Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Why do images not appear inverted when looking directly through a pinhole camera? I understand that the way light takes through a pinhole creates an inverted image on a surface behind the pinhole. I remember this effect from school experiments, it's also described in this wikipedia article. I punctured a piece of paper... | Ignoring diffraction, the pinhole can't change the orientation of what you see because it doesn't change the position or direction of any light rays. It just blocks some of them.
When you put a screen in front of an illuminated object, every point on the object emits light in every direction, which hits the screen at e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/628424",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
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Standing wave equation A question about standing wave equation.
We send a harmonic wave that travels down a rope that is fixed at the end with the equation(like in the picture):
$$y = A\sin(kx-\omega t)$$
The wave that travels down a rope gets reflected at the rope’s end and has the equation:
$$ y = A \sin[k(2l-x) - \... | In this problem, fixed end is at $x = l$. Corresponding boundary condition has a form
$$
y(x = l, t) = 0.
$$
Solutions to the wave equation with this boundary condition have the following form
$$
y(x,t) = f(kx-\omega t) - f(k(2l-x)-\omega t). \quad (1)
$$
In this problem, $f(kx-\omega t) = A\sin(kx-\omega t)$. For $t$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/628749",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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$\beta$-function of general $\phi^6$ in 3 dimensions In 3-dimensions the $\phi^6$ interaction is renormalizable and the $\beta$-function can be found in many reviews in the $O(n)$ symmetric case, $V(\phi) \sim (\phi_a \phi_a)^3$ where $a=1,\ldots,n$.
What I couldn't find, but I can't believe it's not known, is the $\be... | The comment by Connor Behan contains the answer:
arxiv.org/abs/1707.06165
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/628854",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How does a javelin rotate when thrown? As the centre of mass of javelin follows parabolic path, the javelin also rotates about it’s centre of mass while in air. As a result, it hits the ground with it’s nose. Where is this angular momentum coming from? Is there some torque acting on the javelin? Or, Is the angular mom... | Please see the related post here. The answer lies in the the wikipedia section on the modern redesigns for javelin throw competitions. It states that
In 1986 the technical committee of the International Association of Athletics Federations introduced new specification for the standard competition javelin. Among other ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/629006",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Does the age of the universe depend upon a specific choice of referential? Does the age of the universe depend upon a specific choice of referential or is there a way to define it in a referential-independent way?
| No. The age of the universe does not depend on any referential system. In order to measure time, you need some physical quantity that's changing to measure time against. In the case of cosmology, it's the time perceived by a typical observer based on the expansion parameter $a$ --see below. In a manner of speaking, it'... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/629207",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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How to inject the maximum acoustic power into a block of granite? I know that we can use transducers that are glued to a surface to achieve this. If I want, for example, to have 200 watts of actual acoustic power in the audible range in the granite, is a transducer the easiest cheapest way? Are there other methods?
| Here is the challenge you have to overcome.
To actually deliver 200 watts of acoustic power into a solid block of granite requires that the transducer be impedance-matched to the load.
If you press on a piece of granite, it presses back really hard and experiences almost no compression in response. This makes it an ult... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/629492",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why is the half-wave dipole the most used antenna design? When producing em waves using a dipole antenna (of length L), you could theoretically use any L and adjust the frequency of the oscillating voltage to get the desired wavelength. Then why are most antennas half a wavelength long? I'd also like to know why it's u... | A half-wave dipole is fed with the signal at its mid-point.
Consider the current distribution along the antenna. Some current has to flow in and out at the middle, or power cannot be transferred. But at the ends the current has nowhere to flow. So the current distribution along the dipole takes on a distinct "hump" sha... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How do I determine the "recoil permeability" and "remanent flux density norm" of a permanent magnet? I am working on modeling a permanent magnet using finite element analysis.* The magnet in question is a neodymium cylinder 1 cm in diameter, and 5 cm in length.
The program uses the equation
$$
\vec{B} = \mu_0 \mu_{rec}... | In general, the relationship between $\vec{B}$ and $\vec{H}$ is nonlinear and history-dependent. The formula
$$
\vec{B} = \mu_0 \mu_{rec} \vec{H} + \vec{B}_r
$$
is an expedient approximation that often works well for rare-earth permanent magnet applications. It refers to the ‘major hysteresis loop’ which is the path fo... | {
"language": "en",
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Anticommutation of variation $\delta$ and differential $d$ In Quantum Fields and Strings: A Course for Mathematicians, it is said that variation $\delta$ and differential $d$ anticommute (this is only classical mechanics), which is very strange to me. This is in page 143-144:
If we deform $x$ we have
$$\delta L = m \l... | Perhaps the following comment is helpful: If $M=M^{\prime}\times M^{\prime\prime}$ is a product manifold then the exterior differential $\mathrm{d}=\mathrm{d}^{\prime}+\mathrm{d}^{\prime\prime}$ on $M$ is a sum of the exterior differentials on $M^{\prime}$ and $M^{\prime\prime}$. We can assign degree $(1,0)$ to $\math... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/629992",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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Magnetic flux through circular loop due to infinite wire I’m trying to calculate magnetic flux that’s going through circular loop with radius $R$, due to magnetic field of a infinite wire that is in distance $d$ from the center of the loop. $\vec{B}$ vector is parallel to $\vec{dS}$ vector. I know that magnetic field o... |
fig 1: The geometry of the calculation. Note that the distance of the wire from the center has been taken to be $D$, not $d$.
Let the magnitude of the magnetic field due to an infinite constant current carrying straight wire at a distance $r$ from it be $k/r$.
In the given geometry, the wire is co-planar with the loop... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/630086",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What are the weaknesses, if any, of the relational interpretation of quantum mechanics? Carlo Rovelli's 1996 relational interpretation of quantum mechanics (RQM) seems to solve many of the quandaries of traditional theories, including the Copenhagen interpretation (what privileges the observer? Why does he/she instigat... | I personally consider RQM to be an attempt at the "best of both worlds" between Copenhagen and MWI. By making measurements observer-dependent, it essentially accomplishes the same thing as entanglement of the system and observer in MWI. By refusing to speculate on other worlds, it has the veneer of realism of Copenhage... | {
"language": "en",
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A Doubt on Hawking Radiation: What Birrell wants to say here? Well, I know basic General Relativity but I still learning the basics of Quantum Field Theory (therefore without mentions on curved spacetimes). But, I'm trying once and a while to become more used to quantum fields and curved spaces.
Now, the notion of Hawk... | Hawking radiation is observed at future null infinity. One can try to trace back where the radiation observed originated. A common method for this is to use the “geometric optics” approximation, where radiation follows null geodesics. Doing so with the modes of the Hawking radiation suggests that the modes originate ar... | {
"language": "en",
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Active vs passive transformation in right handed particle People often says that active transformation is equivalent to passive transformation.
