Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why a bullet leaves a hole on glass where stone makes scratch? When we throw a stone it breaks the glass with scratches. But when a bullet hits the glass it leaves a small hole(not always) . I want to know the specific reason behind making hole and scratch.
| The stone when hits the glass( like wind shield, or a window pane) the impulse is small as the time of contact to the force applied is more.
But for the bullet the time of contact to the force applied to the glass is small so the impulse of the bullet is large.
The glass is not a solid or liquid entirely. the glass is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/254920",
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Classical Yang Mills vacuum What is the vacuum of classical Yang Mills theory $$\mathcal{L} = - \frac14 F^{a \mu \nu} F^a_{\mu \nu}~?$$ Is it simply $A^a_\mu=0$ for all its components?
| It depends on what you mean by vacuum.
If you mean a field configuration that has $F=0$, then the gauge potential is locally pure gauge (cf. this answer by Qmechanic), so there can only be global obstructions to the gauge equivalence class of the $A$ corresponding to $F=0$ being $A=0$ everywhere. On $\mathbb{R}^{1,3}$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/255077",
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Pressure on the sides of a container? Sorry if this is an incredibly basic question for these categories. Basically, I don't understand these types of problems. I'm sure it's something really simple I'm missing.
Let's say there's an open swimming pool with width $w$, length $l$, depth $d$, and density $\rho$ (equal to ... | You can indeed write $F=\rho gdA$, but the problem is that the force isn't constant throughout the entire area. You need to find an area with constant force, which would be a horizontal strip, because the depth is the same. The force on small strip (at the $w$ side) at depth $x$ with height $\Delta x$ is $\rho g x A=\r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/255425",
"timestamp": "2023-03-29T00:00:00",
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Unpolarized wave, $\Delta\varphi =\Delta \varphi(t)$? I have seen a unpolarized wave defined in a number of places (e.g. here) as a wave such that:
\begin{align}
E_x&=E_0 \cos(kz-\omega t) \\
E_y&=E_0 \cos(kz-\omega t+\varphi)
\end{align}
Where $\varphi=\varphi(t)$ is a random function in time.
My question is why do ... | I'll try to build an answer based on the above comments. There are two things to consider :
*
*Temporal coherence, which has nothing to do with polarization. One simple way to modelize it is the following : imagine you have an incoherent pointlike source that emits EM radiation at some frequency $\omega$. This sourc... | {
"language": "en",
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What is a "Scalar Manifold"? I'm trying to understand a recent paper working within the context of $\mathcal{N}=8$ gauged supergravity with gauge group $\rm{SO}(6)$. There are a number of statements along the lines of:
[...]the scalar manifold parameterized by these 18 scalars is:
$$\mathcal{M}_{18}=[ \rm{SO}(1,1) ... | In general,in a Supergravity theory scalar fields are regarded as the coordinates of a suitable differential manifold with a Riemannian metric irrespective of the multiplet they belong to. The choice of multiplet, the number of supersymmetry and space time dimension set geometrical property of manifold.
Increasing the ... | {
"language": "en",
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What is the difference between these two expressions for the partition function, Z? What is the difference between these two expressions given for the partition function, Z?
$$Z = \sum_{i}e^{-\varepsilon_i/kT}$$
$$Z = \sum_{j} g_je^{-\varepsilon_j/kT}$$
where each energy level has $g_j$ terms of the same energy $\varep... | They are the same expression, just with different accounting of states. (Your energy relation at the end is incorrect.) However, it is sometimes useful to carry the $g_j$ coefficients around, because certain quantities are most easily found by differentiating with respect to the $g_j$. This can even be done when the... | {
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Why the constancy of an observable w.r.t time depends on whether it commutes with $H$ or not? I have been reading Modern Quantum Mechanics by J.J.Sakurai. Under the chapter Quantum Dynamics, the author says if an observable $A$ initially commutes with the Hamiltonian operator $H$, then it remain so for all later times.... | What's special about $H$ is that it generates time translations. This means that operators evolve, by postulate, through Heisenberg Equations of motion
$$
i\frac{\mathrm d}{\mathrm dt}\mathcal O(t)=[H,\mathcal O]
$$
modulo an explicit time dependence. Therefore, if an operator commutes with the Hamiltonian, $[H,\mathca... | {
"language": "en",
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Levitation inside a solenoid Is it possible to levitate something inside a solenoid? If yes, is it possible in any direction (horizontal, vertical)? Also, is it possible when an object is traveling through?
Thanks in advance!
|
Is it possible to levitate something inside a solenoid
Why not? One can levitate a small frog whose mass is less.The skin of most animals are diamagnetic in nature so it repels the external field.One can adjust the mass of the diamagnetic material such that it is repelled by an equal amount of force which increases t... | {
"language": "en",
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Is it possible to have light without heat? I am trying to think of a light source that doesn't generate heat; but I am not sure if such a phenomenon exists.
I am not referring to passive light (such as reflected light, ie, moonlight) but an active light source that does not have heat as a by-product.
Is it possible to ... | There is a phenomenon that generates light without generating heat as by-product*. The phenomenom is called Electroluminescence, and is used in LEDs which are used in many electric equipment (the tiny lights in your computer to let you know it's on).
We can stretch it a bit more with Fluorescence and other forms of cre... | {
"language": "en",
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Baryon / lepton number violation equivalence in Sakharov conditions In the Sakharov conditions for matter-antimatter asymmetry the requirement for the baryon number violation is often interchanged with lepton number violation. In the context of the Sakharov conditions, how is it that baryon number violation can be equi... | In the Standard Model, the baryon and lepton number are accidental global symmetries. However, they are conserved only at the classical level: quantum corrections do not respect them, i.e., they are anomalous.
The interesting thing is that they are violated by exactly the same amount. In terms of currents we write:
$$\... | {
"language": "en",
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How to imagine WiFi signal propagation? When thinking about how the WiFi signal propagates through a household, can I use the following thought experiment?
Assume absolute darkness. Place a strong lightbulb where the WiFi access point is. The illumination that reaches various places in the house is approximately propo... | Hardware hacker CNLohr did a nice time lapse collection of signal strength mapping a 4 foot square in his house, and then a 3d cube with the help of a CNC router table. I saw it on hackaday, his project is here: https://hackaday.io/project/4329-wifi-power-mapping
And he links to a cool video here: https://www.youtube.c... | {
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What are the differences between the differential and integral forms of (e.g. Maxwell's) equations? I would like to understand what has to be differential and integral form of the same function, for example the famous equations of James Clerk Maxwell:
How to know where to apply each way?
Excuse the ignorance, but alwa... | All this tells you is that the fields satisfies both the inategral and the differential equations. The two are related by the mathematical identities called the divergence theorem and Stokes' theorem.
