Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Retarding Potential? Concerning the photoelectric effect, my textbook never defines what retarding potential is, and the internet isn't really clear on it either. I'm getting the sense that retarding potential is just the potential of an EM field, but why is it specifically labeled "retarding"? Is it decreasing with ti... | Retarding potential is not related specifically to change in time. It is related to polarity of the field. A retarding potential is rejecting photoelectrons from reaching the receiving electrode. So it will be negative on the receiving electrode compared to the photoelectrode. If its extremely negative, it will reject ... | {
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If we had enough energy available in particle colliders, what reactions could show up if the quark and electron fields weren't fundamental? Suppose the quark and lepton fields weren't the fundamental fields of Nature, but that a "deeper" Lagrangian connected to a generic model of sub-quarks and
-leptons would take over... | It depends on which particles you are colliding and at which energy. When colliding a fundamental particle (or, fundamental-like at the energy scale of your experiment) with a composite particle, you would observe deep inelastic scattering between the two. This has various consequences, probably the most important bein... | {
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Energy density in string wave The total energy density in a harmonic wave on a stretched string is given by
$$\frac{1}{2}p A^2 \omega^2 sin^2(kx-\omega t).$$
We can see that this energy oscillates between a maximum and a minimum. So the energy is maximum at 0 displacement when the string is stretched and at its maximum... | Since net energy (potential and kinetic) in a stretched string is a constant in space and time for a uniformly travelling wave, the total energy density must also be a constant.
However, the expression you have written is for kinetic energy density. Working from $y= A \cos(kx-\omega t)$ with $\mu$ as the mass density, ... | {
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Ratio of specific heats of mixture of gases Suppose I have $1$ mole of a monoatomic gas and $1$ mole of a diatomic gas. If I mix them, the ratio of their specific heats at constant pressure to that constant volume becomes:$$\gamma = \frac{3}{2}$$
I came up with this result be averaging $C_p$ and $C_v$ of both the gases... | The change in internal energy and enthalpy of mixing ideal gases is zero. According to Gibbs' Theorem, the individual contribution of each species in an ideal gas mixture to the extensive thermodynamic properties of the mixture is the same as that of the pure species at the same temperature and at the partial pressure... | {
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Where is humidity? During hot and humid weather, we sweat incessantly due to high humidity. But when we sit under a fan, we feel cold and comfortable. Why do we feel cold and chilled? Why don’t we feel the humidity?
| The reason you are sweating is not high humidity directly. It is high temperature. But high humidity prevents the body from cooling down and thus indirectly causes sweating.
*
*Temperature: The body starts sweating when it becomes too hot. The evaporation of sweat into the air absorbs energy, so by sweating, the bo... | {
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Supersymmetry beyond $D=11$ spacetime dimensions Taking into account the higher spin theories, from which string theory is an effective field theory, I just wondering if there is something to do to extend supersymmetry to any dimension without any mathematical consistency failure. Could string-theory/M-theory be formu... | The papers https://arxiv.org/abs/1409.2476 and https://arxiv.org/abs/1504.00602 by Choi discuss supergravity in twelve dimensions.
| {
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Why do gravitational mass and inertial mass appear to be indistinguishable? I have learnt that heavier the object is (the more gravitational mass it has), the more resistance to the change of motion it is (the more inertial mass it has).
I can accept this fact but I can't find out the reason behind it. What dynamic, wh... | Picture it like this. Imagine you have 2 crates. In each crate there is pure iron. But one box has 2 times the number of iron atoms, so it is has twice the mass. The weight of box should be negligable.
Now imagine that they are both moving at the same speed. When you apply same force on both boxes, the box with twice t... | {
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Question about the the velocity and acceleration in tensor notation When computing the volicty of a particle moving along a curve parametrized by $Z^i(t)$ for each component i, the components of the velocity $V^i$ are given by $$V^i = (d/dt)Z^i$$ and the components fo the acceleration are given by $$A^i=(d/dt)V^i + \Ga... | “When computing the velocity of a particle moving along a curve“ I think perhaps the confusion arises from the ambiguity in the question: is the velocity of the particle itself is moving along the given curve or is the curve represents particle’s velocity (representing the change in its position ) ; does Z represent a ... | {
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Are those equations in error propagation related? I am trying to prove that the uncertainty of the equation $$Q = xy$$ is equal to $$\frac{\Delta Q}{Q_0} = \frac{\Delta x}{x} + \frac{\Delta y}{y}.$$
However what I am getting is $$\Delta Q =\sqrt{(y\Delta X)^ 2 + (x \Delta y)^²} $$ and I am stuck there.. How to contin... | *
*The formula is
$$\left ( \frac{\Delta Q}{Q_0} \right)^2 = \left ( \frac{\Delta x}{x} \right )^2 + \left ( \frac{\Delta y}{y} \right )^2. $$
*
*Your other, more general formula, is correct.
In your last step, divide by $Q_0 = xy$.
| {
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Why is small work done always taken as $dW=F \cdot dx$ and not $dW=x \cdot dF$? I was reading the first law of thermodynamics when it struck me. We haven't been taught differentiation but still, we find it in our chemistry books. Why is small work done always taken as $dW=F \cdot dx$ and not $dW=x \cdot dF$?
| Because work $W$ is a force $F$ causing a change in position $\Delta x$.
Not just a force $F$ causing a position $x$. Or a change in a force $\Delta F$ causing a position $x$. Neither makes much sense. We are talking about a change in position - that is how work is defined.
And such a change $\Delta x$ is simply symb... | {
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Probability of measuring eigenvalue of non-normalised eigenstate This came up while working on a question about measuring the angular momentum of a particle in a superposition of angular momentum eigenstates:
Given that:
$$\langle\theta,\phi|\psi\rangle \propto \sqrt{2} \cos(\theta) + \sin(\theta)e^{-i\phi} - \sin(\th... | Given a generic vector $\psi$, the expectation value of an observable $A$ over it is given by
$$\operatorname{EXP}_\psi[A] =\frac{\langle\psi|A|\psi\rangle}{\langle\psi|\psi\rangle}.$$
You can check the normalisation by using the identity operator in place of $A$. Hence you get a well-defined state on the C*-algebra of... | {
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Recognizing speech at 1bit quantise depth? i found on german wikipedia an audio example of 1 bit depth quantising, where the speech still can be recognized. how is it possible if at 1 bit depth we have just two values: "signal" and "no-signal"?. here is the examle: https://upload.wikimedia.org/wikipedia/commons/4/43/Am... | 1-bit quantization involves sign-only sampling, which can be done at fantastic rates, well over 10^9 samples per second. For purposes of speech recognition, frequencies over 6 kHz are irrelevant. If a low-frequency signal plus wideband noise is subjected to 1-bit quantization, nonlinear phenomena can sometimes interf... | {
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How does a distant observer see matters that "form" an initial black hole? I did see Can black holes form in a finite amount of time? but it does not seem to discuss how a distant observer would see evolution of collapsing matters that form a black hole. Does it view these matters as disappearing under the horizon, or ... | Strictly speaking the far away observer never seen the black hole forming, and after a while it will start receiving Hawking radiation, until nothing is left.
