Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How noisy are photon detectors? I have a single photon detector and $N$ photons per second arrive at the detector. Then something happens and the number of incoming photons per second changes by the factor of $\alpha$. So now $(1+\alpha) N$ photons per second arrive at the detector.
What are currently the best photon d... | It is certainly possible. It depends, as others have said, on the detector. But it also depends on the detection electronics, and the techniques used to do the measurement. Common sources of noise are shot noise, dark current noise, statistical fluctuations in the detection mechanism, and thermal noise in the det... | {
"language": "en",
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Hermitian conjugate of spinors In any textbook, hermitian conjugate of spinor is defined like $ \psi_{\alpha}^{+}=\bar\psi_{\dot{\alpha}} $ and $(\psi^{\alpha})^{+}=\bar{\psi}^{\dot\alpha}$.
We have Pauli matrices $\sigma^{\mu}_{\alpha\dot\beta}$ and $(\bar\sigma^{\mu})^{\dot\alpha\beta}$ they are hermitian matrices i.... | The matrices $\sigma^{\mu}$, being hermitian, satisfy:$(\sigma^{\mu}_{\alpha\dot{\beta}})^{*}$=$(
\sigma^{\mu *})_{\dot{\alpha}\beta}$=$(\sigma^{\mu\dagger})_{\beta\dot{\alpha}}$=$(\sigma^{\mu})_{\beta\dot{\alpha}}$. So $(\xi\sigma^{\mu}\bar\psi)^{*}$=$(\xi^{\alpha}\sigma^{\mu}$$_{\alpha\dot{\beta}}$$\bar{\psi}$$^{\dot... | {
"language": "en",
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Why would different metals glow red at different temperatures? According to everything I've been taught about incandescence and black-body radiation, and some quick Googling to confirm I'm not crazy, just about everything, regardless of composition, should start glowing red at about the same temperature- 798K, the Drap... | All materials have some color (i.e. are not perfectly black or white
bodies). So, even at incandescent temperatures, if they are illuminated,
there is reflected light with color. A good example of a non-black-body
would be glass; softening a glass rod in a Bunsen burner flame, it does
glow red, but there's little ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/146256",
"timestamp": "2023-03-29T00:00:00",
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Justification of not quantizing small extra dimensions When dealing with extra dimensions ($ x ^\mu $ represents $ 4D $ spacetime and $ y $ the extra dimension) we use what's known as Kaluza-Klein decomposition (basically a Fourier transform),
\begin{equation}
\Phi ( x , y ) = \sum _n f _n (y) \phi _n (x)
\end{equati... | The most general case would of course be to take the fields to be of the form $\Phi ( x , y ) = \sum _n \phi _n (x,y) $. By taking the field to be of the form, $\Phi ( x , y ) = \sum _n f _n (y) \phi _n (x) $ and just carrying out the integral over $y$, we are considering an effective field theory of the full theory. A... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/146392",
"timestamp": "2023-03-29T00:00:00",
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Have we proven that higher dimensions exist? Have we proven higher dimensions exist?
| No.
There are various ways we could prove that extra dimensions exist:
*
*observe Kaluza Klein excitations
*observe microscopic black holes
*observe deviations from the inverse square law of gravity at very short scales
*find proof for string theory
Option 1 would be the most likely option. If there are compact e... | {
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Why does an atom remain uncharged after emission of an alpha particle? When an alpha particle is emitted, two protons and two neutrons leave the nucleus but the electrons remain the same in number. Why does the atom remain uncharged although it appears it should have a net charge of $-2e$?
| You're right, directly after the emission it will have charge -2e if it was neutral before, i.e. be an ion. But within a gas or liquid electrons are very easily exchanged and ejected. This is of course at a much lower energy energy scale than the nuclear emission and therefore less noticeable.
| {
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What's the difference between frequency domain and time domain spectra?
If I have a mechanical oscillator and want to observe the dynamical behavior of the oscillator, is there any additional information to observe it in time domain and frequency domain? Normally, we observe the frequency domain spectra (power spectra... | A problem formulated in the time domain and its equivalent formulation in the frequency domain contain essentially the same information. They just have different mathematical forms. One is easier to solve than the other, that is why we use transformations.
Many problems attempted through the equations of motion obtai... | {
"language": "en",
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Nature of Cooper pairs Some people say it is bound state, some say it is not. Which is more accurate?
Problem is that I read in some books, including Ziman, that Cooper pairs are bound states but my teacher says that it is not true and that Bardeen had to explain it many times even to his peers.Now, i know that it has ... | Yes, Cooper pairs are bound states of electrons held together by an attractive potential mediated by phonons. It's explained pretty clearly in the Wikipedia page. But they're often very loosely bound so the individual electrons remain very far apart, so you shouldn't think of a Cooper pair as a localized particle-lik... | {
"language": "en",
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Is entropy related to Poincare recurrence time? One of the ideas involved in the concept of entropy is that nature tends from order to disorder in isolated systems. But we even know that Poincare recurrence time also is a particular time after which a system of particles get back to their original position,and entropy ... | Yes, entropy and recurrence times are related, indeed proportionally so. The logarithm of the entropy of a well-defined (eg at a single temperature) system contains the density-of-states, the number of quantum levels in the vicinity of the average energy. Entropy increase accompanies an increase in that density- i.e. m... | {
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Does an excited state wave function depend on state preparation? Consider a quantum system with a ground state and many excited states (e.g. an atom).
If the system is in an excited state, to what extent does its wave function depend on the method of state preparation? Does it matter if it was excited directly from th... | A given state has one single wave-function. Thus, the information about the different preparation types is not encapsulated in that wave-function.
But keep in mind that each preparation type has its additional products. For instance if the excited state you obtained came from an even higher excited state, a photon was... | {
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Meaning of Einstein's equation $E=mc^2$? Meaning of Einstein's equation $E=mc^2$? How can a $1\,\mathrm g$ mass possess energy equal to $9\times10^{13}\,\mathrm J$? What does it actually mean?
| It is what it seems to be at first glance: matter intrinsically contains energy even if it is stationary and thus has no kinetic energy. This energy defined as $E=mc^2$ is called rest energy. All matter carry rest energy.
Now, due to the large numerical value of c, even the lightest objects contain such immensely huge... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/147058",
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How is strong time dilation consistent with weak tidal forces? Nolan's latest film, Interstellar, takes pains to explain to lay audience members that the passage of time slows in the presence of strong gravitational fields (as per Einstein's theory of General Relativity). While this certainly makes for an innovative pl... | time slows in the presence of strong gravitational fields
It's not the gravitational field that determines time dilation, it's the gravitational potential. The Newtonian approximation really isn't correct here, but let's use it anyway for insight:
*
*The potential falls off like $1/r$ with distance $r$.
*The field ... | {
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Friction Between Liquid and Solid Surface How does friction between liquid surface and solid surface differ from viscosity, the friction between liquid and liquid surfaces? Also has a word describing the process been invented or is liquid-solid friction suffice? Any ideas are appreciated, I'm looking for various perspe... | The friction between a solid and liquid is a function of viscosity.
