Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Weight in Interplanetary Space How is weight zero in interplanetary
space? The Moon is orbiting the Earth because of the gravitational pull of earth. Then gravity must exist in interplanetary space too. So any body in space must also have an acceleration due to gravity ($g$) but $g$ must actually be 0 for weight to be ... | Weight depends on the reference frame.
In the reference frame of the Earth, the gravitational acceleration onboard the International Space Station is about 8.5 m/s$^2$ (about 90% of $g$).
In the reference frame of the ISS, the gravitational acceleration onboard the ISS is between -0.0001 and +0.0001 m/s$^2$, depending ... | {
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Determining the reverse breakdown voltage of a Zener diode graphically I have been measuring the reverse bias IV characteristics of a Zener Diode BZX (2.7 V) at three different temperatures, -196.2 celcius (liquid nitrogen temperature), 22.0 celcius (room temperature) and 99.0 celcius. Now I need to determine the break... | Function at extremum point (minimum or maximum) does not change, so you need to evaluate differential :
$$ \frac {d}{dx} y = \frac {d}{dx} \left(-e^{-kx}\right) = k e^{-k x} \tag 1$$
Now expand (1) into Taylor series, take couple of terms and set it to zero :
$$ k - k^2 x = 0 \tag 2$$
Solving (2) for $x$, gives approxi... | {
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Order Parameter, Phase transition
*
*Is order parameter for a phase transition is unique?
*Is it always true that in one phase order parameter have zero value and in another phase it has non zero value?
*Is there any standard rules for chosing order parameters?
*Can a system undergoing phase transition can have mo... | Order parameter is defined as a quantity that is zero in one phase and not zero in the other - this answers the second question, but also the first one, since any quantity satisfying this condition can be an order parameter. In particular, if $M$ is an order parameter, then any function of $M$ that leaves it zero in on... | {
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What gives us the equations of motion in GR? Maybe stupid question, but to my understanding, the Einstein equation tells us the differential equation governing the Geometry of spacetime. That's all good and fine , but suppose I had an actual particle with some forces acting on it, how would I find it's trajectory? Woul... | Yes, Newton's first law sort of holds. You have to generalize it to curved geometries. You can think of Newton's first law as the statement that "In the absence of external forces, a particle's velocity gets parallel transported along its trajectory".
In the absence of curvature, the parallel transport is the trivial o... | {
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Experimentally Measuring the Velocity of Water coming out of an Orifice I plan on doing an investigation into Torricelli's Law, where I will be looking at one of the following:
*
*How the cross-sectional area of an orifice affects the velocity of water coming out of it (constant height).
*How the height of an orifi... | Water is incompressible. So you can put a bucket under your stream and let it run for some time. That way you measure the volume of water coming out per time [units m$^3/$s]. Divide by the cross-sectional area of the orifice [m$^2$] to get the water speed [m$/$s].
| {
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Can we determine what the wavefunction (states) of a particle is before we decide which measurement to make? If we are measuring spin-up or spin-down then we write the wavefunction (I think) as
$$ \require{physics} \psi = \tfrac{1}{\sqrt{2}} |{\uparrow}\rangle+\tfrac{1}{\sqrt{2}} |{\downarrow}\rangle $$
But if we emit... | Note that your spin 1/2 wave function:
$$ \require{physics} \psi = \tfrac{1}{\sqrt{2}} |{\uparrow}\rangle+\tfrac{1}{\sqrt{2}} |{\downarrow}\rangle = |\rightarrow\rangle $$
where:
$$|\rightarrow\rangle \equiv |S=\tfrac 1 2, S_x=\tfrac 1 2 \rangle $$
That is, it is an eigenstate of the $\hat S_x$ operator.
| {
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Why is an equilateral triangle not a 2d unit cell? An equilateral triangle obeys the crystallographic restriction theorem, but it is not a part of 2d crystal structure. What symmetry does it lack? Why can't it be a Bravais lattice?
| It is impossible to make a Bravais lattice of triangular cells (equilateral or not). It is the essence of the Bravais lattice concept that it is based on translational symmetry (in 2D, along two independent directions). In order to build a Bravais lattice with an equilateral triangular cell, one would need to ensure th... | {
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Balmer proportionality How did Johannes Balmer arrive at
$$
\lambda \propto \frac{n^2}{n^2-4}, \quad (n=3,4,\dots),
$$
and then how did Rydberg mathematically derive
$$
\frac{1}{\lambda}=R\left(\frac{1}{n^2_1}-\frac{1}{n^2_2}\right)?
$$
I know $n$ stands for the shells but in the textbook, it doesn't define what $n$ is... | They looked at the patterns in the spectra and found formulae that matched them. Physics isn't derived from mathematics: the phenomena drive the mathematical models.
| {
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Difference between Symmetric and Phase difference? For a simple coupled oscillator system such as the one here, with equal spring constants and equal masses (with a displacement from equilibrium of $x_1$ and $x_2$), it follows that:
$(\ddot{x}_1+\ddot{x}_2)\propto x_1+x_2$
$(\ddot{x}_1-\ddot{x}_2)\propto x_1-x_2$
Wikip... | IMHO, the best approach to mass-spring systems is via matrix formulation,
$\underline{\underline{M}}\underline{\ddot{x}} + \underline{\underline{K}}\underline{x} = \underline{F} $,
where the vector $\underline{x}(t)$ collects the degrees of freedom of the problem, and finding the eigensolution of the homogenous system,... | {
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Should a system be “uniform” to qualify for it to be in steady state? I am wondering about whether a system need to be “uniform” to qualify for it to be in steady state or can not uniform systems also act as a steady system.
Can someone please clarify this.
Thanks in advance!
Any help would be appreciated.
| Steady state implies only that local thermodynamic state variables do not change in time. They can be non-constant function of position in space, e.g. there can be a temperature gradient and corresponding heat flux. If temperature function $T(x)$ does not change in time, it is a steady state.
| {
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What is the use of the low pressure helium lamp in this plasma jet experiment? I would like to ask about this experimental set up. What is the use and significance of the reference cell (Low pressure helium lamp)? Why is it necessary on this set up?
Link to paper is as follows.
https://iopscience.iop.org/article/10.108... | This is part of a laser stabilization or wavelength detection setup.