Suppose that we have a right handed particle that is, the spin and the momentum are pointing in the same direction, call this direction right. Under a passive parity transfo... |
if we inverse the particle momentum , does it turn in to a left handed particle?
Particle is right-handed if spin vector is in the same direction as particle momentum vector and left-handed if these directions are opposite :
So basically answer is that you can inverse particle helicity from right-handed to left-hand... | {
"language": "en",
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How do we determine the damping coefficient given the acceleration vs time graph of a 1D mechanical system? Consider a mechanical system about which the only data we have is a graph that shows acceleration vs time. I would like to figure out what the damping coefficient $c$ is.
Instead of displacement as shown in the ... | How to Fit
We have data points the oscillate curve $~x(t)~$.
Step 1: obtain the blue points
The period of this curve is $~T=2~$, hence the points are
$$X=T_0+n\,T~,Y=~x(T_0+n\,T)~,n=0,(1),N_p,$$
where $~T_0=\frac T4.$
Step II
Fit the points $[~X~,Y]~$ to the curve $~a\,e^{-\beta\,t}~$ where $~a=x(T_0)$ and you obtain... | {
"language": "en",
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Can photons only exist in the state of motion in a medium? Photons are known to travel at a speed of $\rm 299 \ 792 \ 458 \ m / s$ in vacuum. Photons can be absorbed, or absorbed and re-emitted by matter. They slow down to $\rm 225,000,000 \ m/s$ in water with a refractive index of $1.3$, to $\rm 200,000,000 \ m/s$ in... | It depends how you're defining "motion". As you're talking about photons as opposed to light generally, I'll talk from the quantum perspective rather than just classical waves. See these related questions for more on the different perspectives:
Do photons actually slow down in a medium, or is the speed decrease just a... | {
"language": "en",
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"source": "stackexchange",
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Phase difference approximation I'm sitting and trying to solve the equation of the phase difference given by:
$\Delta \phi = k (\sqrt{a^2+d^2} -d) \approx \frac{ka^2}{2d}$
Where $a$ is the size of an aperture and $b$ is the distance of the point at the aperture's center as shown in the figure below.
I'm not a math exp... | You need the binomial expansion
$$ \sqrt{d^2+a^2} \approx d \left(1+\frac{a^2}{2d^2}\right) , $$
which assumes that $d\gg a$.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Energy of Hydrogen Atom (Electron vs Proton) In many textbooks, energy changes of the hydrogen atom are attributed to the electron transitioning between energy levels. However, the energy itself is that of the whole system (proton+electron) so how can we attribute its changes to the electron? what's preventing us from ... | The energy is indeed that of the whole system, but the electron has a much smaller mass (1/1836) than the proton, so the latter does not contribute much here. But for accurate results you have to consider the proton as well. When you solve the corresponding two-body problem for two masses $m_1$ and $m_2$, you can reduc... | {
"language": "en",
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"source": "stackexchange",
"question_score": "2",
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Must observables be Hermitian only because we want real eigenvalues, or is more to that? Because (after long university absence) I recently came across field operators again in my QFT lectures (which are not necessarily Hermitian):
What problem is there with observables represented by non-Hermitian operators (by observ... | Given a separable Hilbert space that underlies a quantum system, the observables on this system are the self-adjoint operators on the Hilbert space. The reason they must be self-adjoint is that the spectrum of an operator is real if, and only if the operator is self-adjoint. The spectrum of an operator is the set of po... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/631665",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "33",
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A pedagogical semi-rigorous review of topological phases, topological order, and related subjects I'm looking for a pedagogical review or book about topological phases, topological order, TQFTs, and related subjects.
The ideal thing would be a mix of rigorous definitions and physical examples, with something giving me ... | For topological band theory (single-particle picture) the online course by TU Delft could be a nice starting point. A more thorough approach on topological insulators can be found at the lecture notes by Aboth or at the classic book Topological Insulators and Topological Superconductors by A. Bernevig for instance.
On ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/632052",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Analogy for Lentz soliton Analogy for Alcubeirre Warp Drive:
Every explanation of warp drive in layman terms has this sentence in it:
"The Warp Drive will contract space in thier front and expand space behind."
(I am not sure that this is literally what the alcubierre metric describes)
And then show pictures like thi... | Basically, he came up with a way to generate both the push and the pull force without needing to create negative energy, which as far as we know is impossible to do. Since energy and mass are interchangeable due to the well known equation E=mc^2, and mass can warp space time (aka it creates gravity) that in turn means ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/632143",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Mutual capacitance of a long straight wire and an infinite conducting plate Q. A long straight wire is located parallel to an infinite conducting plate. The wire cross-sectional radius is equal to $a$, the distance between the axis of the wire and the plane equals $b$. Find the mutual capacitance of this system per uni... | The field right above a conducting surface should be perpendicular to the surface. Your choice of field does not meet this condition. That is, your choice of field is not a solution of the Laplace's equation with the boundary conditions set by the given system of conductors
To find the right field you can use the metho... | {
"language": "en",
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Can an LC circuit be used to produce and receive FM signal? By simply changing the frequency of oscillation of an LC circuit (which you can do with the capacitor alone) you could emit (and receive) FM signal.
Are LC circuits actually used to do that? If not, why not?
| FM signal is modulating the frequency of the signal, i.e. 0 will be encoded to a short signal, and 1 will be encoded to a long signal.
To receive an FM signal, we can first use a bandpass to select the frequency we would like to listen to, and then simply 'read' the signal by parsing the short and long signals to 0s an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/632575",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Are soundproof foam shapes reflective of audio frequencies? I came across a previous question regarding how soundproof foam absorbs sound: How does foam "absorb" sound? where the answer explains the properties of the foam itself rather than the shape.
However, in analyzing audio spectrogram images (and messing around w... | Some of the sound is absorbed and some is reflected. A flat surface would reflect more sound than the shaped surfaces which are designed to make more of the reflected wave hit the foam again so more is absorbed.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/632697",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why 2nd Shell can have 8 electrons? I recently watched this video:https://youtu.be/INYZy6_HaQE
and understood why 1st orbital can have only 2 electrons: According to Pauli's exclusion principle, two electrons cannot have the same quantum states.In the first energy level,all other quantum states are same except for the ... | If you are a high school student or a freshman yet, I will try explaining in terms you find easy. As you must already know, an electron in an atom has a set of 4 numbers known as its quantum numbers. They are $n,l,m$ and $m_s$. Now these 4 can not be the same for 2 electrons. Let us calculate the number of states possi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/632872",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why does closing someone's eyes not give them near-sightedness? When we close our eyes aren't we technically looking a really close up piece of skin? That is, our eyelids? If it's so close to our eyes why doesn't it give us bad vision? We know if screens or books or other objects constantly being close to us causes our... | The problem comes only when we try to focus on something that is really close to our eyes. We don't try to focus on our eyelid (may be we cannot), and hence its not a problem
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/633001",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why electric field is scaled by gamma? Two opposite charges are in a spaceship and are attracted by the electric field $E_s$
But for an observer on earth the Electric force is $$E_e=\gamma E_s$$
Normally the forces are scaled down by $\gamma$ in the earth frame and here also the total force is scaled down.