The best way to answer this is with a model setup called Couette flow where a fluid sandwiched between two plates is sped up by the movement of the top plate:
Image source: University of Virginia, Physics 152 taught by Michael Fowler
The friction fo... | {
"language": "en",
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Is it possible to create a parachute large enough to stop all velocity? This idea came to me while playing Kerbal Space Program. I noticed that the larger my parachute was, the slower my rocket would fall back down to Kerbin. I would like to know if it is possible to create a parachute so large in the real world that i... | I will answer "yes" if you think out of the box for a parachute, which is a way for a person ejected from a plane to fall on the earth safely.
Theoretically, one might design a parachute with a layer of helium so as to match the parachute and person downward gravitational force at a certain height, possibly 4 km above... | {
"language": "en",
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Coupled ODEs that model a quad rotor I am working on modeling the vibrations of a quad rotor. The arms that support the rotors are fixed to a center plate; that is, it is pretty much a cantilever beam with an end load. Since this is the case, $m_{eq} = m_{arm} + \frac{m_{motor}}{3}$ and $k_{eq} = \frac{3EI}{\ell^3}$ wh... | From user27118, I was able to grasp a better understanding of what needed to be done to set up the system of ODEs:
\begin{alignat}{2}
m_{eq}\ddot{y}_1 &= k_{eq}(z - y_1) + c(\dot{z} - \dot{y}_1) - m_{eq}gy_1 +
F_1(t)\\ ... | {
"language": "en",
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Statistical physics and momentum conservation In statistical physics one usually looks at energy as a conserved quantity and e.g. in the canonical ensemble assumes a constant average energy of the ensemble. Now why don't we usually do this for other conserved quantities like momentum? Why not do a 'canonical' ensemble ... | Momentum, unlike energy, is a vector quantity. This means that if you have a large number of particle moving at random their momenta tend to cancel out, rather than adding the way a scalar quantity like energy would.
If the total momentum of the component parts of your system does not add to 0, then this simply means t... | {
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Will a person experience micro or zero gravity inside an aeroplane in free fall Let us say that a person is inside a stationary aeroplane being held by a stationary helicopter in the sky. Now, the cable which supports the aeroplane breaks. Thus the aeroplane is now not bound by anything.
1) Will the person inside the a... | In the cases with the aeroplane in air, at first the person will feel zero gravity, but significant air drag will swiftly prevent the plane from accelerating at $g$. Therefore, the person would feel the force of their seat on their bottom disappear, but very soon afterwards the rider will be forced back into their seat... | {
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Is the world we are living in discretized? I do not know how to use professional words to ask my question, so I will try to use a layman language. Please bear with me for a moment.
A ROUGH GUESS
The world our eyes are seeing every moment is a picture reflected in our eyes. I guess our eyes are like cameras, that are ta... | Quite a philosophical approach. There is still the reliance on our four other senses in order to make sense of our physical world, however the same approach can be imply to those senses also with the delay in neurological impulses.
One must also take into account, as you would call it, the in between frames of other p... | {
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Wave packets and half-width at half-maximum Suppose we have a Gaussian wave function and amplitude distribution function
$$\psi(x) = (\frac{2}{\pi a^{2}})^{1/4}e^{-x^{2}/a^{2}}e^{ik_{0}x}, \qquad \phi(k) = (\frac{a^{2}}{2\pi})^{1/4}e^{-a^{2} (k-k_{0})^{2}/4}.$$
Now, according to my textbook, when $x$ and $k$ vary from ... | I was also puzzled with the way Zettili defined $Δx$ and $Δk$ to derive uncertainty relations. His definition is not the same as the well known $\text{FWHM}=2.3548\sigma$. First we need to realize that $|\psi(x)|^2$ and $|\phi(k)|^2$ have the standard Gaussian form
$$\frac{1}{\sigma\sqrt{2π}} \exp\left[−\frac{x^2}{2\s... | {
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How does a giant walk-in fridge maintain a thin temperature gradient at the entrance? I'm standing in a Costco store, and they have a large walled off area for chilled produce. The entrance to this section is a square opening about 10 feet on a side. When you walk in, you notice a rapid change from room temperature to ... | The key here is the air curtain. You can be certain that if it didn't save Costco money, they wouldn't bother with it! It takes a bit of power to push air that much. Two very helpful diagrams are in the youtube video Powered Aire - Cold Storage Air Curtain:
In the first case, the air can mix and change temperature th... | {
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Why we see more diverging light rays than converging light rays? While the apparent fact that there's more diverging light rays than convergings ones seems to be intuitive, mathematically I can't find a reason to be so.
More specifically, given a vector field of light rays $\overrightarrow{v}\left(x,y,z,t\right)$, we w... | By the second law of thermodynamics the stars loose their energies into the space growing older.
But, in addition, the boundaries of our universe are expanding AT LEAST with the light-velocity. The energy (radiation) lost by the stars is not reflected back by these boundaries (and it is not sure whether such boundaries... | {
"language": "en",
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Calculating energy density in the early Universe I've been told to calculate the energy density in the early Universe. It states that it is completely dominated by neutrinos (3 species), photons, electrons, and positrons.
Now, I've found an equation to calculate the energy density for bosons and fermions, with differen... | Normally you would use the effective degrees of freedom $g_\star$, which sums up the particles. This varies from 106.75 at T>200 GeV to 3.36 (after electron-positron annihilation). The values for $g_\star$ may be looked up in a table, e.g. https://arxiv.org/pdf/1609.04979.pdf.
Then the energy density is given as:
$$ \... | {
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Force required to drive car From what I know of Newtonian Mechanics, if an object is moving at a constant velocity, the net force acting on that object is equal to zero. If there is friction, then the applied force required to maintain a constant velocity is equal to the magnitude of the force of friction, regardless o... | power = force × velocity
so at 10 km/h , power is 4000 N × 10 km/h
while at 100 km/h, power is 4000 N × 100 km/h
this way fuel will b consumed approx 10 times faster at 100 km/h than at 10 km/h
| {
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All geodesics are inextendable? I think the title is true, because geodesics has a tangent vector with a constant length parametrized by an affine parameter.
Probably, it is easier to think about timelike or spacelike geodesics. In this case, its affine parameter measures the length of the curve. It is difficult to im... | It is not true. Sometimes the spacetime itself and therefore the geodesics can be extended. Consider for example the manifold described by (t,x,y,z) with $x,y,z> 0$ and Minkowski metric. This is nothing more than Minkowski spacetime truncated to a smaller region, but it is a perfectly valid manifold for all purposes.
... | {
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Is it possible to express various nonlinear motions as straight lines in transformed spacetime? I am trying to understand simple examples of space-time curvature.
Assume for the moment that $c$ is infinite (classical curvature due to Newton's laws). Also, I will only consider 1+1-dimensional space for simplicity: $(x,t... | Ok I solved case 2. Let $t'=\tan^{-1}(\omega t)$ and $x'=x\sqrt{1+t'^2}$. Also observe that $x=A\cos \omega t + B\sin \omega t$ to represent simple harmonic motion. We get $x'=A+Bt'$. So only case 3 remains open.