As long as the laser is on one of the Helium 2P-2S transitions, the beam gets absorbed in the helium lamp and the power on Photo Diode#2 is at a minimum. (Wavelengths: 1082.91, 1083.03 and 1083.03 nm)
With this, you can detect if your laser is at reso... | {
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Why does the kinetic energy of particles increase on heating? One of the obvious facts in thermodynamics is, when we provide heat to a system, some of the heat energy get stored into the internal energy of the system. It is thought that it was stored either in form of potential energy or kinetic energy, but here we gi... | When we add heat to matter its energy increases, both kinetic and potential. How much of the energy we add goes to kinetic versus potential depends on the details of molecular interactions. In the ideal gas state there is no interaction, therefore all heat goes into kinetic energy. When molecules interact, some heat g... | {
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Derivation of path equation, how to derive $$ r''= - \frac{L^2}{m^2}u^2 \frac{d^2u}{d\theta^2 } $$ So specifically I don't know how to go from $r'$ to $r''$. If we start with $r'$, where the substitution $r=u^{-1}$ is used.
$$ r'= - \frac{L}{m} \frac{du}{d\theta } $$
$$ (1): r''= - \frac{L^2}{m^2}u^2 \frac{d^2u}{d\thet... | I assume that with $L$ you mean the orbital angular momentum. Hence, in polar coordinates, $L=mr^2\dot{\theta}=mr^2\frac{d\theta}{dt}$. Moreover, for a function $f(\theta(t))$ we have
$$ \frac{d}{dt}f(\theta(t))=\frac{df}{d\theta}\frac{d\theta}{dt} $$
Hence:
$$ \frac{d}{dt}\dot{r}=-\frac{L}{m}\frac{d}{dt}\frac{du}{d\th... | {
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Propagator for Dirac field The Feynman propagator for Dirac field is defined as:
$$S_{\alpha\beta} = \langle 0 | T \psi_\alpha(x)\bar{\psi}_\beta(y) | 0 \rangle.$$
It should, however, be a transition amplitude so that a particle at location $\mathbf{y}$ is generated at time $y_0$, moves to $\mathbf{x}$ and is destroyed... |
It should, however, be a transition amplitude so that a pond at location $\mathbf{y}$ is generated at time $y_0$, moves to $\mathbf{x}$ and is destroyed at time $x_0$.
...pond? Anyway, the amplitude does not literally have this position-based interpretation. This is more of a rule-of-thumb type of interpretation that... | {
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Experiment preparation - Box to reduce background photons noise I am planning to perform experiment with a photomultiplier tube (PMT) in my lab. The system is not large, with a length scale of about 10 cm. I am looking to reduce the background photons noise as much as I can, and for this I thought to perform the experi... | Use a "Pelican box" or similar black and waterproof cases. Works perfectly.
| {
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Does quantum mechanics require classical mechanics for its own formulation? Is true that quantum mechanics requires classical mechanics (as a limiting case) for its own formulation?
| There are different theories that we call classical theories. There is Newtonian mechanics with all its later developments. Then there is classical field theory, such as Maxwell's equations for electromagnetism. And then there is thermodynamics, with statistical physics. Quantum mechanics is built on concepts from all ... | {
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Why not define tensors under Galilean or Poincare transformations? I have seen vectors (and tensors, in general) defined under rotations,
$$V^i=R^i_{~j}V^j$$
and under Lorentz transformations,
$$V^{\prime\mu}=\Lambda^\mu_{~~\nu}V^\nu$$
where $R,\Lambda$ are the matrices representing rotations and Lorentz transformation... |
Why doesn't one talk about vectors under the Galilean or Poincare transformations (or groups)? Wouldn't that be more general?
The tuple $(V^1,\ldots,V^n)$ is interpreted as the representation of some vector $V$ w.r.t. a basis. That being said, if we fix two bases, then the transformation of vector components is obvio... | {
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In firing a single photon at the center divider of a double slit, does it ALWAYS go through the slits? If we think of a single photon approaching the slits as a wave function, and we fire the photons at the midpoint of the two slits, one at a time, then I would think the probability function is highest at this midpoint... | Don't try to analyze a diffraction problem using particles: you'll just confuse the issues.
Thinking of waves, well, what happens when waves impinge on opaque material? You see this every day. Some of the energy is reflected, some is absorbed. There's nothing particularly profound beyond this that happens in the double... | {
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Why do the units of entropy include energy and temperature? I am trying to learn what entropy actually is, and I read this answer about how entropy is the information needed to specify a full quantum state. However, if entropy is just information, why does it have units related to energy and temperature? So I was wond... | It's a quirk of scientific history that energy is quantified with one set of units (joules, ergs, calories) and temperature with another (kelvins, degrees Rankine). In Thermodynamics and an Introduction to Thermostatistics, Callen notes that energy and temperature have the same dimensions: $\mathrm{mass}\cdot\left(\fra... | {
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Are there materials which allow light beams to interact within them? For example: if you point two perpendicular lasers in air, nothing will happen. I'm wondering if there's any material in which these lasers would combine, bounce off each other, basically anything that would result in a different outcome than just pas... | Nonlinear optics is the study of materials which, if the light is intense enough, do not react linearly to the electromagnetic fields that propagate through them. When this happens, the superposition principle breaks, and beams of light propagating through the material can modify each other's phase, propagation directi... | {
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Why is exhaust stroke isochoric in otto cycle? Please help me clarify this simple concept. In otto cycle, after the power stroke, the gas expands adiabatically and during the exhaust stroke why is the volume of the gas constant? Doesn't the volume of the gas change after the exhaust valve is open? Is the volume conside... |
Doesn't the volume of the gas change after the exhaust valve is open?
Yes it does, for the real Otto cycle which is an irreversible open system. But it does not for the reversible closed system model of the cycle.
The ideal reversible model of the Otto cycle does not include the intake or exhaust strokes because it i... | {
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How are electrons really moving in an atom? Niels Bohr proposed the solar system model of the atom, which is the most recognizable, and assumed electrons revolve in circular paths called orbits/energy levels. However, we know that the Bohr model is incorrect due to later observations, like the Stark and Zeeman effect.
... | There is no such thing as a "trajectory" of a particle in quantum mechanics. If a particle followed a single trajectory -- that is, for every time $t$, you could associate a unique position $x(t)$ where it was located -- then you could also assign a unique momentum $p(t)=m\dot{x}(t)$. This would contradict the Heisenbe... | {
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Orbital motions Suppose two satellites are moving in circular orbits around the earth and then crash into one another.
My Question is this, how do we know that the bodies move in an elliptical orbit after the crash? Why not just remain in a circular orbit with a smaller radius (r)? Why not instead go into a hyperbolic ... | As an intuitive answer to "why can't it result in a smaller circular orbit":
The collision occurs at radius $r$. Therefore the resulting trajectory must pass through a point $r$ distance from the central body.
A hypothetical smaller circular orbit would have some radius $r'$. But a circular orbit by definition has cons... | {
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Does horizontal acceleration affect gravity? If we apply 1G horizontally in some object, will this constant force equal to G affect the time of falling? If the force does not affect gravity, why gravity is prioritized over this force if both are equal?
Edited: For the ones who didn't understand what i mean well, i mean... | The vertical component of net acceleration which is equal to $g$ directed vertically downward is prioritized because this component can only decide the time of flight ,as soon as the distance of projectile from the ground becomes zero then we consider as it has stopped going forward, which mainly is ruled by this compo... | {
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Evolution of a general state - Quantum Quench Suppose we have a state prepared in ground state of some Hamiltonian. Say
$$H \vert\psi_{0}(g)\rangle = E_{0}\vert\psi_{0}(g)\rangle$$
If I evolve this state with a different Hamiltonian
$$ \exp({-iH_{2}t})\vert\psi_{0}\rangle = \sum_{n} \exp(-iE_{n}^{'}t) \langle\phi_{n}\... | You can always write any state in terms of any complete basis, including the eigenbasis of any given Hamiltonian.