So which do you apply? Well, which ever one you want! If you run into an integral, you use the integral form, and if yo... | {
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Are there physical law that are not unit-free? One of the prerequisites of the Buckingham π theorem is that the physical law in question should be unit-free. I couldn't find an example of a physical law that is not unit-free. Is there such thing?
Added later: Here is a definition from Applied Mathematics by Logan:
The... | I'm not sure if this gives you the answer you want in terms of a rigorous physics explanation, but when I studied dimensional analysis, the main point was to ensure all sides were equal when it came to units.
Essentially, the equations, and laws, needed to be unit-free in order to make sense. You can't be left with som... | {
"language": "en",
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Why are the electric force and magnetic force classified as electromagnetism? I confuse the four kinds of fundamental interactions, so I think the electric force and magnetic force should not be classified as a big class called electromagnetism.
Here is my evidence:
*
*The Gauss law of electric force is related to t... | Regarding 1) observe that there is a pattern in common - namely that there is some region (volume for Gauss and a surface for Ampere) and integral of the source on this region is equal to the integral of the field on the boundary. This is a striking similarity.
2) currents are nothing else than moving charges. So both ... | {
"language": "en",
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How to deal with zero uncertainties? Suppose you measure quantity $x$ with an uncertainty ${\rm d}x$. Quantity $f$ is related to $x$ by $f=x^2$ . By error propagation the uncertainty on $f$ would be ${\rm d}f=2x{\rm d}x$. If a certain point $x$ equals zero then the uncertainty on $f$ would be zero, even if $x$ carries ... | This is a situation where naive error propagation breaks down. Those methods (i.e. giving uncertainty for $f(\mathbf{x})$ for some values $\mathbf{x} \pm \Delta \mathbf{x}$) are based on linear approximation, which fails for $f(x) = x^2$ near $x = 0$.
If you're not too worried about statistics issues, you can use the '... | {
"language": "en",
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What does it mean that the laws of physics are time reversible?
The Universe, as far as we can tell, only operates according to laws
of physics. And just about all of the laws of physics that we know are
completely time-reversible, meaning that the things they cause look
exactly the same whether time runs forwar... | It is not really correct to call them " reversible laws of physics"
Laws of physics lead to mathematical models that describe observations. These models are usually differential equations of space and time. The solutions of these equations exist both for time going towards infinity as for time going towards minus infi... | {
"language": "en",
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How is the Rayleigh criterion connected to the Abbe limit? I am interrested whether one can derive a formula for the point resolution (like Abbe did) of an optical system from the Rayleigh criterion (without the use of small angle approximation i.e. $\rm{sin}(\alpha)=\rm{tan}(\alpha)$ which is not really suitable e.g. ... | Both equations are in fact structurally similar with Abbe limit given by
$d= \dfrac{\lambda}{2\mathrm{NA}}$
And Rayleigh limit given by
$d =1.22 \dfrac{\lambda} {2\mathrm{NA}}= 0.61\dfrac{\lambda} {\mathrm{NA}}$
where lambda is the wavelength and $\mathrm{NA}$ the numerical aperture of the light collecting lens.
The f... | {
"language": "en",
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Photons are self-conjugate but neutrinos may or may not: why is that? Caution: This may be a very naive question but I find it confusing. Moreover, I believe this question is based on potential misconception. I would like it to be clarified.
Although the neutrinos are electrically neutral and colorless they have non-ze... | *
*Because we have observed processes where the photon number is not conserved. For example positronium can decay into 2 or 3 (or more) photons. This means that it is not possible to assign a global conserved charge to photons.
*For neutrinos we can assign lepton number and so far we have not observed a process that... | {
"language": "en",
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Why do TM and TE modes coexist in glass fiber? I have read that TM (transverse magnetic) and TE (transverse electric) modes of the electromagnetic field of light travelling in a glass optic fiber cable coexist. I want to know the precise mathematical justification for this (not physical intuition). Is this a banal obse... | Maxwell's equations are linear. As a consequence, if some TE modes and some TM modes can propagate in a given guide (not necessarily a fiber), then their sum can as well.
Note that optic fibers, unlike rectangular waveguides but similarly to two-conductors guides (coaxial or not), can propagate TEM modes. But a TEM mod... | {
"language": "en",
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Does Heat Cause Time Dilation? Since heat is defined as the movement of molecules, and because of relativity time slows for faster moving objects, would a hot object be in a slower time frame then a cooler object, because the hot objects molecules are moving faster?
| A hot gas will exhibit relativistic effects for its particles. A particular particle will have a time dilation effect between collisions with other particles. If its energy is $E = K + mc^2$, $K$ = kinetic energy, and mass is $m$ the Lorentz gamma factor for that particle is then $\gamma = E/mc^2$. This happens to all ... | {
"language": "en",
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Why can the dispersion relation for a linear chain of atoms (connected by springs) be written as $\omega(k)=c_s \lvert k\rvert$? On the german wikipedia site (right under "Akustische Moden"), the dispersion relation for a linear chain of atoms (connected by springs):
$$\omega(k)=2 \sqrt{\frac{K}{M}} \left \vert \sin{\f... | Because by expanding the sinus term into a taylor expansion, you get
$\sin(x)\approx x - \frac{x^3}{6} +\cdots$
So, for small values of k you are allowed to take just the linear term.
| {
"language": "en",
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Difference between sunrise and sunset? Other than knowing which direction is east and which direction is west, or observing for a sufficient timespan (to determine the direction of motion), is there any way of telling whether what one is seeing is a sunset or a sunrise? A priori it seems not but I was wondering if ther... | You got other answers explaining that there are physical reasons in the atmosphere for a sunset to be slightly different from a sunrise. But the problem is that the variations from one day to the other in atmospheric vertical profile (temperature and water vapour) because of meteorological effects are IMHO much greater... | {
"language": "en",
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Components of Velocity in polar co-ordinates Consider a point moving along a curve in a plane. The position of a point P on a coordinate system can be specified by a single vector $\vec{r}$=$r\hat{r}$. A rough sketch describing the situation is shown below:
In order to find the velocity of the particle we take the f... |
\begin{equation}
\mathbf{v}\left(t\right)\equiv \dfrac{d\mathbf{r}}{dt}= \dot{\mathbf{r}}
\tag{01}
\end{equation}
We'll use one upper dot for the 1st derivative with respect to $\:t\:$, for example
\begin{equation}
\dot{\mathbf{r}}\equiv \dfrac{d\mathbf{r}}{dt}\;, \quad \dot{\theta}\equiv \dfrac{d\theta}{dt}
\tag{02}... | {
"language": "en",
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What is exactly the difference between an active and passive frequency standard? In the case of passive atomic frequency standard, we take an atomic reference which has a resonant frequency response centered at certain particular frequency. Then we take a local oscillator and tune its frequency to that particular freq... | In a passive system, you create the frequency externally by some means, then perturb it and check if the quality of that frequency is improved or degraded. In the case of the cesium clock, you see if the fraction of the ions that shift under the reference beam increases or decreases.
