Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What happens if we rotate one gear and this rotates another and this to another and so on. Will the last gear rotate faster than light? what happens if we rotate a small gear attached to a larger one and the large one rotates another small one attached to a large one and the large one rotates another small attached to ... | No. Rigidity in the sense that is frequently assumed in Newtonian mechanics breaks down in special relativity. A torque applied to a gear at one point doesn't immediately start turning each point in the gear at the same angular velocity. The "information" propagates in the form of small deformations within the gear, ro... | {
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What is the difference between a force and a net force? I read in Newton's first law, it states that an object will continue to have a constant velocity unless acted upon by a force whilst for other articles, it states "unless acted upon by a net force." Which one is correct? Are they both interchangeable? Is there any... |
[...] whilst for other articles, it states "unless acted upon by a net
force."
The latter is really the correct expression, the former really being a 'lazyism'.
Consider the following body, subject to three forces as an example:
Newton's First Law refers to the net force $\mathbf{F}$, calculated as the vector sum:
$... | {
"language": "en",
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How does the Brownian motion of air molecules compare to the threshold of human hearing as a function of frequency? This fantastic question essentially asks what is the noise floor of air? Both the answer given on that thread and the value stated by Microsoft are around -23 or -24 dBSPL.
However, overall loudness is on... | My understanding is that we are talking here about the molecules tapping on the eardrum, i.e. the shot noise - similar to the noise of the rain drops. It is a white noise, i.e. its spectrum has the same amplitude at all frequencies.
On a deeper level however there are at least two characteristic timescales that would l... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/561102",
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Difference between vibration and oscillation considering a point in space Most answers and articles I've read so far try to give real world examples such as a spring or a pendulum. However, I'm trying to understand the core difference between the two terms in the most fundamental context.
Do we need the term vibration ... | Lets look at the words:
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin vibrationem ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, such as the movement of a tire on a gravel road.
and
Oscill... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/561219",
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Have we probed beyond Extremely Low Frequency (ELF) light to see is there is anything out in the universe emitting it? I could only find some articles talking about radios used to communicate with submarines and a few now-defunct transmission towers for ELF. I would think this would be something that was studied to see... | Extremely low frequencies (anything below kHz) cannot travel through interplanetary space, because the
plasma frequency is too high.
The plasma frequency is given by
$$\nu_p = \left( \frac{e^2 n_e}{4\pi^2 \epsilon_0 m_e}\right)^{1/2} = 9000 \left(\frac{n_e}{{\rm cm}^{-3}}\right)^{1/2}\ {\rm Hz},$$
where $n_e$ is the el... | {
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Is a capacitor a dipole? A few more questions about understanding dipoles I recently learned about dipoles, according to its definition I was wondering if a capacitor can be considered also as a dipole?
Also I was wondering what is the physical meaning of the dipole moment $\vec{p}=qd$?
And my last question is what is ... | I will answer your first question. A capacitor is not necessarily a dipole. For example, a conducting wire surrounded by a conductor separated by an insulator is a capacitor but not a dipole.
| {
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Does the Ryu-Takayanagi conjecture only apply to vacua? Does the Ryu-Takayanagi conjecture only apply to vacua, or does it also apply to arbitrary excited states?
For excited CFT states, the entanglement entropy can be proportional to the volume, not surface area, or it can even be arbitrarily large.
| The Ryu-Takayanagi (RT) formula certainly applies to more general backgrounds, but it doesn't hold for arbitrary excited states. Remember that generic high energy excited states in the CFT will correspond to a bulk which isn’t at all semiclassical and will look very quantum, i.e. no nice bulk geometry. But of the CFT s... | {
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${\rm 2D}$ isotropic oscillator: Is ${\rm SO(4)}$ a subgroup of ${\rm Sp}(4,{\rm R})$? Consider the ${\rm 2D}$ isotropic oscillator. The hamiltonian is $$H=\frac{1}{2}(p_x^2+p_y^2+x^2+y^2)$$ and the phase space is $4$ dimensional. In this case, the set of all linear canonical transformations that preserve the form of H... | No, $SO(2n,\mathbb{F})\subseteq Sp(2n,\mathbb{F})$ [understood via their standard embedding into $GL(2n,\mathbb{F})$] is only true for $n=1$. This fact can be proved by considering the corresponding Lie algebras.
Specifically, $Sp(4,\mathbb{R})$ is (the double cover of) the restricted anti de Sitter group $SO^+(3,2;\m... | {
"language": "en",
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Is there a smooth transition from inverse quadratic gravity to linear gravity? I can't remember exactly what it was, but I remember going through a problem in physics related to gravity on and inside a sphere, and found that inside, gravity acts linearly as a result of some triple integral cancellation with an assumpti... | For a spherical body of mass $M$ and radius $R$, assuming the density is constant you can calculate the gravitational field strength at any distance $r$ from the centre of the body using Gauss's law. If you work through the algebra (which is a good exercise) you'll eventually find
$$g = \begin{cases}
-\frac{MGr}{R^3}, ... | {
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Finding direction of field when using Gauss law I have seen this stack question Applying Gauss' Law to find Electric Field but I got confused when I saw the comment and the answer because, clearly the flux is a scalar quantity (due to dot product). So after using Gauss law to find magnitude, how do I find the direction... | If you apply Gauss' law to obtain the electric field, the direction of the electric field should be clear before applying Gauss' law, otherwise you will not be able to do the product $\vec{E}\cdot \vec{dS}$ and get the magnitude out of the flux integral. To determine the direction use symmetry arguments; try placing th... | {
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Time evolution of the standard deviation of an operator How would I find the time evolution of the standard deviation of an operator? For example, how might I find the time evolution $\sigma_x (t)$ of the standard deviation
$\sigma_x = \sqrt{ \langle \hat{x}^2 \rangle - \langle \hat{x} \rangle^2}$
of the position opera... | Adding to @Vadim answer's: note that when a system is in an eigenstate of the Hamiltonian, it is stationary. If an operator does not have an explicit time dependence, its expectation value will be constant. This is true regardless of the details of the Hamiltonian or the operator.