For your second question none of the terms in the expansion
$$
e^{-\imath H_2 t} |\psi\rangle = \sum_n e^{-\imath E_n t} \langle \phi_n|\psi\rangle |\phi_n\rangle
$$
ever decay, so the initial state will n... | {
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What is the state of an entangled photon after its twin is absorbed? Let's two photons are entangled in polarization after a laser beam passes through a Betha Barium Borate crystal. They take different paths and one of them (1) is absorbed in a black sheet. What is the state of the leftover photon (2)? Is it in superpo... | What if the black sheet atoms absorb photons only with a certain polarisation?
https://apps.dtic.mil/sti/pdfs/AD1096363.pdf
They have used holes, rather than a black sheet, so this experiment may not be exactly what you want.
But,
https://uwaterloo.ca/institute-for-quantum-computing/sites/default/files/uploads/files/01... | {
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Why there is no $s$-channel for fermion-fermion scattering? I'm learning the Lagrangian for Yukawa theory, where $L_{int} = \phi\bar{\psi}\psi$. For the fermion-fermion scattering, we can draw the Feynman diagrams as
My question is why we can't have $s$-channel here? If it exists, it still seems like we can have a dia... | For $s$-channel, the fermions need to annihilate, so:
$$ e^+ e^- \rightarrow e^+ + e^- $$
is $s$-channel. There is still a $t$-channel, of course, but no $u$-channel as the electron and positron are not identical particles.
| {
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Electrons after Bremsstrahlung radiation Where do electrons go after they have been braked in the Bremsstrahlung effect? In particular, those who have lost almost all their kinetic energy, could they be captured or interact with the nuclei?
| Bremsstrahlung is a name for a general phenomenon, which may happen in many different situations. E.g., in X-ray tube the electrons simply are collected by the anode.
The scenarios described in the OP are more characteristic of Beta-decay - in this case the answer is yes, in some situations electrons are captured.
| {
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Quickway to calculate density matrix knowing $[S_{x,y,z}]$ Consider the spin $\frac{1}{2}$ system. A general quantum state could be written as $|\alpha^{(i)}\rangle=c_i|+\rangle+d_i|-\rangle$ and thus we have the density operator $$\rho=\sum_i w_i|\alpha^{(i)}\rangle\langle\alpha^{(i)}|.$$Suppose we know $[S_x]=\text{T... | Yes. Note that the set of Pauli matrices and the identity operator on $\mathbb C^2$, $\{\sigma_0:=\mathbb I_2,\sigma_1,\sigma_2\sigma_3\}$, is an orthonormal basis in the space of complex $2\times 2$ matrices $M_2(\mathbb C)$ equipped with an inner product $\langle \cdot,\cdot\rangle: M_2(\mathbb C) \times M_2(\mathbb ... | {
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Do we need a quantum gravity theory to model an hydrogen atom on earth? The hydrogen atom is a quantum mechanical system. However, it is also attracted by the gravitational pull of the earth. Therefore, do we need quantum gravity to model its behavior correctly? Conversely, can we study hydrogen atoms on earth to obtai... | No, we do not need quantum gravity to model a hydrogen atom, at least not for any practical purpose. We are in fact able to model hydrogen atoms extremely well with existing theories, so well that quantum electrodynamics is among the best verified theories in all of science.
Gravity is an extremely weak force, and its ... | {
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Why is the stress on a body not a vector? In my textbook, Physics, Part II—Textbook for Class XI, there's a line which talks about why stress is not a vector:
Stress is not a vector quantity since, unlike a force, stress cannot be assigned a specific direction. Force acting on the portion of a body on a specified side... | We can put a wire under tensile stress by pulling each end with a force of equal magnitude. If the wire has an East-West alignment we need to pull its eastern end to the East and its western end to the West (even though one of these forces may be inconspicuously applied by a fixed anchorage to which one end of the wire... | {
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Analysis of the reflection in metal In order to solve the reflexion in a material with a complex index the solution I've found on textbooks is to define $\hat{n}\cos{\phi}:=a+bi$ where $\hat{n}=n_r+n_ii$ is the complex index and then solve the system
$$a^2-b^2=n_r^2 - n_i^2 -n^2\sin^2(\phi)$$
$$ab=n_rn_i$$
Then, with t... | Why are using a law of refraction (snell's law) for reflection in metals?
You can not compute reflections in metal without taking into consideration of wavelength.
Refractive index of metals varies largely for different wavelengths. Different metal absorbs different wavelength that also give metals its color.
The refr... | {
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What would a standing wave of light look like? I want to know what a standing wave of light would like and what properties it might have that are interesting.
| The resonant cavity of a laser is a standing wave. It doesn't really look like anything in particular because the standing waves are not travelling to your eyes. However, you can let some of the wave escape the cavity to do all sorts of interesting things.
The most interesting property is the ability to control cats du... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/742157",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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Some basic questions about applying operator in quantum mechanics Given a momentum operator
$$
\def\bra #1{\langle#1|}
\def\ket #1{|#1\rangle}
\def\braket #1{\langle#1\rangle}
$$
$$
P \equiv - i \hbar \frac{\partial}{\partial x},
$$
I want to calculate $\bra{a} P \ket{a}$. Here are the steps provided by my professor.
$... | Your basic definition is simply wrong/ambiguous. Use @Emilio’s informal rule above, or the correct definition of Sakurai and Napolitano, (1.248), namely,
$$
\def\bra #1{\langle#1|}
\def\ket #1{|#1\rangle}
\def\braket #1{\langle#1\rangle}
$$
$$
P \equiv - i \hbar\int \!\! dx~\ket{x} \frac{\partial}{\partial x}\bra{x},
... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why do we choose the Dirac delta function as the eigenstate of position operator? When we try to find the eigenstates of the position operator, we get that the product of (x-y) and the eigenstate must be zero. It is obvious then that for x different than y, the eigenstate must be zero.
Now for x equal to y, how do we k... | If $\psi$ were $0$ except for some finite value at $x=x_0$, then the integral of $|\psi|^2$ — that is, the probability of finding the particle anywhere at all — would be $0$. Yet experimenters keep finding particles in various places.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/742750",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Is it possible to realize a probabilistic Maxwell's demon using Tesla valve? Imagine a container, with balls of diameter 1x and 10x, moving randomly in all directions. These balls are mixed, so it is a low order system.
Now this container is connected to another container via a slightly modified Tesla valve which has t... | Maxwell's demon highlights the importance of information and ignorance in thermodynamics. By "information" I mean the type of knowledge that is accessible to the observer and by "ignorance" the type of knowledge that remains inaccessible. In the statistical mechanical view of a molecular system the information availabl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/743081",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Maximum Range for Projectile Motion This is a question concerning a trick I observed while solving for the angle responsible for maximum range of a projectile.
