Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Are galaxies really structured the way they look in pictures?
Are real galaxies really structured the way they are in pictures online?
I'm wondering this because if the speed limit of the universe is light speed, which means stuff we see on the sky or detected are delayed. Therefore,
shouldn't galaxies look extremely ... | Let's first assume that we are looking at a distant galaxy, meaning that the distance to the galaxy is much larger than its diameter. This would mean that the apparent angle subtended by the galaxy is very small (e.g. arcsecond to arcminute range).
The result is the ratio of the distance that light rays from the edge o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/427302",
"timestamp": "2023-03-29T00:00:00",
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Does anti-blue coating work less effective on high power lens? I purchased a spectacle from an online website with anti-blue coating. The features of this product is mention here.
Once I receive it, I started using the product without testing the anti-blue coating, recently, I visited the optics store and out of curios... | the optical power of the source is important. your glass with a specific coating can reflect a certain percent of the blue light. i.e. if blocks for example 95 percents of blue photons. and this work for your mobile phone or sunlight, but for a laser because of high optical power that the remaining 5 percents is still ... | {
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"url": "https://physics.stackexchange.com/questions/427477",
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Behaviour of fluids in thin spaces Suppose you have a simple setting: a thin (scale of hundreds of nanometer to single digit micrometer) but in relation to that very wide (up to millimeters) box with an input and an output hole in it.
Given how thin the space is, would a fluid even go in there and fill out the box? Ho... | Your setup is known as a Hele Shaw cell, in which the bulk of the flow is a balance between pressure and viscosity, and around the edge of a region if fluid the balance is between pressure and surface tension.
Also look at the Wikipedia page about Hele-Shaw flow
| {
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Working with Reciprocial Lattice In solid matter physics the lattice structure can equivalently be described via standard Bravais modelling but also by considering it's reciprocial lattice. Mathematically the reciprocial lattice can be indeed interpreted as Fourier trafo of given Bravais lattice.
I often read that by ... | Have you seen so-called tight-binding models yet, describing electrons hopping on a lattice? Here's a simple example with spinless particles in one dimension:
$$H=t\sum_i c_i^\dagger c_{i+1},$$
where $c_i$ annihilates a particle at site $i$, and $c_i^\dagger$ creates one. $t$ sets the hopping energy scale. Since the el... | {
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How do I know that gauge fields are bosons? QED and the Dirac equation have field operators $\psi$ interact with a gauge field $A^{\mu}$.
We identify $\psi$ as a fermionic field and $A^{\mu}$ as a gauge boson - the photon.
Do we or can we know that one is a fermion and the other is a boson?
Or do we get that informat... | By the spin-statistics theorem, half integer spin is associated with fermions whereas integer spin is associated with bosons. Gauge fields transform as vectors under Lorentz transformations therefore they have spin one and are bosons.
| {
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Cubic Beamsplitter Extra Beam? I am filling out a lab report for my optics course, and it asks, "What is the laser beam corresponding to the dashed line of the cubic beamsplitter of the figure below due to?" I have scavenged the internet, the textbook, PhysicsSE, and the lab report and still no dice. Anyone know about ... | from google:
"
Many beam splitters have the form of a cube, where the beam separation occurs at an interface within the cube (Figure 2). Such a cube is often made of two triangular glass prisms which are glued together with some transparent resin or cement. The thickness of that layer can be used to adjust the power sp... | {
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"timestamp": "2023-03-29T00:00:00",
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What transfers energy Suppose a moving object collides with another resting object. First object gives momentum hence mechanical energy to the second object. It shouldn't be like energy suddenly appears on the second object. There should be some way that the second object gains energy from the first object. In theoret... | Forces are transmitted between colliding objects like rubber balls by means of the electrostatic repulsion of the electron clouds that surround the atoms which make up those objects; in addition, those electron clouds strongly resist being forced to overlap because of quantum-mechanical effects. They therefore push bac... | {
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Why does paint mix to produce black, but light mix to produce white? Mixing of different wavelengths of light results in white, but why is that when paint with different colors are mix results in black?
| Mixing light is additive since you are adding electromagnetic waves with different wavelengths together.
The color of materials as paint relies on a different principle. Only certain wavelengths of the impinging light get scattered back and the rest gets absorbed. For example, red paint only scatters back the red wavel... | {
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How can we see stars if their apparent width is less than a pixel? Stars are so far away that their apparent width is essentially zero when compared to any pixel of a camera or TV screen.
And yet we can still see them.
According to our eyes stars have a finite albeit very small width. Why is this, and what is this widt... | The light beam from a very distant star wiggles about in position by a tiny amount due to the effects of passing through the earth's uneven atmosphere on its way towards your eye. In this way it then excites more than just a single photoreceptor in your eye or pixel in an imaging device and thereby produces a "visible"... | {
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Why does only gravity leak into extra non-compact dimensions? This article
K. Pardo, et. al., Limits on the number of spacetime dimensions from GW170817, Journal of Cosmology and Astroparticle Physics, Vol. 2018, 2018.
which was published recently in JCAP states that they put constraints on the number of extra non-c... | The analysis is model dependent, and in a string theory setting would correspond to a brane-world scenario where the non-gravitational fields (open strings) live on a 3+1 dimensional brane. That is, the non-gravitational fields are confined to the 3+1 dimensional space of the brane, while gravity (closed strings) are f... | {
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Modes in optical fibers I am trying to understand the modes in step-index optical fibers and I saw that they say the electric field distribution in the core and cladding is as bellow. my question is that which component of electric field is this?
| "TE" means "Transverse Electrical". That means these modes have E-field perpendicular to the axis of the fiber. Because the fiber is circularly symmetric, the E field could point in any direction perpendicular to the axis (we say that the modes in different polarizations are degenerate).
However, circular dielectric wa... | {
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Why does different part of a spring having mass expand proportional to their distance while the spring has some mass hanged in the bottom? Why do different parts of a massive spring expand proportional to their distance while the spring has some mass hung on the bottom which is comparably very less than the mass of the... | I think it might be because the helical springs when compressed are not actually compressed, they are twisted.The spring as a whole might be acted upon by an axial compressive load but the wire is actually twisted.With twisting, the deformation at the far end(away from fixed) will be more than the fixed end.But Iam not... | {
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Hamiltonian in rotating frame I have a Hamiltonian for spin in a magnetic field
$$ \hat{H}(t) = \mathbf{B}(t) \cdot \mathbf{\hat{S}}$$
$\mathbf{B}(t) =B_x(t) \hat{\mathbf{x}} + B_y(t)\hat{\mathbf{y}} + B_z(t)\hat{\mathbf{z}}$ is the magnetic field, and $\mathbf{\hat{S}}$ is the vector spin operator. If I choose new ti... | You're applying a Rotation Operator into your magnetic field, as follow
$$ B'=R(\theta)B.$$
So we would apply the same for the vector spin operator
$$S'=R(\theta)B.$$
The Hamiltonian becomes
$$ H=(B')^T.S'=BR(\theta)^TR(\theta)S=B.S$$
$(B.S)$ is a scalar product in the spacial sense, yes it is a matrix but it's not a ... | {
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Voltage and current for travel kettle I used a 500 watt travel kettle in France last year and it tripped the electrics in my hotel room so I stopped using it. I assumed the current was too high, even though its wattage rating wasn't that high.