Also as u can see, I just did guesswork, without proper techniques for how to solve this in general.
| {
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Question about wavelength of EM wave in dielectric Many websites (http://maxwells-equations.com/materials/permittivity.php) lists out the following formula as to how you can compute the wavelength of an EM wave in a dielectric
$$\lambda_d = \lambda_o/\sqrt\epsilon_r$$
This doesn't sit well with me.
I wonder where did $... | You're perfectly correct. Referring to Classical Electrodynamics by Jackson, we see that the index of refraction $n$ is given by:
$$n=\sqrt{\frac{\mu}{\mu_{0}}\frac{\epsilon}{\epsilon_{0}}} = \sqrt{\mu_{r}\epsilon_{r}}.$$ But Jackson notes that for most optical frequencies (and non-meta-material media), $\frac{\mu}{\mu... | {
"language": "en",
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If entropy is increasing does it mean universe is non-deterministic? I watched some video where they said entropy can be considered as information.
They also stated that universe's entropy is always increasing...
Now here comes the problem my IT mind can't understand:
If entropy is increasing, in other words universe i... | My two cents to add to the great response from wetsavanna: a short explanation would be the following. Technically, information never increases or decreases at the microscopic level. Entropy is a measure of information about how much do we know about the microscopic levels when making a macroscopic observation. But the... | {
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How does virtual particle become real particle in Hawking radiation? I am new to black hole and general relativity and am just getting introduced to these concepts.
According to my understanding, virtual particle that forms because of quantum fluctuation becomes real particle because of gravitational effects that prolo... | A pair of virtual particles are formed on the event horizon of a black hole--this is a particle anti-particle pair. These form all the time, but they usually just annihilate each other. However, if they form just on the black hole's event horizon, then one will be trapped in the gravitational field of the black hole, w... | {
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Gibbs free energy intuition What is Gibbs free energy? As my book explains:
Gibbs energy is the energy of a system available for work.
So, what does it want to tell? Why is it free? Energy means ability to do work. What is so special about this energy? Can anyone simply explain?
I just want a math-free intuition.
| There are two forces influencing the spontaneity of a reaction:
(1) The tendency of a system to attain a state of minimum energy and maximum order or stability.
(2) The tendency of a system to attain a state of maximum energy and minimum order or entropy.
If a system attains maximum stability, it attains minimum entrop... | {
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How did Rutherford's gold foil disprove the plum pudding model? What stops one of the two following scenarios from happening, consistent with the plum pudding model?
*
*The $\alpha$ particle, attracted by the electrons on the outer shell of the pudding, orbits nearly parabolically around the atom, causing the near-1... | This is the plum pudding model of the atom
Left: Expected results: alpha particles passing through the plum pudding model of the atom undisturbed.
Right: Observed results: a small portion of the particles were deflected, indicating a small, concentrated positive charge.
There are no electrons and no outer shells, ... | {
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Gyroscope motion: Why is $\vec{\Omega}$ vertical? Since I can't sketch here I am referring to: Feynmanlectures-Gyroscope
Assume that you have got a gyroscope (as in Figure 20-3 in the link) that pivoted and can turn around any axis.
Let $\vec{L}$ be the the angular momentum of the gyroscope spinning around its own axis... | Curl your fingers in the orientation of rotation, then the "omegavector" points along your thumb. In this specific case the gyro has two rotations, one of them got $\vec{\Omega}$ associated to it. This is the rotation about the vertical i.e. the whole of gyroscope precesses, hence the associated "omegavector"* points u... | {
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Theoretical limits to specific strength with hierarchical structures Specific strength (measured in units of pressure/density or speed$^2$ which in MKS there is a proposal for labelling it as the Yuri (meter/second)$^2$) is defined as tensile strength divided by material density
Hierarchical structures are on the other... | No, it's not possible.
The general rule of strength in foams is $\rho^3\propto\sigma^2$ so if you cut the density by a factor of 4, then your strength would be cut by a factor of 8.
From a conceptual standpoint slicing a organized shape under a tensile load by a plane perpendicular to the load will show that there are ... | {
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How does a electron revolve in Rutherford's model? How can an electron revolve in a circular orbit because circular motion is an accelerated motion and acc. charged particle is a source of E.M. Wave. So,it should radiate out energy and hence would loose energy; so from where does it get energy from?
| According to Quantum Mechanics, the electron actually has a wave function described by the Schrodinger Equation and it has different energy levels and its energy levels are quantized. At the most stable state the ground state ($n = 1$, $l = 0$, $m_l = 0$), it does not radiate energy, it only radiates energy when going... | {
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"url": "https://physics.stackexchange.com/questions/149983",
"timestamp": "2023-03-29T00:00:00",
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Time slowed by gravity If time moves more slowly on Earth (due to our proximity to a gravitational body) than for someone orbiting Earth in a spaceship, yet the opposite occurs in the frequently cited "twin paradox" of the earth-bound twin vs. the twin in the fast-moving spacecraft, then my question would be this--is t... | You are right, the closer we are to a body and the more the mass of the body, the slower time will run. This is owing to the fact that gravity bends space-time.
In the twin paradox time is slowed down for the fast traveling twin because of the dilation of time due to his fast velocity.
This equation gives the time per... | {
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Introducing angular momentum for the first time to a class What is the best way to introduce the notion of angular momentum to a class without making it appear an unnecessary and artificial construction?
| I suggest a way: bring a toy of a gyroscope form, put it on a table, and give it a brief torque. Although you don't act anymore on the toy, it continues to rotate.
Ask your students WHY does it happen.
I assume that they learned about the conservation of LINEAR momentum. So, we have an analogy:
a body in linear moveme... | {
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Residual Entropy - Third Law I've been told that many systems possess some residual entropy at absolute zero.
This would seem to disagree with the 3rd Law of Thermodynamics? How can this be explained physically speaking?
I am mildly aware that the 3rd law speaks with respect to a perfect system but I've never really u... | In the ideal case, at zero kelvin the system must be in a state with the minimum possible energy, and this statement of the third law holds true if the perfect system has only one minimum energy state, called the ground state. Entropy is related to the number of possible microstates. If the ground state of the system i... | {
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What is the difference between electromagnet and solenoid? What is the difference between electromagnet and solenoid? Both these terms seem as the same thing to me. The only difference that I can find seems to be that an electromagnet contains a soft iron core. I'm sure there must be some other difference between the t... | A solenoid is a cylindrical coil of wire whose diameter is small compared to its length. When an electric current flows through the wire the solenoid generates a magnetic field similar to that of a bar magnet.
An electromagnet is a solenoid wound around a central iron core. The magnetic field generated by the coil ... | {
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Red shifted photons lost energy in which form? Red shifted photons lost energy in which form?