What I have observed is :
If you draw two lines, one opposite to the acceleration faced by the body(i) , another in the direction we want to find the projectile... | Lets call the dimension along which range is to be maximised $x$ and the perpendicular dimension $y$. Let $g_x$ and $g_y$ be acceleration components and $u_x$ and $u_y$ be initial velocity components. Then, the time of flight is given by $t = -\frac{2 u_y}{g_y}$ and the range is given by $R = u_xt + \frac{1}{2}g_x t^2$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/743206",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is household alluminium foil good for observing photoelectric effect? I have built an electroscope(very primitive, just a wire and some aluminum foil). I'm thinking about using it to observe the photoelectric effect. But I don't have any high frequency wave producing equipment.
So, before I try to obtain something for ... | Aluminum foil is covered with a layer of aluminum oxide as soon as it is exposed to air. This tendency for metals to oxidize and also to adsorb water molecules makes work functions difficult to repeatably measure when tested in air.
In addition, certain rare-earth oxides as used to coat vacuum tube emitters dramaticall... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/743343",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Are the field lines around a magnet (and the repulsion felt between magnets) EM radiation? If not, is it those field lines which turn into EM radiation when a charge is accelerated?
| No, because it is a static situation.
An accelerated charge generates EM radiation and if it is strong enough, could make iron filings on a piece of paper oscillate. So yes, theoretically, moving field lines could show EM radiation.
We can make an analogy with gravitational field and how strong is the force downward de... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/743573",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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What does a dot over a spinor index signify? My questions should be rather simple. I was trying to get through one of my professor’s papers, and I saw the following notation, first with regards to Dirac and Weyl spinors, but the notation continues throughout
$$
\psi=\begin{pmatrix}\lambda_\alpha\\\bar\lambda^{\dot\alph... | Starting from the defining representation $A(\vec{\alpha},\vec{u})$ of ${\rm SL}(2,\mathbf{C})$, also $A^\ast$, $(A^T)^{-1}$ and $(A^\dagger)^{-1}$ furnish representations of ${\rm SL}(2, \mathbf{C})$. The representations $A$ and $A^\ast$ are inequivalent and likewise the representations $(A^T)^{-1}$ and$(A^\dagger)^{... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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The relation of time-evolution operators from Schwartz's textbook In the section 7.2.2 of Schwartz's QFT textbook, it says:
define the generation definition of time-evolution operators:
$$U_{21}\equiv U(t_2,t_1)=T{\exp[-i\int^{t_2}_{t_1} dt'V_I(t')]}\tag{7.46}$$
where $V_I$ is the interaction part of Hamiltonian in the... | He must be tacitly using anti-time ordering when $t_2<t_1$. Then the cancellation works.
He should really use the path-ordering symbol "P" rather than "T".
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/743835",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What does it mean to say the universe is not locally real? Pardon me if this is a naive question.
What is difference between saying space-time is not locally real, and saying it is not real?
The proposal that the universe is not locally real seems to imply that it is is non-locally real. But what does this mean?
There ... | Real, but not locally real, means that one can overcome the Bell argument (that there is nothing real being measured in a quantum measurement) by allowing information to be conveyed faster that the speed of light.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/743991",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Peskin and Schroeder eqn 9.14 I am not familiar with functional integral, and in the text like $$\int D\phi D\pi \exp [i\int^T_od^4x(\pi\dot{\phi}-\frac{1}{2}\pi^2-\frac{1}{2}(\nabla \phi)^2-V(\phi))].\tag{9.14}$$ I try to compile it but get:
$$\int D\phi\left[ \prod_{x,t}\int d\pi\ \exp [i\epsilon^4(\pi\dot{\phi}-\fra... | OP's infinitely many Gaussian integrations of the momentum field are essentially the correct method. The infinite product in OP's last line is usually tucked away by normalizing the path integral appropriately.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744140",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Third principle of thermodynamics and the unattainability of absolute zero Consider a $S-T$ diagram (entropy-temperature) and consider cooling a substance by doing a series of succesive isothermal and reversible adiabatic processes between two volumes $V_{1}$ and $V_{2}$.
Now when cooling the substance from $T_{1}$ to ... | Your reasoning proves that we cannot reach absolute zero by reversible adiabatic process from a non zero temperature. I prefer to reach this conclusion as follows:
Your first equation applies to any reversible adiabatic process between states $(T_1,V_1)$ and $(T_2,V_2)$. If we set one temperature to absolute zero the o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744237",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can rigid body have more than 1 speed? I have a doubt that circular ring is a rigid object and we know every point on the rigid obj must have same velocity or speed. But in case of pure rolling of sphere or others we can find topmost point has velocity 2v lowermost have 0 how's that possible..i am not able to visua... | . . . . we know every point on the rigid object must have same [linear] velocity . . . is not true; it is the angular velocity which is the same.
Perhaps the simplest rigid body to think about in the context of rotation is a door.
When a door is opened it is clearly the case that all parts of a door do not travel at th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744315",
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Need help about motion So,In my book it is written that -
Translational motion is the motion when all the particles of a moving body move the same distance in the same same in the same direction.It is of two types-1)Rectilinear and 2)Curvilinear
Now, my question is that to have translational motion doesn't need to have... |
... all the particles of a moving body move the same distance in the same same in the same direction
So if two points of the body $A$ and $B$ move from positions $A_0$ and $B_0$ to $A_1$ and $B_1$ respectively, this says that
$\vec{A_1}-\vec{A_0} = \vec{B_1}-\vec{B_0}$
which can be rearranged to give
$\vec{B_1}-\vec{... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is Newton's second law seemingly not applicable to a ball rolling down incline plane? A homework problem asked us to find the acceleration of a ball (pure) rolling down an incline plane without friction. I thought it was simply $a=g \ \sin(\alpha)$ where $a$ is the acceleration of the CM and $\alpha$ is the angle o... | Your error is here:
... since there is no friction ...
Pure rolling is impossible without friction. No friction would imply no rolling (just sliding smoothly without rotation). Pure rolling implies a static friction force that is exactly large enough to prevent the contact point from moving.
You can solve your task b... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Remote mass detection and location Could a collection of gravitational sensors (eg. MEMS accelerometers), placed in a 3d grid (eg. 10 x 10 x 10 sensors forming a 1 x 1 x 1 m cube) detect the the presence and position of a remote mass concentration, eg. an airplane in the sky?
What accuracy would be needed to do so?
| Gravitational sensors in orbiting satellites have been used to map density variations in the rocks under the ground. (See here for a recent example.)
At shorter range, gravimetric gradiometers are being researched for detecting underground tunnels, objects behind walls, and stealthed aircraft and submarines. (See here ... | {
"language": "en",
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How to prove $\mathrm{Tr}[(\partial_\mu U)U^\dagger]=0$? I am studying ChPT by referring to "A Primer for Chiral Perturbation Theory" by Stefan Scherer.
I'm having a problem with the consideration of terms that appear in the Lagrangian.