However I realised the voltage switch on the kettle was set to 120V and not ... | Suppose that at a voltage of $2V$ the kettle element consists of two parts in series each of resistance $R$ ie a total resistance $2R$.
The power dissipated in the element is $\dfrac{(2V)^2}{2R}= \dfrac{2V^2}{R}$
If the element is to dissipate the same power when the voltage is halved to $V$ then a switching arrang... | {
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Is action for free particle really minimal?
On my mechanics classes I have a problem: show, that the action for free non-relativistic particle $$S=\int\limits_{t_i}^{t_f}\frac{m\dot{x}^2}{2}dt\tag{1}$$ is really the least (but not maximal).
What I do:
$$S=\int\limits_{t_i}^{t_f}\frac{m\dot{x}^2}{2}dt=\frac{mV^2}{2}\i... | Hints:
*
*You are supposed to show that for arbitrary but FIXED values of $t_i$, $t_f$, $x(t_i)$, $x(t_f)$ (with $t_i< t_f$), that the off-shell action functional $S[x]$ for an arbitrary virtual path $t\mapsto x(t)$ is bigger than the on-shell action $S[x_{\rm cl}]$ for the classical path $t\mapsto x_{\rm cl}(t)$.
... | {
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How can velocity be a tensor? I have just begun studying general relativity and have a question.
I know that if a tensor is zero in one coordinate system, it will be zero in all coordinate systems.
So how can the $\mu$'th component of the velocity $dx^\mu/d\tau$ be a tensor?
There must be something I have misunderstood... |
velocity should not be a tensor
Why not? 4-velocity is a tensor: a $1 \choose 0$ tensor. It is the tangent vector to the worldline of a material particle, parametrized by proper time.
Its components obey an identity:
$$g_{\mu\nu} u^\mu u^\nu = 1$$
($g_{\mu\nu}$ the metric tensor).
(I beg your pardon: there are two si... | {
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Neumann function in 2D Schrödinger equation in polar coordinates In the question 2D Schrodinger equation in polar coordinates, @Qmechanic has shown that $\mathrm{Y}_0(r)\sim \ln r$ should be omitted since it's energy expectation value will diverge:
$$
\def\dd{\mathrm{d}}
\def\bm{\boldsymbol}
\int_0^{a} \psi^*\nabla^2\p... | The Neumann function satisfies $\nabla^2Y_0=-Y_0$ only for $r>0.$ If one was to include the origin in the solution, this functional relation is changed.
Indeed, since asymptotically towards the origin $Y_0(r)\asymp\frac{2}{\pi}\ln r$ we observe that:
$$\int\limits_{r\leq \epsilon} dA[ \nabla^2Y_0+ Y_0]=\int\limits_{r\l... | {
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Models in physics As I said in another question I am just a physics enthusiast so I am sorry for my very poor knowledge. What is meant by models in physics? what is their function and why physicists imply them?
Are the actual phenomena the exact reproduction in the real world of a physical model?
| A model in physics usually means a mathematical description of a system which is used to make testable predictions about its behavior. When writing about physics, some people prefer the term "model" over "theory" because most non-physicists don't know the difference between "theory" in the scientific sense and in its e... | {
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Is the Taub-NUT solution stationary? The Wikipedia article about the Taub-NUT spacetime says that it was a first attempt in finding the Kerr solution. Since the Kerr spacetime is a stationary solution, meaning that it admits an asymptotically timelike Killing field (that is, near the future and past null infinities $\m... | A common definition of a stationary spacetime is a spacetime that has a timelike Killing vector (see e.g. Wald, General Relativity, p. 119, or Stationary and Static). In this meaning both the Kerr spacetime and the Taub-NUT spacetime are stationary.
Regarding the second question: consider the Taub-NUT metric in the fo... | {
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If we push a syringe with gas in it In space , would its temperature increase permanently , Violating Boyles Law? On Earth
If we push a gas syringe very fast Inwards , work is done on the gas by
W = PV
which increases the Kinetic energy of molecules in it and since Temperature is Average Kinetic Energy thus T... | Boyle's law is just a special case of the ideal gas equation, for an isothermal change. But you are putting too much emphasis on air and surroundings. This just means: Boyle's law holds, if the change is isothermal - usually that means you have some type of heat exchange that keeps the temperature constant when you are... | {
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Non-acceleration and 0 force If a mass is moving at the rate of 30/ft. per minute for 5 minutes on a straight line and it strikes a second stationary mass and effects a change of position to this second mass, then we know from F=ma that the force is 0 since the acceleration is 0. Then why do we say because it is 0 that... | We never say force acting is zero.We just say there is no external forces to the two masses(external force to the system is zero).This is because only if the external forces are zero(or their effect should be negligible), momentum conservation can be applied.But the force applied by one mass on the other(internal force... | {
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vortex anti-vortex configuration to ground state i'm studying kosterlitz transition. I'm reading this:
https://assets.nobelprize.org/uploads/2018/06/advanced-physicsprize2016-1.pdf?_ga=2.51324009.1302372948.1538119052-1605759177.1538119052
Now at page 5 it says :
"The right panel shows a vortex anti-vortex configurat... | Say $d$ is the distance vortex-antivortex. When $d\rightarrow 0$ the vortex and antivortex annihilate each other. Here's a gif I found on google which makes it clear.
When the vortex and antivortex are at the same position, you get back the ground state of the system (a ferromagnet here if the arrows represent spins).... | {
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Why a metallic mirror temperature cannot be read by a thermal camera? When I look at a first surface mirror with a thermal camera I don't see the temperature of the mirror but the temperature of the reflected objects. It is like if a polished metallic surface don't lose infrared light due to is own thermal agitation. W... | I would imagine that it is because light is a form of electromagnetism, as in, the infrared light the camera is detecting is the light being reflected off of the mirror, as the mirror's personally emitted temperature is simply a reflection of the thermal agitation of the object it is reflecting.
| {
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What's the physical meaning of the gauge invariant quantity $\partial_\mu \varphi(x) - A_\mu(x)$? A famous locally gauge invariant quantity is
$$ F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \, , $$
which is interpreted as the measurable electric and magnetic field strengths.
Now, another locally gauge invaria... | Up to a constant, this is the kinetic momentum, the quantum generalization of $mv$. You know that in a magnetic field the canonical momentum picks up an extra $eA$, and here we’ve just subtracted it back out again. The kinetic momentum measures how much “oomph” is in the particles if they hit you.
| {
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"url": "https://physics.stackexchange.com/questions/431475",
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What makes the disturbance in Electromagnetic waves move? I get that changing electric field will have a curly changing magnetic field and changing magnetic field will have curly changing electric field. So when we move a charge up and down, electric field will change, which will produce this changing magnetic field an... | The general description of dipole radiation is a follows: There is an electric dipole in an antenna (hence an electric field). The charges switch, so their is a current--that makes a magnetic field, until they have switched. Now there is an electric field with opposite polarity. Repeat.
You can find the description in ... | {
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Instantaneous velocity So here’s a question I’ve been thinking of for a while. Suppose we say, “an object is having an instantaneous velocity along a particular direction ( say 10 m/s along the $x$-direction)” . Is it fair to conclude that it is traveling in a straight line along the $x$-axis? Well my opinion on this i... | It is only fair to say "travelling in a straight line" when the acceleration vector points in the same direction (or directly opposite) as velocity. If you accept any looser definition then "instantaneous velocity" would seem to always be in a straight line.