In the active system, there is no ... | {
"language": "en",
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Are neutrinos affected by electromagnetic forces? I know they don't interact with matter nor any electromagnetic forces, but I know they have mass, very little mass but they have. When something has mass it must be attracted by gravity and other objects (electromagnetic) right?
| First, their being influenced by gravity is something completely different than their electromagnetic interaction.
All objects and fields that have a nonzero mass, energy, or momentum interact gravitationally, and so do neutrinos – although they're very light and hard to produce so the gravitational force from any neut... | {
"language": "en",
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Dot product of two vectors in spherical polar coordinates, do I have to convert to cartesian coordinates? For two vectors $p_1=(r_1,\theta_1, \phi_1)$ and $p_2=(r_2, \theta_2, \phi_2)$ I want the dot product $p_1\cdot p_2$. However, the solutions I have seen, involve finding the components in Cartesian coordinates and ... | You can write the dot product of two vectors $p,q$ in the form $\sum_{ij} p_i A_{ij} q_j$ where the matrix $A$ is a kind of "metric" that defines the inner product. In cartesian 3D coordinates this metric is a diagonal matrix, $A = \text{diag}(1,1,1)$, but in the spherical coordinates it takes a different form (and dep... | {
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Coherence length of a single photon If I pass individual photons through a M-Z interferometer with equal arms I will observe interference (eg only one detector will respond). As I increase the path length of one arm I will observe the two detectors responding alternately as I pass through each phase cycle. Eventually I... | Now that discussion of this topic has ceased, may I offer my own simplified answer based on what I have learned?
Firstly, no source of light can produce identical photons with exactly the same energies and direction. If the spread of energies is ΔE then the spread of wavelengths Δλ = ΔE λ2/hc. The maximum number of wav... | {
"language": "en",
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Why is oil a better lubricant than water? How come mineral oil is a better lubricant than water, even though water has a lower viscosity?
When two surfaces slide over each other with a gap filled with a fluid, the different layers of the fluid are dragged at different speeds. The very top layer touching the top metal ... | The parallel plate situation that you describe is not the typical condition encountered in practical lubrication operations. In addition to facilitating the surfaces sliding over one another, the lubricated bearing must also support a normal load. To do this, the gap between the surfaces varies with location along th... | {
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Physics Chain Problem
A chain of length d lies on a table, $d/4$ of it hangs loose on the side of it. Friction coefficient is 0.2. It is released and begins to slide. What is the final velocity with which it falls of the table?
My attempt:
$Wf = \bigtriangleup Ug = - \int_0^{0.75d} \! \mu_k g \frac{m}{d}(\... | The conceptual problem seems to be
however there is no way to define the friction for the rope since it has two parts, with apparently distinct potential energies.
Don't worry about the "distinct potential energies". You can just compute the gain in potential energy for each part separately. For the bit already hangi... | {
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Verify Faraday's law of induction I need to design a procedure for an experiment to verify Faraday's law of induction. I'm given:
*
*A Helmholtz coil of radius 15 cm
*Three plastic spheres of radii 1 cm, 1.5 cm, and 2 cm.
*A spool of copper wire
*A digital multimeter
*A plastic cylinder 5 cm tall and with a rad... | You can wind the wire around the cylinder and measure the voltage in the resulting "new" coil as you move it in the field of the Helmholtz coil (say, along the axis - the field is fairly constant in the center, but varies off the center). However, to verify the Faraday law, you also need to measure time. To this end, y... | {
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Is there scale invariance in the region of QCD aymptotic freedom? It is said that in the deep inelastic scattering, scale invariance emerges. In the scattering of electrons off protons, this reflects the asymptotic freedom.
Now I got a question. Normally, a system has scale invariance because its correlation length bec... | It is not true that scale invariance requires strong interactions. After all, free scalar field theory is scale invariant (and so is classical electromagnetism). In high energy interactions approximate scale invariance emerges because asymptotic freedom implies that free field theory is indeed a useful starting point. ... | {
"language": "en",
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How to pour water from a bottle as fast as possible? When one pours water out of a bottle, it first flows smoothly but then a pressure 'blockage' develops and the pouring becomes interrupted and turbulent, so that the water comes out in splashes. This seems to slow down the flow of water from the bottle.
What is the op... | I can only give you a hand-waving explanation, but the fastest way to empty a bottle I have empirically found is to pour it upside down but rotate the bottle. The main problem is that the empty space above the water needs to be filled again with air which can not get through. If you rotate the bottle correctly, an air ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/261303",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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Can there be an acceleration when no net force acts on a massless object? If no net force acts on a massless object can there be any acceleration of the object?
My attempt:
$$F=ma\\ \implies a=F/m\\ \implies a=0/0 $$
$\implies a$ can be anything.
| On a massless object (like an ideal rod) you can specify the acceleration of one end and derive the acceleration of the other end. But you cannot apply forces and derive the acceleration because the inertial properties are zero.
$$ \vec{a}_A = \vec{a}_B + \vec{\alpha} \times \vec{r}_{BA} + \vec{\omega} \times \vec{\om... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/261387",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is it possible to have solid light? Is it possible to have solid light?
If so, what would it be like?
| No because solid is a state of matter. Light cannot be considered matter since it is made up of particles which have no mass and I'm pretty sure occupy no space (i.e. photons have no volume).
Edit: Since photons are at the quantum level, we can't actually fathom what it would mean for them to occupy space. But on this... | {
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What is the color of a group of trillions of electrons, protons, and neutrons Since an electron is smaller than visible light, then what what color would a group of electrons (trillions of electrons) be if there were enough of them to be seen by the eye? What color would a group of trillions of protons be? Color of tri... | There isn't a simple answer to that.
Colour arises when the light absorption or emission of a system is dependent on the wavelength. For example chlorophyll (i.e. plants) is green because it absorbs red and blue light so only the green light is reflected and reaches our eyes. So the question would be how does the light... | {
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How to find this spin wavefunction? If an electron is in a state that the probability of measuring spin along the +x axis is $P(+x)=\dfrac{1}{2}$ and the probability of measuring spin along the +y axis is $P(+y)=\dfrac{1}{2}$, what is the wavefunction of the electron?
I tried to solve the above problem using a general ... | In such cases it is very helpful to write a and b in such a way that your first equation is automatically satisfied and the overall phase is neglected. I would take:
$$
\Psi = (\cos\theta,e^{i\phi}\sin\theta)^T
$$
You only have to find 2 free parameters now.