The evaporation process can be thought as starting slightly outside the horizon (at a Stretched horizon). This is pictured in the image on the left, a Penrose di... | {
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What is so special about the factor $\sqrt{1-{v^2/c^2}}$ in special relativity? I am studying a book about relativistic equations and special relativity, and I keep seeing $\sqrt{1-{v^2/c^2}}$ everywhere. It is not, as with most of the concepts in special relativity, simply a mathematical construct; it is a logical con... | The reciprocal Lorentz factor
$$\gamma^{-1}~=~\sqrt{1-{v^2/c^2}}~=~\frac{d\tau}{dt}~<~1$$ is e.g. the ratio between proper time $d\tau$ and coordinate time $dt$.
| {
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Does special relativity imply that time dilation is affected by an orientation of clocks? Many texts about STR time dilation use as an example thought experiment with 2 mirror photon clock.
The conclusion of this experiment is: In a frame moving relative to the clock, they will appear to be running more slowly.
As I un... | I would resolve this problem for any arbitrary angle of the light clock inclination to show that the time dilation is independent of the light clock's orientation. If the clock is inclined at an angle $\theta^\prime$ in its rest frame, this angle changes into $\theta$ from the viewpoint of the lab observer WRT whom the... | {
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What should the scale show?
If $g=10 N/kg$ , what will show the Scales?
Yes, I know this is a very simple problem. But, I am stuck.
$$P=mg \Rightarrow m=\frac{100N+100N}{10N/kg}=20 kg .$$
But, I'm worried about this answer. What's the difference between hand holding the scales and putting them on the table? I think,... | The answer is $10 kg$. When you apply Hooke's law to one end of a spring: $F=-kx$, it is implicit that the other end is fixed in place by a force $-F$. This force may be applied by the wall, hand, another mass, etc...
| {
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Magnetic force direction Good day All!
while trying to solve this question
I used the right hand rule and according to it the Force should be directed outwards (pointing toward me)
but here is the answer that puzzeld me
I really don't get why it is down , and would feel very grateful if someone can explain me the rea... | The easiest way to find the force on the coil is probably the magnetic Lorentz force law $$ \vec F=q\vec v \times \vec B$$ The current at any point in the loop corresponds to a positive charges $q$ moving in the current direction with velocity $\vec v$. Thus, at any element of the coil, you take the right-hand -rule fo... | {
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Does an aerial respond to any frequency? what is the range of frequencies that will produce a signal in an aerial?
would a frequncy of 1 Hz be effective with appropriate power? and what about an upper limit, do frequncies in the region of visible light or x-rays produce an oscillation of charges in an aerial?
| Antennas receive electromagnetic radiation by the electrons in the antenna interacting with the electric field of the incoming wave and generating a detectable current.
This is a table of electromagnetic radiation:
As long as the wavelength of the radiation is large, the antenna will respond to the fields , so some s... | {
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Why do electrons emit phonons instead of photons? Why do electrons emit phonons when they "relax" into the minimum energy level of the conduction band after getting into it from the valence band by absorbing a photon with an energy higher than their bandgap? Why don't they simply emit a photon with an energy equivalent... | "To conserve the k-vector." To find a place in the band diagram, an electron should have right k and right energy E. Please see any E-k diagram of the conduction band. Emitting a photon will only lower the energy of the electron with unaltered k value. But if it emits a phonon, both k and E are reduced such that it fin... | {
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Am I checking incompressibility of a velocity flow correctly? My velocity flow is defined by $u_r$, $u_{\theta}$, $u_x$. This makes the strain rate tensor of the velocity flow equal to:
$J_{ij} = \begin{bmatrix} u_{rr} & u_{r\theta} & u_{rx} \\
u_{\theta r} & u_{\theta \theta} & u_{\theta x} \\
u_{xr} & u_{x\theta} & u... | The continuity equation in cylindrical coordinates is $$\frac{1}{r}\frac{\partial (ur)}{\partial r}+\frac{1}{r}\frac{\partial v}{\partial\theta}+\frac{\partial w}{\partial z}=0$$
| {
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Why doesn't my kitchen clock violate thermodynamics? My kitchen clock has a pendulum, which is just for decoration and is not powering the clock. The pendulum's arm has a magnet that is repelled by a second magnet that is fixed to the clocks body. The repelling magnets are at their closest when the pendulum is at its l... | The pendulum is being driven by the magnet: the fixed magnet in the clock is actually the pole of an electromagnet which the clock is using to drive the pendulum: the clock is putting energy into the pendulum via the electromagnet. Almost certainly the clock 'listens' for the pendulum by watching the induced current i... | {
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Incompressible 2D Navier-Stokes equation I am trying to solve for and simulate the vorticity numerically (finite difference method), however there's one part I was hoping to get some help with.
I need to find the fluid velocity $\mathbf{u}$ from the vorticity $\omega$. I can write
$$\mathbf{u} = (\nabla \phi) \times \m... | If you want to solve for $\phi$, you could add in a condition,
$$
\int_\Omega \phi\,{\rm d}V =0,
$$
which would make the solution unique. To do this numerically, you would probably need to use a Lagrange multiplier.
| {
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If fluids have zero shear modulus, how do I make sense of graphs like strain rate vs shear stress (to classify fluids as Newtonian or non-Newtonian)? Following the definition on the wiki: Fluids are substances that have zero shear modulus, or, in simpler terms, a fluid is a substance which cannot resist any shear force... | Solids have a shear modulus that relates the shear stress to the shear strain. Liquids have a viscosity that relates the shear stress to the shear strain rate. Apply a shear stress to a solid and it deforms a bit, reaching a new equilibrium shape that remains motionless until the stress is removed. Apply a shear stres... | {
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Discontinuity of metric derivatives in the Israel junction formalism It is often said that given the metrics $g^+$, $g^-$ on two sides of a hypersurface $\Sigma$, then, with a level-set function $\phi$ such that $\Sigma = \phi^{-1}(0)$, we can describe the metric on the whole manifold by
\begin{equation}
g = \theta(\ph... | FWIW, interestingly, the Israel junction conditions are born out of mathematical necessity to avoid ill-defined products$^1$ of distributions rather than actual physical considerations. See e.g. Refs. 1 & 2 for details.
References:
*
*Eric Poisson, A Relativist's Toolkit, 2004; Section 3.7.
*Eric Poisson, An Advanc... | {
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References for examples of $\ast$-algebra approach to QM and QFT In studying QFT on curved spacetime I've found the $\ast$-algebra approach as one viable approach to the subject on the paper Quantum Fields in Curved Spacetime by Wald.
The $\ast$-algebra approach seems like one quite nice and general approach to both Q... | Lecture notes exposing standard perturbative quantum field theory this way are on PF-Insights A first Idea of Quantum Field Theory. The star algebra perspective ("quantum probability theory") comes alive with the introduction of the free field vacuum state in section 4 of chapter 14. Free quantum fields.
| {
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How do acoustic enclosures for AC condensers work, without stopping airflow? How do acoustic enclosures for AC condensers like THESE work so they allow A) airflow to / from the condensers, B) but also reduce sound output from the condensers ?