In all of the examples given above, there is an acceleration... | {
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Why are transformations that only change something within a finite region redundancies? I'm trying to build some intuition for a very particular definition of the notions global and local gauge symmetries. The definition goes as follows and appears, for example, in "Quantum Field Theory - A Modern Perspective" by V. P.... | Physical systems are described by differential equations plus suitable boundary conditions. (Only when we combine differential equations with proper boundary conditions, we can expect unique solutions.)
For example, we can impose
$$\phi(x) \to \phi_0 \quad \text{as} \quad |x| \to \infty \, .$$
Now, states connected b... | {
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Time evolution of eigenstates superposition If a system is in a state $\psi$ which is superposition of, let's say two, energy eigenfunction, namely $\psi_1$ and $\psi_2$, so that $$\psi(t)=\psi_1e^{-i\omega_1t}+\psi_2e^{-i\omega_2t}$$ (I am omitting normalization constants for simplicity) then $$\left|\psi(t)\right|^2=... | While it's true that
$$\langle\psi_1|\psi_2\rangle = 0$$
it isn't necessarily true that
$$\psi^*_1(x)\psi_2(x) = 0$$
Why? Because we can insert the identity
$$1 = \int\,\mathrm{d}x\,|x\rangle\langle x|$$
in the first equation to get
$$\int\,\mathrm{d}x\,\langle \psi_1|x\rangle\langle x|\psi_2\rangle = \int\,\mathrm{d}... | {
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Confusion with regards to uncertainty calculations Let’s say we have a scenario of a ball being released from the top of the building. This can be modeled simply with the kinematics equation $S=ut +\frac{1}{2}at^2$, which reduced to $S=\frac{1}{2}at^2$. We are given $\Delta t, t, \Delta S, S$, are we are to find $a, ... | My speculation is that uncertainty refers to the range at which the possible value might lie in. Therefore, when we calculate uncertainties, we always add the absolute/fractional uncertainty.
I have discovered that the addition/subtraction of uncertainties is as follows. Let’s say $(A\pm\Delta A)+(B\pm\Delta B)=(C\pm... | {
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In Boltzmann distribution, why is the system at the same temperature as the reservoir? Consider a boltzmann distribution where the total energy of the reservoir and the system is $E$. The energy of the system can be $\epsilon_i$ and the energy of the reservoir is $E-\epsilon_i$.
Now if the system can take on different... | The reservoir is taken to be large enough to provide the system with a very well-defined probability distribution for its energy $\epsilon_i$. For the theorists, this means of course that the reservoir is actually infinitely large.
A system is said to be in thermal equilibrium with the reservoir if its energy is found... | {
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Am I correct to say that ladder operators have complex eigenvalues? From the definition: $$\left. \begin{array} { l } { \hat { L } _ { + } = \hat { L } _ { x } + i \hat { L } _ { y } } \\ { \hat { L } _ { - } = \hat { L } _ { x } - i \hat { L } _ { y } } \end{array} \right.$$
We know that $\hat { L } _ { x }$ and $\hat... | Eigenvectors of ladder operators are called "coherent states". Quoting the Wikipedia article:
Since $\hat{a}$ is not hermitian, $\alpha$ is, in general, a complex number.
So, yeah, you are correct to say that in general the eigenvalues are complex (yet it is possible to have some coherent states with real eigenvalue... | {
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Reverse engineering a time dilation problem Consider the following problem
A rocket with a clock moves at $0.8c$ relative to the earth. An observer A on the rocket measures a time interval of 6 seconds. With respect to an observer B on the earth, the time interval is $$\frac{6}{\sqrt{1-(0.8)^2}}=10$$ seconds.
I got c... | It helps to think geometrically, with a spacetime diagram.
I've drawn one on rotated graph paper so that we can more easily count the tickmarks.
Observer Alice (RED) moves with (4/5)=PQ/OP according to Bob (BLUE). Each light-clock-diamond counts as "2 ticks".
Referring to your original problem, OQ=6 along Alice's worl... | {
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} |
Why do we use the RMS but not the fourth root mean quad? Why do we use the power of $2$? What is the relation between this and having the same heat energy in both AC and DC?
| This particular example happens to have a main reason. The power and hence energy of a signal is proportional to the square of the amplitude (provided other variables like load resistance is constant). So if you take the RMS, you have just summed up the total energy, average it over time and you get average power
RMS a... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can $2\pi/\omega = T$, when it is equal to $\lambda/v$? I can conceptually understand that $2π/$angular frequency will result in the period. $2π$ represents a full cycle, and $\omega$ represents the angle per second of the wave. Then, it follows that a total cycle/the number of waves a second represents the period.... | I think you must have confused the frequency with the velocity of light
| {
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Why are there no vertical normal compressive stresses when a horizontal beam has a vertically applied load? In a beam with a a single vertically applied load and a single vertical reaction force, as well as a reaction moment, for example, this one:
We would typically consider the normal stress ($\tau_{xx}(x,y)=\frac{F... | The normal stress in the transverse direction (y in this case) effectively exist, but the Bernoulli-Euler beam theory does not allow cross sectional deformation (it is assumed to be rigid in its own plane); therefore, although it is possible to calculate the transversal stress generated by Poisson's effect, the results... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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At Home Experiment Shows Permanent Magnetic Field Does Not Refract For an at home experiment I positioned a magnetic field so it would cross a boundary from air into water. I wanted to see if it would experience refraction similar to the refraction seen in electromagnetic fields. I also positioned a laser beam next to ... | Since water and air have similar magnetic permeability the magnetic field $\mathbf{B}$ does not change direction at the interface. So your experimental finding is in accordance to the current knowledge about magnetic fields in matter.
In order to see a change in direction you need to experiment with materials with cons... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Confusion on AC in LIVE & NEUTRAL WIRE So if an AC current means the elctrons are alternating or changing direction in a given time, how does this apply to live & neutral wire, don't they flow in one direction only? Please answer it as simple as possible, I'm only a high school kid.
| In a120 volt circuit the neutral wire carries current at 120 volts every other 1/2 cycle, however the voltage potential voltage potential between the neutral and ground is 0 because the neutral is connected to ground,ie there is no voltage potential difference.
| {
"language": "en",
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Can light be used as a medium to propagate sound waves on? My understanding of why sound cannot travel through space is because sound waves are a disruption wave that require a medium to traverse on, therefore sound can only go as far as the medium it's on goes; in a vacuum, sound cannot be propagated because there is ... | It is possible, but not in the way you are probably thinking.