But why the ... |
In above Figure-01 an inertial system $\:\mathrm S'\:$ is translated with respect to the inertial system $\:\mathrm S\:$ with constant velocity
\begin{align}
\boldsymbol{\upsilon} & \boldsymbol{=}\left(\upsilon_{1},\upsilon_{2},\upsilon_{3}\right)
\tag{02a}\label{02a}\\
\upsilon & \boldsymbol{=}\Vert \boldsymbol{\up... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/633138",
"timestamp": "2023-03-29T00:00:00",
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Why don't evanescent waves give rise to electromagnetic waves? I'm reading about evanescent waves for the first time. I understand that even thought no electromagnetic wave is transmitted across the boundary, an electric field is transmitted which decays exponentially into the material.
As far as I understand this is s... | A propagating wave obeys $\omega^2 = k_x^2+k_y^2+k_z^2$ with $k_i^2>=0$. For an evanescent wave at least one wave vector component has $k_i^2<0$. In this direction the wave amplitude decays exponentially, while it propagates in the other direction(s). Such solutions of the wave equation are only possible near an interf... | {
"language": "en",
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Nonlinear extension of Lorentz Group The Lorentz group is defined to be the set of linear transformations that leave $ds^2 = -dt^2 + |d\vec{x}|^2$ invariant. The Poincaré group contains the Lorentz group, but now we allow transformations of the form $t' = t+a$ where $a$ is some constant.
Is there a name for the group o... | It's called the Lorentz group. No, that's not a joke.
*
*Let $A$ be the group of linear transformations that leave
$$
x^2+y^2+z^2-t^2
\tag{1}
$$
invariant. Nonlinear transformations that leave (1) invariant also exist, as shown in the question linked in the OP, but we've defined $A$ to include only the linear ones.
... | {
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What does it mean for the gravitational force to be "between" two bodies? What is the meaning of the word "between" in the law that the force between two masses at separation $r$ is given by $\frac{GM_1M_2}{r^2}$? I am confused about how can a force be in-between, either it is on body A or on body B, or on both.
Suppos... | One way to look at this is that forces always come as pairs. For example, you start with a universe with only one object in it, then you add another object and nature will immediately create a pair of forces. It’s not like the Moon feels that the Earth is tugging at it, and retaliates by tugging at Earth itself.
You ca... | {
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"source": "stackexchange",
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Problem in wedge constraint
My teacher told all this (u can see in picture)
Here both accelerations have component in -j direction, then why do we say that they cancel out?
[X-axis is surface of wedge]
I have problem in photo 2
Nobody answered so I have to ask it again...
| The answer is quite simple. In the constrained motion problems given above, the main constraint is that both surfaces must be in contact with each other. This is possible only if the component of acceleration of the two bodies in the direction perpendicular to that of motion is equal both in magnitude and direction i.e... | {
"language": "en",
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What is the formula to determine the change in pressure when there is a change in flow? [Updated to help clarify my question]
I have a current water flow of 9 GPM (gallons per minute) at 50 PSI through a 1/2 inch diameter pipe pouring out at the end.
I understand that if I reduce the flow at the end (exit) of the pipe,... | According to Bernoulli’s theorem
$$P_1+\frac{1}{2}\rho{v_1}^2+\rho gh_1 = P_2+\frac{1}{2}\rho{v_2}^2+\rho gh_2$$
Since both ends of the pipe is in the same height
$$h_1=h_2$$
Now the equation can be written as
$$P_1+\frac{1}{2}\rho{v_1}^2= P_2+\frac{1}{2}\rho{v_2}^2$$
$\rho$ is the density of liquid
You can use this eq... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/634145",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Velocity is relative, which means acceleration is relative, which further implies that forces are relative as well So how would we know whether a force truly exists or not. I can be accelerating a car my 5 meters per second squared but another car accelerating with the same acceleration would think that my car is at re... | Within different inertial frames, velocities will be different. However, acceleration will always be the same in any inertial frame. Therefore, so will the forces.
Short proof: suppose $v(t)$ is the velocity in one inertial frame, and $v'$ is some constant shift in velocity due to choosing a different inertial referenc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/634287",
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} |
Does the Oort cloud act as a kind of shield for the Solar System? Does the Oort cloud act as a kind of shield for the Solar System? When an interstellar object impacts the cloud, does its momentum get absorbed substantially?
| No. The Oort cloud is a cloud of comets and icy asteroids, not a physical barrier. Just like everywhere in the Solar system, it is mostly made up a empty space, and wouldn't absorb the impact of an interstellar object in any meaningful way.
The Sun does protect the Solar System from things like the interstellar wind wi... | {
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Can a photon be detected by a "lateral" detector? If I direct a laser pointer north and I put a photodetector eastwards (i.e. at $90^\circ$ ), and I wait for a very very long time (in a perfect vacuum if necessary), will the detector ever be triggered by a photon?
| What the other answers do not address is shielding. Electromagnetism has this phenomenon called shielding and we are able to do it pretty well with our current technologies.
EM waves do spread spherically in space always. The only way to go around this is with shielding, in your case, the laser is using very effective ... | {
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Is there power reflected when Fresnel Transmission Coefficient is 1? Suppose a ray does not meet the total internal reflection condition and is transmitted fully through an interface (i.e. Fresnel Transmission Coefficient = 1), can we still expect any power being reflected for that particular ray? Whether it is a ray o... | To conserve energy,
$$1=R+T+A,$$
where $R$, $T$, and $A$ are the power reflection, transmission, and absorption coefficients, respectively (and we assume that scattering is bundled into $R$ and/or $A$). These are all positive, real numbers.
Therefore, if $T=1$, $R=A=0$.
| {
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Why do I feel electric shock even in the presence of wood? I feel mild electric shock when my laptop with aluminum body is kept on a wooden desk is charging, while both my leg rests on the the leg of the table . Why is that ? Why isn't wood behaving like an insulator here ?
| The conductivity of wood depends on its water content. If you're in an arid desert it probably wouldn't conduct electricity, but if it's somewhat humid or the wood is damp for other reasons it's a reasonable capable conductor.
This website says wood can range from rubber to silicon depending on its water content.
| {
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Why doesn't $v_T = \omega r$ involve the direction of its variables? We derived $v_T = \omega r$ by the following procedure, and it's said that $v_T = \omega r$ "is a relation between the magnitudes of the tangential linear velocity and the angular velocity". Why doesn't the formula involve the direction of its variabl... | The direction is implied to be in the $\hat{\phi}$ direction because it is assumed that (eq 8-9) $r$ is not changing with time. Moreover, it's not really implied since it's the tangential velocity and so is in the tangential ($\hat{\phi}$) direction.