Arent (A) and (B) at odds with each other ?
| No, they aren't, and here's why: an acoustic enclosure is a low-pass filter which allows free movement of extremely low frequencies (i.e., steady flow of air) into or out of the enclosure while blocking the escape of higher frequencies (motor and fan noise). This is the same job performed by the muffler on your car: it... | {
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Sounds in Space, vibration of virtual particles Sound is only available to travel through a transmission medium. My question is due to space not truly being empty, more specifically there are virtual particles in a vacuum, can sound be propagated through space? Further could the speed of sound in this medium be an indi... | @AccidentalFourierTransform's link, which he references above, furnishes a mathematical description of how virtual particles enter the picture of particle-particle interactions. @shai horowitz, the important takeaway for you here is that virtual particles are in principle undetectable in any experiment which means they... | {
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How many watts of electricity can the human body withstand without being killed? I'm talking about DC and/or AC. I've read about people surviving extremely high voltage shock (300kV) but that could be explained by extremely high resistance in the circuit that resulted insufficient current to cause death.
| The main driver for the effect of electricity on the human body is current, not Voltage or Power (Watts).
The interaction is complicated, so you can't easily apply a single number to "safe" or "deadly". Effects are can be neurological, chemical and thermal. See https://en.wikipedia.org/wiki/Electrical_injury
| {
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What is "Symmetry of Infinity" in electricity and magnetism? I have this problem from my E&M textbook:
Two infinitely long wires running parallel to the x axis carry uniform charge densities $+\lambda$ and $-\lambda$ (see photo). Find the potential at any point $(x,y,z)$, using the origin as your reference.
The solut... | I essence this is a two dimensional problem in a yz-plane because you cannot reference an absolute x-position relative to a featureless (infinite) line of charge.
The electric field looks the same at every possible value of x and this is possibly where the term “symmetry of infinity” comes from.
physicspages.com is a g... | {
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Tension in the string of a pulley
In the diagram above why is the tension of the string attached to the pulley at "A"(the string attached to roof) equal to 2T?
Why is it not Mg+(M+m)g?(considering that the pulley is mass less)
I have trouble understanding
| The way I always think of it is that as soon as an object is accelerating, it is "using up" some of the force for acceleration. In this case the heavier object that is falling is "using up" some of the $(m+M)g$ force, so it can not use that full force anymore to pull on the string.
For the smaller weight it is the othe... | {
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If Bohr model is outdated and we know that there is no such thing as an "electron orbital circumference" then how is $2\pi r=n\lambda$ still valid? We know that Bohr model is outdated and we know that there is no such thing as an "electron orbital circumference" then how is $2\pi r=n\lambda$ still valid?
Edit :
If th... | I must add some considerations.
*
*The fact that a model is outdated does not mean it must be discarded. Besides it is really useful to understand the development and the history of what we do, there are still some processes that can be explained with them. Thomson's model can still be used to derive some models of ... | {
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Euler's Equations for Isentropic Flow Derivation I'm reading a book "A Mathematical Introduction to Fluid Mechanics" by Alexandre J. Chorin, and I came across the derivation of Euler's equations for isentropic flow. Page 15, the author goes from
$$\frac{d}{dt}\int_{W_t} (\frac{1}{2} \rho ||\vec{u}^2|| + \rho \epsilon )... | Let's start from
$$
\frac{\mathrm{d}}{\mathrm{d}t} \int_{W_t}\left(\tfrac{1}{2}\rho\rvert\rvert\mathbf{u}\rvert\rvert^2+\rho\epsilon\right)\mathrm{d}V = -\int_{W_t}p\mathbf{u}\cdot\mathbf{n}\mathrm{d}A + \int_{W_t}\rho\mathbf{u}\cdot\mathbf{b}\mathrm{d}V,
$$
and use the transport theorem and divergence theorem to obta... | {
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Is the speed of sound constant? I was looking at lightning, and started to wonder if the speed of the thunder slowed down as it lost energy traveling far distances. I know the amplitude of sound decreases, perceived as volume. Im not certain, however, how to actually calculate the distance of a lightning strike based... | Strictly speaking, the thunder propagation velocity does decrease with distance, as initially lightning generates a shock wave in air, whose propagation velocity is higher than the velocity of sound, however, such shock waves get weaker with distance and become ordinary sound waves at a distance of just about 10 m from... | {
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"url": "https://physics.stackexchange.com/questions/387328",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
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Casimir Operators and the Poincare Group Following along in QFT (Kaku) he introduces the Casimir Operators (Momentum squared and Pauli-Lubanski) and claims that the eigenvalues of the operators characterize the irreducible representations of the Poincare Group. How exactly does this correspondence between eigenvalues a... | Maybe the best way to function is by analogy. For angular momentum the Casimir operator is
$$
L^2=\sum_i L_i L_i
$$
with eigenvalue $L(L+1)$. Thus, it is possible to recover the representation label $L$ from the eigenvalue of the Casimir. Since the Casimir is diagonal and proportional to the unit operator in the re... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/387481",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Electromagnet would emit light? Light is an Electomagnetic wave. When I create an electromagnet by passing electricity wound around a core and keep changing the electric field, does it emit photons?
Is the frequency of electromagnetic radiation equals the frequency of change in the electric field? If yes can it emit vi... | Your question seems to be partly about light and photons. Light, of course, consists of photons. But any electromagnetic wave consists of photons; it's just that some photons carry very little energy (at low frequency and long wavelength) and some carry a lot of energy (at high frequency and short wavelength). When t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/387569",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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A confusion about the naming of orbitals and the values of magnetic quantum number From physics courses, I'm told that (for Hydrojen atom only), for a given $\vec L$ of the electron,
$$|\vec L| * cos(\theta) = m_l,$$
where $\theta$ is the angle between the magnetic field and the orbital angular momentum $\vec L$.
Ther... | The $Y_{\ell m}$ are the spherical harmonics, with $Y_{1, -1}$ and $Y_{1, 1}$ rotating in opposite directions, eigenfunctions in spherical symmetry. Below is a figure of one of these hydrogen $2p$ orbitals, with complex phase coded as color. In an animation (when multiplied with the time dependent complex phase), the c... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why exactly do atomic bombs explode? In atomic bombs, nuclear reactions provide the energy of the explosion. In every reaction, a thermal neutron reaches a plutonium or a uranium nucleus, a fission reaction takes place, and two or three neutrons and $\gamma$ radiation are produced. I know that it happens in a very shor... |
I don't understand why exactly it leads to a powerful explosion instead of just a burst of ionising radiation.
This radiation, representing most of the initial energy output by a nuclear weapon, is swiftly absorbed by the surrounding matter. The latter in turn heats almost instantly to extremely high temperature, so ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/388164",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Projectile motion explanation I’m studying projectiles at the moment and I am sure this is a very simple question, but can someone explain if I have a light object (a tennis ball) and a heavier object (a similar size solid steel ball) and launch them at the same initial velocity and the same angle, will the range be th... | It seems you haven't yet learnt about forces. Need not worry!
In projectile kinematics the motion of a particle is based on certain parameters. And acceleration is one of them. In vertical projectiles the gravitational pull by the earth $mg$ acts on the body.
'Favourite Man' Newton now comes into the scene and states... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Isothermal compression without a heat reservoir I have devised a method to isothermally compress a gas without the use of a heat reservoir.