To see this, you can note that if the ... | {
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Pseudo Force and Inertial and Non-Inertial frames In the figure given below is block placed on an incline $\theta$. Now the lift is accelerating upwards with an acceleration $a_0$. Now if we make our measurements from the lift frame we will have to apply a pseudo force $-ma_0$. Which will have two components one in the... | To avoid confusion caused by gravity, we will assume the lab frame is in an inertial frame, floating in space far from Earth. $F = ma$ works in this frame. In these coordinates, there is no net force on an object that stays at $x = 0$.
Working in the lab frame, you see the lift accelerated upward. Given no friction, th... | {
"language": "en",
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Has the ballistic motion of an electron in gravitational field ever been measured? Reading this question I thought of an argument that an electron's trajectory would bend in the gravitational field despite the electron's being incapable of strong interaction; this would then disprove the conjecture stated in that quest... | After searching online for a while, I found this paper, entitled "EXPERIMENTAL COMPARISON OF THE GRAVITATIONAL FORCE ON FREELY FALLING ELECTRONS AND METALLIC ELECTRONS". The paper refers to two earlier papers:
1.F.C.Witteborn, L.V.Knight,and W.M. Fairbank, in Proceedings of the Ninth International Conference on Low Tem... | {
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The Von Neumann interpretation of the Double Slit Experiment First, I am a philosopher not a physicist, so apologies for limits in my understanding of quantum physics. My interest is in the philosophical implications of physics. I've just joined looking for physicists I can ask questions to, but my first question hasn... | "Consciousness causes Collapse" is based on the idea that the measuring device should be described by a waveform as well as the experiment. Before measurement is done the system under examination is in a mixed state, say
|up> + |down>
Once the measurement is done, the combined system + measuring device is in the sta... | {
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Why don't the nuclear fusion processes inside the sun produce electron antineutrinos $(\bar\nu_e)$? Why don't the nuclear fusion processes inside the sun produce $\bar\nu_e$ despite having the same mass as $\nu_e$? Is the reason as simple as "there is no production channel for $\bar\nu_e$s." ?
| You must convert proton to neutron somehow (pp chain or CNO chain) and this means by charge conservation that a positron must be emitted, and by lepton number conservation to balance lepton number that anti-electron is accompanied by neutrino and not anti-nu.
| {
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Why does water keep dripping out of the bucket even after the faucet is turned off? So I just noticed that when I filled my bucket with water until it overflowed and then I turned the faucet off, the water kept dripping for like 20 seconds. Why does this happens? Shouldn't it have stopped dripping sooner after I turned... | If you are talking about the water overflowing from the bucket, it is because water has a surface tension. This lets the surface, or skin of the water rise slightly above the rim of the bucket before the gravity pulls the water enough to break the surface tension and start it flowing over the edge. Once water stops fl... | {
"language": "en",
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Why is internal resistance of battery considered outside the terminals although it is present between the terminals inside the battery In ideal battery the internal resistance is zero whereas in non-ideal battery there is some internal resistance now this internal resistance is due to the battery material (electrolyte)... | It's just 'empirical' (a rule which is good enough to predict observations, but is not necessarily related to the actual cause). Observations of the current driven by a battery and its voltage show a roughly linear relationship which can't be explained by the external resistance in the circuit alone, but are consistent... | {
"language": "en",
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Deflection of an electron from a charged wire and from an interference grid: In both cases the electron radiates? Near a charged wire a moving electron is deflected. Since the deflection is an acceleration, the electrons emit photons.
What about an electron's radiation, which is affected by an interference grating?
|
Since the deflection is an acceleration, the electrons emit photons.
Not in quantum mechanics/quantum field teory, emission is not obligatory, as it is in classical electrodynamics, when there is a dp/dt. It is an interaction between a particle and another particle, as is the case in diffraction, the other particle b... | {
"language": "en",
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Commuting the time evolution operator Given the time evolution operator $U(t, t_0)$, I don't understand why it is true that for a time-independent operator Q,
$$[Q, U(t, t_{0})] = 0 \Leftrightarrow [Q, H(t)] = 0 $$
where H is the Hamiltonian.
| You can derive the Heisenberg equation from the Schrödinger equation.
$$\frac{dQ_H}{dt}= \frac{d(U^\dagger Q_S U)}{dt}$$
Then after you write it complete and define $H_H=U^\dagger H_S U$ yo see the following:
$$\frac{dQ_H}{dt}=-i[Q_H,H_H]$$
And finally you can say $U$ and $H$ always commute for time dependent $H$ and a... | {
"language": "en",
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Sanity check: can we define "arbitrary" hamiltonians? I just want to do a sanity check on my understanding of Hamiltonian mechanics:
My understanding is: For any number $n$, take the phase space $\mathbb R^{2n}$, and take any arbitrary differentiable function $H:\mathbb R^{2n}\to \mathbb R$ to be the Hamiltonian. Then ... | *
*We only need differentiability of the Hamiltonian $H(q,p,t)$ as long as we stay in the Hamiltonian formulation. In particular, Noether's theorem works with the Hamiltonian action, cf. this Phys.SE post.
