Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Do particles always flow from high to low pressure? In a recent question, it was stated that
particles in high pressure air always flow to lower pressure.
In a pipe with a constriction, fluid flows from from low to high pressure after the constriction. (From here.)
How are these concepts related?
| The net movement of particles is from high to low pressure however individual particles may not move this way.
Let us assume that the particles have negligible inter-molecular forces - ideal gas assumption but probably appropriate in most fluids. This would imply that a particle wouldn't 'know' if it was in a high o... | {
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"timestamp": "2023-03-29T00:00:00",
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Was everything in the Universe "created" from light? Is the following true?
The only matter existing directly after the big bang was electromagnetic radiation.
| I could start by saying that this depends on what your definition of the big bang is, but that would be pointless because the better question is how do you define matter? Or "directly after"?
Firstly, let me say the technical answer is no because electromagnetic radiation is not matter (in a cosmological context). But ... | {
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Maxwell's Equations, cast in terms of magnetic vector potential Derive $$ \nabla \times \frac{1}{\mu_r} \nabla \times A + \mu_0 \sigma \frac{\partial A}{\partial t} + \mu_0 \frac{\partial}{\partial t} \left( \epsilon_0 \epsilon_r \frac{\partial A}{\partial t} - D_r \right) = 0$$ where $D_r$ is a "remnant displacement f... | Gauge transformation.
Let $\lambda$ be defined such that,
$$ \frac{\partial}{\partial t} \nabla \lambda = \nabla V $$
then,
$$ V^\prime = V - \frac{\partial \lambda}{\partial t} $$
$$ \nabla V^\prime = \nabla V - \frac{\partial}{\partial t} \nabla \lambda = \nabla V - \nabla V = 0 $$
You must also transform the magneti... | {
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Why does the diffusion pole universally appear in the two-particle Greens function (diffuson) I've been thinking about the calculation of the diffuson in the context of impurity-averaged Greens functions.
If you calculate the two-particle Greens function in the ladder approximation (for example, in Rammers' "Quantum Tr... | This can be derived using diagrammagic technique (see eg Altland and Simons' book). The more fundamental reason is that the diffuson is a Goldstone mode, which has to be massless (also see Altland and Simons).
But to my knowledge, the direct answer to your question is "no" -- there is no "simple" way because the math u... | {
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Is it true that a processor with a higher temperature uses inevitably more power in comparison with a processor with a lower temperature? If a processor has a higher temperature, can you be sure it it consumes more power than a processor with a lower temperature?
And is the reverse relationship true?
A processorchip wi... | No. Power and temperature are related, but not directly. Thermal environment and surface area also matter a great deal.
A tiny chip has less area to dissipate heat than a larger one. So for the same power draw, it may easily produce a higher temperature than a larger chip.
Imagine a 40W incandescent light bulb. B... | {
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Is differential geometry used in solid state? I'm an undergraduate in physics interested in a career in solid state. While I know that any additional math is helpful--I am on time constraints, and can only take a few supplemental classes.
That said, is differential geometry used much in solid state physics? I'm aware o... | Yes, especially in research-level topics. There are several research groups that work with finding ways to apply differential geometry concepts to solid state systems (although condensed matter seems to be the preferred term nowadays). See for example the book by Altland and Simons, Condensed Matter Field Theory, Chapt... | {
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"url": "https://physics.stackexchange.com/questions/158416",
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Centripetal force in this example? I have a general question regarding the centripetal force. In the example of a ferris wheel where there is a normal force pushing up against the person and the gravitational force pulling the person down, which force is centripetal? I know that the centripetal force counters the linea... | The centripetal force is not a physical force but rather the component of the force which points towards the center during circular motion. For the example of the Ferris wheel, the centripetal force depends on the position. For instance, if the the person is on the top of the ferris wheel, the gravitational and the nor... | {
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If an object falls - regarding air resistance - does the Potential or Kinetic energy get converted into thermal energy as it is falling? I read a paragraph on the transfer of potential energy to kinetic energy and heat from this website:
Even if air resistance slows down the ball, the potential energy is
the same (M... | Heat energy and thermal energy are pretty much the same thing. My science teacher taught me, that because potential energy is related to height, it would be the kinetic energy that is converted into thermal energy.
| {
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What position of the center of gravity can make the front wheels of the car lift off the ground? I have a question regarding the position of center of gravity required to just lift off the front wheel of a vehicle
Consider a vehicle of mass $m$ having a center of gravity at height $h = 0.5m$ from the ground. The coeffi... | I think I understood the reason. I am incorrect in taking the torque of ma directly. This is because ma is the result of the forces acting on the system. Instead I should have balanced the torque about the center of mass, with the equation [4] looking like this
$$mg∗l2−Ftr∗0.5=0$$ [Torque balance about center of mass, ... | {
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How much additional light does Earth receive from the Sun due to Earth's gravitational field? I was reading about how gravity affects light, and that got me wondering how much additional light is collected by the Sun due to the Earth's gravitational field.
Is it a significant amount of light (>1% of total light)? Is it... | Assuming you mean "collected by the Earth"...
These effects are barely measureable when observing the Sun bending light towards itself. Earth bends light even less. The value will be much less than 1%.
The light is red-shifted as it leaves the Sun (effectively becoming less energetic)
It is blue-shifted to a lesser d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/159103",
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Resultant frequency if 3 harmonic notes (a chord) is played If I know the frequency of individual notes being played (let's assume D, F# and A), how do I determine the final frequency if they are played (nearly) simultaneously as a chord.
To put the problem in context, I am writing a program where user inputs are clas... | Here's a minimum working example of a python program which generates a .wav file with a major triad of 440:550:660 Hz using sine waves. Your user input could be used to generate any frequencies for the chord.
import math, wave, array
duration = 1 # seconds
freq1 = 440 # tonic (Hz) (frequency of the sine waves)
freq2 =... | {
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"source": "stackexchange",
"question_score": "3",
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How to visualize the gradient as a one-form? I am reading Sean Carrol's book on General Relativity, and I just finished reading the proof that the gradient is a covariant vector or a one-form, but I am having a difficult time visualizing this. I usually visualize gradients as vector fields while I visualize one-forms w... | In the context of general relativity it is also notable that the manifold is equipped with a metric tensor. This tensor provides a unique way (an isomorphism, s.a. answer by Phoenix87) to map covectors to vectors. The components are computed by index raising/lowering, e.g. for a given covector $w$ with components $w_i$... | {
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"source": "stackexchange",
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Mass in special relativity? Is the mass of a object at rest defined by $$E=mc^2$$
where $m$ is the rest mass. I.e. does the rest mass include every thing from thermal to gravitational potential energy and every other possible energy that it could have at rest. And thus if we write the following:
$$total\ energy=mc^2+p... | The mass term includes all internal "energies". Heating up a body increases the internal kinetic energy. Binding energies also contribute to the mass (when nuclear fission occur, energy is freed and the products of the reaction are lighter than the original element), and this include any bond due to the fundamental for... | {
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Modeling the motion of a bouncing ball I'm writing a program that displays a line of text, and animates a ball that bounces from syllable to syllable (like a sing-along). The program knows the location of each syllable, and it knows at what time the ball should be at each syllable.
