Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why does twisting a cork make it easier to remove from a bottle? When we want to remove a cork from a bottle first we turn the cork. Turning in one direction makes it easier to remove in the axial direction.
Does anyone know something more about this?
| As Steeven said, kinetic friction is a smaller force than static friction. Once the cork is moving in any direction, it is easier to move in the direction you want.
As Anna V said, bonds may be broken that make it easier to move a second time after it has moved once.
So why is rotation easier than longitudinal movement... | {
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What's the difference between a perfect fluid and an ideal gas? This is how I understand it at the moment:
*
*A perfect fluid is a collection of non-interacting particles, which are as a whole characterised by energy and pressure.
*An ideal gas is also a collection of non-interacting particles, but here the ideal ga... | A perfect, or ideal fluid is also incompressible, but an ideal gas is not. Pressure and volume changes on an ideal gas can cause changes in its density.
A perfect fluid is described by an irrotational velocity vector field $\bf v$, so that $$\nabla \times \bf{v} =0$$ and this is not necessarily true for
ideal gases.
Th... | {
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Brachistochrone to a vertical line Just for fun, I am working through some problems in Mathematics of Classical and Quantum Physics by Byron and Fuller. Problem 2.13 reads:
Prove that a particle moving under gravity in a plane from a fixed point $P$ to a vertical line $L$ will reach the line in minimum time by follow... | Hints:
*
*To have a well-defined variational problem, we have to impose adequate boundary conditions (BC). Recall in particular that BCs are necessary$^1$ for the proof of the Euler-Lagrange (EL) equation.
*The initial BC is an essential/Dirichlet BC $y(x\!=\!x_i)=y_i$. However, the final BC is clearly not an esse... | {
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Is it possible to take long-distance X-ray images at a high resolution in Earth's atmosphere? It's my understanding that different wavelengths of EM radiation are affected by scattering and attenuation to varying degrees. Would a camera using only X-rays be able to take a picture of something (for instance) a few mile... | X-ray telescopes (XRTs) need to be above the atmosphere as it is opaque to X-rays. So long range X-ray photography in the atmosphere, unless possibly at very high altitudes, would not be very feasible.
| {
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Why do little chips break off so easily from strong neodymium magnets? I have some strong toy neodymium magnets. Typically after a while little chips start breaking off, unlike from most other small metal objects, like in this image.
It could of course be that neodymium is more brittle than metals used for other objec... | These rare earth magnets are very brittle as you said.
From Wikipedia:
There are two types: neodymium magnets and samarium–cobalt magnets. Rare-earth magnets are extremely brittle and also vulnerable to corrosion, so they are usually plated or coated to protect them from breaking, chipping, or crumbling into powder.
| {
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If I have $N$ particles which move in one dimensions, and that collide elastically, is there a way to solve for their trajectories? There are $N$ particles on a line, and I know each of their masses and initial velocities and positions, and that the total energy and momentum is conserved when they collide.
Is there a w... | It depends on how realistic and how precise you want your model to be.
The first and most obvious simplification is to work in a reference frame in which the centre of mass of the particles is at rest.
After making that simplification, the very simplest model is to model each particle as a point mass, and assume each c... | {
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Bremsstrahlung Radiation A thought experiment.
Consider an electron falling into a black hole. From an external observer to the electron and the black hole, the electron accelerates, and should give off Bremsstrahlung radiation
From the electron's frame of reference, it is travelling along a geodesic in free fall, and ... | Philip's answer is great, I'd just add a couple of things to it.
Generally, it's important to point out that radiation is not an observer-independent phenomenon. For example, ignoring gravity, an accelerating particle will radiate according to an inertial observer, but not according to an observer who is co-acceleratin... | {
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Has a true Superconductor ever been produced? Having a conversation with a friend, we where discussing about the conductivity and resistance changes of superconductors.
He insisted that available superconductors produced by universities or corporate entities that are being produced today worldwide can in practice maint... | Yes, in 1911 by Gilles Holst and Heike Kamerlingh Onnes in Leiden. Kamerlingh Onnes received the Nobel prize in 1913.
| {
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What causes things to roll into potential wells? If an object is sitting on a potential slop, why must there be a force to push it into the well?
| Exactly, it is the force. If there is a conservative force, a potential can be defined as a function $U(\vec{r})$ that satisfies
$$\vec{F}(\vec{r}) = -\nabla U(\vec{r})$$
Therefore the force pushes towards the minimum of the potential.
The common image of a potential "well" into which the objects "fall" is a great anal... | {
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Need help with knowing when I should use $KE = \frac12mv^2$ or $V_f^2 = V_0^2 + 2ad$, in order to find final velocity I'm looking at this pdf for question 15.b) and I figure out $V_f$ by using $V_f^2 = V_0^2 + 2ad$, but the answer says $W = \Delta PE = \frac12mV_f^2$, and our answers ending up totally different, can so... | The $v_f^2 = v_0^2+2ad$ equation only works under constant acceleration.
Based on the graph, you can see that the force $F$ keeps changing, so the kinematic equation above does not apply, since the acceleration $a$ will not be constant.
The work-kinetic energy theorem (or conservation of energy) $W_\text{net}=\Delta \r... | {
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Amount of force required it to tip over a cone Say I have a cone of height $h$, radius $r$, and mass $m$.
How can I determine the amount of force required to tip it over (to have it fall completely to the other side), say exerted (horizontally) at the top of the cone? And in addition, how does the position at which I ... | Hint: Tipping occurs if there is a net moment about a point on the rim of the cone. The net moment is the sum of the moments due to the horizontally applied force and the weight of the cone acting through its center of gravity.
Hope this helps.
| {
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Pressure exerted by an ideal gas according to kinetic theory of gases In my textbook and Wikipedia, I have observed that force exerted on a wall of the container by one molecule is taken into account. Such that $F=\frac{mu} {\Delta t}$ where ${\Delta t}=\frac{2l}{u}$. But this change in time is the time required for a ... | Addition to Al Browns answer.
The change in momentum would be given by $$F\Delta t=2mv_\text{rms}$$ or $$F= \frac{2mv_\text{rms}}{\Delta t}$$ where $v_{\text{rms}}$ is the root-mean-square velocity, usually given by $$v_{rms} = \sqrt{\overline{v}^2} = \sqrt{\dfrac{3k_BT}{m}}$$ where $\bar v$ is the average speed.
The... | {
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How to calculate gas equation (not necessarily ideal) when the internal energy depends solely on the temperature? I know that for an ideal gas it can be shown through the equation of state and the Maxwell relationships, that the energy of the gas depends only on temperature.
But my question is how can I calculate a sta... | It is unnecessary to use Maxwell relations to show that if a gas obeys the equation of state of the perfect gas, the energy depends only on the temperature (and the number of moles).