*However to guarantee the existence of a regular Lagrangian formulation in $n$ variables $(q^1,\ldots,q^n)$ (vi... | {
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Energy of a rotating wheel Why does a rotating wheel have kinetic energy $K=\frac{1}{2}mv^2$ associated with its movement?
I will clarify.
Let's say I have a rotating wheel in an empty void which has an angular velocity $\omega$, then its total energy will be $E=\frac{1}{2} I \omega^2$, as the wheel is not moving. Now ... | You are correct that before contact with the surface the wheel has $KE=\frac{1}{2}I\omega^2$ and after contact with the surface the wheel has $KE=\frac{1}{2}I\omega^2+\frac{1}{2}mv^2$. Since energy is conserved and since $m$ and $I$ are unchanged that implies that $\omega$ must decrease in order to compensate for the l... | {
"language": "en",
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Why is $\Delta x$ or $\Delta p$ constant for a particular $\psi_n$? We were asked to calculate $\Delta x \Delta p$ for the $\psi_0,\psi_1$ of the harmonic oscillator.And so we calculated the answers and verified that $$\langle T \rangle +\langle V\rangle = (n+1/2)\hbar\omega\tag{1}$$ and that indeed they do follow the... | Quantum mechanical measurements are carried not on a single object, but an ensemble of objects prepared in the same state. Measurement on a single object produces a specific value, e.g., of the position - $x_i$. Measurements on the ensemble of $N$ objects produce
$$\{x_i | i=1...N\},$$
which allow calculating sample me... | {
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What is the name of the shape of the iron core in a transformer? I'm researching on transformers and curious to know about what this shape is called (the actual core block, ignore the wires around it).
| That can be called a core-type transformer (with a single window) in contrast to the shell-type transformer. Note also that those types of cores are also constructed with laminated materials to reduce eddy current losses.
The linked definitions from the Electrotechnical Vocabulary of the International Electrotechnical ... | {
"language": "en",
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In the generation of X-Rays, why the incoming electron generated from anode knocks out the K shell electron rather than outer shell electrons? When the high energy beam of particles or photon hits the cathode, electrons from $K$ shell are knocked in the generation of characteristic x-rays. Why do inner electrons get kn... | There is a probability that any of the electrons are knocked out.
However only the most energetic photons resulting from electron transitions would be classed as being in the X-ray part of the electromagnetic spectrum.
If the charge on the nucleus is low, eg for a hydrogen atom, the transitions to the inner most energ... | {
"language": "en",
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Why does the string of a simple pendulum need to be perfectly flexible? The book says:
"The string should be perfectly flexible, if we like to neglect the effects of different velocities of the different parts of the string during the oscillation."
Can anyone explain what actually is going on over here? I mean how do... | Imagine that the string was not perfectly flexible but instead was a length of steel wire, rigidly fixed at its upper end. Then when the weight on its other end tries to swing back and forth, the springiness of the wire applies an extra restoring force in addition to that generated by gravity and the resonant frequency... | {
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Does "adding a constant to the potential energy" imply "adding a total time derivative to the Lagrangian." I am trying to understand why Taylor says in his Classical Mechanics text, "we can always subtract a constant from the potential without effecting any physics."
I assume "doesn't effect any physics" means the equa... | You can add $\dot q=\frac{dq}{dt}$ to the Lagrangian without harm, and this has nothing to do with a potential.
Since the EOM are obtained from derivatives of the Lagrangian, adding any constant (to the potential energy or otherwise) will have no effect.
| {
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To what precision is the heat capacity an extensive quantity We know that heat capacity is an extensive quantity, basically meaning for double the amount of substance you need double the energy to increase temperature. To what extend is this actually true, like:
*
*Are there e.g. (measurable) surface effects?
*Have ... | Experimentally, I think it is easier to do the opposite: cooling bits of heated material in water inside a insulated container and measure the temperature change for example.
When trying to increase the mass of material heated in a furnace to the same temperature, and measure the associated increment of energy (say gas... | {
"language": "en",
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Conserved quantity for any motion in 1D Newton's second law for a nonrelativistic particle of mass $m$ in 1D, reads, $$F \bigg(x, \frac{\mathrm{d}x}{\mathrm{d} t}, t \bigg)=m \frac{\mathrm{d}^2 x}{\mathrm{d} t^2}$$, where $F$ is the net force function. Now, if we assume that $F$ is time-independent and that $v=\frac{\m... | It is all essentially about the energy conservation. When forces do not depend on velocity, they are conservative, and characterized by the potential energy, so the total energy is conserved. When the forces do depend on the velocity, these may be either forces like Lorentz force that do not change the total energy or ... | {
"language": "en",
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Locally flatness in general relativity My professor made following statement:
The spacetime of GR is curved in the presence of strong gravitational fields. The effects of curvature
manifest themselves at large distances. Locally, one can choose a flat Minkowskian metric.