I have a set of equations that work O... | You need the position of the ball $(x(t)$, $y(t))$ for $0<t<1$ if at $t=0$, the ball was thrown with initial velocity $(v_x,v_y)$ at the position $(x_0,y_0)$ in a gravitational field of acceleration $\overrightarrow{a}=(a_x,a_y)=(0,-g)$. The velocity has to be calibrated in order to make the ball arrive the point ($x_1... | {
"language": "en",
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What would be the most general effective Lagrangian involving one Higgs and two gluons? Two different possibilities come into my mind
$\mathcal{L}\sim{}HG_{\mu}G^{\mu}$
where $G^{\mu}$ is the gluon field and $H$ the Higgs, or either
$\mathcal{L}\sim{}HG_{\mu\nu}G^{\mu\nu}$
Where $G_{\mu\nu}=\partial_{\mu}G_{\nu}-\parti... | First of all, since we are talking about an effective theory, there are infinitely many terms. Since the theory does not have to be renormalizable, we can include all operators with $D>4$. So I think you want the easiest one, namely only one additional operator giving you the $Hgg$-vertex.
This would, as you say correc... | {
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Can a conservative field produce a torque? I am asking whether the following Lagrangian for a point moving in a conservative field, can be correct :
$L(r, v, \omega) = \frac {mv^2}{2} + \frac {I \omega^2}{2} - U(r)$.
$r$ is the distance between the equipotential surface on which the movement begins and the equipotenti... | I'm not sure about the notation, so there will be a bit of guessing here. I assume $v = \dot r$, so the kinetic term can be interpreted to be that of a point moving on a plane, described by polar coordinates. Now take any radial potential, which by the rotational symmetry generates a central field. Let us consider Kepl... | {
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Advection operator How are exactly $u_j\partial_ju_i$ and $u_i\partial_j u_i$ related?
And what is their relation to ($\boldsymbol{u}\cdot\nabla)\boldsymbol{u}$ and $\boldsymbol{u}\cdot(\nabla\boldsymbol{u})$ ?
I ask this because:
$$[\mathbf{u}\cdot(\nabla\mathbf{u})]_{i}=u_{j}\partial_{i}u_{j}=u_{x}\partial_{i}u_{x}... | The problem is in the way you wrote your last equation as a matrix multiplication.
You have
$$ [ \textbf u \cdot ( \nabla \textbf u) ]_i = u_j (\partial_i u_j) = (\partial_i u_j) u_j, $$
so if you want to write this in matrix form you have to multiply the vector $\textbf u$ at the right, as a column vector, i.e.
$$[\ma... | {
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How does a supersonic flight speedometer work? I'm sure today they can use GPS and radar, but I was pondering the queation when I saw a film clip of a vintage analog dial labeled in mach number. I'm supposing that the usual way of measuring the pressure drop of the air flow would not work in this case. So what does?
| If we consider a pitot-static probe in supersonic flow we get something that looks like (source):
The probe measures the stagnation pressure in the part of the probe normal to the flow and the static pressure in the part of the probe perpendicular to the flow. There is a small bow-shock around the tip of the probe. Bu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/160413",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Reversible and Quasi-static processes Do we have any proof that reversible processes are always quasi-static or is it just a fact that hasn't been violated till date? If there is a proof then please provide a link.
| This comes from just definations.
In thermodynamics, a quasi-static process is a thermodynamic process that happens infinitely slowly.
Reversible process:Any process which can be made to proceed in the reverse direction by variation in its conditions such that any change occurring in any part of direct process is exact... | {
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Why is an airplane able to increase thrust without moving? I was just watching some documentaries and saw planes building up power in the turbines without moving. I thought about it and remembered, that this happens before every take off.
So, why is this possible? A planes thrust isn't related to the ground, but to the... | In fact, for a short field take off, the pilot's operating handbook instructs you to do exactly that. The brakes are designed for that.
| {
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How does "pushing-start" a dead-battery manual car work? A few days ago the battery of my car went (almost) dead. As it is a manual car, my father once told me that the way to get it going without jumper cables was to push it or let it roll down a hill, sink the clutch, shift to 2nd gear and then let go the clutch.
Aft... | In the days before Electric Rear Window Defrosters, cars still had generators, you could push start the car with a completely dead battery. Generators make electricity, whereas today's cars are equiped with alternators.
Alternators take electricity to make more electricity. They have a much higher output for today's c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/160718",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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The velocity of the flowing coming out of the balloons? Last day , when i was working on two interconnected balloons , a question was kicking my brains !!! This is the explanation of the question:
First , suppose a system that composed of two spherical membranes filled with air (two balloons have different initial volu... | The air flow rate through a tube is approximately given by the Hagen-Poiseuille equation. If the pressure difference between the two ballons is $\Delta P$ then the HP equation gives the volumetric flow rate $Q$ as:
$$ Q = \frac{\pi r^2}{8\mu \ell} \Delta P $$
where $r$ is the radius of the pipe, $\ell$ is the pipe leng... | {
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Which modes are excited when a drum is struck? I've been searching quite extensively for an answer to this question but I cannot find anything definitive. The most I can see is that "one or several" modes become excited, but this is never parameterized by any relevant factors. I imagine it depends on the location of th... | The question
mixes membranes and drums.
Hitting a membrane is different from a drum, because drums
have (more or less, depending on type of drum) a strongly
coupled air volume controlling the vibration of the drum.
A turkish kettle drum will have almost no higher modes,
whereas those membranes as used by Inuit peo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161062",
"timestamp": "2023-03-29T00:00:00",
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Does the escape velocity of a black hole exceed $c$ *before* a singularity is created? As an offshoot of the question Can we have a black hole without a singularity? I'm curious if the point of no return at which the massive object is condemned to become a singularity happens before its escape velocity is greater than ... | To add to John's very good answer, I'll emphasise a point that makes identifying the time when a black hole forms slightly strange: it depends on knowing the entire future evolution.
The black hole interior consists of the points from which you can't escape to infinity. But to be sure that you can escape requires knowi... | {
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If the solar system is a non-inertial frame, why can Newton's Laws predict motion? Since there is no object in the universe that doesn't move, and the solar system likely accelerates through space, how did Newton's Laws work so well? Didn't he assume that the sun is the acceleration-less center of the universe? Shouldn... | Newton's laws work well but if one considers the relativity theory, one finds things not explained by Newton's laws. A well-known example is the "anomalous" precession of the perihelion of Mercury, explained by the general relativity.
| {
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"source": "stackexchange",
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Textbook recommendation for computational physics Can anyone recommend some good textbooks for undergraduate level computational physics course? I am using numerical recipe but find it not a very good textbook.
| I like Bill Gibbs' book Computation In Modern Physics for a couple of reasons (aside from having taken the course from the author):
*
*After introducing basic tools (difference approximations to differential equations, numeric quadratures (i.e. integrals), and eigenvalue problems in a matrix form) it moves right on ... | {
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$v^2 = 2ax$ or $v^2 = ax$? As far as I am aware, $v^2 = 2ax$ is the formula to find the velocity in various questions.