Photons which have experienced a change in frequency (red shift) due to gravity(or other red shifting affects), have necessarily lost energy, total energy is conserved.
| Energy is most definitely conserved in the case of gravitation-ally red shifted (GRS) photons. The sun is 4.6 billion years old and has energy output equal to 3.8x10+26 watts. If 1% of the energy output is lost to GRS, an enoumous quantity of energy is missing. If the lost energy were simply hanging out in the surround... | {
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Why is Graphene So Strong? There has been a lot of news about Graphene since its discovery in 2004. And as we are all told it is a revolutionary material which is very strong, conductive and transparent.
But what is it about the structure of Graphene which makes it so strong?
| In a perfect graphene sheet, all carbon atoms are sp$^2$-hybridized, with three in-plane $\sigma$-orbitals and two out-of-plan $\pi$-orbitals. This means that each carbon atom can form equivalent s-bonds to each of its three neighboring atoms. The bonding energy of one C-C bond in graphene amounts to 4.93 eV [doi:10.10... | {
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Induced EMF of a rectangular loop should be zero? Considering the shape of a rectangular loop in a changing magnetic field:
The induced $\epsilon$ would be zero? Since a rectangular loop is a combination of wires in series to create such a shape. Each wire in this loop induces $\epsilon$ opposes the other, and they sh... | The EMF through the loop is equal to $-\frac{d\Phi_B}{dt}$ i.e., the rate of change of magnetic flux. If the magnetic field is changing, then the EMF is non-zero. You can't really calculate the EMF for an open stationary conductor if only the $\vec{B}$ field is changing. You need to use Faraday's law. How do you find a... | {
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Finding the energy lost due to non-conservative forces I stomped across this question and would very much appreciate any form of clarification.
A otter 75kg slides down a hill starting from rest. Hyp = 8.8, height = 6.5, final speed of otter = 9.2 m/s. And it wants me to find how much energy was lost due to non-conser... | This is literally what I get when I Google "non-conservative force".
From the very first link (to Wikipedia), here's a more detailed explanation:
A conservative force is a force with the property that the work done
in moving a particle between two points is independent of the taken
path. Equivalently, if a partic... | {
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Calculate Initial Velocity For Orbital (Gravity) Slingshot I am trying to find the initial velocity to slingshot a planet around the sun and through a gap.
The green ball is the planet, and the yellow ball is the sun. In this trial I need to get the planet to go around the sun and through the gap at 278Gm. I have tri... | If you are in a circular orbit what you need is a Hohmann transfer, from Wikipedia:
In orbital mechanics, the Hohmann transfer orbit /ˈhoʊ.mʌn/ is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane.
It works like this assuming the planet is in a circular orbit.
Then... | {
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Why is there conservation of kinetic energy in elastic collision and not in inelastic collision? Why is there conservation of kinetic energy in elastic collision and not in inelastic collision? What would be the difference that lead to conservation of kinetic energy in elastic collision and not in inelastic collision?
... | This is the definition of the elastic and inelastic collisions - whether the kinetic energy of the colliding objects is conserved or not.
Note that the total energy is always conserved, but in inelastic collision a part of it is transferred into the internal energy of the colliding objects (typically heat in case of ma... | {
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Do the fields exist without electric charges? I read in an old book on electrodynamics by Pauli that
theoretically there does not exist any need of charges to be there. Fields can even exist without the charges but still independent fields have not been observed still. EMWs are also produced from any accelerated char... | A propagating EM wave is a field that needs no charges. Likewise, a propagating gravitational wave is a field that needs no masses.
However in both cases there is no way (classically) to create the wave without a charge/mass. Considering EM, the divergence of the field is zero unless there is a charge, or put another w... | {
"language": "en",
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Length contraction, front middle or back I still don't have a solid understanding of Length contraction. Imagine we have a ruler of length $L$ that starts at rest upon a ground with markings on it, then accelerates until nearly the speed of light.
For a stationary observer, the ruler accelerates at $a$ metres per sec... |
For a stationary observer, the ruler accelerates at $a$ metres per
second squared.
One must be careful here.
If all points of the ruler have the same coordinate acceleration $a$, then the ruler length remains $L$ for the stationary observer.
If, on the other hand, the ruler is observed to contract, different points... | {
"language": "en",
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Greiner or Landau for Math major student? For textbook series by Greiner or Landau, is it recommended to start reading for math major students, who have no serious physics background, but comfortable with maths ?
It seems that both Greiner and Landau are in same purpose to introduce most areas in a complete and rigorou... | The Landau series is less modern than many of the Griener books from the series, however its much more concise and of very high quality. If you are comfortable with the maths and just need some physics insight, Landau is a fantastic choice. If you want some more modern approaches with more thought put into application ... | {
"language": "en",
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Magnetar field energy density According to Wikipedia a Magnetar...
Earth has a geomagnetic field of 30–60 microteslas, and a
neodymium-based, rare-earth magnet has a field of about 1 tesla, with
a magnetic energy density of 4.0×105 J/m3. A magnetar's 1010 tesla
field, by contrast, has an energy density of 4.0×10... | Yes the energy $u$ stored in a field $B$ in a region with permiability $\mu$ is given by:
$$u = \frac{1}{2}\frac{B^2}{\mu}$$
So if you double $B$ then $u$ gets quadrupled and if you increase $B$ by a factor of $10^{10}$ then $u$ increases by $10^{2\times 10} = 10^{20}$.
I'm not quite sure about the assumptions that go... | {
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QFT and violation of Heisenberg uncertainty principle In some QFT books is said that a free electron can emit a virtual photon as long as it reabsorbs the photon and returns to its original state within a time:
$$\Delta t<\dfrac{\hbar}{2\Delta E}$$
That inequality DOES VIOLATE the Heisenberg Uncertainty Principle. Why ... | I think it is important to emphasize that the notion of 'virtual particles' is a very dangerous one, which seems to lead to countless (unnecessary) misconceptions. It appears to have originated from the diagrammatic technique that can be used to carry out perturbative quantum field theoretic computations (i.e. Feynman ... | {
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Half-integer eigenvalues of orbital angular momentum Why do we exclude half-integer values of the orbital angular momentum?
It's clear for me that an angular momentum operator can only have integer values or half-integer values. However, it's not clear why the orbital angular momentum only has integer eigenvalues.
Of ... | In solving the Schrodinger equation for central force fields (e.g., the hydrogen atom), one generally separates variables using spherical coordinates. The result of the angular dependent equation is
$$\frac{\Phi(\phi)}{\sin\theta}\frac{d}{d\theta}(\sin\theta \frac{d\Theta}{d\theta}) +\frac{\Theta(\theta)}{\sin^2\theta}... | {
"language": "en",
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How to locate the Oil-Water-Contact (OWC) from resisitivity log? What is enough abrupt change in resistivity from resistive gas to conductive water? This is a real petrophysical log analysis chart with resistivity logs (laterolog log on the last row with rainbow plots and induction log on the second row with red, orang... | The region 1277 has the resistivity at about 200 ohms-m while 1291-1292m zone has the resistivity rising abruptly to the range of ~2k ohm-m (and later to 30k ohm-m at 1293m).