Concerning your edit. $\theta$ (your definition) is either 0 ... | {
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What does the geometry of a compactified dimension impact? In Kaluza's original work, he didn't compactify the fifth dimension, rather imposed the "cylindrical condition" where none of the components in the 4D metric depended on the 5th dimension. It wasn't until Klein that the fifth dimension was compactified to a cir... | The significance of the compactified circle as opposed to having a non-compact fifth dimension is that a compact dimension produces the discrete "Kaluza-Klein tower of states" in the effective four-dimensional theory - due to the scalar field then having a discrete Fourier series in the fifth coordinate, which, for sma... | {
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Connection between fractional charge and Schrodinger's cat In the FQHE, it is said that one electron splits into three 1/3-charged entities. Is it like the Schrodinger cat?
|
The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values of e^2/h . It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations have a frac... | {
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AdS Black holes How is the mass of the black hole defined in a asymptotcally AdS solution of the black hole? How can I find it?
Beacause in asymptotcally flat solution I can read it from the $g_{tt}$ component of the metric.
Ps: Someone knows a good lecture about AdS black hole?
| There are two complementary correspondences to black holes. One is a metric where far from the black hole horizon there is $AdS_3$ spacetime. The other occurs quite oppositely where the $AdS_2\times S^2$ spacetime occurs in the near horizon condition of an extremal black hole.
For the asymptotic condition, usually seen... | {
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Growth and Decay, Law or not? The differential equation for decay that applies to radioactive decay is:
$$dN/dt=-kN$$
for a positive constant k and number of particles N. My question is: is this, strictly speaking, a "Law"? I have seen this differential equation refered to as a "Law" and sometimes not, so what is the ... | Maybe your are looking for a more physical explanation.
Imagine you have a material that consists of identical atoms. The atom cores are not stable and therefore we call the material radioactive. With quantum mechanics you can calculate the probability that a atom core that has not decayed yet will decay. If you do th... | {
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Physics of a sprint start I am looking for an explanation to this illustration of a sprinter coming out of the blocks:
Apparently, the production of horizontal force produces a great deal of body rotation (R1) which would quickly rotate the body to an upright position if unopposed. So to counteract R1 the sprinter has... | Thank you for elaborating, Sammy. I think I am starting to grasp it.
The resultant force vector, however, can't be equal to the horizontal force vector since the sprinter needs to apply enough vertical force not only to support his weight but also to raise his center of mass.
So I am guessing that the resultant verti... | {
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Fluid mechanics paradox: The force needed to 'balance' a fluid using a piston We know that the pressure in a fluid (like water) is dependent on the depth. Consider this example:
For the first setup, solving the pressure at the bottom yields
$P_1 = \rho gh = 1000kg/m^3 \bullet 9.8m/s \bullet 1m = 9800Pa$
And from the d... | In addition to @knzhou's fine answer, I'd like to present a more extreme example, which will hopefully provide some more insight!
Solving the pressure at the bottom yields:
$P = \rho gh = 1000kg/m^3 \bullet 9.8m/s \bullet 1m = 9800Pa$
And pressure, $P = F/A$, the fluid exerts a force on the piston equivalent to:
$F... | {
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Why does the frequency of a wave remain constant? They say the frequency of a wave is its fundamental character, thus remain constant throughout its propagation regardless the medium through which it travels. Could anyone explain why frequency of wave is fundamental character but its wavelength isn't?
| You can visualize the situation like this. Lets say there is a source and an observer. They are not moving relative to each other. The source is emitting 10 peaks of wave per second (i.e. frequency is 10 Hz) and observer is observing 8 (only) peaks per time. i.e. due to medium property the frequency is changed. In this... | {
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Why are ceramics good electric insulators? I know it depends a lot on the composition, so not all are great electric insulators. So what makes it good or bad? And is it different from what makes them good thermal insulators?
Power line insulators are ceramic and they have to stave off huge voltages. That's what got me... | Solids can be classified according to their band gaps. The band gap determines how much energy you need to supply in order to free or promote an electron from the valence band to the conduction band. Once in the conduction band the electron can move nearly freely and conduct electricity. A solid with a large band gap (... | {
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What is the velocity in the Navier-Stokes equation? I have been looking at the Navier-Stokes equation, and can't seem to find anywhere a clear description of what velocity it represents.
From what I have read it could be any of the following:
*
*The 'flow velocity'.
*The velocity of an individual particle (I think... | You are correct, it is the velocity of a small volume of fluid centered at the point, that is a macroscopic motion, but it is also the result of the average velocity of the particles in that volume.
| {
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All reference frame are inertial? Where is the flaw in reasoning? This is my first post here. I have a line of thoughts which might be wrong but I couldn't find the error.
Suppose we have a point mass subjected to an arbitrary force $F$. In the lab reference frame we see it accelerating. In the reference frame where t... | The flaw is your assumption that
In this [accelerating] frame we don't see any force so the first law of dynamics is respected.
In the accelerating reference frame you do see evidence of a force, even though you don't see the effect you are expecting (acceleration of the object).
Like an observer standing on the sur... | {
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Can energy conservation be derived from Newton's laws? Can the idea of energy conservation be derived from Newtons's laws? From inspection of his laws you can vaguely discern a relationship but I want to know if you can manipulate his laws to prove it.
If not, what else did it take in history? What other assumptions ab... | Newton's third law tells us that the momentum imparted on one body is equal and opposite to the momentum imparted on another if they interact. We then have
$$
\Delta \vec p_1~=~-\Delta\vec p_2.
$$
The change in momentum is $\Delta \vec p_i~=~m\vec a_i\Delta t$, $i~=~1,~2$. The change in momentum is with Newton's second... | {
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Is reversible work a point function? The potential of a conservative force is equal to the reversible work done on or by a system. But since the potential of a conservative force is represented by a point function, this would seem to imply that reversible work is a state or point function.
But, in thermodynamics, doesn... | Start from the first principle of thermodynamics :
$d U = \delta W + \delta Q$
where $\delta Q_{\text{rev}} = T dS$
so $\delta W_\text{rev} = d U - T d S$
hence at least for an isotherm, reversible work only depends on internal energy and entropy, both of which are state functions. So yes, in this particular case, reve... | {
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Why must $v$ be $< c$ in the Lorentz transformations? Do these equations not apply to light? I was trying to understand how things look from the perspective of light. Looking at the Lorentz transformations, it seems that the universe would contract along the direction of movement into a plane, and time would stop. But ... | To see what's going on, it's enough to do this in two dimensions, with the Lorentz form $\pmatrix{-1&0\cr 0&1\cr}$. (I've set $c=1$.)
The Lorentz group is the group that preserves this form. A typical element is
$$\pmatrix{\pm\sec\theta&\tan\theta\cr \tan\theta&\pm\sec\theta\cr}$$
where $\theta$ runs through the ope... | {
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Metric with Harmonic Coefficient and Stress-Energy Tensor in General Relativity I have two question:
*
*Is there any possible implies or interest to use in general relativity a metric whose coefficients are harmonic functions?