Indeed, from $pV=nRT$, one gets
$$
\frac{p}{T}=\left.\frac{\partial{S}}{\partial{V}} \right|_{U,n}= \frac{nR}{V}
$$
which can be integra... | {
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Do the quark types differ from each other in ways other than charge and mass? I've read things online here and there that seemed to hint that there's more to quark type than mass and charge. Is this true?
For clarity's sake, I'm not asking about properties individual quarks have other than mass and charge, such as spin... | If the six flavors ($d,u,s,c,b,t$) all had the same mass and charge, they'd all still be distinguishable in the sense that the model still includes observables that (if measured) would detect one species and not the others.
Consider quantum chromodynamics (QCD) with $N$ quark flavors of equal mass, without the weak and... | {
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Question about instant axis of rotation The given question is:
A man is rotating a stone of mass 10 kg tied at the end of a light rope in a circle of radius 1m. To
do this, he continuously moves his hand in a circle of radius 0.6 m. Assume, both circular motions
to be occurring in the same horizontal plane. What is th... | If the stone is moving in a circle - as we are told - then the net horizontal force on the stone must be directed towards the centre of the circle. And the only horizontal force on the stone is the tension in the rope. So the centre of the stone's circle must lie somewhere along the line of the rope i.e. along the line... | {
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How do geodesics explain two identical balls thrown up at the different speeds? As stated in the title, two identical balls, both thrown directly upward, but at different speeds. The slower ball will reverse direction at a lower height than the faster ball. But the curvature of spacetime that they are passing through... | The curvature of the spacetime through which the balls are moving is identical, but the balls set off through it in different directions. Whereas in space alone they appear to be heading in the same direction, in four dimensions they are taking different paths. To see this, simply plot two dimensions, z and t, using ev... | {
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Is there a relationship between quantum physics and chaos theory on a classical scale? Im a complete physics lay person and I read somewhere that chaotic systems are subject to tiny differences in initial conditions and that the brain is a chaotic system.
Does that mean our thoughts are subject to quantum randomness?
| I would say that the brain as a physical system is affected by quantum randomness.
But our thoughts are a different thing, thoughts are immaterial, non-physical processes. Mental processes are not governed by causality or any other law of physics.
But I do believe that our minds do use thermal or electromagnetic noise ... | {
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When does the interference pattern of DSE disappear as size of "projectile" is increased? In trying to learn about Quantum mechanics (QM) from popular science books and Stack Exchange (I of course expect my knowledge to be anything but complete) I regularly come up with seemingly childish questions where I wish I could... | What Feynman is pointing out is actually a general wave property. For example, light passing through a slit can also be seen as a a superposition of all possible directions, note however, with an intensity equal to the slit's Fourier transform. At a distant, in terms of wavelength, point P all of these waves arrive, bu... | {
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What are quantum fields made up of? If quantum fields are mathematical entities made up to explain nature, what they explain is definitely something physical and is made up of something. So why can’t there be an answer to what these mathematical quantum fields are made up of?
I mean, if physicists are making them up, t... | "The book of nature is written in mathematics", said Galileo. It is hard to sing a song about a book that cannot be read; here is a song.
Quantum fields are made up of quantum oscillators, an infinity-of-infinities of them. These oscillators are little gadgets, everywhere, that spew out and consume quanta, the building... | {
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Fields as sections of fibre bundles versus functions on spacetime Why should fields be thought of as sections on a bundle? In particular, what is the problem with thinking of them as functions (with additional conditions on target domain and smoothness) on spacetime?
I could come up with one example where there is a cl... | The distinction between functions and sections is only contentful when dealing with a non trivial bundle. One might then wonder when non trivial bundles actually arise in physics. The most famous example is that of a magnetic monopole. However, how did that non trivial bundle "get there"? Well, the answer is, with our ... | {
"language": "en",
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Can we feel heat in outer space? Is there air outside of earth atmosphere? If not, could we feel heat coming from sun?
| I would say yes, one should be able to feel heat in outer space. Heat transfer can be due to contact, convection, or radiation. Although there is practically no air, in outer space there is light, or more precisely, electromagnetic radiation (visible, infrared, etc.) from the sun. So in principle at least, one should b... | {
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Single slit diffraction from Feynman's rotating amplitudes ("Little Arrows") In Feynman's NZ lectures (and consequent book) “QED – The Strange Theory of Light and Matter”, he gives a model for optics.
He describes a probability amplitude for a photon to be detected after being emitted from a source. The amplitude is a ... | It seems that the slit was too close to the source and to the screen. I have also made the wavenumber higher.
When both distances are $50$, and $k=1,000$:
For two slits (source to slits $=500$, slits to screen $=500$, $k=500$, slit-width $=0.2$, slit distance $=1$):
| {
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Magnetic moment and angular momentum of electron I recently got to know about something really interesting.
These are as follows:
1: The magnetic moment of an electron is, $\cfrac{ev}{2πr}$, where $e$ is the charge of the electron, $v$ is its velocity, and $r$ is the radius of the orbit it revolves.
2: The direction of... | Yes and no. While nothing you listed is relativistic, L and M will take on only discrete values based on quantum effects in the bohr model. The orbits are integer numbers of wavelengths of the electron’s debroglie matter-wave. In that sense, yes quantum.
But the formulae considered are all classical Maxwell stuff. The ... | {
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Is there a way to precisely quantify entanglement in general? Entanglement is among the most remarkable features of quantum mechanics. It is pointed out by many as the responsible for breaking Bell inequalities and numerous other surprising aspects of quantum theory. My issue is that I do not understand how to quantify... | Determining whether or not a given mixed state was proven to be an NP-hard problem by Gurvits. Given that, it's quite challenging to have an easy formula for quantifying entanglement, even for bipartite systems! It is worth recalling that nonzero negativity is only a sufficient condition for bipartite entanglement in m... | {
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A Special Relativity question My problem is simple. imagine you have a proton at rest at the origin and an electron traveling along the x-axis with the speed of $0.9c$. (this is our lab frame) now I want to calculate the force on the electron when the electron is at the $x=+d$. I faced a contradiction:
one way of calcu... | In order to abide by the conventions used in Resnick's book, I had to assume that the primed frame is attached to the proton so that we have:
$$x'=d'\space , \space E'_x=\frac{e}{4\pi\epsilon_0 d'^2}$$
According to Resnick, the electric field of the proton (in the place of the electron) is calculated as follows from th... | {
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Deriving the equivalent capacitance in a series circuit formula When we derive the formula for the effective capacitance in series, we say:
$$Q/C_{eqv} = Q/C_1 + Q/C_2 + Q/C_3$$ (if there were 3 capacitors in this case). We would then cancel $Q$ to obtain the formula.
I understand why each capacitor has the same charge... |
I understand why each capacitor has the same charge, but why does the
effective capacitor have the same charge as each individual capacitor?
I'd expect the effective capacitor to store a total charge of 3Q (in
the given example), not Q?