By the chart below we can classify the 200 ohm-m to probably be shale while the high pike to be very resistive zone. Because this is a hydrocarb... | {
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How does electromotive force (emf) influence electrostatic force in a circuit? I am learning about emf and I am using university physics of Hugh D. Young which states that when the emf source is not part of a circuit the non-electrostatic force of the source moves charge form the negative terminal to the positive termi... | As far as I understand the question. The question is when EMF source is attached and detached.
EMF Source Attached.
Consider the EMF source to be a battery in a circuit.A battery maintains a potential difference between its ends and hence provides an electrostatic force for the charges in the circuit.
EMF Source Unatta... | {
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Time Dependent Perturbation Theory Probabilities (This is taken from Griffiths Quantum Mechanics):
So suppose I have two states $\psi_{a}$ and $\psi_{b}$, and the particle starts out in the state $\psi_{a}$:
$$
c_{a}(0)=1\qquad c_{b}(0)=0.
$$
To first order,
$$
c_{a}^{(1)}(t)=1\qquad c_{b}^{(1)}(t)=-\frac{i}{\hbar}\int... | Indeed, to the 1st order, the sum is 1.
Note that $|c_b(t)|^2$ is on the 2nd order of the perturbation.
| {
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Relativistic Kill Vehicle What would happen if a significantly supra-molecular object (say ranking from grams to low kilotons) would be accelerated to relativistic speeds (>.10 c) such that its worldline would intersect with a planetary surface?
Obviously, it would be a highly energetic event, more so with more mass a... | Assuming a direct hit - so traveling through about 50 km of atmosphere - at 0.1 c that would take about 2 ms if it didn't get slowed down too much by the atmosphere.
What about drag force? Let's assume a radius $r$, density $\rho$, mass $m = \frac43 \pi r^3 \rho$. If it is a sphere, it experiences a drag force $F=\frac... | {
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What is the temperature of the clear night sky from the surface of Earth? Before you all jump in with 2.73 K or thereabouts, this is more of an experimental question. It will obviously depend on humidity and radiation being scattered back towards the surface of the Earth. Any ideas? Anyone ever pointed a pyrometer or s... | On 14th Sept 2016 at 20:25 in Woking UK the sky appeared clear to me with a few stars visible, and my infra-red thermometer ( Dr Meter HT550 ) reads -12.9 degrees Celsius when pointed at the sky. OK its un-calibrated, and emissivity of target being measured makes a difference, but the reading may be of interest to som... | {
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What are galactic speeds measured against? The Earth moves through space at 67,000 MPH. The Milky Way travels through a local group at 2,237,000 MPH.
Wouldn't you need a fixed point to be able to measure velocity against? After all, compared to the total speed of our Milky Way, the Earth isn't moving through space. Wha... | Speed is a distance (separation between two well defined points in space) traveled over a time. The speed of Earth you quote is the orbital velocity. We know how far away the Sun is and we know the shape of the orbit, so we know how far the Earth travels relative to the Sun (distance) per year (time). Likewise the spee... | {
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Does spacetime have a "mass" value? or What is "Spacetime" made out of? When measuring the MASS within the Universe, does "space" or "spacetime" have a value?
I only ask, because when speaking of expansion, space is expanding. Could it be possible, to reverse the process, by "uncreating" space?
For if it can be created... | No one really knows the answers to you questions. Spacetime is most assuredly made of something as it is not a void and, by General Relativity, shown to be inhomogeneous: curvature over here in this piece of spacetime can be different from the curvature in that piece over there, so it has position-dependent properties.... | {
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Turning off point for 1g acceleration Let's say I am on a ship accelerating with 1g. I want to keep the engine running for half a year ( to an observer from my point of origin ) but due to time dilation it would have to be sooner than half a year on the ship.. At what time - according to MY clock on the ship - do I hav... | Let's do some math, shall we?
Let's call $t$ the time as measured from Earth, and let's say your engine is running with acceleration $a$ for $0 \le t \le T$. The proper time, that is, the time as measured by a clock on a ship, is given by $\tau = \int_0^T \sqrt{1-v^2/c^2}\ dt$, where $v$ is the velocity as measured fro... | {
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How to find the center of mass of several objects in a 2d plane? We have the following scenario in a 2d plane: a big rectangle with a lot of smaller similar uniform rectangles in it, all of them weight differently.
Where is the center of mass of this object found by a formula?
To generalise it (In a 2d plane):
We ha... |
Let bottomleft point be $(0,0)$ and assuming each small segment is a uniform square of side 1 unit. The $y$ coordinate of the center of mass will be
$y_{cm}=\dfrac{28\cdot4.5+35\cdot3.5+27\cdot2.5+27\cdot1.5+26\cdot.5}{143}\approx2.58$
Similarly the x coordinate will be,
$x_{cm}=\dfrac{23\cdot4.5+31\cdot3.5+21\cdot2.... | {
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What do units like joule * seconds imply? I can easily understand what divisive units imply, but not what multiplicative units imply.
What I mean is, when I read "$12 \:\mathrm{eggs/carton}$", I mentally convert it to, "There are 12 eggs for each carton". I get that.
But, when I see units like joules * seconds, $\:\m... | Reciprocal cartons for storing eggs might make little sense, reciprocal seconds (Hz) do.
Joules times seconds (J.s) is equivalent to Joules per Hertz (J/Hz). It denotes angular momentum, the amount of energy per unit of rotational frequency.
Similarly, reciprocal meters (wave numbers) also make perfect sense. So unit... | {
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Does a static electric field act continuously? Electromagnetic radiation is emitted and absorbed in discrete units, photons.
One photon's energy is described by the well known $E = hf$ formula.
Now, if you a have static electric field that doesn't oscillate or other, then we can say $f = 0$. So the photon energy is zer... | It is really true that the electric field of an electron does not oscillate. It is a static field. If you accelerate an electron - and this one do exclusively by the help of an EM field - the electron absorbs photons and emits photons. And photons have an oscillating electric and magnetic field. However, this is not re... | {
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What can we learn from a band structure diagram? Other than the band gap and its magnitude, what are the things that we can immediately learn about the properties of the material just by glancing at its band structure?
Can we say something about the bonding? Can we see if the material exhibits some exotic properties li... | You can see, where the band maxima and monima are and thus see, which gap is direct or indirect. In the case of a direct semiconductor, the CB minimum would be straight above the VB maximum.
Bonding can not be seen directly, I think. But from the position of the Fermi level, you would see, if a material is behaving lik... | {
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Is wave superposition always equivalent to wave interference? I'm confused when using these 2 words "wave superposition" and "wave interference" since their definition is very similar.
So, are these 2 term the same?
| Diffraction is the result of the influence of an edge on a wave. Behind every edge an electromagnetic radiation forms a fringe pattern. This is an intensity distribution and is called the interference pattern. Behind two close together lying edges (a slit) both EM radiation and water waves form intensity distributions.... | {
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Close or open circuit? A electric source provides a non electrostatic influence on the charges inside the source which pushes the positive charges from the negative terminal to the positive one. Does this happen when the source is part of a close circuit or of an open one?
| Actually the source is capable of creating field around it .The imaginary field lines pass preferably through the circuit(I don't remember that if it was called permeability or somewhat ) and exert force on charges to flow .If the circuit is open it not possible to go to the other side due to resistance offered by the ... | {
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What makes Sun's light travel as parallel beams towards earth?