Consider a container of gas. To compress the gas normally, one would simply move one of the walls of the container inwards, which will do work on the gas when the gas particles col... | Assuming there is only one particle in the container and you can wisely move the piston without colliding with the particle, you then claim that there is no work done.
But don't miss the other side. Macroscopically, with the space reduced, the frequency that the particle collides with the piston increases. There is mo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Question about Charge and Gauge Transformation Does gauge invariance imply charge neutrality? I understand that all physical observables must be gauge invariant. Does this mean that physical observables must be neutral?
If a quark is in red, a gauge transformation can transform it into blue. But gauge transformation c... | You are right of course! Physical observables must be gauge invariant. But this does not mean that they must be neutral. They could be charged under the global symmetry and be neutral under the local gauge symmetry.
In particular, a local gauge symmetry is generated by a function $\alpha(x)$ where $\alpha(x) \to 0$ as... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Why not quarter-life? The number of nuclei left after time $t$ in radioactive decay is given by:
$$N(t) = N_0 e^{-t/ \tau}$$
Now if we put $N(t)$ as $\dfrac{N_0}2$, we get half-life. But, if we had put $\dfrac{N_0}4$, we would have quarter-life, which is also independent of $N_0$.
Is there anything special about half-... | Radioactive decay is an example of an exponential random process. Two key statistics for any exponential random process are the median and the mean. (The standard deviation is equal to the mean for an exponential random process.)
The half life $t_{1/2}$ is the median. The time constant $\tau$ is the mean. There's nothi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does a heat stone heated in microwave oven emits microwave? I have a heat stone which functions just as heating pads.
One concern is that it is heated in microwave.
Sometimes I give it to my kids.
One day a thought came to my mind that what kind of wave does this stone emit after being heated in a MWO?
If it emits wave... | Object which are heated in microwave ovens do not subsequently emit microwaves.
The only thing a microwave oven does is make the molecules of a substance jiggle faster, which makes the substance hotter. It is particularly good at heating water molecules because they have a large permanent electric dipole moment - so f... | {
"language": "en",
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How does a receiving antenna work given that the electric field is 0 in conductors? The question of how a receiving antenna works has been asked on this site before, such as here How does a receiving antenna get an induced electric current? and here How does a receiving antenna work?. I understand the basic principle t... | There are multiple ways in which this is not a contradiction.
*
*By “inside a conductor”, we are referring not to the conductor as a whole but rather the interior volume as opposed to the surface. If the wire segment has a net charge, that charge will be found on the surface.
*The reason the field is said to be zer... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Hubble Parameter as a function of the scale factor in Lambda CDM Model Basically I am trying to plot $H/H_0$ versus $a(t)$ for the Lambda CDM Model. In a paper I am referring to $H/H_0$ decreases with increasing $a(t)$ until a point ($a[t]\sim 0.7$) and then it starts increasing again until today ($a[t]=1$).
When I try... | Below I plot the quantities $H$, $\mathcal{H} = aH$ and $q$
$$
q = -\frac{\ddot{a}a}{\dot{a}^2}
$$
$q$ is known as the deceleration parameter and gives you information about the concavity of $a$: the acceleration
Note that around $z \approx 0.7$ the sign of $q$ changes, meaning that at this redshift the universe start... | {
"language": "en",
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What is the difference between positive negative potential and positive, negative work done? if work is done along the direction of force,then the work is regarded as positive work and if work is done in a direction opposite to the direction of force then it's regarded as negative work.Whereas in electrostatics, if a p... |
Whereas in electrostatics, if a positive charge is brought near a positive charge(which produces an opposing force) the work(electric potential) is regarded as positive.
Here, the work done by the external force (which is you pushing the charge) is positive, cause you displace the charge along the direction in which ... | {
"language": "en",
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What is the difference between $T^\mu{}_\nu$ and $T_\nu{}^\mu$? I do understand why the horizontal order matters for indices on the same vertical position, e.g.:
$$T\left(V_{(1)},V_{(2)}\right) = T_\color{red}{\mu\nu}V^\mu_{(1)}V^\nu_{(2)} \neq T_\color{red}{\nu\mu}V^\mu_{(1)}V^\nu_{(2)} = T\left(V_{(2)},V_{(1)}\right)... | The difference is $(T^{\mu\rho}-T^{\rho\mu})g_{\rho\nu}$.
| {
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"timestamp": "2023-03-29T00:00:00",
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Why is the singlet state for two spin 1/2 particles anti-symmetric? For two spin 1/2 particles I understand that the triplet states ($S = 1$) are:
$\newcommand\ket[1]{\left|{#1}\right>}
\newcommand\up\uparrow
\newcommand\dn\downarrow
\newcommand\lf\leftarrow
\newcommand\rt\rightarrow
$
\begin{align}
\ket{1,1} &= \ket{\... | According to your last question, the singlet state
$\newcommand\ket[1]{\left|{#1}\right>}
\newcommand\up\uparrow
\newcommand\dn\downarrow
\newcommand\lf\leftarrow
\newcommand\rt\rightarrow
$
$
\ket{0,0} = \frac{\ket{\up \dn} + \ket{\dn\up}}{\sqrt2}
$
cannot be valid, while one of the triplet states (assume it the $\ke... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Is there an RMS value for power delivered to an inductor? My textbook defines power delivered to an inductor as:
$$P= V_{L\rm\ peak}I_{\rm peak} \cos ( \omega t) \sin( \omega t)$$
where $\omega$ is angular frequency.
but makes no mention of $P_{RMS}$. It simply says that $P_{av}$ is zero (which makes sense since it's d... | With circuit components, we're typically interested in the amount of energy that's dissipated over time. If we have an average power $\langle P\rangle$, then the energy dissipated over time $t$ is simply $\langle P\rangle t$. RMS power is useless here: there's no way to go directly from RMS power to figure out how much... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/390171",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Potential Difference due to a infinite line of charge When a line of charge has a charge density $\lambda$, we know that the electric field points perpendicular to the vector pointing along the line of charge.
When calculating the difference in electric potential due with the following equations.
$$\nabla V=-\vec{E}$$
... | To elaborate a bit on Bill's comment, you might consider a curve defined as follows in some cylindrical $(r,\theta,z)$ coordinate system:
$$\gamma(t) = \big(r(t),\theta(t),z(t)\big) = (t, 0, 0)$$
$$ t \in [r_0,r_f]$$
The tangent vector to this curve is
$$\frac{d\vec r}{dt} = \hat r $$
so
$$\Delta V = -\int_\gamma \vec ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/390345",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Can electric field be negative? According to the equation ,
$$E = kQ/r^2$$
If the source charge is negative electric field produced by the charge must also be negative. My teacher said electric field can never be negative, it'll either be positive or zero. Online sources pointed out that since electri... | Try to ask yourself the question: what does it mean that anything is "negative"? The term "negative" has no physical meaning in itself before we define it to mean something.
*
*How does a negative number (scalar) make physical sense? What does $-2\;\mathrm{kg}$ or $-10\;\mathrm{apples}$ mean? We can choose to under... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/390461",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Why does oil float on water? This might be a silly question but I want to know why oil actually floats on water. I tried to explain it to myself using Archimedes' principle but that didn't help.