A simple example is to shine a laser pointer at a photoconductor connected to a battery and a loudspeaker. Place a spinning electric fan blade in the light beam so the blade chops it up. Each time a burst of light hits the photoconductor, it conducts and pe... | {
"language": "en",
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Infinitely many conserved currents in any QFT? So I have the following curiosity: Consider for example, in QED, the quantity
$$
j^\mu\equiv\partial_\nu (\lambda(x) F^{\mu \nu})
$$
where $\lambda(x)$ is an arbitrary scalar function of spacetime, constructed from elements of the theory, e.g.
$$
\lambda(x)=A_\mu A^\mu F_... | If we have $\partial_\nu F^{\mu\nu}=0$ on-shell, as happens e.g. in EM without a source current, $F^{\mu\nu}X_\nu$ is conserved provided $\partial_\mu X_\nu$ is symmetric, as happens e.g. with $X_\nu=\partial_\nu\lambda$. Not all these conserved currents are trivial. See Sec. 2.1.2 of my thesis, which generalises this ... | {
"language": "en",
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Will having two water pans in my smoker make any difference? I have a backyard smoker, and I use a tray of water in it as thermal mass to help keep the temperature stable. I don't think the size of the tray is going to matter, but it's roughly 40cm x 30cm x 10cm.
Having to keep the tray full of water is a bit of a chor... | More water in the smoker = more stable temperature. You can prove this by putting in a smaller pan of water than usual and noticing that the temperature swings more.
Does adding more water change the speed the water evaporates at? The answer is kind of yes and kind of no. Here's a vapor pressure diagram:
If we lock th... | {
"language": "en",
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Why does expanding the radius of a drop in contact with a surface by $\mathrm{d}x$ increase the surface area by $2\pi r \mathrm{d}x \cos\theta$? Suppose we have a drop of water sitting on a solid surface in air.
The drop forms a portion of a sphere and intersects the surface in a circle. The radius of the circle, $x$ d... | The new circumference is $2\pi (x+dx)$ and that is multiplied by the length of the inclined bit $dx\, \cos \theta _{\rm E}$ to give the required area if $(dx)^2$ is neglected as a second order term.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Schrödinger's cat bra-ket interpretation Let $\vert\text{#}\rangle$ be the vector state of the cat, $\vert1\rangle$ the "alive" state, and $\vert0\rangle$ the "dead" state. Using the normalization condition $\langle \text{#}\vert\text{#}\rangle=1$:
\begin{equation}
\vert \text{#}\rangle=a\vert1\rangle+b\vert0\rangle
\... | First of all, I do not think $a^2 + b^2 =1$ tells you that a = $\frac{1}{\sqrt 2}$. Basic trignometry.
And to tell the truth, no one knows why $a^2$ is the probability(Or more precisely, the square of the coefficients). It's Born's Postulate.
<0|1> can be viewed as what is the probability density to find state |1> in ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is the meaning of $PV^\gamma=$ constant in an adiabatic process? In an adiabatic process, heat transfer doesn't occur and hence $\Delta U=-W$ (an increase in internal energy due to work done on the system or a decrease in internal energy due to work done on the surrounding).
My textbook then says (for monatomic ga... | It means that during an adiabatic process if you monitor both the pressure and the volume then when you calculate the quantity $PV^\gamma$ every point you will get the same result. For example, $PV=nRT$ can be stated as $PV=$ constant for an isothermal process. You are correct that temperature is also changing for an a... | {
"language": "en",
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How do charges lose electrical potential energy when going through a resistor? I can understand that the charges need to do work against the resistance - which transfers energy to forms such as light, heat, etcetera - using the electrostatic force provided by the battery terminals. But how does this result in a loss of... | Electromotive force is like a push required by electrons to get past the resistor. The loss of energy occurs because work has to be done against the resistance. If there was no resistor in the circuit, no EMF would be required. You can compare resistance to friction and EMF to the force applied in a object. In absence ... | {
"language": "en",
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What causes fluctuations in the inflaton field value? From this article
During inflation there are quantum fluctuations in the inflaton field.
And this
The field φ experiences quantum fluctuations, as the uncertainty principle tells us it must.
And this
However, the field φ, like every other field, is subject to q... | I think the difference between these two explanations is a differing view of a quantum field. I have found that some people define as a quantum field the field itself with the creation and annihilation operators that generate the particles in quantum field theory, while others consider the space filled with a quantum f... | {
"language": "en",
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Electric field in spherical coordinates Let's say I want to find the line integral of the electric field along some path $ab$ as shown here
I imagine taking small segments $dl$ of that path from $a$ to $b$, but as I imagine that, I imagine that the angles and radial distance change, however, that is how it was done, ... | When you have a point-charge $q$ on the point $O$, the potential created by $q$ in a point $M$ in space is Striclty dependent on the distance $|OM|$.
If you move from a point $M$ to a point $M'$ where $|OM|=|OM'|$, the potential is constant, and thus There's no electric field action when you move from $M$ to $M'$. i.e... | {
"language": "en",
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How can the repetition rate of mode-locked lasers be tuned? In my job there is a femtosecond mode locked laser. It is able to operate at a range of repetition rates. I understand the principle behind mode locking of a laser, but I do not know how it would be possible to change the repetition rate of the laser without c... | The cavity length (and therefore the mode-locked pulse repetition rate) of a laser can be changed in any of several different ways. The easiest is to move one of the cavity mirrors using a piezoelectric stack. Another is to insert a pair of optical wedges into the cavity and move them to vary the thickness of glass t... | {
"language": "en",
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A Question about Index Notation of a Scalar Product Could anyone please explain why an index $k$ is added to the scalar product of the velocities (squaring the velocity) in the figure below? Can't we use the same index $j$ for the second factor?
$$\dot{x}_i = \sum^n_{j=1}{\frac{\partial x_i}{\partial q_j}}\dot{q}_j$$
... | It's just an arbitrary labelling choice. You can use $j$ if you want, but to make it clearer that these are two different sums, it's sensible to use a different letter. (e.g. there might be confusion if you were to use $j$ to label two different summations - is that first summation over the sum $\frac{\partial x_i}{\p... | {
"language": "en",
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Why is there a physical preference to real numbers? In quantum mechanics, operators can only be observables if the eigenfunctions they operate on have real eigenvalues. If they are complex, I am told that, surely, some observable of a physical system cannot be an imaginary number. This makes some innate sense to me, bu... | The field of complex numbersis isomorphic to the 2D vector plane, not to the reals. Thus you can use a complex ruler to measure distances and directions in 2D space. The information of that ruler will contain both, lenght and direction. The ruler cannot be a line though, it has to be 2D. Or you can have multiple linea... | {
"language": "en",
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Is the ground state energy always larger for the system with higher potential energy? Say we have two Hamiltonians $\hat{H}_1$ and $\hat{H}_2$ that differ only in their potential energies and $$V_2(x) > V_1(x)$$ for all $x$. Is the energy of the ground state of system 2 necessarily larger than that of system 1?
| Yes, because
$$E_1~=~\langle \psi_1 |\hat{H}_1 |\psi_1\rangle~\stackrel{\begin{array}{c}\text{def. of }|\psi_1\rangle\text{ being}\cr \text{ground state for }\hat{H}_1\end{array}}{\leq}~\langle \psi_2 |\hat{H}_1 |\psi_2\rangle~\stackrel{\begin{array}{c}\hat{H}_2-\hat{H}_1\geq 0\cr \text{semipos. op.}\end{array}}{\leq}... | {
"language": "en",
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Are uncertainties higher than measured values realistic? Whenever I measure a positive quantity (e.g. a volume) there is some uncertainty related to the measurement. The uncertainty will usually be quite low, e.g. lower than 10%, depending on the equipment. However, I have recently seen uncertainties (due to extrapolat... | Uncertainties larger than measured values are common. Especially in measurements where the value is expected to be (close to) zero. For example values for the neutrino mass.