The textbook says only $\mathrm{Tr}(\partial^\mu U\partial_\mu U^\dagger)$ is impo... | Following the detailed hint,
$$
\begin{align}
(\partial_\mu U) U^\dagger
&= \left( \frac{i \partial_\mu \phi}{F_0} + \frac{(i \partial_\mu \phi) i \phi + i \phi (i \partial_\mu \phi)}{2! F_0^2} + \cdots \right) U^\dagger \\
&= \frac{i \partial_\mu \phi \ U^\dagger}{F_0} + \frac{(i \partial_\mu \phi \ U^\dagger) i \phi ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/745200",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 3
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The motion of a rigid body Consider a rigid body with $n$ forces acting on it. What I intend to know is how to determine the motion of the body, more specifically:
*
*How to determine a point through which the axis of rotation of the body passes
*How to determine the direction in which the axis of rotation points
*... | *
*axis of rotation is passing through a point , with respect to which angular velocity of all the point on the body is same.
*this can be determined by right hand palm rule (used in cross product rule to determine the direction)->your thumb should point in direction of axis of rotation,four fingers in direction of p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/745455",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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The conservation of energy in both the cases: Will it be different or the same? On an inclined plane of same height $h$ and every factor the same but the only factor changes is the presence of friction. In the first case the friction is present in the top half and in the second case the friction is present in the secon... | The energy lost to friction will be $F_k d$ where $F_k$ is the magnitude of the kinetic friction force and $d$ is the distance over which the friction acts.
From the description the $d$ is equal in both cases. So which one is greater depends only on the force.
In the usual case $F_k=\mu_k N$ where $\mu_k$ is the coeffi... | {
"language": "en",
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Magnetic force calculation for parallel wires using Maxwell stress tensor. Issue with shear forces I am trying to calculate the forces in between permanent magnets and ferromagnetic surfaces with the Maxwell stress tensor using image theory and the Biot-Savart law. However I discovered a weird behavior regarding shear ... | You've applied the stress tensor incorrectly. If we want to find the force in the $i$-direction on a collection of charges & currents using the stress tensor, then it is
$$
F_i = \oint T_{ij} n_j da,
$$
where $\hat{n}$ is the normal to the surface (and I'm using Einstein summation). In your case, for the lower half-s... | {
"language": "en",
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Product of Pauli-matrix exponentials Given Pauli matrices $\sigma_x = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$ and $\sigma_z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$, can one write $e^{\alpha \sigma_z} e^{\beta \sigma_x}$ in terms of $e^{\beta \sigma_x} e^{\alpha \sigma_z}$ ($\alpha$, $\beta$ are some com... | Use the standard formula,
$$
e^{\alpha \sigma_z}= I\cosh \alpha + \sigma_z \sinh\alpha = , \\
e^{\beta \sigma_x}= I\cosh \beta + \sigma_x \sinh\beta ,
$$
to compute the quadruple product suggested in the comments,
$$
M=e^{-\alpha \sigma_z}e^{-\beta \sigma_x}e^{\alpha \sigma_z}e^{\beta \sigma_x}\\ =
e^{-ia\sigma_z}e^... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Do objects always speed up as they fall? In the thermodynamics video I watched, it was stated that objects at higher elevations have more energy. And that objects must speed up as they fall. My question is, "what happens if an object reaches it's terminal velocity? It's still falling but no longer speeds up" Doesn't t... | Force is spatial rate of energy transference. When it is applied on an object, the object gains momentum or loss depending upon state of motion of an object and direction of applied force. It is never become constant instantaneously. When it becomes constant that means an object reach at equilibirium and rate of gain i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/745835",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do I use the Schwarzschild metric to calculate space curvature and time curvature seperately? I want to understand the math behind the idea that around Earth time dilation accounts for 99.99% of gravity, while around a black hole it only accounts for 50% of gravity while space curvature accounts for the other 50%. ... | I quite dislike this particular turn of phrase - there is no meaningful sense in which curvature can be split into temporal and spatial parts. We can talk about pure spatial curvature in the sense that we can foliate a $d$-dimensional spacetime into spacelike leaves $\Sigma_t$, each of which constitutes a $(d-1)$-dime... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/745960",
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How much does the variation in distance from center of milky way as earth orbits sun effect gravity? As the earth rotates around the Sun our distance from the center of the galaxy is varying - what sort of variations does this cause in the force of gravity here on earth?
[Edit]
Given that Earth orbits around the Sun at... | Easy to estimate: the gravitational force goes like $1/(\mathrm{distance})^2$. With the distances of Earth to Sun and Sun to the Galactic center respectively,
\begin{equation}
\Delta F \sim \left( \frac{150\times 10^6 \mathrm{km}}{2\times 10^{17}\mathrm{km}} \right)^2 \sim 10^{-20} ,
\end{equation}
i.e. by nothing.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/746062",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Convert reflection spectrum to optical density I have the spectrum 380-780 nm at 10 nm intervals of a nearly grey patch. I need to input its optical density into a calibrating programme. This is what a densitometer would do - but I don't have one and I don't know what the densitometer would be measuring. Is there a for... | Here are a couple related questions: How do I convert light with a given spectrum to an RGB color? See this.
How do I convert RGB to grayscale? See this.
The idea is that lighter grayscale colors are those that appear brighter to the eye. Light appears brighter if it is more intense, and if its spectrum in in the regio... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/746238",
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Is Intensive property/Intensive Property an Extensive Property? We know that Extensive property/Extensive Property is Intensive is most of the cases, but is Intensive/Intensive an Extensive property ? if so, is there any examples
| No, intensive divided by intensive is always intensive. Here is the math.
A function $f(x)$ is homogeneous with degree $\alpha$ if
$$f(\lambda x) = \lambda^\alpha f(x)$$
for all $\lambda>0$. Intensive properties are homogeneous with degree $\alpha =0$, extensive properties are homogeneous with degree $\alpha=1$.
*
*R... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Cause non-linear relation between intensity and photo-current I wanted to investigate and validate the relationship between intensity and photo-current with a simple experimental setup. I expected a linear relationship based on the photo-diode's datasheet (I've added the link to the datasheet below).
The experimental s... | As suggested I've used a ND filter instead of a polaroid to control the laser's intensity. This gave me the expected results, as shown in the figure below. As also said before: the beamsplitter affects the polarized light, in a for me, unknown way but it seems to change the relation between the two quantities (as shown... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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"question_score": "1",
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Are the equations of the Poynting vector and energy density of an electromagnetic wave only for the real waves? So, my book says that the Poynting Vector associated to an electromagnetic wave in matter with permeability $\mu$ is $\mathbf{S} = \frac{1}{\mu} \mathbf{E} \times \mathbf{B}$. The thing is, I am unsure whethe... | Complex number expressions for fields in EM theory are just a different mathematical representation of fields to make solving differential equations on paper easier. The actual physical field can be described by either the real or the imaginary component of those complex expressions, depending solely on our choice; usu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/747182",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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What is the relevance of the Lorentz factor in general relativity? The Lorentz factor is ubiquitous in Special Relativity and is used to express "how much the measurements of time, length, and other physical properties change for an object while that object is moving."