It is because each capacitor has a charge $-Q$ on one plate and a charge $+Q$ on ... | {
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How to add two Matrix Product States of different bond dimensions? If I have the MPS representation of two quantum states, how do I add them? Note that the bond -dimensions need not be the same for the two MPSs.
| Say you have two mps to be added together called $\psi$ and $\phi$. At each site, each mps has a 3-tensor with 2 bond indices and 1 physical index. Lets call the 3-tensors of $\psi$ to be M and of $\phi$ to be N. For each physical index value we can view these M and N as matrices because they have 2 indices, namely the... | {
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Where does pseudo force act at? It is known that, to apply Newton's laws in a non-inertial frame, we use the concept of pseudo force. We also know that force is a bound vector. Hence, is there a general way to determine where the pseudo force vector would be located at?
| Pseudo-forces are determined by the acceleration of the reference frame and generally act at all points in space. For a linearly accelerating frame, the resulting pseudo-force is uniform. For a rotating reference frame the force depends on things such as the distance from the rotation axis, the speed of the rotation. T... | {
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It more efficient to generate heat burning electrolyzed hydrogen, or through an electric resistance? It's convenient and simple to use electricity to generate heat, doubtlessly, say in en electric kettle or boiler or heater, but is it more efficient to generate heat burning electrolyzed hydrogen, or through the resista... | Sorry for my poor english. My native language is french.
I think there is something missing in your question. The current in the resistance is not enough to find the energy. You also need voltage. 1 A at 1 V is different from 1 A at 1000 V. So I assume the same voltage : the minimum voltage to produce a certain amount ... | {
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Is it possible to get $\langle AB \rangle$ from $\langle A \rangle$ and $\langle B \rangle$, and vice versa? Assuming that $A$ and $B$ are operators (not necessarily observables) which do not commute and that the quantum system in an arbitrary state $| \psi \rangle$, then ist it possible to get $\langle AB \rangle$ fro... | No, it is not possible for an arbitrary state: Let $\{|n\rangle\}_{n\in \mathbb N_0}$ denote the set of (normalized) eigenvectors of $N\equiv a^\dagger a$. From the ladder operator algebra we find that
$$\langle n|a|n\rangle =\langle n|a^\dagger|n\rangle = 0 \quad , $$
for all $n$. On the other hand, it holds that
$$... | {
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Can electromagnetic standing waves be used to move particulates? As detailed in this paper:
https://www.researchgate.net/publication/3941396_Ultrasonic_separation_of_suspended_particles
The researchers use the formation of acoustic standing waves to deposit particulates into the nodes of the waves. Can this me achieved... | Yes they can, see here for a review of optical dipole traps, page 19 for standing wave traps. The trapping potential for a focused retroretlected beam is
$$U\propto -\frac{\Gamma I}{\Delta}\cos^2(kz)\left(1-2\left(\frac{r}{\omega_0}\right)^2-\left(\frac{z}{z_R}\right)^2\right),$$
where $\Gamma$ is the damping rate, $I$... | {
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How does the small angle approximation lead to 0 here? I'm finding the equations of motion of a mass attached to four springs in a box. See picture:
In the prompt, we're instructed to use "the small-oscillations
approximation, and neglect terms of order $\frac{x^2}{a^2}$ , $\frac{y^2}{a^2}$ , and $\frac{xy}{a^2}$". ... | the force $F_{1x}$ is:
$$F_{1x}={\frac {K_{{1}} \left( \sqrt {{x}^{2}+{y}^{2}-2\,ya+{a}^{2}}-a
\right) x}{\sqrt {{x}^{2}+{y}^{2}-2\,ya+{a}^{2}}}}
$$
take the Taylor series for the denominator
$$\sqrt {{x}^{2}+{y}^{2}-2\,ya+{a}^{2}}\overset{\text{Taylor}}{\mapsto}=a$$
and for the nominator
$$K_{{1}} \left( \sqrt {{x}^{... | {
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Cauchy sequences through examples in Quantum Mechanics (at the level of the rigor of physicists) I have just read the definition of a Cauchy sequence:
A sequence ($\psi_n$) is a Cauchy sequence in a vector space $V$ when $||\psi_n-\psi_m||\to 0$ when $n,m\to\infty$. The limit of every Cauchy sequence $(\psi_n)$ conver... | Here's a concrete example. For a particle in an infinite potential well of width $a$, the normalized energy eigenvectors are of the form
$$\psi_n(x) = \sqrt{\frac{2}{a}} \sin\left(\frac{n\pi x}{a}\right)$$
Most wavefunctions - such as the $\Psi(x) = \frac{1}{\sqrt{a}}$, corresponding to a uniform spatial probability de... | {
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Rigorous proof that a net force of zero guarantees zero linear acceleration in rigid bodies I've never found a rigorous proof of this fact.
The center of mass' acceleration is not necessarily the linear acceleration, specially if the body is attached to a pin or another geometric constrain, then the center of mass spin... | The statement in question is a direct result of the following two statements
*
*Linear momentum of a rigid body is defined as the total mass times the velocity of the center of mass.
$$ \boldsymbol{p} = m \, \boldsymbol{v} \tag{1}$$
*The net force acting on a body equals the rate of change of linear momentum (Newt... | {
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Is a 6-quark particle viable? It is my understanding (which may be flawed) that protons and neutrons are stable because the 3 (R, G, and B) quarks form a "white" color singlet. Wouldn't 6 quarks or even 9 quarks create a white singlet? What about RGBGR?
| In principle, a hadron with any number of quarks can be formed provided that the overall color is neutral.
However, hadrons with more than three quarks (observed in particle accelerators) are unstable$^1$ and decay rapidly.
Tetraquarks and pentaquarks have been observed in high energy collisions, but rapidly decay. A p... | {
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Can we define operators like $\dfrac{1}{a^\dagger a}$? I was recently reading this paper on Enhancement of Few Photon Optomechanical Effects and could not quite understand eq.(2). The author has written an operator like this:
$$\hat \xi=\dfrac{g_oa^\dagger a}{w_m-g_{cK}a^\dagger a}$$
I don't understand how I am suppose... | To supplement Andrew's nice answer, note that vectors in the occupation number basis are eigenvectors of $a^\dagger a$, i.e.
$$a^\dagger a |n\rangle = n|n\rangle$$
As a result, the action of your operator $\hat \xi$ on such a vector becomes
$$\hat \xi|n\rangle = \frac{g_0 n}{w_m - g_c n}|n\rangle$$
which extends by lin... | {
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Basics of centripetal force Suppose an object is moving in a circular path. We know that the net force that is working on that object is the centripetal force towards the center. But the object should have gone closer towards the center in that case due to the radially inward force working on it, but it doesn't. Why do... | That's cause centripetal force is exactly the amount of twist needed for the momentum vector of the particle at an instant so that it sticks tangent to the path at the next.
This works for unit speed, and unit mass, the force is exactly equal to the curvature of the path.
| {
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How does a system with two black bodies connected via a circulator avoid violating the second law of thermodynamics Consider two different temperature black bodies connected by an ideal circulator (or similar passive and directional device) such that thermal radiation emitted from the cooler black body is able to reach... | Let us assume the perfect passive circulator.