*What is the meaning (physical) if the stress-energy tensor ($T_{ij}$) has the components... | I can answer to the first part of your question. A metric with harmonic coefficients is for example the FLRW metric for an universe with positive curvature. In this case the metric takes the form ($c=1$):
$$ds^2 = dt^2 - a^2(t) \left(dr^2 + \frac{1}{\sqrt{k}} \sin(r\sqrt{k}) d\Omega^2 \right)$$
| {
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"source": "stackexchange",
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Third Brillouin zone for a quadratic 2D lattice As far as I understand, the construction of Brillouin zones stems from the relation$$
2 \vec{k}\cdot \vec{G} +G^2 = 0
\,,$$where $\vec{k}$ is the wave vector and and $\vec{G}$ is the reciprocal lattice vector. This condition is supposed to be fulfilled when $\vec{k}$ term... | The first BZ should contain one lattice point, the second BZ two, and the third BZ three, etc. Figure 1 is correct because it is exactly the case. The third BZ in Figure 2 contains 4 lattice points, so it is not correct.
| {
"language": "en",
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How can I send a message to myself in the past? It is easy to send a message to myself in the future: I can put a letter in the post and will receive it tomorrow.
Can you think about a way to send a message to myself in the past; it does not need to be a complex message, only a bit of information would be enough.
Moreo... | We don't believe this is possible. The justification for this belief is nothing less and nothing more than experimental observation. We have never observed a process where an effect comes before its cause, so we simply reason inductively to establish a postulate that the preferred order of events in physical processes ... | {
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What is this shadow being cast upon? The picture below is from on top of Mt. Shasta at sunrise. The sun was directly behind me when I took the picture and it appears to be casting a shadow on.... the sky itself?
Can anyone explain what the shadow is being cast on? There don't appear to be any clouds or anything.
|
What is this shadow being cast upon? The sun was directly behind me when I took the picture and it appears to be casting a shadow on.... the sky itself?
It's the volumetric shadow of the mountain itself being cast on the sky itself. A mountain is not necessarily needed. Sometimes even a bit of smoke can create a nice... | {
"language": "en",
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"source": "stackexchange",
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Why does length of objects seem different in different configurations of object and observer? Today, I had gone to my friend’s garden. There was a dried water well in his garden. We got curious that know how much its depth is. First, we stood on top of the well and estimated its depth.
We estimated that the depth is a... | It is unrelated to physics, but is part of a brand called psychophysics, that is, the study of perception. In the visual psychophysics branch of depth perception, you are interested in finding not only what depth information reaches your eye, but how and if all this information is used by your brain to estimate depth. ... | {
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Physical meaning of enthalpy I've been reading about thermodynamics and reached the topic about enthalpy . I've understood its derivation but I don't understand its physical meaning ... Also I don't understand why they have divided by the mass of gas to get to the specific enthalpy equation . what's the use of it? I kn... | Thermodynamics was developed largely with gases in mind. In this case work can be done on the gas, the $p\Delta V$ term. But there is also the internal energy U to consider, so when one wants to compare experiments done on the same substance under different conditions it is useful to define a new quantity, which is th... | {
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"source": "stackexchange",
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Why is the efficiency of human cells less than the efficiency of an Otto engine? I always used to think (I don’t know why!) that the efficiency of human (and animal and plant) cells should be equal to or near the efficiency of a Carnot engine or at least should be the highest efficiency among all practical engines. But... | First. Carnot engine is the ideal heat engine. It is already highest efficiency possible for its kind
Second. Efficiency need high maintenance cost. You need specific material, specific fuel, specific condition to work and most important it could do only specific task. To make something just work and durable and reuse ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/265285",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Multipole expansion of the electromagnetic field In Jackson's Classical Electrodynamics, section 9.7, he develops the multipole expansion of the electromagnetic fields in terms of the vector spherical harmonics and the spherical Bessel and Hankel functions. His expansion is somewhat confusing, and I was wondering any o... | The Taylor series expansion along with Spherical wave expansion is presented in the book "Theory of Electromagnetic Wave Propagation" by Papas.
http://store.doverpublications.com/0486656780.html
The three dimensional Taylor expansion of the scalar and vector potentials due to a monochromatic current density is used to... | {
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Reason for fluid pressure What is the physical reason that high pressure regions (say, of air or water), want to expand into low pressure regions?
What force is causing them to "equilibrate" the pressure?
The only thing I can think of is that in liquids (or gasses) all molecules are repelling each other, meaning that i... | According to the second law of thermodynamics,entropy of an isolated system tends to increase. Considering the high pressure region and low pressure region as an isolated system, its total entropy goes up, making fluid flow from high pressure to low pressure to increase the disorder(entropy of the system).This behavior... | {
"language": "en",
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Lorentz surfaces, conformal metrics and eigenvalues From what I understand of Lorentz surfaces (spacetimes of dimension 2), it seems that, according to Kulkarni's theorem, two reasonable enough Lorentz surfaces (I am only interested in surfaces with topology $\Bbb R^2$) are conformally equivalent, that is, $g_1 = \Omeg... | The mistake here is to forget that the only coordinate-independent property of the eigenvalues of the metric is the sign. Consider the Minkowski metric in usual Cartesian coordinates
$$d s^2 = -dt^2 + dx^2$$
Or in matrix form
$$\left( \begin{array}{cc}
-1 & 0 \\
0 & 1 \end{array} \right)$$ I.e., the eigenvalues are ... | {
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Heat Pumps and COP? Heat Pump COP (Coefficient of Performance)
$$COP=1-\frac{T_c}{T_H}$$
With Heat Pumps is the efficiency/COP more dependent on the hot or the cold reservoir and why?
| According to this hyperphysics article on heat pumps, the COP is given by
$$\rm{COP}=\frac{T_H}{T_H-T_C}$$
which is not quite the equation you gave (actually it is the inverse).
Once could ask the question: if I change either the high or low temperature by 1 degree, which of these will change the value of COP most?
If ... | {
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Why doesn't this experiment violate the Uncertainity Principle? Is it possible to slow an electron in such a way(for example using a cyclotron to decelerate the electron ) that it completely stops. And since we created the slowing mechanism we might be able to predict its position when it is in rest. But this is in vio... | Quantum mechanics states that an object in its lowest energetic state still has energy (https://en.wikipedia.org/wiki/Zero-point_energy), so it would not be possible to slow the electron to zero velocity. Consequently, the uncertainty principle is not violated.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/266122",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do we know what happened during the Big Bang? Any data that we have on the Big Bang comes from the cosmic microwave background (CMB) which was created about 380,000 years after the Big Bang. From there we have been able to calculate what the Universe was like prior to the CMB's creation by applying the laws of phys... | This seems to be a common misconception about the big bang.
At present our theories can only suggest what happened AFTER the "bang". We cannot formulate what occurred AT the singularity with our current knowledge of physics.