If kinetic energy = work,
$$\frac{1}{2}mv^2=Fx$$
$$mv^2=2max$$
$$v^2=2ax$$
We use this formula to solve some questions in school.
But when i just fiddle around with basic formulas i get this.
$$x/v = t... | In your second derivation, the correct formulas are
$$\begin{align}
\frac{\Delta x}{v} &\approx \Delta t &
\frac{\Delta v}{a} &\approx \Delta t
\end{align}$$
I'm sure you can easily find some examples to show you why $x/v = t$ and $v/a = t$ don't make any sense. Anyway, when you put these together, you get $v\Delta v \... | {
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Mullins effect in the elastic material I was thinking on a experimental question, but I couldn't get the answer:
How can we measure how the Mullins effect influences in the pressure inside a balloon? (I mean that, if there is a formula, tell me!)
| A good way to measure pressure inside a balloon is to create a setup with a balloon, a manometer (long thin liquid filled U shaped tube), and a three way valve. You increase the pressure in the balloon by pumping it up, then measure the pressure with the manometer. Keep increasing the pressure and measure the diameter ... | {
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Deutsch's Algorithm. Unitary Transform $U_f$ I'm studying Deutsch's algorithm and I keep coming across the phrase along the lines of "There is a unitary transform (a sequence of quantum gates) $U_f$ that transforms the state $|x\rangle |y\rangle \rightarrow |x\rangle |y \oplus f(x)\rangle$".
I was trying to figure out ... | Your $U_f$ must depend on $f$. Let's consider the two trivial examples:
*
*$f$ is the zero-function. In this case, $U_f$ is just the identity.
*$f$ is the one-function ($x\mapsto 1$), then $|x\rangle|y\rangle \mapsto |x\rangle|y\oplus 1\rangle$, then $U_f$ is a NOT-gate on the second qubit.
Just a note: The whole ... | {
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Metric tensor in SRT I just read on this webpage that we have (click me) $g_{\alpha \beta} = g_{\alpha}^{\beta} = g^{\alpha \beta}.$
Now, although I understand that the first and the last one are equal, I don't think that the term in the middle is the same as the other two, cause we should have $(g_{\alpha} ^{\beta}) ... | First a word on notation. In special relativity, the Minkowski metric is $\eta_{\alpha\beta}$. The general relativity curved metric is $g_{\mu\nu}$. A lot of texts that only use the Minkowski metric don't make that distinction for some reason. However, when you get to string theory and there are four different metrics ... | {
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Is $∣1 \rangle$ an abuse of notation? In introductory quantum mechanics it is always said that $∣ \rangle$ is nothing but a notation. For example, we can denote the state $\vec \psi$ as $∣\psi \rangle$. In other words, the little arrow has transformed into a ket.
But when you look up material online, it seems that the ... | It is just a label. More conventional notation uses indices for the same purpose, but the latter gets unwieldy if you need more elaborate qualifiers.
One particular application is labeling states by occupation number (cf second quantization).
| {
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Laser, wire, and a circle of light So, when I point a laser at a piece of wire (pointed at a specific angle), a circle of light appears on a wall behind it (see image below). I am trying to see why this happens and if there are any readings on this. Could anyone give some tips on what I should search for or any referen... | So I did it myself and figured it out. It's just really simple reflection.
Basically the wire acts as a mirror, albeit a curved one. Because the light from a laser is straight, we won't have messy light. When a laser reflects off of a flat surface, it keeps going straight. However when it reflects off a small curved s... | {
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Proof that all primitive cells have the same size A primitive cell of a crystal lattice is a set $A$ such that two copies of $A$ which are translated by a lattice vector do not overlap and such that $A$ tiles the entire crystal.
I have read (for example in the german “Festkörperphysik” by Gross, Marx), that all primit... | Let $\mathcal{L}\subseteq\mathbb{R}^n$ be a lattice with a basis $B\in\mathcal{R}^{n\times n}$ and $F\subseteq\text{span}(\mathcal{L})$ be measurable. $F$ tiles $\mathcal{L}$ iff
*
*$(x+F)\cap(y+F)=\emptyset\,\forall x\neq y\in\mathcal{L}$, and
*$\mathcal{L}+F=\text{span}(\mathcal{L})$
It is trivial to show (I'll... | {
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What is the speed of sound in space? Given that space is not a perfect vacuum, what is the speed of sound therein? Google was not very helpful in this regard, as the only answer I found was $300\,{\rm km}\,{\rm s}^{-1}$, from Astronomy Cafe, which is not a source I'd be willing to cite.
| Just want to bring up that most answers seem to be taking "space" to be a nice uniform medium. However, even within our own galaxy, conditions vary wildly. Here are the most common environments in the Milky Way:
*
*Molecular Clouds, $\rho\sim 10^4\,{\rm atom}/{\rm cm}^3$, $T\sim 10\,{\rm K}$
*Cold Neutral Medium, $... | {
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Why would two protons repel? I understand that two protons would repel due to them both being positively charged, however, wouldn't the strong force act on the two protons pulling them together? Would this mean that in this case the electromagnetic repulsive force is greater than the strong force? If so why? If not why... | Yea, a proton and neutron stick together, but two of the sam kind don't. You don't get neutron balls even with only the interneucleon force and no electric repulsion.
I asked about it some years ago in a physics on-line forum, long before StackExchange. Ended up getting a textbook and eventually learning that "the fo... | {
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What does the statement "the laws of physics are invariant" mean? In the first paragraph of Wikipedia's article on special relativity, it states one of the assumptions of special relativity is
the laws of physics are invariant (i.e., identical) in all inertial systems (non-accelerating frames of reference)
What does ... | When constructing equations of motion which are the reflection of laws of nature so to speak, we must make them Lorentz invariant and invariant to spacial rotations. This means that they must have the same form under these transformations. One example is construction of a field theory, in which you begin by forming an ... | {
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Is the Liénard-Wiechert electric field conservative? I know that an accelerated charge should emit an e.m. field and loose energy. Therefore, the Liénard-Wiechert (L.W.) electric field of an accelerated charge should be non-conservative.