To clarify, let's work with an object spinning in a circle in two di... | {
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What is the entropy change of the universe for a rock if it falls from a height into a lake? The rock and the lake are at the same temperature According to my textbook, the entropy change of the universe is $+mgh/T$. I'm confused about why this happens.
after falling (without air resistance), wouldn't the rock possess ... | The first step in determining the entropy change is to apply the first law of thermodynamics to establish the final equilibrium state. In this case, the potential energy of the rock is converted to internal energy of the rock plus surroundings (rest of universe): $$\Delta U+\Delta (PE)=\Delta U-mgh=0$$where U is the ... | {
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Does this research paper prove that warp drives are impossible? Does this preprint prove that warp drives are impossible?
J. Santiago, S. Schuster and M. Visser, "Generic warp drives violate the null energy condition"
It states that the NEC (Null Energy Condition) is violated in this paper and many others: E. W. Lentz,... | No.
Regarding to that specific paper, they analysed only a family of metrics, which apparently does not even cover Lentz ansatz.
In general, be aware of no-go theorems that rely on too many assumptions. Even if you can argue with certainty that in the given mathematical framework something is impossible, you cannot gua... | {
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Angular momentum orientation of the orbits of the two stars with respect to the Solar System Happen to see this in Wiki...
The astronomer Karl Schwarzschild observed the motion of pairs of stars orbiting each other. He found that the two orbits of the stars of such a system lie in a plane, and the perihelion of the orb... | There are lots of observations that show that the line of apsides- the line joining the periapsis points of two stars - changes with time.
The phenomenon is known as apsidal precession.
Apsidal precession can of course be caused by $>2$ bodies in a system, but even for the 2-body systems discussed in the question, ther... | {
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Elastic collision with one moving object hitting a stationary object In an elastic collision, I understand that momentum is conserved and kinetic energy is conserved. If billiard ball of silver (with velocity $v_{(Ag)}$ impacts a stationary billiard ball of aluminum, I am trying to calculate the velocity of the aluminu... | If a small mass collides elastically with a larger one which was at rest, the smaller one will bounce back, not stop.
| {
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Why does the intensity of the bright fringes decrease as we move away from the central maxima in Young's Double Slit Experiment? I studied that in Young's Double Slit Experiment the variation of intensity ($I$) of the fringes on the screen with respect to the phase difference ($Φ$) is given by :
$I = 4I_{0} \cos^{2}\fr... | If you shine a spherical lightwave on the wall, you will observe that away from the line that connects the source with the wall (assuming that the direction of the lightwave is perpendicular to the wall) the intensity of the light will diminish. In the double-slit experiment, you use basically two spherical light waves... | {
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Does Lorentz symmetry breaking always require "stuff"? Following the thread "can Lorentz symmetry be broken?" and the paper "Zoology of condensed matter:
Framids, ordinary stuff, extra-ordinary stuff", it appears that any system with Lorentz symmetry breaking is called a condensed matter system (with some extra details... | Lorentz symmetry is always broken, as a matter of fact, by implied presence of many reference systems (= stuff), between which we make the recalculation rules for observed results. Markers that break the Lorentz invariance are the relative distances between RFs, their relative orientations, their particular physical pr... | {
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Book recommendation: Does anybody know a book adopting a more intuitive approach to the topic of Crystal Vibrations (phonons) than the Book by Kittel? I have tried Simon's 'Oxford Solid State basics' and Kittel 8th edition but I am not impressed by both (I mean the content covered through Chapters 4 and 5 in Kittel)
| I don't know what you would or wouldn't find intuitive, so I'll just say which book I like best: J.M. Ziman's Electrons and Phonons: The Theory of Transport Phenomena in Solids https://global.oup.com/academic/product/electrons-and-phonons-9780198507796?cc=us&lang=en&
A lot of the book probably isn't relevant to you (an... | {
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Why we only need to consider one component of the torque vector when we consider only cases in which the rotational axis is fixed in direction? In my textbook, it is said that "we will consider only cases in which the rotational axis is fixed in direction. As a result, it will be necessary to consider only one componen... | Torque is always given by:- $$\vec{\tau}=\vec{r}\times\vec{F}$$
Since, torque is a vector quantity, it can be broken down into mutually perpendicular components which add up vectorially to give the torque vector just like in the image below.
Though the example is given with acceleration $\vec a$, it is true for torque... | {
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Why is it said that antiparticles are a result of combining SR with Quantum theory? I did understand the historical reasons for the discovery of antiparticles in this context. But are antiparticles really a 'consequence' of combining special relativity and quantum theory? Why isn't it better to say that the existence o... | There are perfectly well-defined non-relativistic theories that contain anti-particles, and perfectly well-defined relativistic theories that contain no anti-particles.
Examples are a dime a dozen. Take a complex scalar field and turn on a Lorentz-violating interaction. Poof: now you have a non-relativistic theory that... | {
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Equipotential as a circle
I just dont understand how with this configuration there could exist a equipotential as a circle. For the assumption that $R>>$ dipole size I think it is there for the approximation of potential due to a dipole $p$ at a distance $r$ $$V=\frac{pcos{\theta}}{4\pi \epsilon_{o} r^{2}}$$
This is a... | Hints:
Do not use the formula for potential. Rather, we know, for a small dipole, the field at an angle $\theta$ and distance $r$ is given by:
$$\vec E=\frac {2kp \cos \theta}{r^3} \hat r+\frac {kp\sin \theta}{r^3}\hat {\theta}$$
Now note that the total electric field at any point on the given circle must be directed t... | {
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Euler-Lagrange equations in relativity (Goldstein) In order to have a covariant formulation of special relativity, we stop using the time $t$ as a parameter and we choose some invariant parameter.
In Goldstein (third edition), chapter $7.10$, it goes through this derivation making an argument about why proper time $\t... | Proper time $\tau$ can be defined as the parametrization of $x^\mu(\tau)$ such that :
$$u_\mu u^\mu = \frac{\text d x_\mu}{\text d\tau}\frac{\text d x^\mu}{\text d\tau} = c^2$$
If you choose an arbitrary parametrization $x^\mu(\theta)$, then you have :
$$\frac{\text d x_\mu}{\text d\theta}\frac{\text d x^\mu}{\text d\t... | {
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Does a object gain heat faster the colder it is? Does an object at $-273°{\rm C}$ gain heat faster than an object at $-1°{\rm C}$
| In order to answer your question definitively, one would need to know from what source the object was gaining heat, and how the heat was being transferred from the source to the object.
However, generally heat will be transferred more rapidly where there is a larger temperature difference between the source and the rec... | {
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What is the $y$-axis in an electromagnetic wave? Apologies if my question is unclear, any help to clarify it along the way is most welcome.