We do not only have 2 heat baths (blue and red). We have a third, at the bottom of the circulator. It surely has some temperature.
Over time, all three heat baths will reach the same temperature.
Suppose T < B < R. Then B is cooling as it sends radiation to R, and R is cool... | {
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How much energy was used to charge the inductor? Electrical systems question I am a math major, and I am taking a mandatory class that looks more like physics and the professor gave us an assignment with a question that I don't have any idea on how to solve it. The question is originally in portuguese, so, I will try m... | For an inductor (with inductance $L$) the defining relation
between voltage ($V$) and current ($I$) is:
$$V(t)=L\frac{dI(t)}{dt} \tag{1}$$
To find the total energy $E$ fed into the inductor
you need to integrate the power ($VI$) over time $t$ (from $0$ to $T$).
Then use equation (1), and finally do the integration by s... | {
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What causes the diffuse reflection of an object onto a nearby object to be colored the same color as that of the object? Assuming a light source, emitting white light,a red colored diffuse sphere lit up by the light, and a white plane below the sphere acting as the 'floor', we find the diffuse reflection of the sphere ... | When you shine white light at a colored object, the light that scatters off it is missing some of its wavelengths i.e., it is tinted: this is why it appears colored to our eyes.
So now you have colored light radiating away from that object, and when it strikes a nearby object and is scattered off, the scattered light ... | {
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Is it possible to create a magnetic environment where it pushes and pulls at the same time, making the target “levitate”? To better understand why I ask this, the backstory is I’m getting more and more annoyed by rolling office chairs rotating, hitting my ankles, hard to switch directions when wheels having ~90 degrees... |
Is it possible to create this environment that the magnets are in
perfect balance in every direction, both pushing and pulling?
If by magnets you mean fixed magnetic moments in a static configuration, then the answer is no per Eanrshaw's theorem.
If the magnets are electromagnets or at least can change their magnetic... | {
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Does relativity mean that the crew of a relativistic rocket would experience less acceleration than in our frame of reference? I have been told regarding a 1 g rocket that "the amount you accelerate would be less due to relativity".
Does that mean that from the crew's time dilated perspective, they would experience les... | There is no frame of reference in SR in which an acceleration can stay constant at a non zero value for an infinite amount of time. This would inevitably lead to a velocity that is greater than the speed of light.
It is well-known that when two frames $S$ and $S'$ move relative to each other with velocity $v$ and a vel... | {
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Is it possible to calculate angular acceleration from a measured linear acceleration? I am trying to use an accelerometer to measure the angular acceleration of a robotic arm.
From rigid body kinematics, the following relation is known
\begin{align*} {^{i} {\boldsymbol{a}}_m} & = {^{i} {\boldsymbol{a}}_l} + ^{i} \dot{{... | I'm not clear on what your equation indicates or exactly what your accelerometer is measuring, but if you need an angular acceleration for an arm, that could be only horizontal or vertical or a vector sum of the two. In each case α = a/r.
| {
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Doubt in derivation of pressure exerted by ideal gas In books the derivation of pressure exerted by a gas on a closed container is derived for a cubical geometry, but since it contains number of molecules per volume (denote it by $n$) the books say it's independent of geometry. My question is how they say it's independ... | You said it yourself , it depends on the number of molecules per volume not the total number of molecules. And by saying so it means you are only considering about the density of gas contained in the closed objest whatever it may be. And also density of gas will not change by changing the shape of container.also the ma... | {
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Simplest exactly solved model displaying a phase transition? The classical example of an exactly solved model which displays a phase transition is the 2D Ising model. However, all the proofs I've seen of this have been very long and complicated.
So, I wanted to know whether there were any other exactly solved models wi... | The quantum Ising model in a transverse field
$$
H=\sum_n \left(\hat \sigma_{z,n} \hat \sigma_{z, n+1} +\lambda \hat \sigma_{x,n}\right)
$$
is easily solvable and has a phase transition. It's a one-dimensional quantum model but, through the usual quantum-classical map that takes the hamiltonian to the transfer matrix,... | {
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When a car accelerates relative to earth, why can't we say earth accelerates relative to car? When a car moves away from a standstill, why do we say that the car has accelerated? Isn't it equally correct to say that the earth has accelerated in the reference frame of the car? What breaks the symmetry here? Do the force... |
What breaks the symmetry here?
The accelerations are not symmetric because (proper) acceleration itself is not relative (frame variant). A simple accelerometer can measure the asymmetry. The car’s accelerometer measures a large acceleration. The earth’s does not. The measured asymmetry in the acceleration is due to t... | {
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Mandl & Shaw QFT chapter 1 question Page 3 of Mandl & Shaw claims that, given a vector $\pmb{A}(\pmb{x},t)=\pmb{A}_{0}e^{i(\pmb{k}\pmb{\cdot} \pmb{x} - \omega t)}$, $\pmb{\nabla} \pmb{\cdot} \pmb{A} = 0$ (eq. 1.6) implies $\pmb{k} \pmb{\cdot}
\pmb{A} = 0$ (eq. 1.7).
I'm having trouble figuring out why (1.6) implies (1.... | $$\mathbf{\nabla}\cdot\mathbf{A}=\frac{\partial A_x}{\partial x}+\frac{\partial A_y}{\partial y}+\frac{\partial A_z}{\partial z}=i\mathbf{k}\cdot\mathbf{A}=0$$
| {
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What is the relationship between the Galilean group and the Poincaré group? What is the relationship between the Galilean group and the Poincaré group?
Are they siblings within the Lie group? Or does the Poincaré group contain the Galilean group as a subgroup?
I'm not so much interested in the Galilean group being the ... | It is assumed you have appreciated Inönü, E.; Wigner, E. P. (1953), "On the Contraction of Groups and Their Representations" Proc. Natl. Acad. Sci. 39 (6): 510–24, and the super-helpful Gilmore text in Group contraction.
Very crudely, the Poincaré Lie algebra,
$$
[J_m,P_n] = i \epsilon_{mnk} P_k ~, \qquad [J_i, P_0] =... | {
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Why won't all voltage be used up on first resistor in series? tldr: I am having trouble conceptually understanding voltage between resistors in series, even though I know how to calculate it using Ohm's law. How do the electrons "know" there are more resistors after going through the first one? Why doesn't it use up al... | Think of it this way.
One battery terminal sits at $10V$, the other at $0V$. The first resistor has one terminal connected to the $10V$ pole of the battery.