But I checked first what happens when the charge is not accelerated, i.e. moves w... | An Electric Field is only conservative if it is static. The propagation of E with a L-W field contradicts this, so it is not conservative.
| {
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Is $ds^2$ just a number or is it actually a quantity squared? I originally thought $ds^2$ was the square of some number we call the spacetime interval. I thought this because Taylor and Wheeler treat it like the square of a quantity in their book Spacetime Physics. But I have also heard $ds^2$ its just a notational dev... | It is a notational device. Note that in $(-+++\cdots)$ the proper length
$$ds^2=g_{\mu
\nu}dx^\mu dx^\nu$$
is negative for timelike $dx$. Thus $ds\equiv \sqrt{ds^2}\in\mathbb{C}$. It (the square root) thus has no physical meaning.
| {
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selection of p substrate as wafer in typical cmos process flow why is p-substrate typically used as wafer in the typical cmos process flow? why not n substrate?with respect to memories, Has it got anything to do with the aplha-paritcle radiation induced errors (soft errors) ? please explain.
| The mobility for electrons is generally higher than for holes, considering typical doping profiles, etc. Therefore, it is easier to achieve higher signal speeds when the conduction flow travels through an n-type silicon. Hence, you would want the substrate to be p-type since you will be doping in the conduction chann... | {
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What physical evidence is there that subatomic particles pop in and out of existence? What physical evidence shows that subatomic particles pop in and out of existence?
| This phenomenon is called Quantum Fluctuations or vacuum energy and it could be described theoretically by Heisenberg uncertainty relation with the energy term.
One of the physical evidences of such phenomenon is ''Casimir effect'' .
when two uncharged plates are put close to each other they exhibit a repulsive force... | {
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Probability wave intuition Basically I am really new with this term. It all came before me when I was reading the Standard Double-Slit experiment.
An excerpt from Principles of Physics (by Resnick,Halliday,Walker) :
. . .by probability wave, to every point in the light wave, we can attach a numerical probability per u... | I think the answer you are looking for is from "Probability Amplitude" on Wikipedia:
Probability amplitudes have special significance because they act in quantum mechanics as the equivalent of conventional probabilities, with many analogous laws, as described above. For example, in the classic double-slit experiment, ... | {
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Ball's opposite rotation caused by friction Assume that you push a ball like in the picture (along the red line) with your hand with a some force.
The ball will move forward while its rotating in this way:
And after some movement, the ball will stop translating(still rotating) and it again moves back towards you. How ... | According to the picture, the ball has acquired a spin which can be described by an angular velocity $\boldsymbol\omega$ emerging from the screen. The contact point is then moving with velocity $\mathbf u=\boldsymbol\omega\times\mathbf r + \mathbf v_{cm}$. As long as this is not zero (i.e. the ball is not rolling), you... | {
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Could dark energy just be particles with negative mass? The title speaks for itself.
Dark matter: We see extra attractive force, and we posit that there are particles which create such a force, and use the measure of that force to guess their locations.
Dark Energy: We see extra repulsive force.
Only thing is, dark ene... | “If dark energy would consist of particles, it would dilute with the growing radius of the universe to the third power, since the total number of particles would stay the same while the volume increases. What observations found was that dark energy rather behaves like a constant which does not thin out, that's why it i... | {
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What information do $|\psi(0)\rangle$ and $|\psi(t)\rangle$ represent? I am starting to feel comfortable with the role of the unitary operator in quantum mechanics. For instance, one of the equations I have seen is
\begin{equation}
|\psi(t)\rangle = U(t) |\psi(0)\rangle
\end{equation}
I understand what a unitary oper... | The state vector ket describes all that can be known of the system at future time. Unlike classical mechanics where two quantities velocity and position are required to describe the future here a single quantity does it, done at the price of requiring the wave function to be complex. The representation in which you des... | {
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Is rate of change of velocity wrt distance and rate of change of velocity wrt time the same thing? Is rate of change of velocity wrt distance and rate of change of velocity wrt time the same thing?If both are same can we define acceleration in the former way?
Please explain using calculus.
| No they aren't. Suppose we have some velocity $v(t)$. The differential with respect to time is just the acceleration:
$$ \frac{d}{dt}v(t) = a(t) $$
Now differentiate it with respect to distance $s$:
$$ \frac{d}{ds} v(t) = \frac{dt}{ds}\frac{d}{dt} v(t) = \frac{dt}{ds} a(t) = \frac{a(t)}{v(t)} $$
| {
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Why is the bottom part of a candle flame blue? What’s the explanation behind the bottom part of a candle flame being blue? I googled hard in vain. I read this. I don’t understand how it’s explained by the emission of excited molecular radicals in the flame. I read that a radical is a molecule or atom which has one unpa... | In a lit candle, when gaseous candle wax reacts with the oxygen in the air, the atoms will be unstably excited. To be stable, the excited electrons will relax to the ground state by emitting photons with energy equal to the energy difference between the 2 states. The photons’ energy doesn’t change much, so the waveleng... | {
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Spacelike to timelike four vectors First at all, let me just say that I'm not a Physicist, I study mathematics. So, I have this question. If you have a spacelike four vector, is there any transformation that could change it to be a timelike four vector? I mean, I know that every Lorentz Transformation (LT) preserves th... | Let's think about this in terms of light cones. At any given point in space-time, we can consider the set of all possible light rays which pass through that particular point. If one now considers the set of all possible tangent vectors to those light rays (these are of course, null) then they form the light cone at tha... | {
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What can take kinetic energy, transform it into potential energy when pressed on, and put back out as kinetic energy when released (besides a spring)? A spring can only hold so much of the kinetic energy. For example, a 1 cm spring can hold less than 5 J. Is there anything that can hold a large amount of energy but be ... | A 1 kg object on the surface of the Earth can store up to $G\frac{M_e}{r_e}\cdot 1$ $kg = 6.3 \times 10^7$ $J$ in gravitational potential energy as long as your pressing direction is up and you press it up far enough.
A compressible thermodynamic system can theoretically hold an infinite amount of energy. See for examp... | {
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Wheel slowing down with constant acceleration A wheel of radius $R$ spins about its center with a centripetal acceleration of $v^2/R$.
I get that the acceleration at all points on the rim of the wheel point towards the center of the wheel. But, what happens when the acceleration of the wheel is slowing down?
Let's say ... | If the wheel is undergoing some sort of angular acceleration, then the magnitude of its velocity - its speed - would be expressed as a function of time, $v\equiv v(t)$.
So what does this mean for the period of rotation? That means the period also becomes a function of time. However, since the period still represents th... | {
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"Find the Lagrangian of the theory" I've heard a few of my professors throw around the term "finding the Lagrangian of a theory". What exactly is this referring to. From what I understand it seems that you determine invariances (symmetries) and they give you a hint for what your Lagrangian is. Furthermore there is more... | Comments to the question (v2):
*
*"Find the Lagrangian of the theory" typically means that you are given the (classical) equations of motion (EOMs) of some physical system, and are supposed to find the action functional $S$ so that the EOMs are (parts of) the Euler-Lagrange (EL) equations for $S$.