At a small neighborhood around a spacetime singularity quantum gravity becomes important and... | {
"language": "en",
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Spinors in 2+1 dimensions I am trying to understand representations of the Poincare/Lorentz group, and in particular spinors, in 2+1 dimensions. I know some of the math, but I'm not sure about the physical interpretation of it all. For example, I know that Dirac spinors have two complex components in 2+1 D instead of f... | For a physical interpretation, spinors are like vectors with a phase. Steane, in his An Introduction to Spinors, describes spinors as flag poles with little stiff flags attached to them. Otherwise spinors have a lot of similarities with vectors, having a direction and magnitude and not inherently quantum mechanical, an... | {
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Why can we see the moon when it is between the Earth and the Sun? A rather stupid question, why can we see the moon when it is between the Earth and the Sun?
| If it is really between the earth and the sun it is called a "solar eclipse" and and the moon's shadow falls on the earth at certain places, because it is not large enough to cover the whole sun except on a shadow path.
A total solar eclipse occurs when the Moon completely covers the Sun's disk, as seen in this 1999 ... | {
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Examples of Matrix Product States Matrix product states (MPS) are a way of representing a (many-body) wavefunction. The method has been described, for example, in
The density-matrix renormalization group in the age of matrix product states. U. Schollwoeck. Ann. Phys 326, 96 (2011), arXiv:1008.3477.
However, would it ... | You can think of an MPS as being built up by objects with three indices. How to easily represent such an object? We can think of this as a matrix where each entry is a vector (in particular the vector will be a vector in the on-site Hilbert space, so e.g. for a spin 1/2 system it will be of the form $\alpha |\uparrow \... | {
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Does cutting of trees affect spin angular momentum of earth? Cutting trees reduces earth's moment of inertia. So the spinning velocity of earth should be reduced day by day. Does it really happen?
| Displacing some mass closer to the axis of rotation reduces the moment of inertia $I$. Considering Earth as an isolated system (which is not), its angular momentum $L$ must be conserved:
$$L=I\omega = \text{const}$$
Therefore if $I$ goes down, the rotation frequency $\omega$ must increase.
But if we should also conside... | {
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Is it possible to create a Faraday cage transparent to only violet/blue light from natural white light? If a Faraday cage’s hole size determines the wavelength of light which can penetrate it then I would imagine this would be possible.
| The blue end of the spectrum is higher frequency, meaning shorter wavelength. A cage that can block blue is going to block (technically attenuate) the given wavelength and any that are longer (lower frequency). If you start blocking at blue, you'll be blocking the entire visible spectrum and on down into the IR, micr... | {
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How did physicists know that only negative charges move? I have phrased similarly another question about how physicists knew that two charges exist, positive and negative. The purpose of the question is not necessarily to educate me historically. It's just that I wish to know about classical subjects without making the... | The Hall Effect shows that negative charge is moving.
In the Hall effect, one passes a current through a wide strip of metal exposed to a perpendicular magnetic field. If positive charges moved, we'd expect the positive charges to be travelling in the same direction as $\vec{I}$, and the magnetic force $q\vec{v}\times... | {
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What Postulate States Entropy must be Positive? I've been reading the Postulates of Classical Thermodynamics, and I haven't found anywhere to be said that the Absolute Entropy of a system has to be a positive number.
The third one states that the Temperature, $dU/dS$, must be Positive, since $S$ is monotone increasing ... | In classical physics, the absolute entropy is not well-defined - only entropy differences matter, so shifting your entropy by an overall additive constant doesn't matter. So entropies can indeed be negative, just as energies can, and that doesn't say anything at all about your system, just about your choice of coordin... | {
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In geometrical optics, how can we say that rays coming from a distant object are parallel to one another? If two rays are not parallel in the start, how can they become parallel at the instant when they strike the lens of a telescope?
If they don't become parallel, why do we consider them to be, in the ray diagrams of... | In the limiting case, consider that the object and your lens are finite in size and infinitely far apart. Then each appears as a point when viewed from the other. Two rays passing from the object to your lens would then follow the same path and would thus be parallel.
| {
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Can sound waves be used as simple explanation of relativity effects in STR? There are so many similarities (Doppler Effect, independence of wave velocity from source speed etc..). Try moving in your car with music and ask you friend outside record it while you moving towards him (playback speed faster + “blue shift”) a... | No, they can't. In fact sound waves would lead you to Galilean relativity, and in all the cases where it differs from Einsteinian relativity they would lead you to the wrong result. This is a catastrophically bad model for Einsteinian relativity.
As a simple example of where things go most horribly wrong consider a s... | {
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Does the speed of light in vacuum define the universal speed limit?
*
*Is light the thing causing the universal speed limit to be $299\,792\,458\,\mathrm{m/s}$? So the universal speed limit would be different if light travelled faster or slower?
*Or, is $299\,792\,458\,\mathrm{m/s}$ the universal speed limit anyway ... | Even if nothing propagated at the speed $c$, it would still be a universal speed limit, and we could still measure it.
In fact, it's not impossible that light has a (very tiny) mass in reality. If it does, that wouldn't change anything about special relativity. It would make teaching it even more of a nightmare than it... | {
"language": "en",
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Simple analytic examples of Multi-scale Entanglement Renormalization Ansatz (MERA) I want to understand Multi-scale Entanglement Renormalization Ansatz (MERA) with very elementary examples. So far I could find references which are mostly based on numerics. It would be a great help if someone could give a very simple ex... | The canonical example for MPS (in fact, the first MPS ever) is the AKLT model (http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.59.799, https://projecteuclid.org/euclid.cmp/1104161001). The 2nd reference also discusses the 2D (=PEPS) version of the state.
Another example of an exact MPS/PEPS model are (nearest-... | {
"language": "en",
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Electromagnetic lifts, and work Magnetic field doesnt do any work, so when an electromagnet lifts, say a car or something, where is the energy coming from?
| A constant magnetic field doesn't do any work on a moving charge. This, however, doesn't mean that a magnetic field can't do work if it is not constant. The field has an energy density of ${1 \over {2\mu}}B^2$ and this energy can be converted into work if the field changes, e.g. by introducing a magnetic material. It's... | {
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Why doped silicon does not undergo electrostatic discharge? Doped silicon is charge neutral overall, but since the extra added carriers are only weakly bounded (~45meV) they become delocalized. Since the concentration of silicon is 5-9 orders of magnitude higher than the concentration of dopants, the delocalized charge... | Doping introduces allowed energy states within the band gap of the material, and these energy states are very close to the energy band that corresponds to the dopant type.
From the Wikipedia article on doping in semiconductors:
[For example] electron donor impurities create states near the conduction band while elect... | {
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How does the "Look Else Where Effect" affect the chances of detecting a false diphoton excess at the LHC? Back in December 2015, there was found a 750 GeV diphoton excess in both CMS and ATLAS at the same location with a significance well above $3\sigma$; a 0.13% chance of being false.
However, there hasn't been any r... | The exact answer depends on the specifics of the analyses, and also on the overall number of analyses performed.