The particle data group lists these as smaller than some value with a 90 % confidence limit. But I have seen papers where $m^2$ was given as a neg... | {
"language": "en",
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Covariant and contravariant coordinates - index notation I am learning about electrodynamics and have recently been introduced to the four vector. I also come fresh to the idea of covariant four vectors and contravariant four vectors.
My question concerns the notation used and I would like to gain some insight into it... | The position of the indices contains real information about how a vector or tensor transforms under a change of coordinates (node: coordinates are themselves not vectors). For two things to be equal, they have to be equal in all coordinate systems. This means that the uncontracted indices (i.e. the ones that are not su... | {
"language": "en",
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What are the differences between anything at just above absolute zero and something just above the event horizon? I believe an item that has a half-life would decay at the same rate regardless of temperature (maybe I am wrong on this assumption) but it would definitely slow down due to time dilation above an event hori... | Event horizons represent regions of strong spacetime curvature and gravitational potential. Hence they affect the flow of time in characteristic ways. Clocks (including radioactive decay) run slower as seen by infinity, signals from them are redshifted, there is Hawking radiation, there are big tidal forces if the cent... | {
"language": "en",
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Can any body be uniform in the universe? If I take any body in the shape of a rod and stretch that, after it reaches breaking stress it breaks at one point.
Even though we apply the same the stress on each and every part of the rod it broke at one point. If it's uniform it should break at all points because breaking st... | TL;DR: No
One way of looking at this is to recognise that Physics is a series of constructed narratives involving modelling (or simulating) observations, mainly using (and developing) interpretations from mathematics (which is also a collection of powerful modelling languages).
The notion of idealised objects (includin... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Oscillator with decaying restoring force Suppose a system that is described by the equation of motion:
$$
\ddot{x} = -k\cdot x\cdot \exp\left(-\frac{t^2}{2\sigma^2}\right).
$$
(For example a spring with decaying stiffness.)
I'd like to obtain the corresponding motion $x(t)$ however I'm not sure how to tackle that probl... | It is possible to solve this problem simply by using power series. To simplify notation say $k_t=k*e^{-\frac {t^2}{2\sigma^2}}$. Then assume the solution can be written as:
$$x(t)=\sum_{n=0}^\infty c_n t^n$$
Then, inputing this into the given differential equation:
$$r.h.s.:~~\ddot x(t)=\sum_{n=2}^\infty (n)(n-1)c_n t^... | {
"language": "en",
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Can one find Dirac matrices for any spacetime metric? For any metric $$g_{μν}$$ is there always a linearly independant spacetime algebra satisfying $$\{\bar{γ}_μ,\bar{γ}_ν\} = 2 g_{μν} I?$$
For a diagonal metric I was able to work out that $$\bar{γ}_μ=\sqrt{n_{μμ}*g_{μμ}}γ_μ$$ satisfied these conditions (the minkowski ... | Yes, tetrads are the way to go. Suppose we have Dirac matrices for Minkowski space,
$$
\{ \gamma^a, \gamma^b \} = 2 \eta^{ab} I,
$$
and we also have a tetrad/vierbein, $e_a^\mu$, [1]
$$
g_{\mu\nu}\ e_a^\mu\ e_b^\nu = \eta_{ab},
\qquad
\eta^{ab}\ e_a^\mu\ e_b^\nu = g^{\mu\nu}.
$$
Then we can define $\bar{\gamma}... | {
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Modeling water flow between two tanks To familiarize myself with concepts from my system modeling class, I have posed myself the following problem, which I have been struggling with for a good while now. I am an absolute physics beginner, so it is likely I fundamentally misunderstood some things about pressure etc.
Th... | This is for @David White.
What I have in mind is $$F=-A_1\frac{dh_1}{dt}=A_2\frac{dh_2}{dt}$$
For the tube: $$\rho l\frac{dF}{dt}=\rho g A(h_1-h_2)-\frac{1}{2}\rho \left(\frac{F}{A}\right)^2f\left(\frac{4l}{D}\right)A$$where f is the friction factor, A is the cross sectional area of the tube, and D is the tube diamete... | {
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Lorentz invariance from Dirac spinor I have a really naive question that I didn't manage to explain to myself. If I consider SUSY theory without R-parity conservation there exist an operator that mediates proton decay. This operator is
$$u^c d^c \tilde d^c$$
where $\tilde d$ is the scalar superpartner of down quark. No... | Ah: The $C$ is key. The spinor $d^TC$ is the charge-conugate spinor (often denoted $d^c$), which behaves like a barred spinor as far as Lorentz transformations are concerned.
You can look up charge conjugation, Majorana spinors and similar things in most QFT textbook, e.g. in Sohnius' introduction to SUSY (the Appendix... | {
"language": "en",
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How can a particle in circular motion about a fixed point accelerate, if the point doesn't too? When a particle is performing uniform circular motion attached to a string about a fixed centre, at any instant of time its acceleration is directed towards the centre but the centre has no acceleration. But I was taught in ... | I'm guessing you mean the string constraint that Tension must be equal in both directions at all points in the string except the endpoints, where the tension at the endpoints must be equal and opposite?
So for an object moving in circular motion around a fixed point attached to a string, you're right that the object is... | {
"language": "en",
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Commutation relation in quantized electromagnetic field theory I have a question regarding a proposed problem (Problem 4.8) in Rodney Loudon's book "The Quantum Theory of Light". Let $U(t)$ be an operator defined by
$$
U(t)=\exp\left\lbrace\frac{i}{\hbar}\int\text{d}^3x\,\mathbf{V}(\mathbf{x})\cdot\mathbf{A}(t,\mathbf{... | Your $V_T(x)$ and $X(t)$ are commute, because $V_T(x)$ onlys has a $x$ in expotentional, use series expansion that the component $\frac{(i k\cdot x)^n}{n!}$ and $X(t)$ is commute, that $\frac{(i k\cdot x)^n}{n!}X(t)=X(t)\frac{(i k\cdot x)^n}{n!}$, so you can pull $X(t)$ to the right of $V_T(x)$ or the left of $V_T(x)$ ... | {
"language": "en",
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Can someone explain why there is water in this vacuum chamber? I work at a water treatment plant that uses a vacuum system to pull the water into the filters and backwash the filters. In the middle of the vacuum system there is the vacuum chamber. What I don't understand is why is there water in the bottom of the chamb... |
When the water rises, there is "high vacuum" and when the water is low
there is "low vacuum."
I would read it the other way round: when there is "high vacuum", the water rises, and when there is "low vacuum", the water is low. The reason there is water in the vacuum chamber seems to be the pressure difference betw... | {
"language": "en",
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Sum to an integral in deriving equipartition theorem I'm reading this derivation of the equipartition theorem for ideal gases. On the second page, it is mentioned that the partition function as a simple sum,
$${\displaystyle Z=\sum _{i}e^{-\varepsilon _{i}/kT}}$$
is not adequate to describe a classical gas as the distr... |
But why is this conversion from a sum to an integral correct?
There is no conversion. The partition function is defined as integral in classical statistical physics, because the possible states form a continuous set and it is the most natural definition.