However, in my fairly introductory study of Genera... | The Lorentz factor turns up in GR when physical observables are involved, particularly under transformations between different (local) frames. Sadly there is usually little attention given to such observables in textbooks and courses, which is why you haven't seen the Lorentz factor there. The formula $\gamma = -\langl... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does a double star system have more mass than its constituents? According to Einstein, energy is equal to mass. Consider a planet that is in gravitational attraction to two stars. Normally I would say that the gravitational attraction is proportional to the masses of the two stars. But if they are orbiting each other, ... | The sum of the kinetic and potential energy of a bound system is negative. This must be the case, because you would have to inject more energy into the system to separate the components to infinity.
Therefore the "gravitational mass" of the binary - what you would measure with another orbiting test mass at greater dist... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/747546",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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In the context of the holographic principle, is the bulk-boundary correspondence due to entanglement? According to the holographic principle, a "bulk" region of D dimensions corresponds to a "boundary" region of D-1 dimensions. In this context, the laws of physics of the bulk can be "encoded" on the boundary, so there ... | The idea of holography is that the bulk degrees of freedom and the boundary degrees of freedom are the same. They can't be entangled with themselves.
In a simple holographic universe consisting of a single qubit, there is a description of an arbitrary state $α|0\rangle + β|1\rangle$ as a configuration of the bulk, and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/748496",
"timestamp": "2023-03-29T00:00:00",
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How to justify this small angle approximation $\dot{\theta}^2=0$? Suppose the equation of motion for some oscillating system takes the following form:
$$\ddot{\theta}+\dot{\theta}^2\sin\theta+k^2\theta\cos\theta=0$$
Applying small angle approximation to $\theta$ gives $\sin\theta\approx\theta$ and $\cos\theta\approx1$,... | By drawing a phase plot you can more visually see where the approximations are valid. Define
\begin{align}
x&\equiv \theta\\
y&\equiv\dot\theta
\end{align}
This transforms your initial equation into the following first order differential equations:
\begin{align}
\pmatrix{\dot x\\\dot y}=\pmatrix{y\\-y^2\sin x-k^2x\cos ... | {
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Higher-order perturbation in Kondo problem In chapter 6 of the book about condensed matter physics written by Gerald Mahan, the self-energy of the conduction electron is calculated to the third order in $J$ (the Kondo coupling) to show that the imaginary part of the self-energy diverges logarithmically as the energy s... | Yes, indeed. See, e.g., Perturbative approach to the nonequilibrium Kondo effect in a quantum dot (also published as a PRL paper), where the perturbation theory is carried out up to the fourth order in $U$.
Note also that Kondo effect in Kondo and Anderson models was solved exactly by Bethe ansatz respectively by Andr... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What does squaring a vector mean? So,in the 3rd equation of motion,i.e $v²=u²+2as$,what does the square on the final velocity and initial velocity actually mean?And how does it make an effect on their direction?
suppose upwards vector is positive and downwards vector is negative.And,we are throwing a ball from a height... | This equation should be written:
$$
v_{x}^2 = v_{0x}^2 + 2 a_x (x - x_0)\,,
$$
where $v_x = v_x(t) = \vec{v}(t) \cdot \hat{i}$ and $x = x(t) = \vec{r}(t) \cdot \hat{i}$, meaning that it is an equation for the components of the vectors, under the assumption of constant acceleration vector, $\vec{a}$, and a choice of coo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Setting of the canonical ensemble for actual interacting systems The canonical ensemble formalism is usually derived by considering a given small system (the system under study) weakly coupled to a huge system (the thermal bath), so that the microcanonical ensemble computations can be applied to the pair of system, reg... | A rather general consideration usually given in statistical mechanics books is that the energy of the system of interest is proportional to its volume, whereas the interaction energy (with the bath) is proportional to the size of the contact surface. This means that for a sufficiently big system (i.e., in thermodynamic... | {
"language": "en",
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How did Enrico Fermi compute when the Chicago Pile-1 nuclear reactor would become critical? I'm trying to understand the first nuclear reactor, the Chicago Pile-1, specifically the math Fermi did to figure out when the reactor would go critical. There's a nice report available from Fermi, where he tracks the value of $... | This kind of plot is typically called a "1/M Plot", where M is the reactor multiplication. To measure the multiplication, you need a neutron source and a detector. As you add more and more material to the reactor, the detector signal increases. When the reactor goes critical (or more precisely supercritical), the de... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/750081",
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"source": "stackexchange",
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Is $\phi^5$ a descendant in $\phi^4$-theory (at the conformal Wilson-Fisher fixed point)? I'm wondering if $\phi^5$ is a descendant in $\phi^4$-theory in $d = 4 - \epsilon$ at the conformal Wilson-Fisher fixed point, where the coupling constant is $\lambda$. The e.o.m. tells us that $\phi^3$ is a total derivative (and ... | Your last equation does not follow from the others.
The combinations of fields and derivatives which give primary operators in Wilson Fisher are almost the same as those for the free theory. Due to multiplet recombination, there is one exception at spin zero ($\phi^3$) and one exception at each odd spin $\geq 5$. If $\... | {
"language": "en",
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What exactly does a Lorentz transformation provide?
The primed reference frame is moving relative to the unprimed frame. So if we were to take the lorentz transformation of point P from the unprimed to primed, would it be the point A or B that it returns ? Assuming that the Lorentz transformation is passive i.e. we ar... | See below for an update to address the "passive transformation".
The [active] Lorentz-boost-transformation of event P is neither your events A nor B,
but an event between your A and B
that is on the hyperbola centered at the origin that passes through P.
The boosted event is joined to the original event by a line
that... | {
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4-Vector Potential, transformation under Lorenz Gauge I am given an initial vector potential let's say:
\begin{equation}
\vec{A} = \begin{pmatrix}
g(t,x)\\
f(t,y)\\
0\\
g(t,x)\\
\end{pmatrix}
\end{equation}
| i think you are misunderstanding slightly, to obtain your potentials, you must have a specific chosen gauge that these potentials satisfy already.
Suppose my vector potential satisfies a specific gauge already,
$$\nabla \cdot \vec{A} = G(x,y,z,t)$$
I now perform a gauge transformation,
$\vec{A} \rightarrow \vec{A}'$ su... | {
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Making sense of band theory for nonmetals For the case of metals, we observed that metals often have nearest-neighbours in excess of the maximum valency (for example, 8 for Li, which has only one valence electron) and that metals display great conductivity. On this basis, it was suggested that electrons are delocalised... | Existence of band structure is the result of Bloch theorem, which predicts that electron spectrum in a periodic potential consists of continuous patches, states being label by a continuous number/vector $\mathbf{k}$ and a discrete band index $n$. Thus, the existence of bans is the consequence of crystal structure.
Exce... | {
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Why does magnetic force only act on moving charges? I don't understand why the magnetic force only acts on moving charges. When I have a permanent magnet and place another magnet inside its field, they clearly act as forces onto one another with them both being stationary. Also, I am clearly misunderstanding something.... | A magnetic field does have an influence on a stationary electric charge.
"when i have a permanent magnet and place another magnet inside its field they clearly act a forces onto one other with them both being stationary"
is exactly the case that is also true for an electron.