Speaking however about the first time that the specific diphoton excess was announced by both experiments, you can find here the values for the significance before and after the look elsewhere effect being ... | {
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Best way to estimate a coefficient when data have errors I am a little bit confused about some tecniques concerning error-analysis.Consider this situatiuon:
During an experiment I collected a $x,y$ table of data that are expected to satisfy a linear relation $y=kx$. For any $x_i$ I have an associated error/uncertainty ... |
During an experiment I collected a $x,y$ table of data that are expected to satisfy a linear relation $y=kx$. For any $x_i$ I have an associated error/uncertainty $\delta x_i$ and the same applies to the $y_i$'s. What is the best thing to do in order to have a good estimate of the parameter $k$ and the associated erro... | {
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Principle of Least Action Question Let's say we have a particle with no forces on it. The path that this classical particle takes is the one that minimizes the integral
$$\frac{1}{2}m\int_{t_i}^{t_f}v^2dt.$$
So if we graph this for the actual path a particle takes it is a straight, horizontal line on the $(t,v^2)$ pl... | You have to minimize the integral subject the the constraint that the initial and final positions $x(t_i)$ and $x(t_f)$ are held fixed. In particular, $\Delta x = \int_{t_i}^{t_f} v(t)\, dt$ is held fixed. If the particle slowed down than sped up as you suggested, the action would be less, but it wouldn't have a high... | {
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How many photons are needed to make a light wave? What is the smallest number of photons needed to make a "light wave"?
In other words, how many (coherent?) photons start to exhibit classical behavior?
For example, how many photons are needed to get linear polarization? (Single photon has circular polarization.)
| Light never completely behaves as a particle. Light never completely behaves as a wave. As pointed out by hsinghal, the Michelson interferometer showed that, even at the "single photon" level, we still see wave behaviors. These behaviors are well modeled by quantum mechanics, which treats light as neither a pure wav... | {
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Which temperature does $T$ in Clausius inequality ($\oint \frac{\delta Q}T\le 0$) refer to? I got a little confused about the temperature in Clausius inequality. As you can see in this answer of Luboš Motl, it seems that temperature is the temperature of the system.
But in some answers of Chester Miller e.g. this and t... | The temperature appearing the the Clausius inequality is definitely the temperature of the "boundary interface (with the surroundings)", or simply the temperature of the sources. One of the best places I have seen this discussion is in Fermi's book, chapter 5, section 11. He is explicit about it. To see this you have t... | {
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Why is the resistance in a parallel circuit smaller than the resistance in a series circuit? So I was told in the physics class that the resistance in a parallel circuit is smaller than the resistance in a series circuit. Why does that happen?
Is this statement also true for circuits which have no resistors or resistan... | It seems like you get the rational answer but lack the ability to feel it:
imagine you have 5 doors of different sizes and a thousand people to pass from a to b. If all the doors are in a row (so everyone has to pass every door), it will take a lot more time compared to the situation, where you place all the doors next... | {
"language": "en",
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Plane waves in special relativity I don't understand how there can be plane waves that by definition are spread through all of space if nothing can travel faster than light.
Wouldn't every wave have to spread over time with at most the speed of light?
I could understand when they are only appearing in the mathematics o... | Plane waves are fully compatible with special relativity, since they are Lorentz-invariant objects:
$$\psi_k(x) = e^{i px/\hbar} = e^{i(Et-\vec{p}\cdot\vec{x})/\hbar}$$
You seem to be concerned with the fact that plane waves are spread through all space. But in fact, they're spread through all spacetime! They are perfe... | {
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What's smaller: a neutrino, or a string from string theory I've recently read an article that stated "If an atom were as big as the solar system, a neutrino would be the size of a golf ball". I watch the science channel, and on (I believe) the show How the Universe Works they mentioned that if a hydrogen atom was the s... | The mass of the neutrinos are estimated to some tenths of an $\mathrm{eV}$. The masses of atoms are mostly between 1 and 300 $\mathrm{GeV}$. Thus, considering the masses, this golf ball comparison isn't okay in my opinion. In my mind, comparing the mass of the Moon to the mass of the Solar System would be more realisti... | {
"language": "en",
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Born & Wolf; Alkali metals transparent to UV? Cesium transparent to blue? Most optics texts will mention that alkali metals can become transparent in the near ultraviolet in the sections on reflections from metals, plasma frequency, and electron density. I remembered this again just now when I saw Table XXVII in Born a... | It is absolutely accurate that two continuous functions (the magnitude and imaginary component of the optical index, in this case) will cross if they trend in opposite directions. Therefore, there must be a very specific wavelength at which the the real and imaginary components are exactly equal.
There are many reason... | {
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Why is black hole entropy not an extensive quantity? The Bekenstein entropy for a black hole is proportional to the surface area $A$ of the black hole
$$
S_{BH} = \frac{k_B}{4 l_P^2} A
$$
with the Planck length $l_P = \sqrt{\frac{\hbar G}{c^3}}$.
The area is the surface of a sphere with Schwarzschild radius $r_s = \fra... | I'd like to add to BobBee's insightful answer, which one can summarize as: we need to broaden our notion of extensive for systems Gibbs, Boltzmann and all the others could not conceive of.
Another point, which is implicit in the notions that BobBee's answer discusses is that entropy is always extensive in the following... | {
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Could a radar pulse be considered particular in nature? I ask because I have a real problem with wave/particle duality (one of the biggest cop outs in the whole of physics, in my opinion)
A radar pulse is definitely a wave.
It is spatially bounded. (at least in one dimension!)
It has energy.
It is a 'quanta'.
Is this n... | Quanta of a electromagnetic wave or photon is the minimum amount of energy that can be transferred from one place to another. Increasing the energy of a pulse means you are increasing number of photons in the pulse and we can write
$$E=nh\nu$$
Where equivalent mass can be written as
$$E=pc$$
$$p=\frac {h\nu}{c}$$
a... | {
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Radius of centripetal acceleration Suppose you are moving in circle of radius $r$. So there should be centripetal acceleration towards the center. Now you want to decrease the radius of the circle, so someone should apply more centripetal acceleration in order to decrease your radius. But I had read that with the incre... | The key point that is missing from your two contradictory "explanations" is this:
While you are changing the radius, you are not moving in a circle around the original center point. You are moving in a spiral of some kind.
Think about a stone tied to a string being whirled in a circle. If you pull harder on the string ... | {
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Is Hilbert Stress-energy tensor always same as Belinfante stress-energy tensor? The canonical stress-energy (SE) tensor arises from Noether’s Theorem by employing the conserved currents associated with translational symmetries.
It's defined as
$$T^{ab}=\frac{\partial \mathcal{L}}{\partial(\partial_a\phi)}\partial^b\phi... | Yes, provided we work with Torsion-free connections. This is explained in the original papers of Belinfante and Rosenfeld that are cited on the Wikipedia page.