In pseudo-quantum (or old quantum) statistical physics, "state"... | {
"language": "en",
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Predicting the future In the special theory of relativity, each event is a point in 4d spacetime. And we can represent our life as a world line in the spacetime. Then, if we somehow find out the mathematical equation of somebody's world line, then can his future be predicted?
| Your thoughts are similar to that of Laplace's Demon, and may be better suited for a philosophy board.
Wikipedia sums it up well:
According to determinism, if someone (the Demon) knows the precise location and momentum of every atom in the universe, their past and future values for any given time are entailed; they ca... | {
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How can the $v$ coordinate be null if $g_{vv}\neq 0$? I'm probably missing something very basic here. As far as I know, a coordinate is called null when its coordinate lines are null. This means that if $(M,g)$ is spacetime and $x^\mu$ a coordinate chart, the coordinate $x^\nu$ is null when $\partial_\nu$ is null. This... | In the case of Minkowski space time, start with the line-element in the form
$$
ds^2 = -c^2dt^2+dr^2 + r^2(d\theta^2+\sin^2\theta\,d\phi^2)\,.
$$
Consider a light ray which travels radially. In this case $\theta = const., \phi = const\,.$
This reduces the line element to
$$
ds^2 = -c^2dt^2+dr^2\,.$$
Now let $v = ct +... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/439190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Is it possible to squat quicker than gravity? It's definitely possible to propel your body using muscle to move towards the ground quicker than gravity.
But is it possible to squat quicker than gravity?
Assuming squatting from your knees and not you bending down from your back like a lever, and that you're not grippin... | Yes it would, and in fact if you make any effort at all, this is inevitable.
This answer doesn't disagree with or contradict the others.
Provided you squat quickly enough that the part of your body not dropping, i.e. the part below the knees, is not applying all of its weight to the ground, this means your top half is ... | {
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Divergenceless of energy momentum tensor for any metric $g_{\mu\nu}$ As suggested by @my2cts, from this post, I want to know if the divergenceless of energy-momentum energy tensor is valid for any metric $\eta_{\mu\nu}$ (i.e for example with $\eta_{\mu\nu}=g_{\mu\nu}$)?
Here the formula with $\eta_{\mu\nu}$ (I think t... | Yes. The Einstein tensor has zero divergence for any metric. The Einstein field equations equate the Einstein tensor to the stress-energy, so if the field equations hold, the stress-energy must be divergenceless.
| {
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Where does the unused generated electricity go? Assume there is a nuclear reactor consuming nuclear energy of one mega watt. The energy is converted to electricity by a generator with some energy loss.
For the sake of simplicity, let's assume the generated electricity is about 0.9 mega watts. If the load only consumes ... | So if I take an alternator and make a water wheel, it will just spin freely, not generating any electricity until an electrical load is put on it. Then the electrical load will add some resistance to the wheel which the flow of water will have to overcome, thus generating exactly the amount of electricity consumed by t... | {
"language": "en",
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What is the geometric interpretation of the Einstein tensor $R_{\mu \nu} - \frac{1}{2} g_{\mu \nu} R$? The Riemann curvature tensor $R_{\mu \nu \rho \sigma}$ has the geometric interpretation of giving how much parallel transport fails to close around tiny loops. The Ricci tensor $R_{\mu \nu}$ is the Riemann curvature a... | At the risk of being downvoted, without any good arguments, I can tell you that you can understand these equations as a relativistic equations for a fluid dynamics, so the G equation can be viewed as sort of continuity equation. It indicates energy-momentum conservation. My advice: google relativistic fluid dynamics.
| {
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Magnetism and magnetic fields Why does a magnet attracts iron? Why does not the reverse case happens?
When a magnet attracts a metal, does it induce a current in it or does that happen only in the coil wound around a metal?
| The reverse happens, also iron attracts magnet. It is also the consequence of Newton's Third Law.
If the magnet is static (in the frame of the iron), then there is no induction. Magnetic field is created only by moving charges and affects only moving charges.
| {
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Why does the fine-structure constant $α$ have the value it does? This is a follow-up to this great answer.
All of the other related questions have answers explaining how units come into play when measuring "universal" constants, like the value of the speed of light, $c$. But what about the fine-structure constant, $α$... | I know for sure why it is about 1/137. Because it never comes alone, but with some other dimensionless combinations of a problem parameters, so its value is only a part of a whole expression.
Some say it determines the strength of EM interaction. Let us see. We will proceed from QED, which is QM of Electrodynamics. An... | {
"language": "en",
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Will hydraulics lever ever stop if we exert some force to it? Suppose there is a simple hydraulics lever (like the one often shown when discussing about Pascal's Principle). If we exert some force into one of the piston without having any weight on the other piston, will the lever ever stop? I am guessing the lever wil... | It depends in what you mean with "there is no weight on the other piston" .
If you mean that there isn't an object on the other piston but you're performing the experiment in an atmosphere then the piston will stop when there is equilibrium of forces between the force you're exerting and the force the atmosphere exe... | {
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Angular momentum of a system about the center of mass Let $\mathbf{R}$ be the center of mass of a system of particles. Then the angular momentum of the system is
$$\begin{align}
\mathbf{L} &= \sum \mathbf{r}_i \times \mathbf{p}_i\\\\
&= \sum \left(\mathbf{R} + \mathbf{r}_i^\prime\right) \times \mathbf{p}_i\\\\
&= \math... | The answer by AccidentalFourierTransform is incorrect in that Goldstein doesn't define $\sum_i m_i {\bf r}'_i = 0 $. Between 1.27 (which states: $\bf{r_i}=\bf{R}+\bf{r'_i}$) and 1.28 there is an argument (he doesn't put everything in symbols!),
[T]he factor $\sum m_i \bf r'_i \bf$, which, it will be recognized, define... | {
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Is it possible to suggest a physical experiment in which measurement errors are dramatically increasing? (due to the accumulation of errors) Is it possible to suggest a physical experiment in which measurement errors are dramatically increasing? (due to the accumulation of errors)
Maybe some magnetic field can be used ... | There is a opportunity for cumulative errors to slip in whenever one uses one set of measurements as a proxy for a fundamentally different parameter. This is particularly so if the measured values are some kind of derivative (e.g., time or position derivatives) of the desired parameter.
An example is "dead reckoning." ... | {
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Water at 0 atmospheric pressure Suppose I put a bucket of water on the surface of the Earth. Then somehow the atmosphere disappears. My question is:
Would the water fly out of the bucket, or would it be still there?
My reasoning is that it will stay in the bucket since gravity is acting on it. Is this correct?
| The water will evaporate and fly out of the bucket; the process will not stop until there is enough water vapor in the atmosphere that the vapor pressure stops the water from boiling further. If the scenario happens in a confined space, this has a chance of happening while there is still liquid water in the bucket, but... | {
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Are there any cases where Stokes law does not apply in viscous fluids? A friend of mine and I are conducting an experiment to find the relationship between terminal velocity and radius of a sphere (i.e trying to confirm Stokes law). We are using spheres ranging from 1.5mm radius to 3mm, and dropping them in a large bea... | Stokes law is a corollary of the Navier-Stokes law.