Now assume, as you did, that the voltage is "all used up" after the first resistor (i.e. if $2A$ flows through it). In that case the voltage would be $0V$ at that ... | {
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Maximum value of angular acceleration In a video of Prof. Walter Lewin, in which he is talking about the maximum value of angular acceleration, he says that it does not imply that the angular acceleration is zero if the angular velocity is zero and that when the object conducting some angular motion is stationary the a... | It's similar to SHM. When an object performs SHM the displacement from the equilibrium is
$$x=A\sin (\omega t) $$
by differentiating, there are equations for velocity and acceleration
$$v=A\omega\cos (\omega t) $$
$$a= - A\omega^2\sin (\omega t) $$
from graphs of those functions it can be seen that at positions where ... | {
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Mechanism of Relativistic Momentum The formula for relativistic momentum is $\vec{p}=\gamma m\vec{v}$.
To derive this formula, one analyzes a collision while assuming the principle of relativity and the conservation of momentum principle are correct:
https://www.feynmanlectures.caltech.edu/I_16.html
I'm fine with all t... | I think what you are looking for is an understanding of 4-force, that is the vector which describes force in relativity. Without getting into the details (which are easily accessible by a google search), the key aspect is that the relativistic four force for a given classical force depends on the velocity of the object... | {
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How come black body have more emissivity and more absorbtivity(a) at same time? We have two definitions to look at
Absorbtivity(a): the ratio of absorbed energy and incident energy on a body
$a_{BlackBody} = 1$
so if i have a tourch light that gives red light, in a dark room I point this tourch light at this black bod... | You are mixing up two concepts, namely the emission of light as a consequence of temperature and the reflection of incident light.
When you look at objects in daylight, their apparent colour is caused by the fact that they absorb some of the incident daylight and reflect the rest. It is the combination of the frequenci... | {
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Conservation of angular momentum in an inelastic collision
I have a question about the second method used to solve the problem above.
The moment of inertia with respect to the stick's midpoint after the collision is $ml^2/12 + ml^2/4$ or $ml^2/3$ so the angular momentum with respect to the stick's center after the co... | The CM of the system (the mass and the stick together) moves in a straight line and every point of the system rotates about the CM.
I think the mistake arises from considering the mass m and the stick together as a whole system and writing the conservation of angular momentum about a point (middle of the stick) which i... | {
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Eigenvalues of Product of 2 hermitian operators Let $A$ and $B$ be two Hermitian operators. Let $C$ be another operator such that $C = AB$. What can we say about Eigenvalues of $C$? Will they be real/imaginary/complex? What I did was to search for examples. The following were examples (in matrix representation) I looke... | In general, we can say that $C=AB$ will have real, imaginary and complex eigenvalues (complex of the form $z=a+ib$ where and $\{a,b\in \mathbb{R}\mid a,b \ne 0\}$ as shown in the comments by Mark and Qmechanic's answer). For example, if
$$A=\begin{bmatrix}
0 &1 \\
1& 0
\end{bmatrix}\ \ \text{and}\ \ B=\begin{bmatrix... | {
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A lens with a high permeability In real life materials with high $\mu$ values are not realistic, so lenses are made with high $\epsilon$ materials. But what would be the impact of achieving the same refractive index by increasing $\mu_r$ too.
For instance, if we made a lens with $\epsilon_r=\mu_r$ the wave impedance of... | The refractive index is $\nu = \sqrt{\epsilon_r \mu_r}$ because the speed of light is $c/\nu$ in that medium. At this level of idealization it does not matter what the relative permittivity or relative permeability is, only their product matters when it comes to ideal propagation in a homogeneous medium.
If the two med... | {
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If the probability of a point (photon) hitting another point (electron) is zero why do they collide? If the probability of a point (photon) hitting another point (electron) is zero why do they collide? To have a probability greater than zero almost one of them should be not a point. Correct me, please if I am wrong.
| In popular presentations of particle physics you often find the statement that photons and electrons are "point particles", while protons and other composite entities are not. However to call a photon or an electron a "point particle" is quite misleading unless you immediately add that we are dealing with quantum physi... | {
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What is light cone? Explain to mathematicians who understand the Lorentz group but not light cone Mathematically the Lorentz group is precisely the $O(1,3)$ is the 4-vector rotation preserving the inner product of 4-vector under this metric
$$
\eta_{\mu \nu}=(+1,-1,-1,-1).
$$
There are four distinct sectors of this $O(... | Given a four-vector $A^\mu$, define the “interval” associated with $A$ as
$$
\Delta s_A = \eta_{\mu\nu}A^\mu A^\nu = \left(A^0\right)^2 -\vec A{}^2
$$
We say that $A$ is
*
*“spacelike” if $\Delta s_A < 0$. An example is $(0, \vec A)$.
*“timelike” if $\Delta s_A > 0$. An example is $(A^0, \vec 0)$.
*“lightlike” if $... | {
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Provided a unit vector and Force, how can I calculate it's components? Say I have a $F=kQ_{1}Q_{2}/r^{2}$ and a direction vector $(x, y, z).$ How can I find the component forces $F_{x}$, $F_{y}$, and $F_{z}$?
| You need to know the direction of the force as well as its magnitude. The force’s component along the $x$ axis is then
$F_x = |\vec F| \cos \theta$
where $\theta$ is the angle between $\vec F$ and the $x$ axis etc.
If the force is radial i.e. $\vec F = |\vec F| \vec {\hat r}$ then its components at $(x,y,z)$ are
$\disp... | {
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Does transmutation of nuclear waste need more energy than it originally produced? Nuclear transmutation has been proposed as a method to reduce nuclear waste from nuclear power plants:
*
*https://en.wikipedia.org/wiki/Nuclear_transmutation
I recall reading somewhere that this is economically not very attractive, beca... | This article describes some of the reasons we don't use nuclear waste as fuel.
The biggest problem is that we have plenty of uranium (and other energy sources) and burying the waste is not very expensive so there is not a large economical incentive to burn the rest of the fuel. This in turn leads to less interest in de... | {
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Inverse Square vs Exponential I feel a little foolish asking this, but I keep reading sources which say that for an inverse square law relationship, e.g. light intensity vs distance from source, the intensity decays exponentially.
Are inverse square and exponential the same? I would think not, as I cannot find an alge... | Inverse square is not the same as exponential dropoff. Any source which says this is using "exponentially" in a colloquial way. Hopefully they don't then try to do mathematics immediately afterwards!
There are some exponential dropoffs in physics, such as the intensity of evanescent fields, but the drop off of normal... | {
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Do electromagnetic waves contain electrons? I understand that EM waves are oscillating electric and magnetic fields. But doesn't this mean that the wave itself contains charged particles that generate the fields?
| Weirdly, they don't contain electrons, but are actually made up of photons - even those waves that are not in a frequency we know as visible light.
Here's a source from Nasa.gov -
https://imagine.gsfc.nasa.gov/science/toolbox/emspectrum1.html#:~:text=Electromagnetic%20radiation%20can%20be%20described,energy%20found%20i... | {
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What does it mean for a field theory to be invariant? In this paper A. N. Schellekens, Conformal field theory p.8 they mention the following
If a field theory has a conserved, traceless energy momentum tensor, it is invariant
both under general coordinate transformations and Weyl transformations.