You can see the torsion-free necessity by using a vierbein formulation. Just varying the vierbein alone usually gives the asymmetric Noether tensor. If you de... | {
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What forces cause the wetting of a brick when water is poured over it? When water is poured over a porous material, like brick, which forces are causing the wetting of brick (i.e., absorption of water by brick)? Is it gravity, capillary force, or both? Normally capillary action causes rising of water rather than suckin... | Capillarity is responsible for wetting the brick. It is better to think in terms of surface energy. Water has two surfaces, one in contact with surrounding air, and one in contact with brick. If surface energy of water-brick interface is lower than water-air interface, then water will flow in such a way as to increase ... | {
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What does "non-normal parity" mean? Nuclear physicists seem to use the term "non-normal parity" a fair bit. Googling for the term yields some 840 results, and the same search on Google Scholar indicates that about 430 of those are research papers.
Unfortunately, those searches seem to only yield research-level papers t... | Going back to A.M. Lane, Reduced Widths of Individual Nuclear Energy Levels one finds the quote:
At this stage we introduce a separation of the discussion
which is carried through to the end of the
section, namely, nuclear states are discussed according
to whether they are of "normal" or "nonnormal"
parity. Th... | {
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Problem with how to apply pseudo force in this situation This is a situation, where both the bodies move with a constant angular velocity. M1 is connected to a rotating rod and M2 is connected to M1 with a string. There is no tangential acceleration.
I want to figure out the forces on M2 w.r.t M1. I say, there is
1-mg
... | Your definition of $r_2$ in the figure and in the text are inconsistent.
I will assume your text is the correct one and let $r_2$ be the distance of $m_2$ from the center.
For an observer at the center, you only need to add the centrifugal force
$$m_2 \omega^2 r_2$$
For an observer at $r_1$, it is orbiting and spinning... | {
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Is it possible to measure specific gravity (SG) with two pressure sensors? I am looking into the subject of continuous specific gravity (SG) measurement of my beer during primary fermentation. I am wondering if attaching two pressure sensors on different heights on my fermentor wall and then calculating SG from pressur... | Yes it is absolutely possible; in fact this method is somewhat common among larger breweries.
From the book Brewing Yeast and Fermentation:
'Density may be computed from differences in pressure measured simultaneously at different depths within vessels. Thus, at a constant vertical distance between two points the diff... | {
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Are Newton's 1st and 3rd laws just consequences of the 2nd? Can Newton's 1st and 3rd laws be assumed given just $F=ma$. I know that the argument would be, "No, then there would only be 1 law". But I can't think of any situation where 1 and 3 aren't superfluous.
If you just told me $F=ma$:
I would assume nothing else c... | There's a modern re-interpretation of the first law in terms of differential geometry.
Here, velocities live in the tangent space and accelerations in the double tangent space. However, not arbitrary vectors of the double tangent space are valid accelerations - they neeed to be 'second order': If you think of the doubl... | {
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Why is the wave function inside a delta potential non-zero? The wave function outside an infinite well is zero, owing to the fact that we assume particles to have finite energies. But in the case of a delta function potential $\delta(x-a)$, the wave function is non-zero at the point $a$.
To find the states of a delta f... | The $\delta$ potential is a special case, as approximation, of the square potential barrier:
$$
V(x) = \begin{cases}
V_0,\quad -a\leq x \leq a\\
0\qquad\textrm{otherwise}
\end{cases}
$$
where $V_0\to\infty$ and $a\to 0$ such that the product $V_0a$ is a constant.
Outside the interval $[-a,a]$ the Schrödinger equation i... | {
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Difference between analog signal and digital signal There is no perfect generator of a true digital signal in the real world natural phenomenon. Most of the physical signals produced by humans and animals like roaring, speaking, playing, clapping, electrostatic charging, drumming are all analog in nature. Even physical... | There is a sense in which everything is quantized, therefore an analog signal is really a digital signal in disguise.
If you take a very sensitive detector of say a radio signal and then turn the signal down low enough, you will begin to see the signal strength varying in small steps that match the energy of one photon... | {
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Is the superposition principle a postulate in electrostatics? Consider two electrical point charges $q_1$ and $q_2$ described by the total charge distribution $\rho = \rho_1 + \rho_2 = q_1 \delta(\vec{r} - \vec{r_1}) + q_2 \delta(\vec{r} - \vec{r_2})$. The total electrical potential could then be calculated by
$$
\phi... | Maxwell equations for electrostatics are $\nabla\cdot\vec D = \rho, \nabla\times \vec E = 0$. The second one tells you, that there is a potential field $\phi$ generating electric field as $\vec E = -\nabla \phi$.
Both equations are linear, it means if there is $\rho_1, \rho_2$ satisfying $\nabla\cdot \vec D_1 = \rho_... | {
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Interacting fields and Hilbert space "Two fields with different mass parameters lies in two different Hilbert space."
How am I supposed to prove this using the concept that a field consist of a collection of harmonic oscillators? Tom banks in his book on qft gives a suggestion of using overlap of ground state to arrive... | A thorough statement, proof, and discussion is given in Theorem 3.1 (Haag's theorem for free fields) of the recent Ph.D. thesis http://edoc.hu-berlin.de/dissertationen/klaczynski-lutz-2015-11-06/PDF/klaczynski.pdf by Lutz Klaczynski.
''different Hilbert space'' must be viewed with a grain of salt as all separable Hilbe... | {
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What is the shape of a deuterium nucleus? What is the shape of a deuterium nucleus?
I can think of two obvious extremes.
A positive proton end intersecting with a neutral neutron end.
Or a cylinder with spherical caps on the ends that is positive on one end and neutral on the other.
| This is an extended comment on count_to_10's answer, please upvote that answer not this one.
It's tempting to think that because a deuterium nucleus is made up from two different particles, one positive and one neutral, that it must necessarily be asymmetric. However a hydrogen atom is also made up from two different p... | {
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Why only electromagnetic energy during electron relaxation? When an electron relaxes to a lower energy state in an atom, it emits photons. But why does it produce only electromagnetic energy and not other forms of energy? For example, why doesn't it emit a Z boson, or simply increase in mass?
| At the energy scales of an atom, the photon is the only thing of all the things the electrron can theoretically couple to in the Standard Model that can be produced at the available energy. Producing other particles, such as a Z boson or an electron-positron pair, can't happen because their mass is too learge.
And an i... | {
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"url": "https://physics.stackexchange.com/questions/273825",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Attraction between two wires with parallel current I'm self-studying electric and magnetic forces, and I'm stuck on one concept that I can't seem to resolve.
The book I'm using (College Physics Reasoning and Relationships, Giordano) explains a situation between two horizontal parallel wires. If a parallel current is r... | Of course there is superposition. There will be cancelling out of fields in some places. If the currents are of equal magnitude, that 'null' point will lie somewhere midway between the wires. The more you increase the current in one, more will the 'null' point shift towards the other wire.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/274018",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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