traveling from star A to star B at some significant fraction of the speed of light. In the frame of the ship, the distance A to B is less than the distance in A and B's rest frame. Is it possible for the ship to quickly increase its speed so that in its frame the ship... | This is an interesting puzzle and I don't think I agree with the previous answer.
Suppose the ship is stationary, halfway between A and B, which are $L$ apart. In a very short (negligible) time it accelerates towards B at high speed. A and B are now $L/\gamma$ apart. The ship is still halfway between A and B (playing ... | {
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What does it mean to say that glass has refractive index 1.5? The refractive index of a material depends on the wavelength of the light incident upon it which is why dispersion happens. When we say that glass has refractive index 1.5 which wavelength do we have in mind?
| In this Wikipedia page it says:
Standard refractive index measurements are taken at the "yellow doublet" sodium D line, with a wavelength of 589 nanometers.
Therefore it's in the middle of the visible light band. In the list provided in that page you can see that glass (it calls it fused silica) at 20 Celsius degrees... | {
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When is the order of magnitude not equal to the exponent of scientific notation? Explain why the order of magnitude is sometimes not the same as the exponent in scientific notation. It is because of the units?
| $n \,e \,m$ is just usually thought of as $n \times 10^m$, coming from the early age of computers/pocket calculators, it's a historical way of writing the scientific notation. On the contrary, $n \times e^m$ is just that, it is never written as $n \,e \,m$.
| {
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Unclear assumption in deriving fluid energy conservation laws I am currently working through Alexandre Chorin's Mathematical Introduction to Fluid Mechanics. In the first chapter, he treats the change in Kinetic energy of a fluid region $W\subset D$ subject to the fluid flow map $\varphi_t:\mathbf{x}\mapsto\varphi(\mat... | Indeed, there is no assumption.
You can use the Reynolds transport theorem https://en.wikipedia.org/wiki/Reynolds_transport_theorem
With the Green theorem , it gives :
$\frac{d}{dt}\int\limits_{\Omega (t)}{f\rho d\tau }=\int\limits_{\Omega (t)}{\left( \frac{\partial f\rho }{\partial t}+\nabla \cdot (f\rho \overrightar... | {
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Entropy of the big bang At the moment of big bang, all the matter was in perfect order, that is entropy 0 so what force or disturbance would occur to begin the chaos and the entropy start to increase?
|
At the moment of big bang, all the matter was in perfect order, that is entropy 0 [...]
This is not true as far as we know. We think it was in a state of less than maximum entropy (else heat death would have occurred instantly), but there is no reason to think it had 0 entropy. "Typical" initial conditions would have... | {
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Why do electromagnetic waves have the magnetic and electric field intensities in the same phase? My question is: in electromagnetic waves, if we consider the electric field as a sine function, the magnetic field will be also a sine function, but I am confused why that is this way.
If I look at Maxwell's equation, the c... | E and B are in phase for a running plane wave, but are 90 degrees out of phase for a standing wave. This can be easily seen by considering the vector potential, $A(t, x) $. Using $E = \partial_t A$ and $B=\partial_x A$. For $A=sin(\omega t - kx) $ you find that E and B are in phase. For $A=sin(\omega t) sin(kx) $, a st... | {
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Variational Navier-Stokes: where to find study material "for dummies"? I have worked with the Navier Stokes equations before but I'm a physicist. I was talking to a mathematician and they use a complete different notation and I am very lost.
First of all, I use the Control Volume method for discretization and they use ... | I'm a physics undergrad student. I've been to self-studying continuum mechanics, and as a part of that reading some fluid dynamics stuff. At first I faced similar difficulties. Kip S Thorne's Modern Classical Physics helped me to grasp the physical intuition behind most of the concepts. Then I was motivated to study th... | {
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Why is blowing so different than sucking? Why is it so easy to blow out a candle from a significant distance, but nearly impossible to suck enough air to do the same?
Even without focusing the airflow through a nozzle or something, this affect seems to be present. For example, it's easy to feel the air coming out of a ... | Assume a constant density of the air $\rho$.
Consider an imaginary tube of air in the region of the candle, of area $A_{\rm open}$ and speed $v_{\rm open}$, being reduced to an area $A_{\rm lips}$ and speed $v_{\rm lips}$ at the lips.
Using conservation of mass $A_{\rm open}\, v_{\rm open}\, \rho =A_{\rm lips} \,v_{\rm... | {
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Resistor Capacitor circuits I am a high school physics teacher and came across some issues today that I am unable to explain.
We made a circuit with an $11$ V power source connected to a $100~k\Omega$ resistor and $100~\mu F$ capacitor. We used a Vernier voltage probe to observe the potential across the capacitor incr... | For one, at $11\,\text{V}$ you are using the probe outside its specifications (up to $10\,\text{V}$). The $6\,\text{V}$ issue might have to do with the black lead of the sensor being directly connected to ground through the interface connector (or whatever potential your measurement device like a tablet or laptop is at... | {
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Why don't you get burned by the wood benches in a sauna? When you go to the sauna you may sit in a room with 90°C+. If it is a "commercial" sauna it will be on for the whole day. How does it come that when you sit on the wood you don't get burned?
I believe this question is different than the "classical" one concerning... | Wood is a poor conductor of heat. The thermal conductivity of wood is relatively low because of the porosity of timber. Thermal conductivity declines as the density of the wood decreases. ... For example, the thermal conductivity of pine in the direction of the grain is 0.22 W/moC, and perpendicular to the grain 0.14... | {
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Why can all solutions to the simple harmonic motion equation be written in terms of sines and cosines? The defining property of SHM (simple harmonic motion) is that the force experienced at any value of displacement from the mean position is directly proportional to it and is directed towards the mean position, i.e. $F... | These are all good and correct answers, but I will answer from a different perspective.