Archimedes’ principle, physical law of buoyancy, states that any
body completely or partially submerged in a fluid (gas o... | Water is heavier that oil for the same unit volume due to its higher density. Due to its larger mass, it settles at the lowest level to have the smallest potential energy and it able to do so as water is fluid. So water body is positioned below the oil body.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How to code Tensor Networks? I'm interested in learning tensor networks, I've been reading some introductory articles about this. The problem is that these articles mostly discuss the theoretical definitions for tensor networks such as MPS, PEPS, etc.. The problem is that discussions regarding how to program these for ... | An online platform where you can learn about tensor networks, their definitions, index juggling, Python/Matlab/Julia codes describing MERA, TRG, TNR, Exact Diagonalization is -- https://www.tensors.net/.
A very useful routine (which the above website uses for handling and contracting indices is known as "NCON" mention... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/390646",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Sound an amplifier makes when you plug / unplug a cable When you plug, unplug or even touch a jack cable of an aplifying system with speakers, one can hear a low-pitch sound that is of roughly always the same frequency, which does not seem to depend on the device (Hi Fi chain, guitar amplifier...)
*
*How is this sou... | Your body acts as an antenna and depending on your location your surrounding is covered by 50,60 Hz EM waves. That could be what you are hearing. There are also other signals but eiher they are too weak or out of hearing spectrum. You can also confirm this by touching an oscilloscope probe.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/391348",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How come the following equation produce a straight line? Time period for bar pendulum= T;
$$T=2\pi\sqrt\frac{\frac{k^{2}}{l}+l}{g}$$
where,
l=distance of center of gravity(C.G.) from point of suspension
k=radius of gyration about an axis passing through the CG of the body
upon solving,
$$lT^{2}=\frac{4\pi^{2}}{g}l^{2}... | Check the x-axis variable - it's not linear, instead it's $T^2$ and y-axis reflects this by its notation $l(T^2)$. The x-axis variable is chosen like this in order to make the dependence linear, so the coefficient of $l$ can be solved by linear fit.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Notation of Maxwell relations The Maxwell relations are often given as for example
$$\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V.$$
What does the $S$ and the $V$ in the index of the parantheses mean? I guess that $S$ and $V$ should stay constant for the derivation, but i... | Your system has two degrees of freedom. So any of your quantities $V$, $E$, $P$, $T$, $S$ can be viewed as a function of any two of the others. The expression
$$\left(\frac{\partial T}{\partial V}\right)_S$$
means "the derivative of $T$ with respect to $V$ when viewing it as a function of $V$ and $S$ (i.e. $T(V,S)$)". ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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In 1D wave mechanics, is there a counterexample to the relation $m \frac{d \langle x\rangle}{dt} = \langle p \rangle$? The standard physicists' proof of the identity $m \frac{d\langle x\rangle}{dt} = \langle p \rangle$ involves integration by parts. For example, in Griffiths's "Introduction to Quantum Mechanics", the d... | I would say the usual proof of this statement comes from Ehrenfest's theorem:
$\frac{d<Q>}{dt} = -\frac{i}{\hbar} [Q,H]$
Then with the usual single particle Hamiltonian one has $H=\frac{p^2}{2m} +V(x)$ and so $\frac{d<X>}{dt}=\frac{1}{2m}[p^2,x]$ This evaluate via standard commutation rules to your identity $m\dot{<x>... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/391856",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is this interpretation of quantum fluctuation in eternal inflation in Wikipedia correct? Wikipedia's article on inflation says
Although new inflation is classically rolling down the potential, quantum fluctuations can sometimes lift it to previous levels. These regions in which the inflaton fluctuates upwards expand m... | Classically, a particle rolls down a potential viz. $\frac{d}{dt}\mathbf{p}=-\boldsymbol{\nabla}V$. The equivalent for a classical field is $\frac{d}{dt}\pi=-\frac{\delta V}{\delta\phi}$. The first of these equations is quantum-corrected to $\frac{d}{dt}\langle\mathbf{p}\rangle=-\langle\boldsymbol{\nabla}V\rangle$, whi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Calculating the matter-energy density of the Universe Reading about the value $\Omega$ which is the ratio between the mass-energy density of the universe and the required mass - energy density of the universe to ensure linear expansion. I understand that if the value of $\Omega$ < 1 then space-time will warp into a sad... | The CMB has a lot of information in it, that's the reason missions such as COBE, WMAP or Planck are so important. Simply put the CMB is the result of the interaction among the various components in the universe before decoupling. This implies that a slight different universe to ours would generate a whole different pow... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/392052",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Information from four point correlation functions in Ising model For a one-dimensional classical Ising model with the Hamiltonian $$H=-J \sum_{i}\sigma_{i} \, \sigma_{i+1}$$ where $\sigma=\left\{+1,-1\right\}$ one can calculate two point correlation for the spins $$\left<\sigma_{i} \, \sigma_{j}\right>.$$ I understand ... | Let me answer a more general question (which might not be what you are after...): what information is encoded in general correlation functions $\langle\sigma_A\rangle$, where $A$ is a finite set of vertices and $\sigma_A=\prod_{i\in A} \sigma_i$?
It turns out that one can prove (it's actually easy) that, for any local ... | {
"language": "en",
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Relativistic velocity addition from time dilation I'm trying to derive the relativistic velocity addition equation using the time dilation equations but I get a wrong result.
Assume the widely used scenario in which there are 3 clocks: O, A and B.
A is moving relative to O at velocity $v$.
B is moving relative to A at ... | The clocks on ships A and B are not just running slower compared to clock O. They are also offset from each other due to their different locations. If you look at the Lorentz transform for the time coordinate
$$t' = \gamma\left(t - \frac{xv}{c^2}\right),$$
you can see that the distance between the clocks is also a fact... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why doesn't a new ball-point pen write as smoothly as one being written for a little? Why doesn't a new ball-point pen write as smoothly as one being written for a little? You will say that the friction is more first up.Then why is that so?
| A ballpoint pen consists of an extremely hard ball (tool steel or tungsten carbide) seated in a soft metal shank tip (usually brass). This will form a low-friction bearing but to do so, some initial wear between them is required for the ball to "seat" properly in the shank. In the process of seating in, tiny asperities... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/392636",
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What do quantum spin hamiltonians describe? I've learned all particles are either fermions or bosons, obeying their respective operator algebras, and then I've seen Hamiltonians describing models carrying one of these two types of particles. So far it made sense.
But then I started seeing Spin Hamiltonians describing, ... | Concerning the spinless fermions, it should be considered that Pauli's spin-statistics connection (fermions have half-odd integer spins, bosons have integer spins) applies to Lorentz invariant systems. So, it is possible to have fermions with $S=0$ in non-relativistic systems. Usually, this kind of fermions appears as ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Confusion on quantum numbers So, I've known for a long time the famous quantum numbers $n, l, m, s$ and I thought these were all of the quantum numbers, and then when applying the Schrödinger equation to orbital angular momentum and getting the spherical harmonics, with their numbers $l$ and $m$, I thought, okay here t... | Brief answer.
for each electron we assign $n$, $l$, $s$
e.g. 2p electron $n=2$, $l=1$, $s={1 \over 2}$
In the presence of a magnetic or electric field we need to think about $m_l$ and $m_s$ the projections of $l$ and $s$ in the direction of the magnetic or electric field
e.g. 2p electron $n=2$, $l=1$, $m_l = +1,0,-1$... | {
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Does reversing time give parity reversed antimatter or just antimatter? Feynman's idea states that matter going backwards in time seems like antimatter.