What is meant with '... | The action, yes. The equations of motion, therefore also yes. But the fields themselves, no. That's like expecting a rotation of axes to preserve Cartesian coordinates in Newtonian physics.
| {
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Understanding Space-time intervals and its types I am taking Introduction to Modern Physics class. There, we were studying spacetime intervals as a subsection of Lorentz's transformation. My professor said that $\Delta x^2-c^2\Delta t^2$ is invariant, and then he said us that it is a lightlike event if $\Delta x^2-c^2\... | "Events" are akin to [localized] points.
It's not the "events" that are spacelike, timelike, or lightlike.
Rather, it is the "relationship between pairs of events" that are spacelike, timelike,or lightlike.
The pair of events "A and B" is timelike related if there is a timelike path in spacetime (say the worldline of ... | {
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How to simplify this complex circuit? I am new to circuit solving and I tried to simplify this circuit, but I am unable to do so. I can't figure out which resistances are in series and which resistances are in parallel.
Do I have to use star-delta conversion here or the circuit can be solved without conversion?
I just ... | I would define 5 current loops (making sure that each resistor is in at least one loop). Then write 5 voltage loop equations (summing voltage drops). Solve for the currents.
| {
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How to demonstrate that light carries angular momentum by making an object rotate? Electromagnetic fields, carry angular momentum. However, I want to demonstrate by an experiment and convince a bunch of high school students, that electromagnetic fields do carry angular momentum. To that end, can we design an experiment... | One example can be found in Introduction to Electrodynamics by Griffiths, example 7.8.
Horizontally suspend a uniformly-charged insulating ring from its center (perhaps by attaching spokes from the ring to its center, and then attaching a string to the center). Place a solenoidal electromagnet directly below the center... | {
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How can a person be hit by a high-energy proton beam? There is this somewhat famous story of a Russian particle physics Ph.D. student from the 70s, who stuck his head into a particle collider and got hit by a beam of high-energy protons. For more details see here, here or here.
I am confused about how exactly this is e... | Here is a slide that I found by Goggling "Proton beam in air"
| {
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"source": "stackexchange",
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Linearization of 1D maps about a fixed unstable point Recently, I was going through the paper Controlling Chemical Chaos in a three variable autocatalator system, by Peng et al. Here are the references
Although I have been introduced to 1D maps and the logistic map as well, but a certain point has been bugging me for... | It's a simple Taylor expansion, but their notation maybe is not great.
When they write $f(\beta_n -\beta_s)$ it might look like $f$ is a function and $\beta_n -\beta_s$ its argument, when actually $f$ is essentially a constant number that is multiplying $\Delta\beta=\beta_n -\beta_s$, which is the distance from the $k$... | {
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Would a pressurized container move by itself if opposite edges have different size surface area? If inside a closed container there is gas with higher pressure than outside the container, and one edge of the container has a larger surface area than the opposite side, would the container move by itself? Wouldn't there b... | No, you are forgetting that the pressure on the two other slanted faces also contribute a component of force opposite to the largest face. The net forces still balance.
This is because the vector area (the integral of all infinitesimal area vectors) of any closed surface is zero.
| {
"language": "en",
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How is Newton's third law working here? I understand that if I were, for example, to throw a bowling ball in outer space then the ball would move away from me by the force I generated. But the ball would also exert a force on me in the opposite direction and move me away in the opposite direction of the bowling ball.
I... | The gas molecules next to the metal of the fire extinguisher push on it. When these molecuoes bounce off the metal surface, the rest of the gas molecules in the container push them back towards the metal, keeping the pressure on.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does light have multiple frequencies? The wavelength of visible light ranges from 750 - 400 nm, and so do the corresponding frequencies. However, a photon only has one frequency, given by $E =h\nu$, at a given time, and it can’t be changed unless the photon gets energy from somewhere, which isn’t possible in the va... | Light comes with so many wavelengths because it is made of so many photons. A typical lightbulb puts out something on the order of $1\ \mathrm{W}$ of power in the visible spectrum, while individual photons in the visible spectrum each have an energy on the order of $10^{-19}\ \mathrm{J}$. Therefore, a typical lightbulb... | {
"language": "en",
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"source": "stackexchange",
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Temperature rise in IC engine without heat flow In an IC engine, the air fuel mixture is ignited in a cylinder resulting in temperature rise of the mixture. However, there is no heat flowing into the engine cylinder from some heat reservoir. Yet, in the P-V graph below, it says that heat $Q_H$ is flowing into the cylin... | The part of the cycle where the red arrow is pointing is the 'ignition'.
That's when the new fuel/air mixture taken into the engine is ignited and provides the energy input. So the heat comes from the ignition of the new fuel.
| {
"language": "en",
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What does $F$ in the equation of surface tension $(T=\frac{F}l)$ mean? As far as I knew or assumed: If an imaginary line is thought to be present on a surface, then molecules of the surface will attract or exert equal forces throughout the length of the Line. So in a nutshell let say the centre of mass or the centre of... | For a disc or ring
this time tension equals to the ratio of net force acting on a small straight linear fragment of circumference to the length of that fragment
seems like a reasonable definition.
It's true that the total force has no resultant direction, but it's often the case that energy is used to deal with such ... | {
"language": "en",
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Direction of supersonic shockwave on a bullet with lateral velocity When a bullet travels at supersonic speeds, it generates a shock-wave. For a bullet traveling in a straight path, the shock-wave is oriented in the same direction as the bullet. But if a bullet is being deflected by the wind, the nose of the bullet wil... | A shock wave will obey the Rankine–Hugoniot relations, which means the normally incident flow direction is the relevant direction.
My question: is the shockwave oriented to the nose of the bullet, or is it oriented to the direction of flight?
What you are looking for is called aberration. So first find the angle bet... | {
"language": "en",
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Absolute zero: how close can we go? Kinetic theory says that the minimal temperature is zero kelvin, at which every motion is stopped.
However, we do know that quantum theory says that we have unavoidable quantum fluctuations, so: what is the minimal quantum temperature that can be reach? Is there any known closed form... | Approaching absolute zero means subtracting smaller and smaller amounts of energy from the system. Using the energy-time uncertainty relation, $\Delta E\Delta t\geq \hbar/2$ we conclude that the minimum attainable temperature is greater than:
$$
T_{min}> \frac{\Delta E}{k_B}> \frac{\hbar}{2k_B t_{universe}},
$$
where $... | {
"language": "en",
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Derivation of anomalous commutators of currents in Fradkin's book I am trying to understand the derivation of the anomalous commutators of the left- (and right)-moving currents in Fradkin's book (see e.g. here). I am not sure I understand how (6.71) leads to (6.72).