I'm confused about what we mean when we say electromagnetic 'waves' (say visible light). In the usual mental picture we have of a simple sine wave, what does the y-axis correspond ... | Of course what is reported onto the $y$-axis is a matter of arbitrary definition. But usually the standard way to depict an electromagnetic wave is to report onto one of the three orthogonal axis the strength of the electric field, on another one the strength of the magnetic field, and the last third axis is taken to b... | {
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Wave packet in quantum mechanics? When we talk about light waves or EM waves, we simply say that the wave packet is the superposition of other waves of different wavelengths. In quantum mechanics, we say the same thing; the superposition of many waves associated with electron form a wave packet. I don't understand this... |
Bcs one wave is associated with one electron.
This is not true! You should rather say, There is a unique wave function $|\Psi(t)\rangle$ (or In position basis $\psi(x,t)$) associated with a particular state of system.
There is something very nice about $|\Psi(t)\rangle$ but not very new, If $|\psi\rangle$ and $|\psi'... | {
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Why don't electrons accelerate in a circuit? In a circuit, electric field exerts force on electrons, so they must accelerate. Every text book I have read, points that electrons move with a constant drift velocity. How can this happen? Does Newton's law not apply there?
| Yes Newton's law is applied here, and the electrons accelerate in response to the electric field. However, the electrons also undergo collisions with the atoms of the conductor, so on an average, they acquire an initial velocity of zero just after each collision. The electrons then acquire a final velocity $\vec v_f$ b... | {
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Why light shows its wave-like properties only when it interacts with objects with dimensions close to the wavelength of light? In Young's Double Slit Experiment, we were taught that light behaves as a wave here because the width of the slits are very close to the wavelength of light itself. But why does light behave li... | If you send a water wave (with a fixed wavelength) to an object, a diffraction pattern will form behind the object (assume you send the wave perpendicular to the length of the object). If the wavelength of the waving water is very small compared to the object, the wave will not notably curve around the edges. Almost no... | {
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Gauge-fixing conditions in Einstein-Cartan gravity What are the gauge-fixing conditions one needs to impose on the tetrad one-form $e^a$ and the spin-connection one-form $\omega^{ab}$ while working in the Einstein-Cartan formalism where both are independent objects? I am more interested in the case of 4D gravity.
| Analogous to Equation 3.3 of this paper https://arxiv.org/pdf/gr-qc/9406006.pdf, one can propose the following gauge conditions in all dimensions $D > 3$
$$*D* e^a = *[d*\omega^{ab}+(\omega \wedge *\omega)^{ab}] = 0$$
| {
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EMF generated by moving square
I have been studying electromagnetic induction and I have trouble understanding some things.
Say we have a square wire going through a magnetic field like in the picture (height is "h" and total length in a magnetic field is "x"). If we moved that whole conductor to the right because of ... | Might as well answer the question in case someone in the future is stuck here as well.
The change in flux is 0 but the EMF in the case of an infinite magnetic field should be 0.
That's because while the force you get using Lorentz force law is indeed still there, now you have to take into account the force that the rig... | {
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Why isn't the formation of a black hole stopped by the uncertainty priciple? As long as spacetime is smooth (that is, not quantized), the uncertainty principle can be applied. When a black hole forms the particles that are collapsing get closer and closer (though the metric of space changes). Won't the uncertainty prin... | The uncertainty principle does not prevent indistinguishable fermions getting arbitrarily close. All it says is that if they do, they must have an arbitrarily large difference in momentum (or different spin quantum numbers).
In other words, you can cram ideal (i.e. non-interacting, point-like) fermions to as large a de... | {
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Dirac Current Derivations I am currently self-studying Quantum Field Theory and am using the book An Introduction to Quantum Field Theory by Peskin and Schroeder. I am confused about a derivation presented in section 3.5 (called "Quantization of the Dirac Field"). Equation 3.111 derives a "rotation current density" J w... | For the commutator $[J_z, a_{ 0}^{s\dagger}]$ we have non-zero terms only for those that have an $a$ in $J_z^{(s)}$
\begin{align}
[J_z, a_{ 0}^{s\dagger}] = &\, \int d^3 x \, \int \frac{d^3p\, d^3q}{(2\pi)^6} \frac{1}{\sqrt{2 E_{ p} 2 E_{ q}}} \sum_{r, r'} e^{+i ( p - q)\cdot x}
\Big[\Big(a_{ q}^{r \dagger} ... | {
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Understanding a Solution to QFT I am self studying QFT from An Introduction to QFT and currently, I am completing problem 3.3(a). Here are some sample solutions that I am using to understand this problem: (https://theoreticalmaximum.files.wordpress.com/2017/07/intro-to-qft-solutions2.pdf). In the middle of page 9, the ... | As @Cosmos Zachos comments, the contraction of an antisymmetric tensor with a symmetric one vanishes. By antisymmetry of $\sigma$,
$$p_\mu p_\nu \sigma^{\mu \nu} = -p_\nu p_\mu \sigma^{\nu \mu},$$
But as the indices are summed over we can relabel $\mu \to \nu$ on the RHS and we have
$$p_\mu p_\nu \sigma^{\mu \nu} = -p_... | {
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Where is energy in energy density? I was learning about energy density and it seemed to be defined as the potential energy per unit volume in an electric field
$\frac{dU}{dV} = \frac{1}{2}\epsilon E^2$
But how can just the electric field have a potential energy on its own without presence of any charge? What is causing... |
But how can just the electric field have a potential energy on its own without presence of any charge? What is causing this energy to be present in an electric field?
Remember the mechanical definition of energy. Energy is the capacity to do work. The electric field can exert a force on a moving charge, so it does ha... | {
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Geodesic incompleteness of static spherically symmetric solution Static spherically symmetric solution of Einstein equations is given by the metric
$$
ds^2=f(r)dt^2-\frac{dr^2}{f(r)}-r^2d\Omega^2,
$$
where $f(r)=1-(kr)^2$, $d\Omega^2$ is the metric of unit sphere.
I struggle with the notion of geodesic incompleteness. ... | Geodesic incompleteness is defined by the existence of a geodesic that, under the evolution of time from $-\infty$ to $\infty$, terminates at some finite affine parameter. Hence, it is enough to construct a geodesic (by computing the Christoffel symbols and solving the geodesic equation with respect to the given metric... | {
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Name for critical lines in parameter space and plots thereof Suppose I study a dynamical system as a function of some control parameters, and I find that the nature of the attractors changes discontinuously (or non-analytically) at certain critical values (or along critical lines) in the space of control parameters. Th... |
What do you call a plot of these basins in the space of control parameters?
Such a plot is called "parameter space" (for example), but the specific regions are not usually called "basins" (a term more associated with the system's phase space), but simply "region" or "set" (e.g., here).
A phase diagram of the dynamic... | {
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Why is power transmission carried out at low current high voltage? My textbook states that power is transmitted at high voltage and low current since $P=I^2R$ and as the current has a small magnitude, the heat dissipated across the transmission lines is less than when we carry it out at high current and low voltage. Bu... | As we have $P = I\Delta V $, the same amount of power can be delivered either at high currents and low potential differences or at low currents and high potential differences. In either case, the same amount of internal energy is transferred to the surroundings by heat as you correctly pointed out, so the decision is m... | {
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How is light emitted by an incandescent lamp? I am looking for better understanding of how light is produced in an incadescent lamp. More specifically: how is the kinetic energy of electrons converted to light?