But, since nature is $CPT$ symmetric, reversing time ($T$) is equivalent to $CP$ operation. So, reversing time gives parity reversed antimatter, not just antimatter.
... | The statement that antimatter is matter going back in time is usually associated with Feynman diagrams in QED, so we're talking about electrons, and electrons have parity +1, so:
$$ CPT = C1T = CT = 1 $$
So the parity part doesn't come into play, but it is required in general.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Very basic question on AdS/CFT I was going through the introductory material by Horatiu in Ads-CFT.
It says that $N+1$ D-branes are split into $N$ D-Branes and a probe D-Brane. The Wilson loop is located on the probe D-brane, which is at the Minkowski boundary of the AdS space.
The AdS space is given by $f^{-1/2}dx_{|... | Here is an answer to the question of why the $AdS_5\times S^5$ metric is appearing. This is taken almost directly from the TASI lectures I cite at the end.
If you consider N coincident Dp-branes, the background solution has a metric and dilaton which we can write as
$$ds^2 = H^{-1/2}(r)\left[-f(r)dt^2 +\sum_{i=1}^p(dx^... | {
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What is the precise definition of a 4-vector? In Minkowski space, I know that there are some vectors such as the ordinary velocity that are not proper 4-vectors.
But what is the exact definition of a 4-vector? For any fixed numbers, say 1,2,3,4, does $(1,2,3,4)$ become a 4-vector in Minkowski space with the invariant i... | In Euclidean space, we can define vector as an object which transforms in a specific way under rotation.
To define vector in special relativity, we use Lorentz transformation instead of rotation. (Actually, Lorentz transformation is a kind of rotation in 4-dimensional space,)
Suppose that the events of stationary obse... | {
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Minimum Thickness of Insulation of a Pipe We know that there is the critical radius of insulation where heat transfer is maximum at that radius. Heat Transfer vs Insulation Thickness]1
From the graph, we can see that as long as the radius of the insulation is between r1 (Radius of pipe) and r*, the insulation increase... | While the full equation for heat transfer through insulation as $r_2$ changes is:
$$q_r = {T- T_\infty\over{{ln\big({r_2\over r_1}\big)}\over 2\pi Lk}+{1\over {h(2\pi r_2L)}}}$$
(ref), differentiating $q_r$, i.e. $dq_r/dr_2$ gives this equation also found here (under 'Insulation of cylinders'), the critical insulation ... | {
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Geometric optics question (from 2001 GRE)
In the diagram above, two lenses with focal lengths $f_1 = 20$ cm and $f_2 = 10$ cm are placed $40$ cm and $70$ cm from an object $O$, respectively. Where is the final image formed by the two-lens system, in relation to the second lens?
(a) 5 cm to its right
(b) 13.3 cm to ... | It works because the thin lens equation works for virtual images (i.e. $s'<0$) and virtual objects (i.e. $s<0$). To see why that is true, lets derive the thin lens equation with the following two assumptions:
*
*A light ray passing through the center of a lens does not bend.
*a light ray entering normal to the lens... | {
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Does Hyugens principle apply in three dimensions? Does Hyugens principle apply in three dimensions ?
If a surface wave (for simplicity an ocean wave) is propagating along the x axis we know that this wave ray is a point source for wavelets on the y axis but what about the z axis.
If this diagram was 3 d would we see a ... | Yes, absolutely, in general. The Huygens' principle is an intuitive picture of the solution of the Helmholtz equation through superposition of Green's functions. The basic solution is $E(\mathbf{r})=\frac{\exp(i\,k\,|\mathbf{r}|)}{|\mathbf{r}|}$ and you're simply building solutions out of sums of this one ("sums" in th... | {
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Solar Sail and GR In Newtonian gravity a theoretical reflective sail could be made such that gravity pulling it down toward the star is compensated by 'light pressure' coming from the same star.
In both cases the force drop like $\frac{1}{r^2}$
therefore the forces will compensate at any distance.
If we introduce GR w... | First, if you have an extremely large sail near a very powerful star, the 'photon pressure' on the sail can be greater than the pull due to gravity. Even though both forces decrease as $r^{-2}$ this doesn't necessarily mean that the two forces will always cancel, one of them can be always greater than the other (in the... | {
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Boson or Fermion How do you deduce that an atom is a fermion or a boson? Do you determine it from the number of neutrons because "electrons and protons cancel out each other in a neutral atom"? What does this have to do with spin? Somebody please help.I am really confused here.
| It has to do with the overall spin. Bosons have integer spin $(0, 1, 2, \dots)$ and fermions have half-integer spin $(n+\tfrac{1}{2})$.
They can be either elementary or composite. Fundamental fermions that we discovered so far are the quarks and the leptons of the Standard Model. Fundamental bosons that we discovered s... | {
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Is there an "invariant" quantity for the classical Lagrangian? $$
L = \sum _ { i = 1 } ^ { N } \frac { 1 } { 2 } m _ { i } \left| \dot { \vec { x } _ { i } } \right| ^ { 2 } - \sum _ { i < j } V \left( \vec { x } _ { i } - \vec { x } _ { j } \right)
$$
This is just a typical classical Lagrangian for $N$ particles. Sinc... | In general, there is no reason to expect that there exist conserved quantites for a symmetry which is not a symmetry of the action, but merely of the equations of motion.
The case of the non-relativistic Lagrangian and Galilean transformations is a special case. As Qmechanic works out in this answer, the Galilean trans... | {
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Euler-Lagrange Equation Proving Maxwell Equation When quantizing the EM Field, we get the Lagrangian density,
$$L=\frac{1}{2}\left(\epsilon \vert E\vert ^2 - \frac{1}{\mu}\vert B\vert^2\right) = \frac{\epsilon}{2}\vert\nabla\phi + \dot{\textbf{A}}\vert^2 - \frac{1}{2\mu}\vert\nabla\times\textbf{A}\vert^2$$
My professor... | HINT :
Note that
\begin{equation}
\sum\limits_{i=1}^{3}\frac{\partial}{\partial x_i}\left[\frac{\partial L}{\partial(\partial\phi / \partial x_i)}\right]=\mathrm{div}\left[\frac{\partial L}{\partial(\mathrm{grad}\phi)}\right]=\boldsymbol{\nabla}\boldsymbol{\cdot}\left[\frac{\partial L}{\partial(\boldsymbol{\nabla}\phi)... | {
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Why is the energy of quantum harmonic oscillator independent of its amplitude? The energy of a harmonic oscillator with amplitude $A$, frequency $\omega$, and mass $m$ is
$$E=\frac 12 m \omega^2A^2 \, .$$
It is intuitive to think that the energy depends on the amplitude because more the amplitude means that the oscill... | You can calculate the variance of the position coordinate, $\sigma_x^2$, for a general eigenstate of the energy $\psi_n$ to be
$$\sigma_x^2=\frac{\hbar}{m\omega}\left(n+\frac{1}{2}\right) \, .$$
We can replace the $n$ dependance by energy dependence using the relation
$$E_n = \hbar\omega\left( n+\frac{1}{2} \right)$$
a... | {
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Bogoliubov Transformation with Complex Hamiltonian Consider the following Hamiltonian:
$$H=\sum_k \begin{pmatrix}a_k^\dagger & b_k \end{pmatrix}
\begin{pmatrix}\omega_0 & \Omega f_k \\ \Omega f_k^* & \pm \omega_0\end{pmatrix} \begin{pmatrix}a_k \\\ b_k^\dagger\end{pmatrix}\tag{1}$$
for bosonic operators ($+$) or fermio... | There are two methods to tackling this problem:
*
*As pointed out in Yen-Ta Huang's answer and also in this Everett You's answer (EY16) to this related question we can split the creation and annihilation operators into a real and an imaginary part.