*Note that an act... | {
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$\mathrm{\rho^0}$ meson decay via the weak interaction? Of course, the $\mathrm{\rho^0}$ meson can decay in $\mathrm{\pi^{+}\ \pi^{-}}$ through the strong interaction. Using Feynman diagrams, I cannot understand why the same decay couldn't happen through the weak interaction. I attach the diagram I've drawn.
Strong dec... | As far as I understand, the decay of an anti-u quark into an anti-d quark will emmit a $\mathrm W^+$ boson. But the anti-u and d quarks into which the boson would decay, have charges $-2/3$, $-1/3$ respectively. So their total charge will be $-1$. A $\mathrm W^+$ boson cannot decay into two particles whose sum equals $... | {
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Why doesn't the speed of the wind have an effect on the apparent frequency? A boy is standing in front of stationary train. The train blows a horn of $400Hz$ frequency . If the wind is blowing from train to boy at speed at $30m/s$, the apparent frequency of sound heard by the boy will be?
The answer: The frequency rema... | Because that is the result when you examine the process in detail.
For example:
The boy and the train are in a static relationship. The train could sound its whistle for as long as the power source held out. If the boy received more waves per second than the train produced, where would the extra waves come from?
Or:
... | {
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Conservation and forces/energy Are there really non-conservative forces in actuality ?
Feynman states in his book that in fact, all forces are conservative ( originating from conservative vector-fields ), provide we look close enough ( microscopic level ). The reasoning is that we can't allow non-conservative for... | There are macroscopic forces that admit no description in terms of a potential, for example, any friction force proportional to the velocity of a moving object as path-dependent integral, and is hence non-conservative.
But we know the macroscopic description is not the fundamental description. In terms of the interacti... | {
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Can one define wavefunction for Bogoliubov quasiparticle excitation in a superconductor? Wavefunction is essentially a single particle concept. It is easily extended to multiparticle system as follows- if one has say five electrons the wavefunction of this five electron state is any completely antisymmetric function of... | The localization of Majorana zero modes has a well-defined meaning: consider a Kitaev chain with two ends. Because of the zero modes, there are two nearly degenerate ground states, let us call them $|0\rangle$ and $|1\rangle$, which have opposite fermion parities. They are localized as "single-particle wavefunctions" i... | {
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Eigenstates into which a system can be projected after a measurement I'm currently reading Dirac's Principles of Quantum Mechanics, on page 36, he says:
Another assumption we make connected to the physical interpretation of the theory is that, if a certain real dynamical variable $\xi$ is measured with the system in ... | When you measure an observable over a certain state, any possible outcome lies within the physical spectrum of the observable itself (which can be shown to coincide with the algebraic notion of spectrum for linear operators). So after the measurement has given you a value, say, $\lambda$, any other measurement on the s... | {
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How could a cord withstand a force greater than its breaking strength? How could a 100 N object be lowered from a roof using a cord with a breaking strength of 80 N without breaking the cord?
My attempt to answer this question is that we could use a counter weight. But I don't really understand the concept behind coun... | The simplest approach (and what the person asking this question probably was getting at) is to use a pulley like so:
The weight of the object is now shared between the two sides, with each carrying a 50 N load. You end up using twice as much cord. The other advantage is that you now have a "mechanical advantage" and y... | {
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What is the correct way to treat operators that has "time" in QM? I don't know if this question has already been resolved but considering that $i\hbar\partial_t$ is the energy operator, and $\partial^2_t$ is the waves operator (or helmholtz), I can't accept that $t$ itself isn't an operator
What is the argument here th... | You are touching on the subject of relativistic quantum mechanics where time and space $(t,x)$ are handled on the same footing as operators. The accepted description is to not use quantum wavefunctions as describing one particle but rather the state of a quantum field. Doing this turns into the subject of quantum fie... | {
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What is basically the difference between static pressure and dynamic pressure? What is basically the difference between static pressure and dynamic pressure?
While studying Bernoulli's theorem, I came before these terms. The law says:
When the fluid flows through a small area, its pressure energy decreases & kinetic e... | Under common assumptions and ignoring potential energy, static pressure is the expression of the fluid's temperature (internal energy) and dynamic pressure is the expression off the fluid's velocity, so if the fluid is brought to a rest adiabatically, their sum is equal to the stagnation pressure. The stagnation pressu... | {
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Calculate the approximate number of conduction electrons So i have the following problem: A cube of gold 0.1 meters on an edge, calculate the approximate number of conduction electrons whose energies lie in the range from 4.0 ev to 4.025 ev.
But I'm not clear on how to start. could someone offer any help?
| mmm. I don't think that's quite right. I'd rather use the equation for the number of electrons in any given energy state,
$N(E) = \int_0^{\infty} \frac{1}{e^{(E - E_F) / K_B T}} \frac{V (2 m) ^{3 / 2}}{2 \hbar ^3 \pi ^2}\sqrt{E} dE$ where $E_f$ is the fermi energy and $E$ is the energy of the electron. To do this, ... | {
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When does Pauli's exclusion principle kick in? Imagine that I prepare a fermion in the $\left|\uparrow \right\rangle$ state and a second one far away in the $\left|\downarrow \right\rangle$ state and set them in a path for collision.
According to Pauli's exclusion principle, the composite wave function must be anti-sym... | Let's ignore the position-momentum observables. Your definition of far away has a precisely definition. We can treat one electron and ignore the another. So we don't have to worry about pauli principle. When we want to collide this two electrons, and no more work in far away paradigm, we need to define some length when... | {
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Understanding magnetic force on charged particle if we put any charged motionless or static particle in the constant magnetic field, then why does it don't feel a magnetic force?
Mechanism by which electric and magnetic fields interrelate
I have read the above article which suggested that the magnetic field is the re... | Magnetic field is not a type of electric field, though the 2 are intimately related. Otherwise, every charged body kept in a magnetic field would experience a magnetic force and basically a lot of stuff would go out of control.
(For example, if you kept a magnet close to a circuit, then there would be a electric fiel... | {
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Are electrons miniature black holes? For something to be a blackhole, it must have gravity and the radius must be smaller than the schwarzschild radius for its mass.
-Electrons have gravity
-Electron are theoretically believed to be infinitely small points
Since it has gravity it is capable of being a black hole. Since... | Well, according to the wild ER=EPR conjecture by Maldecena and Susskind, two entangled electrons are connected by a quantum wormhole. The mechanism and details of this quantum wormhole are left unspecified by these authors, though.
| {
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Do transferring energy and applying force to a body imply same? Do transferring energy and applying force to a body imply same meaning? When we say, "I throw a ball using my pushing force so on the other hand, can I say that I transferred my kinetic energy to the ball therefore it became moving.
| No. In a uniform circular orbit the orbiting body maintains constant energy while a constant force, only changing in direction, operates on that body.