It is not applicable in cases where
*
*Reynolds number is too high: For particles, the regime in which Stokes law is applicable - the Stokes regime - is when $Re=\dfrac{d_p\cdot v\cdot \rho}{\mu}<<1$. If Re is too high, then drag forces will cause deviations from ... | {
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Conversion from Planck unit to SI Good evening, I'm reading the paper Prehawking radiation by William G. Unruh where it says:
...a time scale of order of $m^{3}$ in Planck units, or $10^{53}$ ages of the current universe for a solar mass black hole"
How do I perform the conversion from Planck units to seconds?
| Another way to say what John Rennie said is:
A formula such as $$t=m^3$$ written "in Planck units" means $$\frac{t}{t_P}=\left(\frac{m}{m_P}\right)^3$$ in non-Planck units, where $$t_P=\sqrt{\frac{\hbar G}{c^5}}$$ is the Planck time and $$m_P=\sqrt{\frac{\hbar c}{G}}$$ is the Planck mass.
So in SI units the formula wou... | {
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How do know that Goldstone Boson actually become the longitude degrees of freedom in W+,W- and Z boson? In many Quantum Field Theory text books they says these about Spontaneous Breaking and Higgs mechanism like this
In unitary gauge, the Goldstone Bosons are eaten by $W^\pm$ and Z and become their longitude degrees of... | A massless spin-1 gauge boson (such as a photon) has two degrees of freedom (m=+1 and m=-1) which are called "transverse" (Think of an electromagnetic wave.) A massive spin-1 gauge boson has an additional "longitudinal" degree of freedom (m=0). Saying that the W+, W- and Z bosons get a longitudinal degree of freedom is... | {
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Why can't the collision be elastic if after the collision the two objects move together with the same velocity? I don't quite understand why two bodies can't 'stick' together in elastic collision. I have found several sources that say that if two objects collide and end up moving at the same velocity their collision is... | Let's assume the bodies do stick together and move with final velocity $v$, and also assume that kinetic energy is conserved. Let's also just work with a collision in one dimension.
Then we have our two conservation equations
$$m_1v_1+m_2v_2=(m_1+m_2)v$$
$$\frac12m_1v_1^2+\frac12m_2v_2^2=\frac12(m_1+m_2)v^2$$
Rearrangi... | {
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Will a warm object in a vacuum cool more quickly than a warm object surrounded by an atmosphere containing CO2? I have gotten stuck on an endless thread about Global Warming, in which skeptics sometimes make the claim that an object surrounded by a "heat absorber" like CO2 will cool more quickly than one not surrounded... | The object can be the planet Venus. If Venus would be a shiny white rock without an atmosphere, its surface temperature would about -40 C. But the surface temperature is about 460 C.
The CO$_2$ in the atmosphere radiates as much as it absorbs, half of it downward half of it upward.
https://www.acs.org/content/acs/en/cl... | {
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Why we can't take torque equation for the mid point of the ladder in the question **Source IIT JEE 2005 PHYSICS** Question (Source IIT JEE 2005 Physics)
Two identical ladders, each of mass M and length L are resting on the rough horizontal surface as shown in the figure. A block of mass m hangs from P. If the system is... | Consider a ladder leaning against a smooth wall at 45 degrees (no friction), assume force on ladder is 100N due to gravity at the centre of mass, length 4m. Use the some of torques at the bottom (floor has friction) and you should get 35N is a force at the top perpendicular to the later, resolve this force at 45 degree... | {
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If the dimension of a space is prime, are quantum states in it guaranteed to be entangled? A rather obvious question perhaps but if I have a Hilbert space of dimension $d$ and $d$ is prime, I cannot possibly write my state as $$\rho = \sum_i p_i\rho_a\otimes\rho_b$$ simply because the dimensions don't add up correctly,... | If the dimension of the Hilbert space is prime then the state is guaranteed to be unentangled, simply because it can't have any tensor factor spaces to count as subsystems.
| {
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What is the difference between the voltage in the electrical circuit and electrostatics? In electrostatics it depends on the distance from the charges, should it also be in the circuit? But in practice, the voltage depends on the resistance, for example on a resistor. And the distance itself does not play any role. Why... |
But in practice, the voltage depends on the resistance, for example on a resistor. And the distance itself does not play any role. Why so?
Because in practice, often voltage in circuits is determined by external agent, such as battery or a power grid. Distance between elements or their length does influence voltages ... | {
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image formation by lenses
Why is the image formed by an object as described in the picture can be derived only from these three ray of lights?Every point on the object has multiple ray of lights going in every direction, how do we know that the other ray of lights(other then these three) don't converge at some other p... |
Why is the image formed by an object as described in the picture can
be derived only from these three ray of lights?
Actually two rays are enough. But no real lens (or system of lenses)
will behave that way. I wonder if your teacher or textbook didn't tell
you that this is an approximation, called after Gauss, good... | {
"language": "en",
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"source": "stackexchange",
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How does the energy of a solar flare propagate? Does it radiate outward, spherically, or is it more directed? Is there some opening angle? Is it more complex than this?
| Since the original definition of a solar flare only depended upon an increase in x-ray flux in a small spatial region on the sun1, the energy of a solar flare would then propagate in the form of electromagnetic radiation.
However, our current understanding would require that we include the beaming of ions and electrons... | {
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Focusing Sunlight with Flat Mirrors- solar barbecue Say somebody had 48 1sqft glass mirrors (almost 4.5 sq.m total), because these tiles cost about $1 each.
If mirrors are all tediously aligned to redirect sunlight onto a Weber BBQ, the air temp inside the BBQ quickly rises to 260F (400K), and the irradiated surface (i... | Let's ignore conduction, and pretend that the only way the BBQ gains/loses heat is by radiation. If this bothers you, just build a transparent pressure housing around the BBQ and evacuate it.
Whether just sitting in the sunlight or at the focal point of your array of mirrors, the BBQ will reach an equilibrium temperat... | {
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Rest mass of electron-positron would be the same as their energy in annihilation? If the combined mass of an electron and a positron was approximately $1$ MeV/$c^2$, then would the total energy of their annihilation be equal to $9 \times 10^{16}$ MeV? Why do we not multiply the rest mass by $c^2$ to get the energy that... | We do multiply the mass by $c^2$ to get the energy. The mass is roughly $1$ MeV/$c^2$ and when we multiply this by $c^2$ we get $1~c^2$ MeV/$c^2$ = $1$ MeV.
| {
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Does a mirror reflecting a mirror's image go darker than the original mirror image or remain constant? Is there a constant ratio of decreasing light? I noticed before that mirrors don't adequately reflect the light level of the room. My question was if there were two same caliber mirrors, one reflecting image of the fi... |
would it go darker again
Yes. You're losing light with every bounce. A typical household mirror is somewhere around 80 to 85% efficient, so with every reflection you're going to lose 15 to 20% of the image. From the images I've see the losses seem less, perhaps 10%. For instance, you can see that it is getting darker... | {
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Why is $E=mc^2$ and not $E=m\frac{c^2}{2}$? Kinetic energy for a moving object is the integral of force with respect to distance, often given as:
$$E=m\frac{v^2}{2}.$$
This would imply that for mass moving at the speed of light, the kinetic energy would be:
$$E=m\frac{c^2}{2}.$$
This puts it off from the Einstein resul... | As the other answers point out, the full relativistic energy expression is
$$E^2=m^2c^4+p^2c^2$$
where $E$ is the energy, $m$ is the rest mass of the particle, $c$ is the speed of light and $p$ is the momentum of the particle.