*As hinted at in (Capri, 2002; pg448) we can generalize the Bogoliub... | {
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How fast does an electron jump between orbitals? I'm wondering what speed electrons jump from level to level. I've been told only that they emit light when doing so and need energy to be inputed in order to occupy orbitals closer to the nucleus.
I will explain the reasoning for asking this question after I understand t... | If you look at the spectral lines emitted by transiting electrons from one energy level to another, you will see that the lines have a width . This width in principle should be intrinsic and calculable if all the possible potentials that would influence it can be included in the solution of the quantum mechanical stat... | {
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Curl and divergence I am trying to understand curl and divergences in a more intuitive manner, especially the curl. And is curl a surface phenomenon, if yes then how?
| A discussion on the intuitive interpretation of the curl from math SE. And a quote from Wikipedia:
If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid.
For divergence, I'd also point you to Wikipedia:
More technically, the divergence represents t... | {
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Why does the Hamiltonian define symmetry/invariance? In Sakurai's Modern Quantum Mechanics, in Chapter 4, he effectively states that the operation of rotation or translation, represented by a unitary operator $U$, is customarily called a symmetry operator regardless of whether the physical system itself possesses the s... | I interpret your question as "why would one want to call this the definition of symmetry?"
My imagination of symmetry: different "view" of the states such that the physics looks the same. Specifically, the states evolve in the same way.
In quantum mechanics, the unique role played by Hamiltonian is that it's the opera... | {
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Is it possible to harvest the energy from the movements of a satellite in orbit? I was thinking about how energy is harvested on Earth from movements of certain forces like wind and ocean currents. Could similar principles be applied in space?
Satellites are virtually in perpetual motion when orbiting the Earth. Is the... | What knzhou and nicael said is absolutely true, you cannot extract from the satellite itself more energy of that you have put in it when you launch it in orbit.
Maybe you're interested in knowing how that energy could be extract, and I think that a space tether could be a proposal.
| {
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Is specific radioactive activity constant? We have been learning a lot on the topic, and my professor introduced a couple of formulas that can help me evaluate specific activity:
$$a = \frac{A}{m};$$
$$a=\frac{\lambda}{m}N_0e^{-\lambda t}$$
Knowing this, it is obvious that $a$ is not constant and that it changes expone... | I think it is easier to understand if you write the variables as functions of time. Activity is defined as
$$A(t)=\lambda N(t) =\lambda \frac{m(t) N_a}{M}$$
where $N(t)$ is the number density as a function of time, $\lambda$ is the decay constant, $m(t)$ is the mass as a function of time, $N_a$ is Avogodro's number, a... | {
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If momentum and kinetic energy are related, how loss in energy doesn't cause loss in momentum? Kinetic energy and momentum are related to each other by the following equation:
$$K.E.=\frac{1}{2}\frac{\textbf{P}^2}{m} $$
In inelastic collisions the momentum is conserved but the energy isn't. How can this be correct in t... | The momentum of one system is conserved if no force acts on it.
Your problem is that you look at one system alone, and when force acts on it, you think that momentum isn't conserved.
If for example a clay ball A of mass $m$ and velocity $v$ collides with an identical ball B moving at opposite direction. They both stop... | {
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If I have an electrical point dipole inside a grounded sphericall shell, what is the electric potential outside of the sphere? In particular, I am confused about how the distribution of charge will take place, and how it will affect the outside.
It seems to me that charges induced by the dipole (positive and negative... | Starting with an ungrounded spherical shell, we can determine the electrical field outside the shell using Gauss's law:
The net electric flux through any hypothetical closed surface is equal
to 1 / ε times the net electric charge within that closed surface.
Source: Wikipedia.
Since the dipole, as a whole, is n... | {
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On the Robertson uncertainty relation when $\big|\dfrac{1}{2} \langle\{A,B\}\rangle - \langle A \rangle \langle B \rangle \big|^2 \neq 0$ The Robertson uncertainty relation is
$\sigma^2_A \sigma^2_B \geq \big|\dfrac{1}{2} \langle\{A,B\}\rangle - \langle A \rangle \langle B \rangle \big|^2 + \big| \dfrac{1}{2i} \langle ... | You might profit from calculating a few expectation values for, e.g. the oscillator, for which $a^\dagger |n\rangle= \sqrt{n+1} | n+1\rangle$.
Take $A=a$ and $B=a^\dagger$, so that
$$
[a,a^\dagger ]=1, \qquad \{ a,a^\dagger \} =a a^\dagger + a^\dagger a=1+2N.
$$
Look at the first excited state, $|1\rangle$, so $a|1\ran... | {
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According to Conservation of Momentum, a gun in a sealed box should not have recoil? According to the law of Conservation of Momentum, there is no way to increase the momentum of a system, except by momentum transfer from interactions with the external. If I fire a rifle while sitting on a go kart, the go kart is going... | If the gun is somehow not anchored to the inside of the box when it is fired (say the hook that holds it releases it at the right instant), the gun and bullet will travel in opposite directions with opposite momenta. They may strike the box at different times, but the momentum of gun+box+bullet will always be zero. Aft... | {
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How is the centripetal force of a car when turning distributed over the wheels?
The centripetal force can easily be calculated as: $F = (M*v^2)/R = (M*v^2)*sin(\delta)/L$. But how is this force distributed over the (front and rear) wheels? My initial thought was to just divide it by 4 for each wheel, but when you turn... | Try considering this
Since the car is driven by one engine let us assume all 4 wheels have same velocities at all time for simplicity.
And the weight of car is divided quite uniformly over the 4 wheels as well
Sonnow that we have made the m•(v^2) part of the equation same for all the wheels let us move on to the Raius ... | {
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Preferred fluid flow As I’ve read in the book “Fluid Dynamics” by Yunus Cengel, The Pressure Drag decreases and the Skin Friction Drag increases when fluid flow over body transitions from laminar to turbulent thus, resulting in overall decrease in Drag Coefficient.