Kinetic energy changes when a net force is applied in the direction that an object is moving. It will reduce if the net force opposes velocity, or increase if net force ... | {
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Can mass be uncertain? If you can have uncertainty in momentum, then wouldn't you have uncertainty in mass and velocity?
Why can't mass be uncertain?
| Uncertainty is a property of observables. Mass is not normally taken to be an observable, so it does not obey uncertainty relations.
Why isn't mass an observable? There is a superselection rule that forbids it in the presence of reasonable symmetry assumptions. See the discussion here for more.
EDIT: In "true" relativi... | {
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What observations would be needed to falsify the law of conservation of energy? I've been doing some thinking, and began to wonder: What observations have led us to the conclusion that ‘energy can neither be created nor destroyed’?
Essentially, this means that the big bang supplied our universe with all the matter that... | Conservation of Energy can be derived if one accepts that $F = ma$. I won't include the derivation here unless you ask. This means that to prove Conservation of Energy wrong, one must prove $F = ma$ wrong. This could be attempted in a variety of ways. One such way would be applying a force to an object and noticing the... | {
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Flux linkage of 2 coils in series I have a question about magnetic circuits. I am an engineering student, therefore I will neglect some minor errors.
There is a simple magnetic circuit with 2 coils ($C_1$ & $C_2$), with $N_1$ & $N_2$ turns and $i_1$ & $i_2$ currents. Coils are in series and connected with 1 magnetic co... |
I know that magnetic circuit resembles electric circuits.
Yes, but the analogy works between certain specific quantities, and you are considering the wrong ones: the electromotive force does not correspond to the flux linkage, but to the magnetomotive force.
For lumped magnetic and electric circuits, the main corresp... | {
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Can an object appropriately isolated from its surroundings become colder than its surroundings? Consider a sealed box, well-insulated on all sides, except for the lid which is transparent to infrared. An object is placed inside the box and the box is evacuated (purpose being to thermally isolate the contents of the box... |
With nothing but clear dark sky above, I assume there is nothing to radiate appreciable heat back into the box and maintain the object's temperature.
In this case there wouldn't really be an "ambient temperature" though.
To elaborate: The inside of the box would cool down until thermal equilibrium is reached between ... | {
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Predicting Polarity of capacitor in the given diagram I have to determine the polarity of the Capacitor in the given diagram.
I Approached the problem as follows:
When Magnet 1 moves with its North pole towards the coil, emf is induced in the coil as the magnetic flux through the coil changes. So, when seeing from the ... | The best way to think about this is imagine the capacitor plates A and B to be behind the paper plane and then think about the direction of current induced. Observe it from the right magnet's side whose South Pole is approaching so the face of coil facing that South Pole will itself produce clockwise current in the coi... | {
"language": "en",
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What is the dyad corresponding to a stress tensor? (As I understand it ... qualifies every sentence in what follows).. a stress tensor is a rank 2 tensor that maps a unit vector normal to a surface to the stress (or traction) vector corresponding to that surface. A rank 2 tensor can be represented by a 3x3 matrix, and... | A rank-2 tensor is a linear combination of dyadic products, simply because the space of all such tensors is spanned by the dyadic products of the basis vectors of the underlying vector space. Each dyadic product is also known as a rank-1 operator, where rank here refers to the matrix rank rather than the order of the t... | {
"language": "en",
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If a bullet is fired vertically upwards, when it comes back does it fall to the same spot? What I'm basically asking is that if a body is projected with sufficiently high velocity so that it doesn't escape from the earth's gravitational field but reaches an appreciable height with respect to the radius of the earth, th... | Even if I ignore wind and the drag forces and only consider the rotation of the earth the bullet will not hit the ground at the same place from where it was projected.
There will be Coriolis effect.
Coriolis effect: The Coriolis effect is a deflection of moving objects when the motion is described relative to a rotatin... | {
"language": "en",
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Why is most probable speed not equal to rms speed for an ideal gas? The rms speed of ideal gas is $$\mathit{v_{rms}} = \sqrt{\dfrac{3RT}{M}}.$$
The most probable speed is the speed where $\dfrac{dP(\mathit
{v})}{dv} =0$ where $P(\mathit{v})$ is the probability distibution. Solving for $\mathit{v}$, we get $$ \mathit{v_... | We're used to thinking of "most probable" and "mean value" as the same thing, but it need not be so. It's worth remembering that the "expectation value" of a six sided die is 3.5, but this is not a very probable result. You might object that this is due to discrete effects, but consider this example: you have two ident... | {
"language": "en",
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Why are solar panels blue, rather than black, when black absorbs more light? This is an image of a solar panel array, courtesy of Wikipedia.
Some of these look rather black, but most of them are blue.
As far as I know, solar panels work by absorbing "light energy", and then converting this to "electrical energy". Some... | The colour you're seeing is from the very small fraction of light that the panels are reflecting. The vast majority of light is being absorbed to generate electricity.
Why some of the panels appear slightly blue while others don't I don't know. Presumably there must be small differences in the manufacturing process. Th... | {
"language": "en",
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Distribution of dark matter in galactic halos Often dark matter around galaxies is referred to as a 'halo'. I've seen the galactic rotation curves, but I'm having trouble visualizing how the dark matter is distributed for a typical rotating galaxy.
I'm familiar with the expected relation $v \approx \frac{1}{\sqrt{r}}$ ... |
Is there a function with respect to r that can describe the distribution of dark matter in galactic halos?
Yes, it is called the NFW-profile and it looks like this:
$$\rho_{(r)}=\frac{\rho_0}{\frac{r}{r_s}\left(1+\frac{r}{r_s}\right)^2}$$
where $\rho_{(r)}$ is the dark matter density inside the radius $r$, and $\rho_... | {
"language": "en",
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Electricity is the movement of electrons or ions? Electricity is the movement of electrons from one atom to another or the movement of charged negative particles (ions)?
| An electric current is the flow of electric charge. But electric charge is not an entity, it is a property that must be 'carried' by a charge carrier.
An electron current, the flow of electrons, contributes to an electric current since the electron 'carries' negative electric charge. However, an electric current is n... | {
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Why can't we define a unique wavelength for a short wave train?
Here we encounter a strange thing about waves; a very simple thing . . .namely, we cannot define a unique wavelength for a short wave train. Such a wave train does not have a definite wavelength; there is an indefiniteness in the wave number that is relat... | I would say that an answer is that length of wave packet and width of spectrum are related by:
$\Delta\omega \Delta t\approx 1$
"Width of spectrum" here is characteristic range of frequencies that signal contains, that is width of Fourier transform of the signal. Infinite sine wave contains only 1 frequency, that is it... | {
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Finding the appropriate coordinate transformation given two metrics Given the two-dimensional metric
$$ds^2=-r^2dt^2+dr^2$$
How can I find a coordinate transformation such that this metric reduces to the two-dimensional Minkowski metric?