Any linear-differential equation of degree $n$ has $n$ linearly independent solutions, ie. these $n$ solutions span a vector space, with sets of solutions forming a basis.
For simple harmonic motion, the differential equation is:
$$... | {
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Rand-walk/Brownian-motion on 2D lattice I started to learn stochastic processes this year. Only had two classes, but I already have some problem. We learned about Einstein's and Langevin's description of Brownian-motion and now I need to solve a task, related to Brownian-motion/rand-walk.
The task's text is the followi... | Just to make this post clear for anyone, who comes here in the future: Case closed, I actually had the right answer in the post, and Aaron Stevens confirmed it in a reply, thank you.
So for the 2D diffusion, $\left< r^{2} \right> = 4Dt$.
| {
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Could magnetic fields really be completely substituted by relativity and electric fields? In many textbooks (especially those for undergraduate level), magnetic fields are described merely as a relativistic side product of electric fields when considering frames in motion relative to moving charges. Everybody knows the... | No, this is a common misunderstanding of the relativistic argument.
Consider the three spatial dimensions of height, width, and depth. You describe paintings in terms of their height and width, but one day you discover that if you rotate the painting, some of the height and width can turn into depth. That tells us that... | {
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What's the variation of the Christoffel symbols with respect to the metric? By the Leibniz rule, I expected it to be
$$\delta \Gamma^\sigma_{\mu\nu} = \frac 12 (\delta g)^{\sigma\lambda}(g_{\mu\lambda,\nu}+g_{\nu\lambda,\mu}-g_{\mu\nu,\lambda}) + \frac 12 g^{\sigma\lambda}(\partial_\nu (\delta g)_{\mu\lambda}+\partial_... | $ \Gamma^{a}_{bc} = \cfrac{1}{2}g^{ad}(\partial_{b}g_{dc} + \partial_{c}g_{bd} - \partial_{d}g_{bc}) \Rightarrow $
$ δ\Gamma^{a}_{bc} = \cfrac{1}{2}δg^{ad}(\partial_{b}g_{dc} + \partial_{c}g_{bd} - \partial_{d}g_{bc}) + \cfrac{1}{2}g^{ad}(\partial_{b}δg_{dc} + \partial_{c}δg_{bd} - \partial_{d}δg_{bc}) \Rightarrow$
$... | {
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"timestamp": "2023-03-29T00:00:00",
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Do orbiting planets have infinite energy? I know that planets can't have infinite energy, due to the law of conservation of energy.
However, I'm confused because I see a contradiction and it would be great if someone could explain it.
Energy is defined as the capacity to do work. Work is defined as Force x Distance. Fo... | Power expended when moving in orbit $\vec {F}.\vec {v}=-\nabla \phi .\frac {d\vec {r}}{dt}=-\frac {d\phi}{dt}$ , $\phi$ is gravitational potential. Hence the work of gravitational forces is $W=\int {\vec {F}.\vec {v} dt}=-\int {\frac {d\phi}{dt}dt}$. For a periodic motion, the integral $W$ over the period is zero. For... | {
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Electric charge of the Higgs field The Higgs field is
\begin{equation}
\Phi = \frac{1}{\sqrt{2}} \left( \begin{array}{cc} \phi_{1} + i\phi_{2} \\
\phi_{3} + i\phi_{4} \end{array} \right) \tag{1}
\end{equation}
with $\phi_{1}$ and $\phi_{2}$ carrying electric charge $+1$ respectively, while $\phi_{3}$ and $\... | Simply read the WP article and heed its consistency. It is in P&S conventions, so please do not look at Srednicki, whose opposite conventions evidently confuse you consistently. Now,
$$Q=T_3+Y_w/2, $$
so for the Higgs doublet, Y =1, hence Q = +1 for the upper component and 0 for the lower component, the one that pick... | {
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} |
How do I determine the components of a cinematic jump, for vertical and horizontal velocity? I have been tasked with determining the feasibility of The Rock's jump in the movie 'Skyscraper' I am using projectile motion equations to determine it, but have gotten stuck whilst calculating my horizontal and vertical veloci... | Of course the three numbers don't describe the sides of a right triangle. You are incorrectly assuming that $v_0=v_{0,x}+v_{0,y}$
and then also expecting the Pythagorean theorem to work out with the then incorrect value of $v_0$. This makes sense because, in general,
$$v_{0,x}+v_{0,y}\neq\sqrt{v_{0,x}^2+v_{0,y}^2}$$
Th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463251",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Do Chern Insulators (QAHE) have topological order (long-range quantum entanglement)? I know IQHE is a example having "invertible" topological order from Professor Wen's definition. And Topological Insulators is SRE because of necessary of underlying symmetry protection. After that, the Chern Insulator (QAHE) needs a un... | An "invertible" topological order characterized by a gravitational Chern-Simons term.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463466",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Why is the central maximum of single slit diffraction pattern wider than other fringes? I had answered a question Single Slit Diffraction Experiment, telling why the central maximum is the brightest one, but it asks:
Why is the central maximum twice as wide as the others?
Now, that is tricking me, I have tried my bes... | You can know that from the derivation of fringe width in single slit experiment, though I will give you a simple answer, without much mathematics.
If you look at diagrams of Fraunhofer single-slit diffraction patterns, you will see that the central maximum is symmetrical about the center line. All the other maxima and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463640",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
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