The Pressure Drag is reduced during the transition imp... | Laminar flow is clearly preferred. But a turbulent one has its uses, too
Not only will a laminar boundary layer result in much less friction drag (the velocity gradient at the wall is much less steep than with turbulent flow), but for the same reason it will extract much less energy from the flow so its ability to endu... | {
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Are random errors necessarily Gaussian? I have seen random errors being defined as those which average to 0 as the number of measurements goes to infinity, and that the error is equally likely to be positive or negative. This only requires a symmetric probability distribution about zero. However typing this question in... | There are many examples of physical phenomena that seem to be governed by non-Gaussian statistics. For instance, the Levy distribution arises in the multiple scattering of light in turbid media, where the photon path length follows this distribution.
I think any time you have rare, but important events, you will see no... | {
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Can there be general relativity without special relativity? Can General Relativity be correct if Special Relativity is incorrect?
| No, there can't be general theory of relativity without its special part. Why, what is relative in general theory, length and time interval. From where relative space and time came, from relative speed. But in general theory, there is no more need of relative motion but absolute motion and gravity is just frame of refe... | {
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Is momentum perfectly conserved at the particle level given the Heisenberg uncertainty principle? Discussions of conservation of momentum frequently use the metaphor of two billiard balls colliding. My impression is that this is not valid at the quantum scale - an illustration of the particles' trajectories should show... | If you initially knew the incident momentums, the sum of momentums will be preserved, but its difference almost certainly (it depends in the kind of interaction, but with probability 1) will have some uncertainty, thing that after the collision didn't happen.
| {
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Regarding absorption of light I have a question regarding absorption of light. When looking at the absorption spectra of for example "Chlorphyll a", two absorptions peak can be seen in the visable spectra of light ( one at around 425 nm and one at 680 nm). I have been told that if a photon has suffient energy to excit... | In order for the excitation to occur there must be resonance. The energy of the absorbed photon must match the energy of the transition. In this case the transition is between bound states with well defined energies.
| {
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How can a body have two axis of rotation at the same time? I m not concerned with rotation of a body with two simultaneous axis but concerned with how we choose the axis,while going through pure rolling I have observed that there are two axis of rotation one is passing through the center of mass and the other is throug... | It isn't so. You can't have two axes at once. You can combine rotation along two axes to give a effective rotation along a single axis and the other way round.
| {
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Stern-Gerlach experiment with a magnetic field inbetween An experiment is set up so that a beam of spin-1/2 is prepared for $S_{z} = \hbar/2$, it then passes a constant magnetic field $\textbf{B} = B_{0}\textbf{e}_{x}$ with the velcity $v_{0}$ for a distance of $L$ before it passes an aditional Stern-Gerlach apparatus ... | As pointed out in another answer, your Hamiltonian is wrong. In the $z$-basis, the representation for the $x$-component of a spin $1/2$ can be written as:
$$
S_x = \frac{\hbar}{2}
\begin{bmatrix}
0 &1 \\
1 &0
\end{bmatrix}
$$
This leads to the following Schrödinger equation:
$$
\left\lbrace
\begin{matrix}
\dot{a} = i... | {
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What is the relationship between the integrability of a quantum many-body system and thermalization? If a quantum many-body system is integrable, does it imply the system would always thermalized or many-body localized?
| *
*First of all, I only discuss closed quantum system here.
*Usually integrable systems do not contain disorders (but 1D Kondo model has impurity while being integrable), hence generally not many-body localised.
*Integrable systems do not thermalise in a conventional way (I mean it does not thermalise to a Gibbs ens... | {
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How are real particles created? The textbooks about quantum field theory I have seen so far say
that all talk in popular science literature
about particles being created spontaneously out of
vacuum is wrong. Instead, according to QFT those virtual particles are
unobservable and are just
a mathematical picture of the pe... | *
*leptons (electron) and quarks, that build up matter, were created with pair creation.
*that means, that a matter-antimatter pair can be created out of vacuum (and can annihilate too into vacuum), this pair creation (and annihilation) is going on in every neutron and proton all the time, because neutrons and proton... | {
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Nuclear Physics Modeling Software I have a nuclear reactor design I would like to model. I would like to show the individual atoms and how they interact with each other in the reactor (specifically, I would like to model decay modes, interactions with photons). I was wondering if there was any software which would help... | A "general" reactor solver and GUI doesn't really exist. Especially one where you want to show individual particles. (I'm not sure how you would show individual particles, there are approximately $10^{10}$--$10^{20}$ particles in a reactor system.)
If you have a new reactor concept that you want to model, you would n... | {
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If I pointed a laser directly at Sagittarius A* from Earth, how likely is it to reach the event horizon? Given the extreme low-density of space, is it likely to reach the event horizon without interference from other matter?
| Sagittarius A* is hidden behind dust clouds that block all visible light. The only reason that we can observe it is that we use infra-red wavelengths that can penetrate the dust clouds. So if you shone a visible laser at Sagittarius A* there is absolutely no chance of it reaching the event horizon.
On the other hand if... | {
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"answer_id": 0
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Resistance and resistivity: which one is the intrinsic and which is the geometric property? Why? The electrical resistance $R$ and electrical resistivity $\rho$ of a metal wire are related by $$\rho=\frac{RA}{l}$$ where $l$ is the length and $A$ is the cross-sectional area of the wire. One could also have written $$R=\... | Let me remark, that from microscopic point of view it is more common to talk about the conductance and conductivity, which are inverse to the resistance and resistivity. Thus, I might use below these terms interchangeably.
Resistivity is a property of a material
Within classical electrodynamics (i.e., when the averagin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/403100",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 1
} |
What is the physical meaning of the third invariant of the strain deviatoric? In continuum mechanics of materials with zero volumetric change, the material condition can be expressed by the strain deviatoric tensor instead of the strain tensor itself. To express the plasticity of the materials, the plasticity surface i... | For a general $3\times 3$ matrix $\mathbf{A, you have:
$$I_3 = \frac{1}{3!}[\mbox{tr}(\mathbf{A})^3 -
3\mbox{tr}(\mathbf{A}^2)\mbox{tr}(\mathbf{A}) + 2\mbox{tr}(\mathbf{A}^3)]$$
If you have $\text{tr}(\mathbf{A}) = 0$ (this is the case for $\mathbf{A} = \boldsymbol{\varepsilon}_{dev}$), then you get:
$$I_3 = \frac{1}{3... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/403220",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Does increasing tension on a string reduce or increase the harmonic wavelength for a standing wave? I had thought that increasing tension on a string increases the frequency and thus decreases the wavelength. My book says otherwise. Which is correct?
| Possibly you are being confused by the $c=f\lambda $ formula. This applies twice, once in the string (where $\lambda$ is fixed and the tension affects $c$) and once in air (where $c$ is fixed and $\lambda$ changes). The frequency is the same in both.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/403336",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Physical processes taking place inside Germanium detectors Reading about differences between Silicon detectors and Germanium detectors, I decided to learn a bit more about the latter, since I've always used Silicon detectors in all the experiments I worked for. While reading about them, I found that Germanium detectors... | The gamma photons produce highly energetic electron in Ge which by ionization generate a large number of electron-hole pairs proportional to the energy of the electron in the depletion or intrinsic zone of the Ge pn-junction. This is similar to a ionization gas chamber detector. This charge generation leads to a corre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/403485",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 0
} |
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