*
*Are we dealing with interband transitions or with intraband relaxation involving photons? Is this Bremss... | The only requirement for radiation to occur, in insulators or conductors, is acceleration of charges or magnetic fields. Bound electrons surrounding a nucleus can be stimulated to radiate by thermal agitation of the nucleus. Rotations, vibrations etc. All atoms have either dipole or multipole magnetic moments, these w... | {
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Is there a special quantity for direction? As in, since vectors have magnitude and direction. And scalars have only magnitude, is there a special quantity for direction?
| You can represent a vector as
$$\mathbf{v}=v\ \hat{v}$$
where $v$ is the magnitude of the vector (that is the length of the arrow if you like) and $\hat{v}$ is the unit along the vector $\mathbf{v}$. You can refer to the former as magnitude and later as the direction of a vector.
For example: In
$$\mathbf{v}=2\hat{i}$... | {
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Does mass have an effect on Centripetal Acceleration? I am using an online simulation for a lab concerning Centripetal Acceleration. When I change the mass the graph indicates that the magnitude of the acceleration is constant. According to the Centripetal Acceleration formula: $a=v^2/r$, this is true because no mass i... | It depends on what you are looking at.
If you are applying a constant centripetal force to objects of different masses, then they will each experience a different centripetal acceleration.
If a bunch of different masses are under going circular motion around a circle of radius $r$ with speed $v$, then they will all be ... | {
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Why doesn't current flow through an open branch? I know that current doesn't flow through open branch because current can't flow through air due to its high resistance .But i was thinking , what's the problem if current flows through an open wire (assumed 0 resistance for matter of circuit solving). I mean, isn't there... | The answer is current actually does flow and charges do accumulate at ends. That's why arcs form in open circuits at high voltage. And as you mentioned the flow would be a momentary one and not continuous.
When we connect a battery to an open wire, the potential of the battery does push charges around. But as soon as t... | {
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In LED's do the number of charge carriers (electrons and holes) decrease with time? According to page-1268-69 of Halliday, Walker & Resnick's Fundamentals of Physics (10th edition),
To emit enough light to be useful as an LED, the material must have a
suitably large number of electron-hole transitions....What we need ... | No, the current won't stop flowing as the battery maintains constant electromotive force. Some free electrons will lose their kinetic energy and become gridlocked. You can view this phenomenon, that is, free electrons losing their kinetic energy, as free electrons losing kinetic energy to a resistance, say a light bulb... | {
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Why is entropy of gas reamains constant during adiabatic expansion? In adiabatic compression, we add energy to the gas via piston and decrease volume. Now the increase in energy and decrease in volume will cause increase and decrease in entropy respectively, but it turns out(according to the books) that the entropy of ... | We measure change in entropy according to the following integral from state 1 to 2:
$$dS = \int_1^2 \frac{dQ}{T} $$
For adiabatic change $dQ = 0$ from 1 to 2
Therefore the integral becomes
$$dS = \int_1^2 \frac{0}{T} $$
Since $dS=0$, no entropy change from 1 to 2.
What might be confusing you is whether the Piston itsel... | {
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Can information travel faster than speed of light in this situation? I know the answer is no but I have a thought experiment that seem to be violating that. Imagine two persons living on two different planets namely A and C which are 10 light years apart. There is a planet in between, B, which is located exactly at the... | The limit here is about how far the information can travel between two points. If people who originate at those points move while the message is propagating, that can reduce the time it takes for the people to get the message, of course, because it cuts the distance that the message has to travel to reach them. (But i... | {
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Can atom be excited above ionisation level? I know this sounds dumb, but it puzzles me when I search for ArI levels catalogue in NIST. It shows argon's first ionisation level as $15.7596119 \; \text{eV}$ in row 427, with more rows after with energy above that.
This is puzzling. How can atomic energy levels go beyond io... | The atom is a whole quantum mechanical entity, the electrons occupying orbitals at definite energy levels. Scattering photons of the appropriae frequency an electron has a probability to be removed, it does not need to be in the shallowest energy level.
If one could radiates the atom with the frequency/energy of a low... | {
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Can it be shown in experiment that the momentum (or position) states of the electron and proton in hydrogen are entangled? The states of the electron and proton in hydrogen are entangled. Which means that the momentum and position of both are entangled. Can this be shown in an experiment, so if you measure the momentum... | Indeed, the states of the electron and the proton in a hydrogen atom are entangled. The wave function of a hydrigen atom has form
$$
\psi(\mathbf{x}_e, \mathbf{x}_p) = e^{i\mathbf{k}\mathbf{R}}\phi(\mathbf{x}_e- \mathbf{x}_p),
$$
where
$$
\mathbf{R}=\frac{m_e\mathbf{x}_e+ m_p\mathbf{x}_p}{m_e+m_p}
$$
is the position of... | {
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Are the accelerations the same at either end of a moveable pully? Given a moveable pulley with a fixed pulley on either side,
Is the acceleration of the left weight (m1) the same as that of the right weight (m2)?
Intuitively, I would imagine it to be, since if m1 drops by 10 metres, then m3 would rise by 5 metres, and... | While it is certainly possible that $x_1 = - \frac{1}{2} x_3$ and that $x_2 = - \frac{1}{2} x_3$, as your intuition suggests, it is not necessarily the case. (We define $x_1$, $x_2$, and $x_3$ to be the displacements from the original positions of the masses.) If both of the equations were automatically true, then ro... | {
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Time derivatives of the unit vectors in cylindrical and spherical In cylindrical and spherical coordinates, the position vectors are given by $\mathbf{r}=\rho \widehat{\boldsymbol{\rho}}+z \hat{\mathbf{k}}$ and $\mathbf{r}=r \hat{\mathbf{r}}$, next to next, and their derivatives with respect to time are
$$
\dot{\mathbf... | It doesn't make a lot of sense to talk about the "time derivatives of the unit vectors of the basis themselves", because the unit vectors themselves are constant with respect to time. Instead, in curvilinear coordinates, the basis vectors are vector fields, with different values from point to point in space. The unex... | {
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Motivation of Keeping Supersymmetry in String Compactification In Candelas, Horowitz, Strominger, and Witten's famous paper [1] about string compactification, they ask that supersymmetry should not be broken in the resulting 4d theory. Then combined with other reasonable requirements, they concluded that the 6d compact... | The motivation is that supersymmetry is actually a consistency condition for string theory. Non-supersymmetric string theories exist but all of them have problems such as tachyons or anomalies.
Other interesting point is that we don't know any single example of a stable non-supersymmetric vacua constructed within strin... | {
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Indistinguishability of Quantum States and its Consequences In the book Quantum Computation and Quantum Information, there is a discussion about how if states are not orthonormal then there is no quantum measurement capable of distinguishing the states.