My understanding is that we can work out identities w... | Note that these equations are (5.244) and (5.245) in the book version, compared to the online notes. Luckily I still have my own notes scribbled in this section of my book copy. Here it is:
$$
\begin{split}
[j_+(x), j_+(x')] &= \lim_{\epsilon, \epsilon' \rightarrow 0} \left( \frac{i \delta(x' - x + \epsilon' + \epsilon... | {
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Graph for Coulomb Force vs $1/r$ My teacher told me that the graph for the coulomb force $F$ vs $1/r$ where $r$ is the distance between the 2 charges should be parabolic but I can't seem to understand why. I am aware that equations of the form $y^2=4ax$ are parabolic but why should $F$ vs $1/r$ graph be parabolic?
| Assume $F$ to be $y$ and $1/r$ to be $x$
Then, according to coulomb's law
$$y = cx^2$$
where $c = \frac{q_1 q_2}{4 \pi \varepsilon_0}$
Now you can rearrange the equation as follows.
$$x^2 = c' y$$
where $c' = \frac{1}{c}$
Now you can take $c' = 4a$, and this will give you your familiar expression for a parabola with th... | {
"language": "en",
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What is wrong with the high-school definition of a vector? Why is the high-school definition of a vector as "a quantity with a magnitude and a direction" incomplete? For example, Griffiths Introduction to Electrodynamics book says:
The definition of a vector as "a quantity with a magnitude and direction" is not altoget... | The definition is not satisfactory because vector spaces do not come equipped with a notion of direction or magnitude. The matrix
$$
\begin{pmatrix}
1 & 1 \\ 0&1
\end{pmatrix}
$$
defines an automorphism of $\mathbb{R}^2$ as a vector space, but preserves neither magnitude nor direction (understood as the angle between v... | {
"language": "en",
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Direct experimental observation of magnetic orbital quantum number $m_l$ Is there an experimental way to observe magnetic quantum number $m_l$ values directly, the way electron spin was detected by Stern Gerlach experiment or proton's spin by nuclear magnetic resonance experiments? The Zeeman effect comes to mind, but ... | A hint to the literature of fine-structure spectroscopists: an $ℓ=2$ state is sometimes known as a “quintet” because of its splitting into five sublevels. See also singlet, doublet, triplet, etc.
You suggest in a comment that we consider the famous sodium doublet, which is visible without any magnetic field. That doubl... | {
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Isn't it possible for a matter to have mass of an electron but opposite charge? I read that "Positrons" have the same mass as of an electron but it is oppositely charged but we don't call it a normal matter we have given a special name to it "anti matter". But why ? Why can't a matter particle have those properties ? W... | Because it's not just mass that's identical, all properties of an electron are shared by the positron except opposite sign for charge (and also handedness).
| {
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Basic question about orbital speed I was reading a Sci-Fi book recently and had a weird thought:
I know that objects closer to a gravitational well need to move faster to stay in orbit and objects further away move slower. But if you want to increase your orbit/escape the gravitational well you have to speed up while i... | This is the well-known satellite orbit paradox. The key point is HOW you thrust in a cicular orbit. When you do a so-called impulsive thrust, i.e a thrust for a short time (small relative to the orbital period), you do it at that given position and the thrust energy goes only into the kinetic energy, i.e. you locally i... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Mathematical justification of the Born-Huang expansion in the derivation of the Born-Oppenheimer Approximation In the book K. Huang and M. Born, Dynamical Theory of Crystal Lattices (1954, Appendix VIII) and also in the Wikipedia article https://en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation#Derivation, t... | Let
$$
H = H_e + T_n
$$
Where $H$ is the full Hamiltonian and $T_n$ is the nuclear kinetic energy. Notice that the only dependence on $R$ in $H_e$ is through the position operator, i.e. there is no dependence on $\frac{\partial}{\partial R}$. This means we can treat $H_e(R)$ as a (Hermitian) operator on the space of fu... | {
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Is the intensity of light dependent on number of photons per unit area? I was learning about the photoelectric effect of light and there it says more the intensity of light, the more number of electrons will be ejected from the metal surface given that the frequency of light is more than its threshold frequency.
Now wh... | Number of photons per unit area is proportional to intensity. That’s because intensity = power/area = (energy/time)/area. A photon has energy $h\nu$, where $\nu$ is the frequency. So intensity is $N h\nu$/(time x area), where $N$ is the number of photons.
| {
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If our solar system and galaxy are moving why do we not see differences in speed of light depending on direction? May be a silly and simple question, but I've been wondering if:
The speed of light is constant, and
*
*When we're moving in the same direction (where both the emitter and the receiver move with the light ... |
The speed of light is constant
is one of Einstein's postulates of relativity and says something profound that can take time to realise.
It means that the light is measured to have the same speed independent of the motion of the source.
So for example if a light was shone from a stationary spaceship we would receive i... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is there a single slit in the Young double-slit experiment? I am studying waves these days and my teacher just introduced Young double-slit experiment, which has always been brilliant (see picture below).
However, I have a question: why is there a single slit in the experiment?
My teacher says that the single slit ... | The single slit is used to create light from a single source.
Even what we regard as a single source of light e.g. a bulb, can have different parts to it, e.g. different parts of the filament, emitting light at different frequencies and amplitude and varying with time in different ways.
The single source is then split ... | {
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Confused about the Pauli exclusion principle I've been struggling to understand this: Let's say I have a gas of one million electrons. Does every single one of those electrons have a different energy (up to the degeneracy from the different momentum components)?
| Avogadro constant, which is a good estimate of the order of magnitude for a macroscopic number of particles, is much bigger than a million ($N_A\approx 10^{23}$). Yet, there is nothing difficult in giving every pair of electrons (with different spins) their own momentum state, for momentum is continuous - i.e., the num... | {
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Why does stimulated emission not contribute to linewidth? The rough quantum mechanical explanation for linewidth is that the lifetime $\tau$ of an excited level is associated with an uncertainty $\Delta E$ in its energy satisfying $$\Delta E\tau=\hbar$$ and so there is a linewidth $$\Delta \omega=\frac{\Delta E}{\hbar}... | The short answer: the relevant lifetime is not the one of an individual excitation, but the first-order coherence time, the timescale at which the phase diffuses.
The longer answer is very interesting. On the quantum level, both the photons coming in and out of the cavity are described by a Lindblad process. For the g... | {
"language": "en",
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"source": "stackexchange",
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Matrix element and Dirac notation If
$$
T=
\left[
\begin{array}{cccc}
e^{\beta J} & e^{-\beta J} \\
e^{-\beta J} & e^{\beta J} \\
\end{array} \right]
$$
and
$$Z = \sum_{S_i=\pm 1} ... \sum_{S_N=\pm 1} \exp{\beta J(\vec{S_1}\vec{S_2}+\vec{S_2}\vec{S_3}+...+\vec{S_{N-1}}\vec{S_N}+\vec{S_N}\vec{S_1})}
$$
Then why c... |
Then why can we say that:
Because, each $S_i$ can only take on two values: +1 or -1
For example, if $S_1 = +1$ and $S_2 = +1$ then the $e^{\beta J S1S2}$ is ${e^{\beta J}}$, which is exactly what the ++ matrix element of $T$ says.