I know that $g_{\mu\nu}=\begin{pmatrix}-r^2&0\\0&1\end{pmatrix}$ (this metric) and... | You can also do the following, which may not be as general as you want it, but the idea might be usefull for other problems. You already know that the given metric is Minkowski metric in different coordinates, so look at the null geodesics. In the usual coordinates $(t',x')$ they are given by $x'\pm t'=const$. Then fin... | {
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White, is it a colour or absence of colours? Our chemistry sir and we had an argument today at the lab, he says that white actually is not a colour, it is the abscence of colour, but we say that it is a colour and we gave the following point to substanciate our point that white is a colour:
When we see an object in red... | we define color based on which range of wavelength it reflect. as u said a red object is red because it can only reflect red , so it is not any other color. maybe we could call black colorless, and i think our teacher just used a conventional form of speech (dont u think?)
ask our teacher what he would call the colour ... | {
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Frequency dependence of the speed of light in air According to this link, the speed of light of different colors in a medium should be different. But if the refractive index of light in air is 1 then this means that the speed of light in air and vacuum should be the same. Could anyone help me out here?
Thanks
| You have two different concepts intertwined in your question. You begin by asking about the speed of light in a medium varying with color (i.e. wavelength). This phenomenon is called dispersion and it is present in all materials including air. Dispersion shows up in many places in the field of optics, but the case y... | {
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Time dependence of the Lagrangian of a free particle? I am working through Landau's book on Classical Mechanics. I understand the logic and physics of isotropy and homogeneity of space-time behind the derivation of the Lagrangian for a free particle, but I am confused regarding its time dependence. When we calculate th... | You say " When we calculate the action as the integral of the Lagrangian for a wiggly trajectory, the velocity is obviously dependent on time and so is the Lagrangian".
How exactly is the velocity dependent on time? Before applying the least action principle and find the trajectory of the object, we have a Lagrangian ... | {
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Mass, energy, and entropy. I have a seemingly simple question about the relation between these three that for some reason doesn't make sense to me. If entropy is the disorder of a system, then a low entropy state is one of higher energy. As we know, mass is energy. From here we must say that the more mass something has... | A quote from comments:
how is a higher temp and faster moving particles not an increase in available energy and therefore a decrease in entropy?
Maybe higher temperature means more available energy and more unavailable energy! It definitely sometimes means that.
We have devices that decrease entropy of heat energy, ... | {
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A Proposed Improvement to the Diet Coke and Mentos Experiment I am sure most of you are aware of the Diet Coke and Mentos craze - put a few mentos in a bottle of diet coke and whoosh!
Equally, I am sure most of you are aware that this occurs because the gas is able to form bubbles in rapid succession at 'nucleation sit... | Yes you can :) How did it work out for you?
| {
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Spectral lines and QM In the various presentations I've seen so far in atomic physics of series such as the Balmer series, the wavelength of each spectral line is definite - but in QM, free particles have no definite energy if I understand correctly: none of the photons in a beam of photons that would interact with the... | Of course the photon will have an amount of energy and that is radiation energy which if defined by Planck's equation. Radiation energy is also related directly to wavelength,frequency and wavelength number.The higher the energy, the less is the wavelength ( all this from Planck's equation). What Heisenberg equation is... | {
"language": "en",
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Does the Earth revolve around the Sun? I am aware of this Phys.SE question: Why do we say that the earth moves around the sun? but I don't think this is a duplicate.
In a binary star system, where the masses of the 2 stars are not so different from each other, can we say that each star revolves around the other?
If yes... | Both the the Earth and the Sun orbit around the solar system barycentre. This is defined as the centre of mass of all the bodies in the solar system. Because the Sun contains the vast majority of the mass of the solar system then the barycentre is very close to the Sun. The picture below, from the wikipedia entry on th... | {
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If the Earth's atmopsphere spins with the earth due to friction, why is there no horizontal spiralling drag? Imagine a bucket of paint with a spinning ball in it. The paint would form a spiral and would not all move in synchronous movement with the ball.
To clairfy - In order for the Earth's atmosphere to appear to us ... | The same happens with the air around the earth, this phenomenon is called the Coriolis effect, and it affects our atmosphere. You also have to keep in mind that there are a lot of other variables to take into account when talking about atmosphere, like the angle of our axis towards the sun, etc...
| {
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Why does Li+ ion move to cathode in Li-ion battery? When Li-ion battery is discharged or being used, the positive lithium (Li+) ions move from anode to cathode through the electrolyte. Meanwhile the electrons move in the same direction through the external circuit. Why does this happen? I mean, why does a Li+ ion get a... |
Why does Li+ ion attract to the positive electrode (cathode)?
Let's first see how we define the Cathode and Anode based on electron movement.
A cathode is the electrode from which a conventional current leaves a polarised electrical device.
Now, importantly, Cathode polarity with respect to the anode can be positive ... | {
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Is there a curve for which a particle restricted to move within it under the gravitational force will always exhibit a pure harmonic motion? A simple pendulum, for example, is not isochronous for large amplitudes (that is, the frequency will depend on the amplitude). So a particle confined in a circumference will not... | If you built a surface such that its height was proportional to a horizontal coordinate $x^2$, $h = k x^2$, then the potential energy at point x would be $mgh = m g k x^2$, which is a harmonic potential. In other words: yes, the curve exists and it's a parabola. This assumes uniform $g$, though, I guess if you want to ... | {
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Approximations of the kind $x \ll y$ I have an expression for a force due to charged particle given as
$$F=\frac{kQq}{2L}\left(\frac{1}{\sqrt{R^2+(H+L)^2}}-\frac{1}{\sqrt{R^2+(H-L)^2}}\right) \tag{1}$$ where $R$, $L$ and $H$ are distance quantities.
Now I want to check what happens when:
*
*$H\gg R,L$
*$R,H\ll L$
... | Your final expression is off by a minus sign, and is not what you want. For #1, $H$ is large, so I'd factor $H$ out. For #2, $L$ is large, so I'd factor $L$ out.
When you factor out a large thing, the remaining things are either numbers (which are what they are) or small things. And when something is small you can a... | {
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100°C = 100 K =? I'm in first year. Our class is in lesson " Heat and Thermodynamics". While solving a numerical problem of a reversible engine he told us that 100 degree Celsius is equal to 100 kelvin. I inquired but could not get satisfactory answer. Pleas help me understand it.
Here is the numerical, please consider... | What your instructor has said is right. While taking Temperature differences (delta T), etc. we take x Celcius = x Kelvin, so we can take any delta T value in Celcius in our numericals interchangeably.
| {
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Does the wave/particle duality exist across the entire electromagnetic spectrum? Does the wave/particle duality exist across the entire electromagnetic spectrum?