An electron is both an electric charge and... | {
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What is happening at the particle level in the Bernoulli Principle? One might think that increasing the speed of particles would increase pressure -- if I understand what the Principle states, it is very counterintuitive.
My guess is, the pressure has something to do with particles moving perpendicular to the fast moti... | The particles, on average, keep their energy, but the motion becomes more organized. They have more velocity along the streamlines, and less toward the sides.
| {
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Why do we drop the renormalization term in momentum Klein-Gordon Field Theory? I'm following Peskin & Schroeder's book on QFT. I managed to prove expression (2.33) which gives us the 3-momentum operator for the Klein-Gordon Theory:
$$\mathbf{P}=\int \frac{d^3p}{(2\pi)^3}\mathbf{p}a_\mathbf{p}^\dagger a_\mathbf{p} + ren... | That term has nothing to do with renormalization, it’s just a result of ordering ambiguity in transitioning from classical physics to quantum physics.
| {
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Why do some objects tend to sink after some time in water even if they float at the start? I have observed this phenomenon in swimming pools: I have seen many dead insects floating on the surface, but after some time some they tend to sink down without any external influence. Why does this exactly happen? It even happe... | In order for an object to float, its density has to be less than or equal to the density of the liquid.
The objects you describe sink after a while because a sufficient fraction of the volume of air originally in each object, due to its porosity, is replaced by water which has a higher density than air. The end result ... | {
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What if the universe was not uniform...? In this popular science article they say that if our universe resulted to be non-uniform (that is highly anisotropic and inhomogeneous) then the fundamental laws of physics could change from plate to place in the entire universe.
But what theoretical basis does this claim have? ... | It sort of happens by definition. The wordings are a bit circular in this sense. Isotropy speaks to a symmetry in the universe which we can use to predict that things operate the same in all directions. If it is anisotropic, then there is no such symmetry. "Anisotropic" is less of a cause of the fundamental laws ch... | {
"language": "en",
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What is sound and how is it produced? I've been using the term "sound" all my life, but I really have no clue as to what sound exactly is or how it is created. What is sound? How is it produced? Can it be measured?
|
What it sound?
Sound is nothing but a mechanical wave. The human ear can detect mechanical waves from 20 Hz to 20,000 Hz.
How is it produced?
It is produced when energy transformation occurs. For eg. beating a drum - mechanical energy.
Can it be measured?
Yes, it can be measured by the frequency of the wave.
| {
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How to show that the Coriolis effect is irrelevant for the whirl/vortex in the sink/bathtub? There is a common myth that water flowing out from a sink should rotate in direction governed by on which hemisphere we are; this is shown false in many household experiments, but how to show it theoretically?
| The calculation of the Coriolis force is dependent on latitude:
$F = m a$
where $a = 2 \Omega sin(lat)$, with $\Omega$ being the Earth's angular velocity
$m$ is the mass of the object in question
The Earth's angular velocity is (about) $7.29 \times 10^{-5}$ rad/sec
So, for a sink with a couple gallons of water in it ... | {
"language": "en",
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Mnemonics to remember various properties of materials I'm trying to figure out how to remember that
*
*hardness: how resistant it is to deformation
*toughness: how resistant it is to brittle failures
*stress: force on a surface area
*strength: ability to withstand stress without failure
*strain: measurement of d... | I would suggest learning about some of the formulas relating them - that way you're not just memorizing things but actually have some grasp of what goes into them. In particular, I only really know about stress and strain, and it's because I think of them as being the analogue in linear elasticity theory of "force" and... | {
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Is Newton's Law of Gravity consistent with General Relativity? By 'Newton's Law of Gravity', I am referring to
The magnitude of the force of gravity is proportional to the product of the mass of the two objects and inversely proportional to their distance squared.
Does this law of attraction still hold under General ... | To be direct: the answer is no. There's no spatial curvature for Newtonian gravity, when it is rendered in geometric form as a curved space-time geometry. All the curvature is in time.
One of the most prominent ways this stands out is in the relation between radial distances versus circumferences. For Newtonian gravity... | {
"language": "en",
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Book about classical mechanics I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical consideration related to these to formalism (like tangent bundle, cotangent bundle, 1-for... | As already mentioned the standard introductory books in hamiltonian geometrical (point-) mechanics are Foundations of Mechanics by Abraham and Marsden and Arnolds Mathematical Methods of Classical Mechanics. Another standard book is: "Classical Mathematical Physics" by Walter Thirring.
You may also have a look at "Symm... | {
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What will happen if we add salt to boiling water? I would like to have a good understanding of what is happening when you add salt to boiling water.
My understanding is that the boiling point will be higher, thus lengthening the process (obtaining boiling water), but at the same time, the dissolved salt reduce the pola... | I think the dominant effect might actually be the fact that the salt you add might not be at boiling temperature. But this is just based on the fact that the boiling-point elevation due to salt in water is actually quite low for typical amounts of salt used in cooking, say. I'm not too familiar with the second effect... | {
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Intuitively, why is a reversible process one in which the system is always at equilibrium? A process is reversible if and only if it's always at equilibrium during the process. Why?
I have heard several specific example of this, such as adding weight gradually to a piston to compress the air inside reversibly, by why ... | As I am new to Stack Exchange, I happened to see the question only now and mine is a belated answer. If Mark is still interested in an answer, then:
It is a good question gaining added strength with the EDIT.
For thermodynamic analysys, a process must connect two equilibrium states A, B of a system. Take a state C of ... | {
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Would it help if you jump inside a free falling elevator? Imagine you're trapped inside a free falling elevator. Would you decrease your impact impulse by jumping during the fall? When?
|
Would you decrease your impact impulse by jumping during the fall?
Yes
When?
Soon enough that it's before impact, late enough that you don't hit the ceiling of the elavator.
Beyond that I don't think it matters much.
Would it help if you jump inside a free falling elevator?
Probably not. Indeed I expect it would ... | {
"language": "en",
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Finding the volume of this irregular shape I have I have an approximately basketball-sized non-hollow piece of aluminum sitting in my house that is of irregular shape. I need to find the volume of it for a very legitimate yet irrelevant reason.
What is the best way I can do this? In fact, what are all the ways I coul... | Eureka! As Archimedes said, according to legend.
In principle, "TheMachineCharmer's" answer is feasible, but I would recommend recording the change in the volume of water instead (if you need an accurate measurement), because (1) it could be difficult to measure the volume of the spilled water, and (2) it is also a lit... | {
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Why don't spinning tops fall over? One topic which was covered in university, but which I never understood, is how a spinning top "magically" resists the force of gravity. The conservation of energy explanations make sense, but I don't believe that they provide as much insight as a mechanical explanation would.
The hyp... | when the mass is spinning it has an angular momentum pointing in a direction perpendicular to the plane it's spinning on.
The angular momentum has to be conservate: i.e. has to keep pointing in the plane-perpendicular direction. As cedric said, the gravity, works for the axis of the spinng mass to fall horizontally on ... | {
"language": "en",
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How do subgrid-scale parametrisations in climate models work? Global Circulation Models typically have grids of 100-300km on a side. There are obviously lots of atmospheric processes that happen at smaller scales than this. Convection, cloud formation, the effect of mountains...