I dont get it:
I... | Sitting in your chair, you are not in an inertial reference frame. The equivalence principle states that a local accelerating frame is not distinguishable from the effect of gravity. This has no bearing on curvature. If you are sitting in your chair, you have chosen an accelerating frame. You have not chosen a Minkowsk... | {
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Two-particle system wave function I have a similar question as Two particles system
That is:
why for two-particle without interaction will have wave function $\psi(x_1,x_2)=\psi_a(x_1)\psi_b(x_2)$
And when we exchange it will have the form
$\psi(x_2,x_1)=\pm\psi(x_1,x_2)$.
and expression
$\psi(x_1,x_2)=A[\psi_a(x_1)\... | This is done for identical particles (really in QM we cannot distinguish between the two particles for ex. electrons or bosons)
consider some operator $\hat{\rho}$ which swaps two particles A and B.
$\hat{\rho} \psi(A,B)= e^{\iota\theta} \psi(A,B) $,
where $\psi(A,B)$ is the amplitude of wavefunction, which under swapp... | {
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Is it correct to say that; an object moving at a constant velocity is moving in a straight line? I think it is correct because:
v = displacement/time, if the direction changes, the displacement changes so the velocity is not constant anymore.
Please correct me if I'm wrong
| Yes. Velocity has both magnitude as well as direction, so a constant velocity would imply constant direction as well. Constant speed, however doesn't necessarily mean straight-line motion (e.g. uniform motion along a circular path).
| {
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Angular momentum and Potential field In addition to total energy, which components of the angular momentum $(\mathbf{L}_x,\mathbf{L}_y,\mathbf{L}_z)$ are conserved in the presence of an external potential field $V(x,y,z)$? I've learnt that it is usually the $\mathbf{L}z$, but how should I prove it? There seems no way t... | The general statement is that if $V$ is rotationally symmetric about a given axis, then the component of $\vec{L}$ parallel to that axis is conserved. This is easiest to demonstrate by rewriting the potential in terms of polar coordinates and showing that the torque is always perpendicular to the axis of symmetry.
Alt... | {
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Failure of wave theory in explaining photoelectric effect What property of waves makes it unable to explain to the photoelectric effect, and how does that property make the wave theory fail in explaining the photoelectric effect?
| If light was only a wave increasing the intensity of light would have increase the kinetic energy of photo electrons as intensity of the wave represents it's energy but it was found out that kinetic energy is unaffected by the change in intensity , it simply increases the number of electrons (all with the same energy)... | {
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Why is the field quantization applied to the free particle? This post claims that there is no real photon (particle) with a plane wave solution well-defined momentum state).
It makes sense somehow to me. I can think of several arguments:
*
*The plane wave solution doesn't have well-defined probability as it exists in... |
Besides 'it works' argument, do we have any explanation why this quantization process makes sense?
Quantum field theory (QFT) is used for interacting elementary particles, and also as a tool/model for other quantum mechanical states (condensed matter for example).
Your premise:
we apply quantization rule to the free... | {
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What is the point of a voltage divider if you can't drive anything with it? The voltage divider formula is only valid if there is no current drawn across the output voltage, so how could they be used practically? Since using the voltage for anything would require drawing current, that would invalidate the formula. So w... | This is perhaps a niche concern, but one advantage of voltage dividers is that they also cleanly divide down the noise.(*)
In very low temperature electronics experiments, you might want to drive your very sensitive device that can't handle more than 10 microvolts of applied voltage, but your voltage source might be wa... | {
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Specific note that is not clear for me in and the derivation of maxwell equation $\oint \vec{B} \cdot d \vec{r}=\mu_{0} I_{e n c}$ I know this is not the full equation but right now in this path of the course that what we learned so far.
We studied that a wire along the $z$ axis produces magnetic field $\vec{B}=\frac{\... | Given,
$$\oint \vec{B} \cdot d \vec{r}=\int \frac{\mu_{0} I}{2 \pi \rho} \rho d \varphi=\mu_{0} I$$
There can be 2 reasons your teacher said that the $\rho^{-1}$ is crucial for the proof.
*
*Consider the equation, $\int \frac{\mu_{0} I}{2 \pi \rho^{n}} \rho d \varphi=\mu_{0} I$
where n is a real number. This clearly ... | {
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Why symmetric potential has even bound ground state and does odd ground state exist? I have read that symmetric potential has even bound ground state, but I don't know how to derive it? The only conclusion I can derive is for even potential I can take real wavefunction.
I also want to ask, if odd bound ground state eve... | One particle wave function for a bound ground state does not have nodes. This is obviously not the case for the wave functions of several fermions, which necessarily have zeros to satisfy the Pauli principle. Note also that the wave functions of the eigenstates of a scalar potential can also always be chosen real.
| {
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Photon description of quantum-optical interference experiments I am currently studying the textbook The Quantum Theory of Light, third edition, by R. Loudon. In the introduction, the author says the following:
In the customary photon description of quantum-optical interference experiments, it is never the photons them... | The term photon applies to an electromagnetic wave packet of finite size and a total energy determined by the frequency of the wave. The strength of the two fields at any point determines the probability that all of the energy and momentum of the packet will be absorbed by some other entity (often an electron) at that... | {
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Where is energy dissipated on charging a capacitor? The energy lost on charging a capacitor can be easily found from the change in energy of the components of the circuit and the energy supplied by the battery.