Sun's light appear to travel as parallel beams towards earth $_1$. Sun produces electromagnetic radiations through pp chain and other reactions in Photosphere $_2$.
I don't see whether these reactions send photons in that neatly arranged parallel rays,... | Suns rays are isotropic, but if we assume a small area $dA$, then the rays would be perpendicular to that crossection, and parallel with eachother.
| {
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Is there a commonly used unit of measure (other than temperature units) that is not absolute? I live in a country where we use Degree-Celsius(°C) to measure the temperature.
Sometimes from one day to the other, the temperature rises from 10°C to 20°C and I hear people say, "Wow! Today is twice as hot as yesterday!".
I ... | Stellar magnitudes are generally measured relative to Vega
| {
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What is the initial angular momentum of a rigid body given an offset impulsed force? What is the imparted angular momentum to a rigid body if the impulse force is offset by a distance $h$ from the center of mass and the imparted momentum from the center of mass is $mv$?
For a homogeneous sphere I said the imparted angu... | In general if the imparted momentum vector $\vec{J}$ goes through a point $\vec{r}$ relative to the center of mass then the change in speed of the center of mass is
$$ \begin{aligned}
\Delta \vec{v} &= \frac{1}{m} \vec{J} \\
\Delta \vec{\omega} & = I^{-1} (\vec{r} \times \vec{J})
\end{aligned} $$
where $\times$ is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/155425",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
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} |
Soft-Supersymmetry Mass (Direct contact term) I found this term/operator in some papers that can generate masses, e.g Riva-Biggio-Pomarol(2012), Fox-Nelson-Weiner
$\int d^4\theta \frac{X^\dagger X}{M^2}Q^\dagger Q$
Could anyone explain about this term?
Is there any references that explain this term?
| The term give a mass for the squarks. This is easy to see by expanding the superfields,
\begin{equation}
\frac{ F ^4 }{ M ^4 }\int \,d^4\theta \bar{\theta} ^2 \theta ^2 \left( \tilde{q} ^\dagger + \bar{\theta} \bar{q} + ... \right) \left( \tilde{q} + \theta q + ... \right)
\end{equation}
Only the first squark-squa... | {
"language": "en",
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"source": "stackexchange",
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Does a positive or negative charge attract a neutral object?
Three objects are brought close to each other, two at a time. When objects A and B are brought together, they attract. When objects B and C are brought together, they repel. From this, we conclude that:
(a) objects A and C possess charges of the same sign.... | -
B: +
C: +
A and B attract, so I thought they have to be opposite signs. B and C repel, so they must be the same sign. I was surprised when I saw solutions, the selected answer was just (e).
Answer: (e). In the first experiment, objects A and B may have charges with opposite signs, or one of the objects may be n... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Metallic to insulating spin density wave transition in Hubbard model For a half-filled Hubbard model with weak on-site Coulomb interaction ($U/t<<1$), it's quite intuitive that very likely the system will be in metallic phase. However, there is also such a statement that "the commensurability of the Fermi wavelength wi... | The half-filling case is very special because you can easily see that the Fermi surface of the non-interacting system ($U=0$) is a square. As a result, a wave vector $Q = (\pi,\pm\pi)$ will connect opposite sides. This commensurability is the so called "nesting effect" and it induces instability of the system. If you c... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Field operators in Klein Gordon field: creation of a particle at position $x$ Let's start with the quantised field operators $\phi(\mathbf{x})$ and $\pi(\mathbf{x})$, defined as usual, and the relativistic normalisation $|\mathbf{p}\rangle = \sqrt{2E_p}a_p^{\dagger}$.
I know that :
$$\phi(\mathbf{x}) \left|0\right> = \... | OK in the end I think I got somewhere on my own. I am just posting this here in case it is useful for someone else.
The reason $\phi(\mathbf{x}) \left|0\right>$ can be interpreted as creating a particle at position $\mathbf{x}$ is because: $$\phi(\mathbf{x}) \left|0\right> = \int \frac{d^3p}{(2\pi)^3}\frac{1}{2E_p}e^{-... | {
"language": "en",
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Why do square shaped cups spill easier than round cups? I've noticed that when I use a cup that is square shaped with convex sides, it spills more easily than a circular cup. Why does this happen? What is the most spill-prone cup shape? What is the most spill-resistant basic cup shape?
| It is the corners where the liquid molecules collect (for a very short time), collide and some of them tend to go upwards because that is the only available direction to move freely. The smaller is the angle between two sides, the greater the chance that liquid will spill from that corner (given that the motion of mole... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Flakes of Ice in Frozen Milk and Orange Juice When I was a kid, my family used to put our gallon jugs of milk and orange juice into the freezer when we'd go away on vacation so that they would keep longer. As I remember it, if we were gone for a week or more the jugs would be frozen solid, but if we were only gone for ... | It's because orange juice and milk are both colloidal suspensions
That suspended stuff (proteins and lipids generally) won't freeze until long after the ice does. Some gets trapped in the ice lattice, transforming it to some extent. Since it happens somewhat randomly throughout, you get lots of distinct shards forming.... | {
"language": "en",
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What makes an insulator good for polarizing? Water in an electric field become polarized easily, since the natural dipoles twist and turn to align with the field.
In non-polar insulating materials, a redistribution of charge can happen in the material when placed in an electric field, which gives the material induced d... | The most important factor for getting a large polarization in a solid is how close the material is to a distorted crystal structure which breaks inversion symmetry (e.g., a ferroelectric or piezoelectric instability). The closer a material is to being a ferroelectric etc., the larger the polarization because it is easi... | {
"language": "en",
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What is antimatter? Can you give a visual example of what is antimatter?
With the re-opening of Large Haldron Collider scheduled in Mar 2015, I'm reading that they smash two particles together to try to re-create particles that might have been there are the beginning of the Big Bang, and this includes antimatter?
Is an... | To complete the good answer by Photonic, one should add that antimatter has been observed in the laboratories and experimented with for over 60 years, in terms of individual antimatter particles. It is also continually created by cosmic rays impinging on our atmosphere.
The easiest to create in the lab and the atmosphe... | {
"language": "en",
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Who is doing the normalization of wave function in the time evolution of wave function? In the Schrödinger equation, at any given time $t$ we should jointly add another sub equation, like $$||\psi_t(x)|| = 1$$ where $\psi_t(x) = \Psi(x,t)$, and then try to solve the two equations simultaneously. Why not? I know it does... | Suppose $\psi$ satisfies the (dimensionless) time-dependent Schrödinger equation:
$$
i\frac{\partial\psi}{\partial t}=-\frac{\partial^2\psi}{\partial x^2}+V(x)\psi.
$$
It will also satisfy the conjugate equation:
$$
-i\frac{\partial\psi^*}{\partial t}=-\frac{\partial^2\psi^*}{\partial x^2}+V(x)\psi^*
$$
Now consider ho... | {
"language": "en",
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What would a very massive rocky body look like? I have a basic understanding of how gaseous bodies behave according to their mass:
*
*"Low mass" bodies are gas giants (or brown dwarfs),
*Beyond a certain mass, hydrogen fusion starts, making a star,
*More massive bodies burn shinier and faster,
*Beyond a certain m... | If you put a lot of rocky planets together they will result in either a neutron star or a black, depending on the mass. The reason is that there is not much fuel left to fight against a gravitational collapse.