If the particle isn't moving (i.e. has $p=0$) then this expression reduces to the famous
$$E=... | {
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Solid foundation for obtaining the band gap from density functional theory Looking around a lot of solid calculations, the band gap is usually estimated by DFT. But I have some doubts of that within my knowledge, so I'm asking the question.
The usual process to generate density is the Kohn-Sham approach where a density... | In band theories, electrons are independent in the crystal. Unit cells have an average density, but variations would be as random as in the free electron gas. This is a poor approximation for narrow bands, like the $3d$ bands of the transition metal compounds or the $4f$ bands of the rare earths.
Then on-site Coulomb i... | {
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Cat falling from a tree When a cat or any body falls over to the ground, how is momentum conserved?
I was working on a problem of a cat falling on top of a skateboard, and the system travels together with a new velocity. That seemed intuitive enough for me. This is how I was thinking through:
The cat had momentum that ... | Both @Farcher and @PhysicsDave answers are correct.
The key point is the momentum of a system is constant only if the system is isolated (for example, not subjected to forces external to the system). So far as we know there are not truly isolated systems- you cannot shield a system against gravity. This is why @Farche... | {
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Can we say that bosons attract each other? We know that bosons donot follow Pauli exclusion principle, thus they can occupy the same state. But is it equivalent to say that bosons attract each other?
| Saying that bosons attract each other would require a careful analysis of what do we mean by attraction. In classical physics (and in everyday life), attraction between two subsystems implies the existence of some force which makes more probable to find the two subsystem close each other rather than distant. Thus, the... | {
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Why is the potential difference across a conductor is equal to the battery voltage when it is connected to it Why is the potential differencel across the conductor is equal to the battery voltage?
| Edit: I thought the question was referring to a resistor, not a conductor. If you connect an ideal conductor to the positive and negative terminals of a battery, then the simplified picture of conductors as equipotentials will break down. To avoid this complication, you always need to include a resistor in such a cir... | {
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Derivation of 2nd law of Thermodynamics from ergodicity assumption In Wikipedia it is claimed that:
Assumption of the ergodic hypothesis allows proof that certain types of perpetual motion machines of the second kind are impossible.
Since perpetual motion machines are machines which would violate the 2nd law, shouldn... | Ergodicity is also compatible with violations of the second law of thermodynamics, because of the simple reason that if $T_t$ is an ergodic time-evolution which is invertible, then also $T_{-t}$ is ergodic. But obviously, if one of them leads to an increase in entropy, the other one violates the second law. Therefore, ... | {
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Mathematical question on Mathisson-Papapetrou-Dixon equations I am studying about Mathisson-Papapetrou-Dixon equations which govern the motion of a test particle around a central massive object in the pole-dipole approximation.
Given that $S_a=-\frac{1}{2}\epsilon_{abcd}V^bS^{cd}$ I want to prove that $S^{cd}=-\epsilon... | In Minkowski signature (-,+,+,+) we have
$$
\epsilon_{0123}= - \epsilon^{0123}
$$
so I think your identity should read
$$
\epsilon_{abcd}\epsilon^{aijk}= -\delta^i_b\delta^j_c \delta^k_d\pm {\rm perms.}
$$
which is minus what you have have. The same is true for the (+,-,-,-) signature.
| {
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Confusion on real space renormalization group for Ising model on lattice For the Ising model with only nearst neighbor interaction on square lattice, if we do the RG by integrating out half degree of freedom, then we would get a new Ising model with many kind of interactions, so Ising model with only nearst neighbor i... | You had stopped your consideration and didn't made a final conclusion. The renormalization transformation based on decimations has no fixed point. The accepted answer in this topic Critical 2d Ising Model contains a link to the notes about this matter.
| {
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Can I apply the standard Runge Kutta 4th order method to the Langevin Equation? If I have a Langevin Equation with an external force term (which may be time dependent), is it possible for me to apply the standard 4th order Runge Kutta algortihm to solve it numerically?
Edit:
I would like to mention the use case for th... | You can, but you need to be careful.
The external force is a probabilistic function, but in the simulation you need to make sure you only sample one function value for any particular time, and use that consistently. In RK4 you do several sub-steps for each time step, and if you use different a "random" value of the for... | {
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Linearization of MHD equations for a cold plasma and low frequencies I'm trying to convert the next equations for a cold plasma (consider $P=0$ the pressure), for low frequencies and ignoring dissipative effects:
$$\rho \left(\left(\frac{\partial \vec{v} }{\partial t}\right)+ (\vec{v}\cdot \nabla)\vec{v}\right)= \frac{... | As a matter of preference, I will use $\mathbf{Q}_{o}$ and $\delta \mathbf{Q}$ for the quasi-static and fluctuating terms.
Next, recall from vector calculus that the following holds:
$$
\mathbf{A} \times \left( \mathbf{B} \times \mathbf{C} \right) = \left( \mathbf{A} \cdot \mathbf{C} \right) \mathbf{B} - \left( \mathbf... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444089",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
How to derive the formula for the radius of a Fermi sphere? I'm trying to figure out how the radius of a Fermi sphere
$$p_F = \hbar (3 \pi^2 \frac{N}{V})^{1/3}$$
is derived from the formula
$$dN_{spatial}=\frac{V \ d^3p}{\hbar^3}.$$
The solution states that I should arrive at the following
$$\frac{2V}{(2 \pi \hbar)^3}... | I think it should be $h$ in the denominator of your second equation,
$$
{\rm d}N = \frac{V}{h^3}{\rm d}^3{\bf p}
$$
Integrating at both sides, and taking into account the degeneracy
$$
N = \frac{2 V}{h^3} \int{\rm d}^3 {\bf p} = \frac{2 V}{h^3} \int {\rm d}\Omega\int_0^{p_F}{\rm d}p ~p^2 = \frac{2V}{h^3} \frac{4\pi}{3... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444240",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Reason for very low speed of sound in rubber I just came by a table in the Class 11 Physics NCERT textbook, listing speeds of sound in different media.
Vulcanised rubber has an unusually low speed of sound $54\ \mathrm{m}/\mathrm{s}$ as compared to the other solids, e.g $6000\ \mathrm{m}/\mathrm{s}$ for granite and $35... | Remember that sound is a vibration of kinetic energy passed from molecule to molecule.
At the particle level, a rigid material is defined by atoms and/or molecules with strong forces of attraction for each other. You must have learnt that the particles vibrate about their mean positions like springs. They quickly retur... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444304",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
How to do dimensional analysis? $$mgh = \frac{mc^2}{\sqrt{1-(v/c)^2}}-mc^2.$$
In dimensional analysis do we just ignore the square root? Or do we solve what’s inside first then we do the square root? Do we say $(v/c)^2$ is 1 as dimensions cancel? Then say each term now has the same dimension, so this is correct? I’m s... | Since $v/c$ is dimensionless, the function $1/\sqrt{1-v^2/c^2}$ is dimensionless and dimensional analysis gets no information from this factor. It's not so much that you ignore this factor, but just it plays no role in dimensional analysis, just like "$3$" or $\pi$ does not enter in this analysis.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444504",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
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