On charging a capacitor I know that the energy loss appears as heat in the internal resistance of the battery... | When charging a capacitor the energy from the battery is transferred to the capacitor. If the wires have resistance, some of this energy is lost, i.e. dissipated. If the resistance is zero, there are no losses - but there is still the energy transfer from the battery to the capacitor.
| {
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Why didn't heavier elements settle at the core of the solar system? As the solar system formed, why didn't all of the heavier elements such as iron, collect where the sun is leaving the lighter elements in the outer solar system?
| Most of the iron and heavy elements in the solar system are in the Sun.
They aren't all in the Sun, because the material from which the solar system formed was well-mixed and turbulent.
The reason that the concentration of heavier elements is higher in the small, rocky, inner planets (the gas giants have an abundance m... | {
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Does seeing an object modify it state? I took a dive into the concept of information in physics and from what I have read, I which someone to confirm if looking at something really modify the state of that thing.(modify state here refers to any small change in the object "information arrangement")
| Having read the comments to the post I think you're talking about collapses. In quantum mechanics, a physical state is, in general, in a superposition of states with each state corresponding to a specific possible value you could measure. When you do measure however you only get one result and an "explanation" is that ... | {
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Can circularly polarized light resonate in a Fabry-Perot cavity? I am curious as to how a standing wave of circularly polarized light may be forced to resonate in a Fabry Perot cavity as in this paper - https://doi.org/10.1103/PhysRevD.98.035021
I know that in a standard Fabry Perot cavity with incident linearly polari... | Circularly polarised light is two linearly polarised electromagnetic waves with their electric fields at right angles to one another and $\pi/2$ out of phase.
So if it works out for each component of the electric/magnetic field what does superposition imply?
| {
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What is that which is magnetic force? I believe a magnetic field is caused by movement of charged particles.
But, what is it that is actually making the force between two magnets repel or attract to another? For repelling, I'm mentally visualizing a water balloon between two magnets. What is the water balloon composed ... | The magnetic force can be understood as a relativistic effect on the electric force. It results from Lorentz transformation of the electrostatic force for a stationary charged particle.
| {
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In what sense is a quantum damped harmonic oscillator dissipative? The classical Hamiltonian of a damped harmonic oscillator $$H=\frac{p^2}{2m}e^{-\gamma t}+\frac{1}{2}m\omega^2e^{\gamma t}x^2,~(\gamma>0)\tag{1}$$ when promoted to quantum version, remains hermitian. Therefore, the time evolution of the system is unitar... | I'll use the convention of writing the exponent as $\gamma t / m$ rather than $\gamma t$.
The actual energy of the HO is
$$ E = \frac{1}{2}m\dot{x}^2 + \frac{1}{2}m\omega^2x^2 = \frac{1}{2m}p^2\mathrm{e}^{-2\gamma t/m} + \frac{1}{2}m\omega^2x^2 = \mathrm{e}^{-\gamma t/m} H$$
since $p = \partial_{\dot{x}}L = \mathrm{e}^... | {
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Where can i get the step by step expression for CMB anisotropy? I never able to wrap my head around alm term used in expression
If you know the expression, kindly explain but also give textbook references. It would be helpful.
| Any function on a sphere can be expanded as a linear combination of spherical harmonics $Y_{\ell m}$. The numbers $a_{\ell m}$ tell you “how much” of each spherical harmonic is needed. This is similar to a Fourier series for decomposing any periodic function $f(x)$ into its sinusoidal “harmonics”.
Conceptually, the sph... | {
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Can Maxwell's equations be generalized to all fields? For having studied both classical and quantum optics, I regard Maxwell's equations as the grand "cheat sheet" from which (almost) all optical/photonic phenomena can be derived. Yet, I also know that wave-particle duality extends to all other fields and particles in ... | This is because of special relativity. The fact that the speed of light is finite can be packaged nicely im saying that we live in a space where the notion of proper distance makes sense:
\begin{equation}
ds^2=-c^2dt^2+ dx^2+dy^2+dz^2
\end{equation}
In particular, the only things we can talk about are things which are ... | {
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How does light get energy when moving from one medium to another? It is said that the speed of light increases when moving from optically denser medium to rarer medium but
as light can be considered as a particle how does it get the energy to increase it velocity
| I would just add to Emilio Pisanty's comment by saying that the frequency remaining a constant as light travels across a boundary separating two media is required because it is required that the tangential component of E be continuous across the boundary.
In turn, that the tangential component of E must be continuous a... | {
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Are there any physical processes of which we have a full understanding? Are there any physical processes of which we have a full understanding? For instance, we know that each orbit has a different energy, and electrons can move to a higher orbit by absorbing energy and drop to a lower orbit by emitting energy. However... | No for philosophical reasons.
The closest science can come to knowing fundamentally reality would be a Theory of Everything. But TOE's are a dime a dozen. It-from-bit, constructor theory, mathematical universe, geometric unity. None of them make unique predictions, or ones we could test.