How are these processes built in to the ... | In general small scale motions (like convection and formation of local eddies) in geophysical fluid dynamics are treated as turbulence, that is a regime characterized by chaotic motions and rapid, quasi random variations of pressure, temperature and velocity. Those random processes cannot be neglected in boundary layer... | {
"language": "en",
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Planet orbits: what's the difference between gravity and centripetal force? My physics teacher says that centripetal force is caused by gravity. I'm not entirely sure how this works? How can force cause another in space (ie where there's nothing).
My astronomy teacher says that gravity is (note: not like) a 3D blanket... | cetripital force only exists when you have prescribed motion (due to constraints). Think of a roller coaster car riding on a rail. To keep the car on the rail and tangetial to its direction a force and moment need to be applied to the car. When the path is circular we call the cetripetal force. In fact, with any path, ... | {
"language": "en",
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How can I measure the mass of the Earth at home?
*
*How can I measure the mass of the Earth at home?
*How was the mass of the Earth first measured?
| You can make estimates of the Earth's mass $M_\mathrm E$ by estimating its average density $\rho$ and using the formula $M_\mathrm E = \rho \cdot V$, where of course $V= \frac{4}{3} \pi R^3$, so you have to know the Earth's radius $R$. This method is rather a gamble because you don't know the Earth's average density (s... | {
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Advantages of high-energy heavy-ion collisions over proton-proton collisions? Some high-energy experiments (RHIC, LHC) use ion-ion collisions instead of proton-proton collisions. Although the total center-of-mass energy is indeed higher than p-p collisions, it might happen that the total energy per nucleon is actually ... | As a clarification the energy per nucleon is always lower: for example, currently in the LHC the proton top energy is 3.5 TeV. Now the Pb energy is 3.5 TeV times Z so the energy per nucleon is 3.5*Z/A and A is greater than Z for every nucleus (except the proton where it is equal to one).
But the goal of ion-ion collisi... | {
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What software programs are used to draw physics diagrams, and what are their relative merits? Undoubtedly, people use a variety of programs to draw diagrams for physics, but I am not familiar with many of them. I usually hand-draw things in GIMP which is powerful in some regards, but it is time consuming to do things ... | I use TKPAINT which still works very well.
http://www.netanya.ac.il/~samy/tkpaint.html
First, one has to download ActiveTcl for Windows or its Tcl counterparts for Linux or whatever you use. It can draw filled or empty disks, ellipses, squares, rectangles, splines, rotate them, quickly copy them, move them, texts with ... | {
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Would a magnet attract a paperclip indefinitely? Let's say we have a magnet stuck to a metal bar, suspended above the ground. If I attach a paperclip to the magnet, where is the energy to hold the paperclip coming from (against the force of gravity), and for how long will the paperclip remain there - will it remain the... | When the magnet attracts and moves the paperclip, moving it in the gravitational field of the earth, the energy comes from the potential energy that [in that case] we can associate to the magnetic field.
By attracting the paperclip you increase the gravitational potential energy of the paperclip but you reduce the one ... | {
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Distance travelled in free-fall When an object is in free fall, we have:
$$a(t) = g - \frac{c}{m}v(t)^2$$
where $g$ is acceleration due to gravity, $m$ is the mass of the object, and $c$ is the coefficient of air resistance.
How does one get the distance traveled after t seconds? I tried integrating it, giving
$$v(t) =... | When accelereration is given as a function of velocity only then the following apply
$$ x(u)=\int\frac{u}{a(u)}\,\mathrm{d}u+K_{1} $$ and $$ t(u)=\int\frac{1}{a(u)}\,\mathrm{d}u+K_{2} $$
the rest is solved similarly to David Z (above).
| {
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Notation of plane waves Consider a monochromatic plane wave (I am using bold to represent vectors)
$$ \mathbf{E}(\mathbf{r},t) = \mathbf{E}_0(\mathbf{r})e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t)}, $$
$$ \mathbf{B}(\mathbf{r},t) = \mathbf{B}_0(\mathbf{r})e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t)}. $$
There are a f... | Stationary field or monochromatic field. Yes, basically that is the field including the $e^{i\omega t}$ term, but even when it is omitted one still knows what is meant.
| {
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How are neutrons produced from cosmic ray particles? What are the details of how neutrons are produced as a result of cosmic ray particles hitting our planet's atmosphere?
For instance, what is the pathway that creates the highest number of neutrons from cosmic ray particles?
The article "Single event upset" states:
A... | Spallation of air atoms' nuclei is the easiest way - there are neutrons kicked out of the nucleus directly or emmited by radioactive elements, which were activated by cosmic rays.
Also neutrons can be produced upon hadronization of quark-gluon-plasma or from electron capturing in air nuclei.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does kinetic energy increase quadratically, not linearly, with speed? As Wikipedia says:
[...] the kinetic energy of a non-rotating object of mass $m$ traveling at a speed $v$ is $\frac{1}{2}mv^2$.
Why does this not increase linearly with speed? Why does it take so much more energy to go from $1\ \mathrm{m/s}$ to... | In comes down to definitions.
Momentum is defined as $p = mv$. Momentum grows linearly with velocity making momentum a quantity that is intuitive to understand (the more momentum the harder an object is to stop). Kinetic energy is a less intuitive quantity associated with an object in motion. KE is assigned such that t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Material resistency to lasers beam Keeping the average power constant, why some materials are more eager to be damaged by pulsed laser with respect of C.W. lasers, or viceversa?
When i talk about pulsed lasers i think for examples of duty cycles in the order of $10^5$.
For example optical elements (such as a vortex pha... | Not being an exhausting list. Some phenomena that allows for this to happens is non-linear effects. A short pulse allow a higher intensity for a small period to time which enhance non-linear effects such as two-photon absorption and self-focusing. Two photon absorption will make a material absorb light which it wouldn'... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
} |
Chosing a reference frame in which the Earth is at rest and doesn't rotate We may choose a non-rotating earth as our reference frame and ask ourselves: how about the planetary and stellar motions. A star at a distance of 10 million light years would turn around the earth in 24h with a velocity of 10^18 m/s.
A friend o... | Planetary motions in such a frame would be depicted properly by the deferent an epicycle model of Ptolemy:
http://en.wikipedia.org/wiki/Deferent_and_epicycle
So, the question is actually answered by Ptolemy. For more reference, look up details in the Almagest! :-)
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/603",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 3
} |
Evolution in the interpretation of the Dirac equation As I understand, Dirac equation was first interpreted as a wave equation following the ideas of non relativistic quantum mechanics, but this lead to different problems.
The equation was then reinterpreted as a field equation and it is now a crucial part of quantum f... | In my opinion, a good introductory text for Relativistic Quantum Mechanics is Quantum Field theory- by Itzykson and Zubor. Another text is Relativistic quantum mechanics of string fields by - Greiner and Muller
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/634",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 7,
"answer_id": 5
} |
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