For instance, the mass limit to make a black hole is a function of the mass, not of the composition. More o... | {
"language": "en",
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What are the latest findings on the topology and size of the universe? The paper
G. Aslanyan & A.V. Manohar, The Topology and Size of the Universe from the Cosmic Microwave Background, JCAP 06 (2012) 003, arXiv:1104.0015,
uses the 7-year WMAP data. Has any additional checking been done on newer data (e.g. Planck)?... | The latest constraint on the curvature of the universe comes from the Planck Mission which indicates that the universe is very flat today.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/156519",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Time Dilation Back to Original Frame is Inconsistent? I am watching someone jog at nearly the speed of light, and they snap their fingers. In my frame (A), it takes $\Delta t$ seconds.
Using $\Delta \bar{t}=\frac{\Delta t}{\gamma}$ to bring you from frame A to B, and then dividing by gamma again to get back to frame A ... | In the jogger's frame of reference, the event that the finger snap begins and the event that the finger snap ends are (assumed to be) co-located. Thus, in this frame
$$\Delta \bar x = 0$$
According to the Lorentz transformation, the elapsed time between the events in your frame of reference is (setting $c = 1$)
$$\Del... | {
"language": "en",
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Sign of the totally anti-symmetric Levi-Civita tensor $\varepsilon^{\mu_1 \ldots}$ when raising indices I am confused with the sign we get when we want to raise or lower all indices of the totally anti-symmetric tensor of any rank. Take the metric to be mostly plus ($-+\ldots+$). Then is it
$$\varepsilon^{ijk}=\varepsi... | In flat spacetime, the isomorphism between contra- and covariant components is furnished by the Minkowski metric $\eta_{\mu\nu}$. The Minkowski metric in $n$ spacetime dimensions is just $\operatorname{diag}(-1,1,\dots,1)$. Thus for all dimensions, $$\operatorname{det}\eta=-1$$
For any $n\times n$ matrix $A_{\mu\nu}$, ... | {
"language": "en",
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How to diagonalise the Lagrangian mass term with SU(4) symmetry and self-dual tensors I should write the mass term of the Lagrangian with global SO(4) symmetry in tensor representation with anti-symmetric tensors and then diagonalise this term with defining a new set of tensors (self-dual and anti self-dual) and writin... | I think you can write
$$\psi=\psi^++\psi^-$$
$$\psi^\dagger=\psi^+-\psi^-$$
and then you will get something like
$$\psi^\dagger\psi=(\psi^++\psi^-)(\psi^+-\psi^-)=(\psi^+)^2-(\psi^-)^2$$
Which is decomposed
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Defining Reference Directions for Voltage and Power (sign convention)
My professor decided to use the above reference directions when calculating power in circuits. He says that when power > 0, power is consumed. When p < 0, power is generated.
This definition is counter intuitive to what I would have assigned--I wou... | Assuming $i_1$ and $v_1$ are both positive or negative (such that their product is positive) then positive charge enters the more positive terminal and exits the the more negative terminal; the charge exits the device at a lower potential
Thus, the charge has less potential energy after passing through the device and s... | {
"language": "en",
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Do particles always flow from high to low pressure? In a recent question, it was stated that
particles in high pressure air always flow to lower pressure.
In a pipe with a constriction, fluid flows from from low to high pressure after the constriction. (From here.)
How are these concepts related?
| The determinants of the net velocity of particles is a combination of the kinetic energy and the potential energy. In a venturi the kinetic energy is higher than on either the inlet side or the outlet side. At the outlet side the kinetic energy will be decreasing as the particles exit the pipe into the high pressure "r... | {
"language": "en",
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Is gravity a force? If gravity just emerges from the curvature of spacetime, is it actually a force?
Why is it one of the 4 fundamental forces of nature?
| It is certainly true that our (classical) theory of gravity describes gravity in a geometrical way as the curvature of spacetime, and this seems very different to the other three forces. What is less well known is that the other forces can also be written as a geometrical theory and described using curvature. This form... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Spherical phase space dynamics I have a hamiltonian of the form
$$H(\phi,z) = (1-z^2)\cos(2\phi) + \chi z^2$$
with position $\phi$ and conjugate momentum $z$. It has this form provided that $z \in [-1,1]$ and we have natural representation of the dynamics on sphere with $z$ being distance on the $z$-axis and $\phi$ - a... | They are fixed points because the location is well defined.
You think that it is a problem only because you are represented it in $(z,\phi)$. If you write it in Cartesian coordinate, the fix points will be clear to you.
For the dynamics around a fixed point, first you should calculate the dynamic equation $(z,\dot{\phi... | {
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Representations of subalgebra in the super virasoro algebra In the Virasoro algebra, which is generated by $L_n$, one has the obvious subalgebra spanned by $L_{-1}$ ,$L_{1}$ and $L_{0}$ which is isomorphic to the Lie algebra $\mathfrak{sl}(2,\mathbb{R})$.
The Neveu schwarz super virasoro algebra, as defined in http://e... | The (super-)algebra you are referring to is called $\mathfrak{osp}(1,2)$, where osp stands for orthosymplectic. I am not sure about the matrix representation, but a google search about "orthosymplectic superalgebra" will give you plenty of references.
| {
"language": "en",
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How do we stabilise satellites so precisely? Look at the Hubble Ultra Deep Field photo. The stars in it are on the order of 1 arcsecond across. To an order of magnitude, this is $10^{-6}$ radians in a $10\text m$ telescope which was held steady for $10^6$ seconds.
In other words, the velocity of the aperture of the tel... | Three capabilities are needed to precisely control of the orientation of high precision spacecraft such as the Hubble. The spacecraft must have
*
*A notion of where it is supposed to be pointing,
*Equipment that can detect the spacecraft's attitude and attitude rate,
*Equipment that change the spacecraft's attitud... | {
"language": "en",
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Why can't the electron enter the nucleus? Actually, there exists an attractive force between an electron and the protons inside the nucleus, but the electron cannot be attracted towards the nucleus! What force balances that attractive force? Explain.
| The electron is attracted by the nucleus. In the Bohr model it was said that the electron rotates around the nucleus and the centrifugal force compensates the nuclear attraction. But the Bohr model is outdated. The electron is a quantum particle in a electrostatic field, and its behavior is dictated by the Schrodinger ... | {
"language": "en",
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Baryogenesis via Leptogenesis Baryon number is directly violated through electroweak anomaly and so does the Lepton number, for each transition from one vacuum to another. The two violations are of equal amount $\Delta B=\Delta L=N_f[N_{CS}(t_i)-N_{CS}(t_f)]$ since $(B-L)$ is anomaly free. Both the violations (i.e., $\... | I will try to give an answer, that contradicts a little my comment. I did not do any calculations, but I don't think that sphaleron processes have any influence here, since this should not only hold at very high temperatures. (BTW: this is the partial answer to one of your questions on how leptogenesis can lead to bary... | {
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What would happen to matter if it was squeezed indefinitely? I hope that this is a fun question for you physicists to answer.