Science can just make more accu... | {
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Lagrangian potential for Newtonian gravity In the Wikipedia site for Lagrangian (field theory) the Lagrangian density for Newtonian gravity is given by
$${\cal L}(\mathbf{x},t) = \frac{1}{2}\rho(\mathbf{x},t)\mathbf{v}^2 -\rho(\mathbf{x},t) \Phi(\mathbf{x},t) – \frac{1}{8\pi G}(\nabla\Phi(\mathbf{x},t))^2$$
I understa... | The last term represents the energy that is carried in the gravitational field itself. If you are familiar with electrostatics, this would be the equivalent of the statement that the energy stored in an electric field is $\frac{1}{2}\epsilon|\mathbf{E}|^2=\frac{1}{2}\epsilon(-\nabla V)^2$, where $V$ is the electric pot... | {
"language": "en",
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Why does mass-spring system tend or prefer to oscillate with natural frequency? Can you explain it theoretically rather the derived version of it? Why the mass spring system prefers to oscillate at natural frequency, why does it rather oscillate at other frequencies? Every object in the universe is always vibrating, i... | The frequency depends on the spring stiffness, k, and the mass, m, as the math shows. For a more intuitive explanation, suppose we watch as the mass moves through the middle (equilibrium) position and the spring starts to stretch. There are two competing factors: the stiffness of the spring, which wants to pull the mas... | {
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Relativity without constancy of light speed Using homogeneity of space, isotropy of space and the principle of relativity (without the constancy of light speed), one can derive:
$$x' = \frac{x-vt}{\sqrt{1+\kappa v^2}}$$
$$t' = \frac{t+\kappa vx}{\sqrt{1+\kappa v^2}}$$
$\kappa = 0$ denotes Galilean and $\kappa < 0$ deno... | There has been much discussion on one-way speeds of light and simultaneity etc. in the philosophy of physics literature. Most famously, Reichenbach introduced a parameter $\epsilon$, which gives the (one-way) light speed in opposite directions as $c/2\epsilon$ and $c/2(1-\epsilon)$. Here $c$ is the "two-way" speed of l... | {
"language": "en",
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Polarization of sunlight by the earth's atmosphere I have just learned that sunlight traveling through the earth's atmosphere picks up a net polarization by collisions with molecules ($O_2$, $N_2$, etc.) that the photons encounter. One would think that those molecules would have to possess some degree of common alignme... |
One would think that those molecules would have to possess some degree of common alignment in order to produce light that possesses nonrandom polarization.
Molecules are quantum mechanical entities and light interacting with individual molecules should be thought of in photons. Nevertheless, the classical elecromagne... | {
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Origin of $\ell \leq n-1$ orbital rule I am wondering about the origin of the $\ell \leq n-1$ orbital filling rule. For the hydrogen atom, I believe the reason is because in the spatial wave function there is the term
$$\psi \propto \sqrt{(n-\ell-1)!}$$
so if $\ell > n-1$, by the definition of the factorial, $\psi$ goe... | TL;DR: The quantization condition
$$n_r ~:=~ n-\ell -1 ~\in\mathbb{N}_0 \tag{A}$$
follows by looking for normalizable wavefunction solutions $R(r)$ to the radial TISE.
In more detail: Schematically, one first solves $R(r)$ in the regions for small & large radial coordinate $r$. After factoring out the newly found asymp... | {
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Does dark matter follow all principles of regular physics? Is dark matter bound by all the laws of regular physics?
i.e. laws of thermodynamics, speed of light, length contraction, mass-energy relation.
What about Newton's laws of motion (since all of Newton's laws assume an interaction between particles)?
| If dark matter consists of particles it would follow all the rules of regular physics.
If dark matter is caused by entropic gravity though (also called emergent gravity; see for example this discussion about Erik Verlinde's theory) dark matter doesn't consist out of dark particles. I think there is proof that contradic... | {
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Why are aerodynamic / streamlined shapes always stumpy at the front? I'm building an autonomous boat, to which I now add a keel below it with a weight at the bottom. I was wondering about the shape that weight should get. Most of the time aerodynamic shapes take some shape like this:
The usual explanation is that the ... | You are correct if your boat will only travel in a straight line.
In real life the motion of the boat will often have a yaw angle, so that it is moving slightly "sideways" relative to the water. For example it is impossible to make a turn and avoid this situation.
If the front is too sharp, the result will be that the ... | {
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Difference between Mixed and Pure states Suppose that there is a system of two photons 1 and 2, each of which is in a mixed state $1/2|R\rangle\langle R| + 1/2 |L \rangle\langle L|$, where $|R \rangle$ and $\langle L|$ are two orthonormal pure polarization states. (So the composite state would be a product of two mixed... | The thing is whether those two photons are independent or not.
A single photon can be $|L\rangle$ or $|R\rangle$, which are pure states, or any linear combination of them (normalized).
However, whtn you have two photons as a compound system, you can have these 4 pure states: $$|LL\rangle, |LR\rangle, |RL\rangle, |RR\ra... | {
"language": "en",
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Why is maximal kinetic energy lost in a perfectly inelastic collision? A perfectly inelastic collision is one where both of the colliding objects stick together and move as one.
My question is, why, of all possible combinations of final velocities that conserve momentum, does this one lead to the greatest loss in kinet... | For a perfectly inelastic collision, there is a reference frame (the center of momentum frame) in which the final state has zero kinetic energy, and zero is the absolute minimum.
| {
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Is it possible the many-worlds hypothesis explains dark matter? To provide context for the title, is it possible that dark matter is just gravity from other 'branches' of the universal wave function that have split from ours, that are weakly interacting with the gravity in our branch? Is this an idea anyone has explore... | Interesting idea, but ... no. It does not work like that. The branching idea is a bit misleading. Instead, the Many Worlds interpretations refers to the terms in the superposition of the wave function of the universe. Each terms in this superposition is viewed as a "world," which is perhaps a bit misleading. So all pos... | {
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Force on charged particle when moving along magnetic field lines I was thinking, what happens to the force on a charged particle when it is moving along the magnetic field lines?