If theory says so, then to what extent have physicists confirmed by experimental means?
| Wave/particle duality is present across all particles, an equation to show this is:
$$
p=h/\lambda
$$
where p is the momentum of the "particle", lambda is the wavelength and h is Planck's constant. From this it can be seen that anything can be considered a wave, but they must have a very small mass to have a wavelength... | {
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What do spacelike, timelike and lightlike spacetime interval really mean? Suppose we have two events $(x_1,y_1,z_1,t_1)$ and $(x_2,y_2,z_2,t_2)$. Then we can define
$$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 + \Delta y^2 + \Delta z^2,$$
which is called the spacetime interval. The first event occurs at the point with co... | Timelike is when an event is inside the lightcone (as you have mentioned) and as a result, one event CAN affect the other event (there can exist a causality between the two events. E.g. lets say there are two events, where I shoot a laser and another event where someone gets hit by a laser. If they are timelike seperat... | {
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Can net torque $\sum_i\mathbf r_i\times\mathbf F_i$ be expessed as $\mathbf r\times$ (net force) for some $\mathbf r$?
Let $\mathbf F_i$ be forces each of which is applied on $\mathbf r_i$ of a rigid body. Then is there a position vector $\mathbf r$ that satisfies
$$\displaystyle\sum_i\mathbf r_i\times\mathbf F_i =\m... | Let me introduce the notation
$$\sum F_{i,x} = F_x, \ \ \ \sum F_{i,y} = F_y, \ \ \ \sum F_{i,z} = F_z, \tag{i}$$
Since the determinant is zero, there may be indeed, no solution of the system. But if the system of equations has a solution, recall that the body doesn't rotate around a point, but around an axis. So, your... | {
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What is the mass of a sphere? A solid sphere of mass M is rotating along an axis.
We can consider it as a collection of large number of point masses, every point mass is moving with respect to center of mass with velocity which depends on its radius from rotating axis.
Then, according to relativity, the mass of every ... | In relativity (but often not Newtonian physics) there is a huge difference between a static mass distribution and a stationary one. A static distribution is one in which there is no velocity, whereas a stationary one is defined by looking the same at any given time. All static distributions are stationary, but your rot... | {
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Hula-hoop physics What are the important parameters to consider when trying to keep a hula-hoop in the air by spinning it around the waist?
For instance, when shopping for hula-hoops, one can commonly find its diameter and weight, but how do they affect the actual ease of keeping it in the air? What's the physics behin... | The ratio of the circumference of the body and the hulahoop (HH) is an important parameter. The greater the ratio, the more the HH will rotate - and the more it rotates, the greater its angular momentum. When you have an object spinning with its axis vertically, and apply a torque, it will precess - instead of falling ... | {
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Biot-Savart law from relativity Few days ago I came by a derivation of STR from Bio-Savart law. Since then I have been trying to derive Bio-Savart law from STR. The derivation mentioned previously used two parallel current-carrying wires of unit length and used the change of their current density to achieve Lorentz con... | Consider a positive point charge moving in positive $z$ direction at a constant velocity, at that instant when it's at the origin. The magnetic-field lines generated in plane $z=a$ are closed loops, further we observe circular symmetry in the problem about $z$-axis, henceforth the loops are circles.
A image to develop ... | {
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Parity transformation is proper orthochronous? In 3+1 dimensional spacetime the parity transformation is $$P^\mu_{\;\,\nu}=\begin{pmatrix}+1&&&\\&-1&&\\&&-1&\\&&&-1\end{pmatrix}.$$ This is orthochronous but not proper and thus is not the result of compounding infinitesimals.
However, in $(2n)+1$ dimensional spacetime, ... | Parity and Time reversal are by definition elements of the full lorentz group with which you need to supplement the proper orthochronous subgroup in order to be able to span the entire group.
As noted, the proper way to define parity in any dimension is to flip one of the spatial axes. In even space-time dimensions it ... | {
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A cup of water in ZERO gravity What will happen if I try to pour a cup of water in zero gravity, into another empty cup? Will the water come out of the cup? The adhesive force between the water molecules and the interior of the cup should prevent the water from coming out. Is it correct? Or is there something more to t... |
The adhesive force between the water molecules and the interior of the
cup should...
Even in absence of adhesive force, the water will never move in 0-gravity, because there is no up nor down, no force is acting on it.
You can clearly see in this video at 1:15 that in order to get the water out of a plastic cup you... | {
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Deriving the equations for a moving inertial reference frame I assume $c=1$ in the following derivation:
In order to derive the equations for a moving inertial reference frame, I immediately wrote down the following:
$$ x'=Ax+Bt, \tag{1}$$
$$t'= Dx+Et. \tag{2}$$
In order to solve it I would need 4 independent equations... | I am sorry, but I have no time to find your mistake for you. However, I can give you a tip that I am 100% sure would work.
Your mistake can be very easily found by dimensional analysis. Start from the beginning of your derivation and check all formulas. The first one which makes no sense due to dimensions is wrong.
You... | {
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Heuristics for the Hawking mass I have the following definition of Hawking Mass. Given a spacelike 2-surface $S$ embedded in a 3+1-dimensional Lorentzian Manifold $L$,
$$
M(S) := \sqrt{ \frac{\text{Area}(S)}{16 \pi}} \left(1- \frac 1 {16 \pi}\int_S H^2 d_{\sigma_S}\right),
$$
where $\sigma_s$ is the induced volume form... | A small note on the definition. It should be
$$
M(S) := \sqrt{ \frac{\text{Area}(S)}{16 \pi}} \left(1- \frac 1 {16 \pi}\int_S \theta^-\theta^+ d_{\sigma_S}\right),
$$
where $\theta^\pm$ are the divergences along the two null directions. It is equal to what you have written if the 2-surface $S$ lies in a space-like 3D ... | {
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Do photons with a frequency of less than 1 Hz exist? A photon with a frequency of less than 1 Hz would have an energy below
$$
E = h\nu < 6.626×10^{−34} \;\rm J
$$
which would be less than the value of Planck's constant. Do photons with such a low energy exist and how could they be detected? Or does Planck's constant ... | The shortest answer for why such photons "exist" is that whether a given photon qualifies depends on your rest frame. Take your favourite high-frequency photon in the universe, say of frequency $n$ Hertz in your rest frame. With a Lorentz boost $-\beta$, I multiply this by $\gamma (1-\beta)=\cosh\phi-\sinh\phi=e^(-\phi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/170828",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 5,
"answer_id": 3
} |
Average Energy of a coherent state The question is relating to a previous problem concerning the harmonic oscillator.
Determine the average energy < E > in a coherent state |alpha>.
From my understanding the expectation of the energy would simply mean calculating
< alpha| H | alpha>. Where < H > = < T > + < V > for a... |
From my understanding the expectation of the energy would simply mean
calculating < alpha| H | alpha>. Where < H > = < T > + < V > for a
harmonic oscillator. Is my approach valid?
Yes. This is a valid approach. This is what is meant by the expectation value of the energy.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/170920",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
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