Say you had a perfect piston - its infinitely strong, infinitely dense, has infinite compression ... you get the idea. Then you fill it with some type of matter, like water or dirt or something... |
Then you fill it with some type of matter,
Why do You want to do that? Your piston is ", infinitely dense, "
so You are going to compress matter with a black hole piston :=)
| {
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conservation of volume in phase space I was reading through a proof of Liouville's theorem on conservation of volume in phase space from David Tong's lecture notes (Chapter 4: "Hamiltonian formalism") and on page 89 it says that $\det(J)=1+\mathcal{O}(\mathrm{d}t)^2$ which then implies that the derivative of $\det(J)$ ... | With
$$ \tag{1} \det(J) = 1 + \mathcal{O}(dt^2)$$
he means that when $dt \to 0$ the quantity
$$ \tag{2} \frac{ \det J -1}{(dt)^2}$$
is bounded. Now what is the derivative of $\det J$? Using the definition we have
$$ \tag{3} \frac{d \det J}{dt}
= \lim_{dt \to 0} \frac{ \det J - 1}{dt}
= \lim_{dt \to 0} \frac{ \det J - 1... | {
"language": "en",
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Forced Oscillations & Resonance I need a very much physical explanation for the phenomenon of Resonance associated with forced oscillations (damped). I have gone through HRW and Concepts of Physics by H C Verma, but that wasn't of much use for me.
I got some mathematical idea of the thing, but still I'm not confident.
| Resonance is when you push a kid on a swing.
If you do it right, you make him swing higher (You push him in the same direction as he is moving). If you do it wrong, you stop his swinging (e.g. pushing, when he is on the way backwards).
When you "add to" or "build up" the amplitude of the oscillations, this is resonanc... | {
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Polar moment of inertia of a cylinder So I know the polar moment of inertia of a solid cylinder is:
$$
I= \frac{1}{2} mr^2
$$
My question arises with the polar moment of inertia uses for solid cylinders in my mechanics of materials book, which is:
$$
J=\frac{\pi}{2}r^4
$$
Don't these describe the same thing? Or am I mi... | For a cylinder with density $1/\ell$, the mass is $\pi r^2$ and the moment of inertia $\frac{\pi}{2}r^4$. This makes a bit more sense for a disk than for a cylinder (you don't have to fret over the $1/\ell$ term). I hope you can now see the relationship between the two formulas.
| {
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Why are heat-shields on re-entry vehicles smooth and not textured to increase drag? Meteorites naturally texture themselves via the formation of regmaglypts, 'thumbprint-shaped' indentations caused by ablation of their surface, during entry into the atmosphere.
This appears to naturally increase atmospheric drag on the... | Heat shields do not experience flow across them. There is a hyper-compressed layer of atmosphere next to the shield, which (due to said compression) gets very hot. The atmospheric flow is external to this compression layer, so there's no value to a roughened surface.
Now, keep in mind that the original concept for th... | {
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Gravity and bottomless pits Assuming that someone is theoretically able to make a hole through the center of a large planet, and then jumps down the hole, what will happen? Given my understanding of gravity and energy, my estimate is that in the absence of any resistive forces, the person would fall right through to t... | Ignoring the engineering difficulties of constructing a tunnel through the molten core, and ignoring the effects of the rotation of the Earth which would complicate things, yes, you are correct - you would fall through and come to a stop on the other side, then go back the other way. If you add in resistive losses, yo... | {
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Faraday cage in real life In electrical engineering we talk about using a "Faraday Cage" all the time. In general we mean putting the circuit in a metal box and grounding it, or putting a EMI shield over the top of a chip. My question is how perfect is a real faraday cage, can electro magnetic signals escape it or en... | The theory for a tinfoil screen is fairly straightforward.
There are two things going on: first, a lot (most) of the signal is reflected. Second, what penetrates into the foil is attenuated and dissipated by currents.
The impedance of the aluminium "tinfoil" is given by $\eta_{\rm Al} = (\mu_r \mu_0 \sigma / \omega)^{1... | {
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Born-like measuring rule in classical experiments this 2011 paper "Born's rule from measurements of classical signals by threshold detectors which are properly calibrated" by Khrennikov investigates the theoretical possibility of Born-like measurement rule/ dynamics for classical systems but appears largely theoretical... | The oldest work on this preceeds quantum mechanics by more than 100 years. it was done by Malus in 1809 about experiments with polarized light. See http://arnold-neumaier.at/papers/physpapers.html#CQlightslides
| {
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Kinetic energy for rotating round body having its COM not at the centre Say I have a round object, whose center of mass is NOT in its center. This can be caused due to a hole or non uniform distribution of density. The object rolls on the ground with velocity of $\omega*R$, radius being $R$ & angular velocity $\omega$... | The Kinetic Energy can be calculated as:
$K = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$
where $v$ is the velocity of centre of mass, $I$ moment of Inertia about it's centre of mass and $\omega$ being its angular velocity.
Thus Kinetic Energy can be calculated, at that instant by substiuting $v = R\omega$ in the first equ... | {
"language": "en",
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What enables protons to give new properties to an atom every time one is added? How does adding one more particle to the nucleus of an atom give that atom new properties? I can see how it changes it's mass, that's obvious... But how does it give that new atom different properties like color?
A good example would be: st... | One more factor:
Adding protons to the nucleus increases its charge and so the attraction between the nucleus and the electrons becomes stronger. As a result the atom radius decreases which plays a role in chemical interactions. Another consequence is that now more energy is required to make the atom lose an electron.
... | {
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} |
Force between two point dipoles What would the force between two parallel point dipoles be?
I was thinking of doing it the way force between two point charges is found out, by finding the field and then the force but I am not able to formulate it.
| Going from the field to the force will be difficult, because you don't know a priori how a dipole reacts to a field, particularly if the field is not homogeneous. The way to do this is the same as you find the field for the first dipole: find the net force on the two charges of the second dipole, and then take the limi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/160649",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 1,
"answer_id": 0
} |
How does "pushing-start" a dead-battery manual car work? A few days ago the battery of my car went (almost) dead. As it is a manual car, my father once told me that the way to get it going without jumper cables was to push it or let it roll down a hill, sink the clutch, shift to 2nd gear and then let go the clutch.
Aft... | Actually, you can push/roll start a manual car in this fashion with no battery at all. The momentum of the car is used to turn over the engine when the clutch is released, hence why the car slows noticeably at this point.
Second gear is used to get the engine turning fast enough that the alternator provides sufficient... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/160718",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
"answer_id": 0
} |
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