I am familiar with the right-hand-rule and it seems to me that RHR does not apply in this situation. Since the RHR, the field lines, directio... | Because $\mathbf F=q\mathbf v\times\mathbf B$, if $\mathbf v$ is parallel to $\mathbf B$ then $\mathbf F=0$ and the particle experiences no magnetic force.
This (which uses a RHR to get the directions right) is always valid.
| {
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What is the direction of the frictional force acting on a rolling wheel? Let's keep things simple and assume that the wheel does not slide. Assume you are in a car that moves with constant speed. Obviously, the wheels exert a tangential force to the surface on the road in the points of contact, P. According to Newton's... | If a car is gaining speed, the force from the road is forward. If it is breaking, the force is backward. If the speed is constant, the force is forward and large enough to overcome various sources of drag.
| {
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Why is the electromotive force (EMF) highest in the loop when $\theta$ = $90$? My question is in regard of the following snippet provided by my textbook.
So why is the electromotive force (EMF) highest in the loop when $\theta$ = $90$ or $270$?
So the magnitude of the induced EMF will be determined by the rate at whic... | "Since there is no magnetic field penetrates the area at that instant shouldn't there be no current?"
I'm afraid that this is a bit like saying about a ball thrown upwards that has reached its highest point: "Since there is no velocity there can be no acceleration". In other words, you do need to consider carefully tha... | {
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What principles of physics restrict a disintegration ray? If a vehicle were to move horizontally through solid stone by separating it into pieces, moving the pieces behind it, and reassembling them precisely as they were, the net change in energy ought to be zero. The actual cost of boring a hole appears to depend on ... | A basic principle behind the minimum energy requirement is that of a potential barrier.
Consider a very simplified model: the object to disintegrate is a pair of oppositely charged particles which are at a small distance apart. There is an electrostatic attraction between them, so they have less energy being close than... | {
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Heat energy change in adiabatic process We know that when a system gains heat energy from the surroundings through conducting walls of the container , then the temperature of the system also increase till it reaches an equilibrium value .
Whereas in an adiabatic compression of a gas where temperature increases but the ... | The definition of adiabatic expansion is that the heat exchanged by the surroundings and the system is zero.
Also,
∆Q = ∆U + work done
The work done in an adiabatic process is compensated by the change in internal energy, making sure that no other external factors supply energy to the system.
| {
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Lorentz boost expressed as Hyperbolic versors At this link https://en.wikipedia.org/wiki/Versor#Hyperbolic_versor it is claimed that an hyperbolic versor, defined as:
$$
\exp(a \mathbf{r})=\cosh a+\mathbf{r}\sinh a
$$
where $||\mathbf{r}||=1$ correspond to a Lorentz boost. But I cannot work out a proof. Can anyone help... | It isn't a Lorentz boost by itself, but it can be used to easily derive one (at least in 1+1 dimensions). It's similar to the expression of spatial rotations in term of Euler's formula:
$$ x'+iy'=e^{i\phi}(x+iy),\ \left[e^{i\phi}=\cos\phi+i\sin\phi,\ i^{2}=-1\right]$$
which gives
$$ x'+iy'=x\cos\phi-y\sin\phi+iy\cos\ph... | {
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Difference between Doppler effect and relativistic Doppler effect? When the source of a sound wave is moving in the direction of the sound wave it is a different scenario than if the receiver of the sound wave is moving in the direction where the sound waves are coming from. Why is this not the case in the relativistic... | For sound, when we speak of the observer moving or the source moving we mean moving with respect to the medium through which, and by means of which, the sound travels, so the two cases can be distinguished. The relativistic Doppler effect is for electromagnetic waves, which don't use a medium. So the only source or obs... | {
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Does position-momentum uncertainty principle apply to a two-body wavefunction when we frame boost to its center of mass reference frame? The heart of my question is below in bold. The rest is clarifying information or additional points of discussion - in case my assumptions are the heart of my misunderstanding.
In a tw... | Yes it holds because the corresponding operators satisfy the standard commutation relations. It can be proved in various ways. The most elementary way is to describe the system using the so-called Jacobi coordinates (in the phase space) which include the coordinates of CM and the total momentum. Assuming that the posit... | {
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Why rotating objects stops? Sorry for asking this simple question, but really I couldn't find a good document discuss what I need exactly.
I am implementing a flight simulation, but my question is related to physics rather than aerodynamics so I find to ask the question to physics experts.