As another example, If $S_1 = +1$ and $S_2 = -1$ then the $e^{\beta J S1S2}$ is ${e^{-\... | {
"language": "en",
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Which of these sentences best describes the equivalence between mass and energy?
Which of these sentences best describes the equivalence between mass and energy?
*
*mass is a form of energy.
*mass and energy are two manifestations of the same property: mass-energy.
*mass is energy confined to an object.
*energy a... | I would say 5. "$m^2 c^2 = E^2/c^2 - p^2$". This is closest to your 4., but includes what happens when $p\ne 0$
| {
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Proof that you can't disentangle two parties if you only operate on one Let $A$ and $B$ be two entangled systems. Can someone prove or sketch a proof of why you cant unentangle $A$ and $B$ by only acting on $A$ or $B$ alone? i.e. by only applying $\mathbb{I}_A\otimes U_B$, with $U_B$ unitary.
| If there was some unitary operator factorized as $\mathbb I_A \otimes U_B$ that would send the entangled state $|\psi\rangle$ to a factorized state $|\phi_A\rangle\otimes |\phi_B\rangle$, ie :
$$|\phi_A\rangle\otimes |\phi_B\rangle = (\mathbb I_A\otimes U_B)|\psi\rangle$$
Then, we would have :
$$|\psi\rangle = (\mathb... | {
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Why bother buying efficient lights if you are already heating your house? Assume I live in a location where at any time of day and any time of year, I need to heat my house. Assume further that I have a room with no windows. In this case, does it make sense for me to buy efficient light bulbs, considering that any inef... | Hot air rises
You'll have noticed the radiators around your house are close to the floor - under it if you're lucky enough. Your lighting, on the other hand, is close to the ceiling. The hot air they produce will do little to warm you where you actually are, usually seated and close to the floor.
| {
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How do stars produce energy if fusion reactions are not viable for us? From what I've learned, fusion reactions are not currently economically viable as of right now because the energy required to start the reaction is more than the energy actually released. However, in stars they have immense pressures and temperature... |
However, if these reactions are considered endothermic for us, how are they exothermic in stars?
The reactions are still exothermic for us. In fact, they are very exothermic. The fact that they are not net energy producers is due to inefficiencies in our existing technologies for producing these reactions, not becaus... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/674089",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Concept of Gravitational potential energy Change in Potential energy corresponding to a conservative force is defined as $$\Delta U = U_f - U_i=-W_f$$ and gravitational potential energy is $$\Delta U = U_f-U_i = -W_g $$ Suppose a mass $m_1$ is kept at a fixed point $A$ and a second mass $m_2$ is displaced from point $B... | No the equation that you have derived isn't wrong. What actually is at fault here is the logic that potential energy at infinity must be infinite. This is completely incorrect. For example consider the following equation:
$$a-b = c$$
In this equation the only given information is the difference in magnitude of the two ... | {
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Local order parameter for confinement in gauge theories I would like some help clarifying what Zinn Justin is saying in his book "Quantum Field Theory and Critical Phenomena" p.805 on detecting confinement of gauge theories.
In particular, I understand Elitzur's theorem just states that there is no such thing as gauge... | The reason is that non-abelian gauge theories are asymptotically free. This means that at short distance, one cannot distinguish between the confined and deconfined phase because the gauge interaction turns off. Therefore it is hard to imagine what kind of local observable could measure the confinement phase transiti... | {
"language": "en",
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Locally-Flat Minkowski limit of Schwarzschild Metric I've seen questions and answers dealing with similar topics, but none that seem to provide what I'm looking for.
The Schwarzschild metric (and indeed any valid metric) should reduce to the Minkowski metric over a sufficiently small, linearized region.
I am trying to ... | You can always choose locally-inertial coordinates to see that any metric (Schwarzschild, or otherwise) at a given point assumes the Minkowski form, its first derivative vanishes (therefore Christoffel connection vanishes too), but the second derivative does not vanish. The fact that the second derivative cannot be mad... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why can a very large body of water not store summer heat? On this page, it states "The key disadvantage of using a very large body of water to achieve heat exchange with a relatively constant temperature is that you are not able to store summer heat in that body of water – to have the benefit of retrieving those higher... | I think you may be misinterpreting the statement. It is not claiming that heat of summer cannot enter a lake (and be stored in it), but rather that 'you' in your actions with the heat pump cannot 'store' useful energy into the lake.
If you had a large (say a few tens of cubic metres) insulated tank of water in your bas... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/674852",
"timestamp": "2023-03-29T00:00:00",
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How do we measure time? I'm having a little trouble trying to put to words my problem and I apologize in advance for any causation of trouble in trying to interpret it.
We define periodic events as those events that occur over equal intervals of time. But, don't we use periodic events themselves to measure time (like a... | When we think about time, we naturally go to the processes of how we measure it. But time is not the ticking of a clock, or the oscillations fo an atom. Time is the construct we use to differentiate events. (No time based terms in the definition.) Just as space is the construct we use to differentiate objects. We need ... | {
"language": "en",
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Is an expression of a quadrupole as an expansion of dipoles possible? Would it be possible to express a quadrupole as an expansion of dipoles? Because a possible definition of a quadrupole seems to be: an electric field equivalent to that produced by two electric dipoles.
| Actually, for any kind of magnetic field or electric field when a multipole expansion is done in different poles, as dipole, quadrupole, sextupole, octupole and so on, it is like a Taylor expansion:
$$ B_z(x) = \overbrace{B_{z0}}^{dipole} +\overbrace{\frac{dB_z}{dx} x}^{quadrupole} + \frac{1}{2!} \overbrace{\frac{d^2 B... | {
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Second Kepler's law explanation What is the explanation for the second Kepler's law? Why is the law valid?
Is it that the total energy of a planet equals to the kinetic energy plus the potential energy?
| Kepler's second law (a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time) is a consequence of conservation of angular momentum. It applies not just to gravity, but also to motion under any central force i.e. a force that is always direct towards a fixed point.
Of course, Ke... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/675822",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 3,
"answer_id": 2
} |
What does rotational balance mean? For example, in many badminton rackets, it says that the balance point is rotational. How does this actually work?
| I am not sure but here is a guess. It may mean the racket is dynamically as well as statically balanced about the balance point. The racket is balanced statically in that the racket is stationary with a fulcrum at the balance point. The racket is dynamically balanced in that rotation (spinning the racket) about a princ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/676123",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Doppler Effect and Relativity paradox Let, Alice is moving towards Bob at very high speed. Therefore, events in Bob's frame will appear to happen slowly in Alice's frame due to time dilation. Since velocity is relative, the same is also true for Bob.
Now, since Alice is moving towards Bob, Bob's light will be blueshift... | The Doppler effect and time dilation are two separate phenomena- the first will either reinforce or counteract the apparent effect of the other, depending on the direction of the relative motion concerned.
The Doppler effect is an apparent change in clock rate that results from changes to the distance light has to trav... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/676214",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
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