I am interested in the consequences of this. What does this mean p... | Let assume two states $|x\rangle$ and $|y\rangle$ and their inner product $\langle x|y\rangle$. If $\langle x|y\rangle = 0$, then both state can be perfecly distinguished and there is no uncertainty which is which. Examples of such states are $|0\rangle$ and $|1\rangle$ or $|+\rangle$ or $|-\rangle$. As $\langle x|y\ra... | {
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When I walk down the stairs where does my potential energy go? When I leave my room I walk down three flights of stairs releasing about 7kJ of potential energy. Where does it go? Is it all getting dispersed into heat and sound? Is that heat being generated at the point of impact between my feet and the ground, or is it... | Into the motion of your body.
When you go down the stairs, your muscles take the vertical motion down the stairs and add a horizontal component to it. As you travel down the stairs, you will be accelerated vertically by gravity, as your potential energy is converted into kinetic energy. The faster you go vertically, th... | {
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Mechanical energy in a body moving upwards Why is it that mechanical energy is always conserved, I mean when an object is thrown in air, why does the kinetic energy convert to potential energy and not any other form of energy?
| Mechanical energy is not always conserved. It is only conserved if the system is not subject to a net external force.
In your example the object and the earth are the system.
If you throw an object in air mechanical energy of the system will not be conserved because the air exerts an external force due to air resistanc... | {
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Graph Interpretation of Gravitational Waves In the image is the data recorded by the LIGO's 2 observatories in USA. What is its interpretation? I mean what does the zig zag lines represent? Similarly, what does the blond red and blue lines (that seem like exponentially increasing up) represent? Could you please clarify... | This is showing what is called a black hole merger. It is two black holes that are orbiting each other, and after time, they get closer to each other and then finally combine.
These graphs show the frequency spectrum versus time of the gravitational wave signal (each graph is from each detector of the LIGO). As time pa... | {
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Why do I feel centrifugal force If I move with constant speed on a turn? Title sums it up pretty much, I'm studying for my physics exam right now and I just can't wrap my head around this
| Because as the car turns around a corner it is forcing you away from your straight inertial path so your path has to curve with the car. As the seat, seat belts, or whatever part of the car you are touching curves away from your straight inertial path it applies pressure on you forcing you away from the straight line y... | {
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Scalar field displacement from the minimum of the potential gives rise to particles/dark matter, why? In This paper (Kobayashi et al -- Lyman-alpha Constraints on Ultralight Scalar Dark Matter: Implications for the Early and Late Universe) it says, at the beginning of Section 3.1:
A light scalar field stays frozen at ... | The answer seems to be much less deep than what OP expects. The field $\phi$ is to be thought of as a purely classical field, its magnitude literally representing the density of matter. So if its value is large, it means there is a lot of matter, and if low, very little.
As the field is locked to its initial value, if ... | {
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Why is difference of points not a valid definition for a vector in curved space? In page-49 of MTW (1973 edtn), the following picture is shown:
After seeing this picture, the question which arose in my head is why exactly can we not define a vector as difference of points in curved space?
| Because in curved spacetime you can't take the difference of a vector at point P and point P' unlike in Minkowski spacetime.
Imagine abovementioned two points separated by $dx^{\mu}$ and let's call the vector at point P $a_{\mu}(P)$ and the other $a_{\mu}(P')$. You can infinitesimally transport the vector at P by $dx^{... | {
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Why is the work done by internal conservative forces equal to negative of the change in potential energy of the system? In my Physics class I studied that work done by an internal conservative force is equal to the negative of the change in potential energy of the system. That is,
$$dW_{internal conservative force} = d... | In short, because:
Conservation of energy theorem =>
$T + V = Constant$
So: $dT + dV = 0$
So: $dT = - dV$
| {
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Unexpected different results from Newton's second law Please don't ban me. I read through Homework-like questions and I know they should ask about a specific physics concept and show some effort to work through the problem. I hope the question is ok.
I recently came across a mechanic basic problem which I wanted to sol... | The first solution is wrong. When you calculate the torques relative of the right edge of the bar you forgot about the torque of force $N$. The correct equation should be
$$ f\cdot L \sin\theta + N \cdot L\cos\theta = P \frac{L}{2} $$
and then you'd get the result that agrees with the second solution.
| {
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If $E=mc^2$, then why do different substances have different calorific values? Today during a classroom discussion, I realised that if we consider the equation $E=mc^2$, then we are establishing a relation between energy and mass but we often observe that different substances produce different amount of energy when the... | Different $E$. Burning is a chemical process that releases some amount of chemical energy, which is vastly less that the total rest energy contained in the initial substance. The $E$ in $E = mc^2$ is how much energy you'd get if you converted all of the mass into pure radiation and left nothing left, which is a totally... | {
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Does light travel in a straight line from a third observer's view? We are always taught that light travels in straight path in a homogeneous medium, we even do experiments in primary school with cardboards with holes, "proofing" that light does not bend.
But on a wider perspective, let's say sending a pulse of light fr... | According to the GTR, there is no such thing as a classic straight line in a universe with Gravity - they are replaced by the concept of a geodesic.
The weaker the gravity, the closer the geometry approximates Euclidean geometry with straight lines. Since gravity "curves" space-time, and light travels through space-tim... | {
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Could metal rods conduct geothermal energy to the surface? Currently geothermal heat pumps circulate a working fluid through a loop running in either a deep well or a long series of more shallow trenches. Boring a well is expensive and digging trenches chews up a large chunk of land.
Could an array of metal rods (reba... | Since the characteristic time of diffusion is L²/D, where L is the characteristic length and D is the diffusivity (here, the thermal diffusivity), the characteristic speed is D/L, or 10-7 m/s for a 1 km deep probe and very thermally conductive copper. We can pump liquid far faster than this.
Looking at the conductive p... | {
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How can the Wigner function of squeezed states be non-negative? It is always said that when the Wigner function of quantum states takes a negative value, then it is a clear signature of non-classicality of this particular state. It is also well-known that the Wigner function of squeezed states is completely non-negativ... | There is no contradiction because positivity of the Wigner is not enough to guarantee classicality: squeezed states are precisely examples of this. What is known for pure states (Hudson’s theorem) is that only Gaussian states have non-negative WFs (at least in the $xp$ plane), but the theorem is silent on the classic... | {
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Double Slit Interference pattern - horizontal or vertical? What determines whether in a double slit experiment the interference pattern will be horizontal or vertical for example? Is it mostly seen horizontal because the slits are small enough horizontally for interference pattern to be seen? Also, I sometimes see a "r... | TL;DR
*
*If the slits are sufficiently long the diffraction pattern will be spaced in the same direction as the slits.
*If the length of the slits is of the order of the wavelength then the diffraction pattern will appear "rectangular".
*One should only expect a circular interference pattern if the aperture has a c... | {
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Why is acoustic intensity inversely proportional to density of the medium? The definition of sound (acoustic) intensity is given by
$$ I = {p^2 \over {\rho c}} \;\;\;\; \text{or} \;\;\;\; I = {p^2 \over {2\rho c}}$$
I've seen both definitions in different textbooks and am not sure which equation is more accurate. But... | A candid way to visualise that $density / amplitude$ relationship is the following image:
*
*Imagine the medium as a 1 or 2 or 3 dimensional lattice of marbles linked to their nearest neighbors by springs (a N-dimensional array of harmonic oscillators, if you wish).
*The density (of the simplistic medium) is relat... | {
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Do $2s$ and $2p$ orbitals have same energy? While solving the Schrodinger equation for the H atom, we get $E_n$ depending exclusively on $n$ (actually on $\frac{1}{n^2}$). Then I thought 2s and 2p orbitals must have the same energy.
But while reading Molecular orbital theory in Atkin's Physical chemistry book, I found ... | In a multielectron system by solving the Schrodinger equation you will see that the energy of the orbital doesnt only depend on n ,it depends on l as well.
| {
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What are the symmetries of circular billiards that makes it integrable? I have often heard that integrability in is equivalent to extensively many conserved quantities $A_i$, i.e. the Poisson bracket $\{H,A_i\}=0$ or in quantum mechanics $[H,A_i]=0$.
*
*What are the conserved quantities $A_i$ for classical circular b... | 2D circular billiard is Liouville integrable:
*
*The Hamiltonian $H$ itself is always an integral of motion for an autonomous system.
*The boundary force is a central force, so the angular position variable $\theta$ is cyclic, and hence the angular momentum $J_3$ is an integral of motion.
Linear 2-momentum $\vec{p}... | {
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Entanglement in 2D Harmonic Oscillator system Let's assume a 2 dimensional harmonic oscillator system with the Hamiltonian $\hat{H} = \frac{1}{2} p_x^2 + \frac{1}{2} p_y^2 + \frac{1}{2} \omega_x^2 x^2 + \frac{1}{2} \omega_y^2 y^2$ with the solution of the ground state being simply the product of the the ground state of... | Entanglement means the system not separable in any basis (or coordinate system). It’s not always easy to show there is no transformation (such as the inverse of the one you propose) that would bring a system to an explicitly separable form.
The development of practical entanglement witnesses to show entanglement irres... | {
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Experimental result of the atomic nucleus volume by scattering alpha particles from the atomic nucleus. Investigation of the electron volume by what? Rutherford's alpha particle experiments marked the beginning of the determination of the volume of the atomic nucleus.
How were the experiments conducted that led to the ... |
How were the experiments conducted that led to the statement of the point-like electron?
The particle physics experiments are mainly scattering experiments, and the theory that fits the existing data and predicts future data is the quantum field theory, QFT, of the standard model, SM.
The axiomatic table in the SM ha... | {
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Uniqueness of the definition of Noether current On page 28 of Pierre Ramond Field theory - A modern primer the following is written:
"we remark that a conserved current does not have a unique definition since we can always add to it the four-divergence of an antisymmetric tensor [...] Also since $j$ [the Noether curre... | In Noether's first theorem, the continuity equation$^1$
$$ d_{\mu} J^{\mu}~\approx~0 \tag{*}$$
is an on-shell equation, i.e. it holds if the EOMs [= Euler-Lagrange (EL) equations] are satisfied. It does not necessarily hold off-shell.
Hence we can modify the Noether current $J^{\mu}$ with
*
*terms that vanish on-shel... | {
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Does real life have "update lag" for mirrors? This may sound like a ridiculous question, but it struck me as something that might be the case.
Suppose that you have a gigantic mirror mounted at a huge stadium. In front, there's a bunch of people facing the mirror, with a long distance between them and the mirror.
Behin... | If there were such a lag, you could use a moving mirror to measure the speed of light.
This was first done in the 1920s by Michelson. (See e.g. this link which hosts papers from 1924 and 1927.) Michelson built an octagonal solid with mirrored sides which spun at several hundred times per second, and used this spinning ... | {
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Smallest proposition given a state $\psi$ Today, in my lecture the following was mentioned:
Given a state $| \psi \rangle$ in a Hilbert Space $H$, the smallest proposition which is true given this state is given by the projection operator $| \psi \rangle \langle \psi |$, which is the smallest projection operator that ... | This terminology is not familiar to me, but I can think of only one possibility :
For Hermitian operators, there is a notion of positivity (and therefore an order). In this case we would say that a hermitian projector $P$ is smaller than another $Q$ if :
$$\forall |\varphi\rangle, \langle \varphi|P|\varphi\rangle\leq \... | {
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What does it mean for a nucleus to be more stable? When we say that a nucleus is more stable than another nucleus, are we saying that the nucleus is at a lower energy level than the other nucleus? In chemistry, a more stable compound is one that is at a lower energy level, is this the same when we talk about a nucleus?... | Your reasoning based on the ‘rest mass energy’ is not really relevant to the analysis. On earth, a nucleus at higher altitude would hold more gravitational potential energy. But I don’t think you would intuitively imagine that this would make it less stable. My point is, you could define many different kind of energies... | {
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Why is centrifugal force called fictitious? When an object undergoes rotation, from the object's reference frame, which is a non-inertial reference frame, the object feels there is a radially outward force, a centrifugal force, acting on it. However, from an inertial reference frame, this force doesn't exist at all. Th... | I disagree that you feel centrifugal force. A person in a centrifuge actually feels their reaction to the centripetal force. If you sit in a car that is subject to harsh acceleration, you 'feel' as if you are being pushed back in your seat. There is no force pushing you back- it is simply the result of your inertia.
| {
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Can we cool Earth by shooting powerful lasers into space? In a sense, the climate change discussion revolves around the unwanted warming of the earth's atmosphere as a whole.
It seems a bit too obvious to be true, but could we cool the atmosphere by simply shooting that unwanted energy somewhere else?
Energy might be c... | Cheap and effective method: We should paint roofs and streets white.
Besides, a small part of the Sahara would currently be enough to supply humans with electricity from solar cells. On the rest of the Sahara there could be solar cells to power your lasers. But this is only possible if the power loss of cells and laser... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/650490",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
"answer_count": 8,
"answer_id": 2
} |
What's the difference between inelastic X-rays scattering and Raman scattering? In solids, inelastic scattering of X-rays can produce or absorb a phonon, which is equivalent to saying that solid ends up in excited vibrational level ( or if it was in a vibrational level to begin with, it ends up in ground state). But is... | Raman Scattering is indeed an inelastic scattering process. Raman scattering is synonymous to inelastic scattering of photons.
Raman scattering is usually done in IR region, the reason being vibrational spectra of most molecules are in this region. That doesn't mean Raman spectroscopy can't be done with high frequency ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/650892",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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