Suppose that I am having a cu... | for your flight simulator you can applied braking torque and then stop the simulation when the angular velocity is zero.
your equation
$$I_y\ddot\varphi(t)=\tau_m(t)+\tau_b(t)$$
where $I_y$ is the inertia about the y axes and $\tau_m$ is the applied torque to accelerate the cuboid and $\tau_b$ to decelerate the cuboi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/574275",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What do maufacturers do to ensure that a valve is capable of containing hydrogen gas? I am a researcher working to develop a hydrogen fuel system for use in a specialized internal combustion engine. The biggest challenge from an engineering standpoint with a project such as this is the inherently volatile nature and sm... | I am also in the hydrogen business and yes this is a big problem. We create gas by electrolysis on 16 stainless plates, each about 20cm x 20cm. We use neoprene gaskets about 1cm wide and 2.2mm thick, in between each of the plates to maintain proper separation. All tightened with 8 bolts. For fittings, we coat the thr... | {
"language": "en",
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"source": "stackexchange",
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Why do motorcycles front wheels lift of the ground when accelerating quickly When motorcycles accelerate quickly they do a wheelie. Where is the torque provided to lift the motorcycle?
| It is due to the conservation of angular momentum. As soon as the motorcycle is accelerated, there's a rotation of the rear wheels, associated with it will be an angular momentum. So, one is introducing an angular momentum into the system. As there was no angular momentum before accelerating, the net angular momentum s... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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In Rayleigh scattering do the frequencies scattered correspond to the discrete energy level transitions available to atmospheric particles? I have read that for Rayleigh scattering the photons are absorbed by the atmospheric particles then re-emitted (albeit very quickly) and the shorter wavelengths scatter better whic... | Rayleigh scattering is scattering. The photons are not absorbed and the scattering can take place at all wavelengths. The scattering is caused by both oxygen and nitrogen in the atmosphere and they have very similar Rayleigh scattering cross-sections.
The sky is not violet because there is little violet in the solar sp... | {
"language": "en",
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Probability in classical physics I have read lots of thing on probability in QM and the different ways of intending it. Now, I am wondering how physicists intend probability in classical physics. To be more specific, I have read some articles about the fact that probability in classical physics is seen by physicists as... | For better understanding of yours, the implementation of Probability, both in QM and CM can be presented as following:
In QM, the probability of any attribute can be used for two different aspects:
*
*For determining the distribution of constituents, within a system, &
*For determining individual attributes of the ... | {
"language": "en",
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How do I categorize material as having uniform or non-uniform tension? From what I've learned tension uniform/constant throughout the body only in massless objects eg: massless ropes, but when is it non-uniform?
EDIT: By uniform/constant tension I mean the value of tension in the object is the same at any point in the ... | Massless ropes will normally have uniform tension, since the weight of the rope itself doesn't factor into any tension calculation. Ropes with mass tend to have nonuniform tension, since their own weight needs to be accounted for - the top of the rope has to support everything below it, while the bottom of the rope doe... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Lorentz Force on a Current Carrying Wire Does the Lorentz Force on a Current Carrying wire given by the equation
$$\mathbf{F} = I \int \text{d}\ell \times \mathbf{B}$$
constitute an action reaction pair? That is, if i have two arbitrarily shaped current carrying wires, is it true that force on any one of them due to th... | edited
No, it seems that the law of action is true for the cherry-picked case of parallel wires as shown by @Sagigever's response. For instance, this is certainly not true for the case of magnetic Lorentz force exerted by two charges (yellow in figure) moving perpendicular to each other (along the blue and red lines). ... | {
"language": "en",
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Do photons lose energy after radiation pressure is applied to a perfect reflector? I was readng Wikipedia article (English one) about radiation pressure because there is something I still cannot figure out. As I understand it, radiation pressure emerges from conservation of momentum. Photons or electromagnetic waves po... | Your intuition is correct: each photon loses a very small amount of energy when it reflects from a perfect teflector that can move. The reflected photons will have slightly longer wavelengths than their incident counterparts.
| {
"language": "en",
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Why do fluids not accelerate? A fluid flowing in a horizontal pipe must be flowing at a constant velocity because of the conservation of mass.
However, considering how there would be a pressure and hence force acting behind the fluid, for it to have a constant velocity, there must be an equal force slowing it down (dep... | The fluid is accelerating. The continuity equation simply states that at any instant $A_1v_1=A_2v_2$ where $A_1$ and $A_2$ are the cross-sectional areas of the upper pipe and lower pipe respectively, with $v_1$ $v_2$ being the fluid velocities in the same. The potential energy of the fluid stored in the upper pipe is b... | {
"language": "en",
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Accelerometer and Static Force I'm studying the principles of accelerometer and given below is what is stated in LiveScience
An accelerometer is an electromechanical device used to measure acceleration forces. Such forces may be static, like the continuous force of gravity or, as is the case with many mobile devices, ... | Acceleration and Force are two different concepts. The first has S.I. Units m/s$^2$ and the second Newtons.
Accelerometers measure acceleration. Force sensors measure forces.
A static force (such as the force of gravity) is a force with constant magnitude. therefore a constant force induces a constant acceleration.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/576128",
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"question_score": "1",
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Can rolling without slipping occur without friction? If a body is rolling without slipping is it necessary that there is friction acting on it ? I encountered a question in which there is a spherical body and a force is being applied on its top point ...so if there is only force then it should do translation motion on... | Rolling without slipping occurs when for the revolutionary body (RB, i.e. sphere, cylinder, disc, ring etc) the following relation holds:
$$v=R\omega$$
where:
*
*$v$ is the translational velocity,
*$\omega$ is the angular velocity,
*$R$ is the object's radius.
Now imagine we make a sphere rotate at $\omega$ and we... | {
"language": "en",
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Wave motion in a transverse wave I was learning about wave motion and how in transverse waves, each particle executes SHM up and down. If that is the case, how is it so that energy is still transferred onto the next particle? The logical answer should be that it disturbs the other particle, but if it moves up and down ... | It depends on the type of wave. In the derivation of waves in a string, we come to the equations:
$$\frac{\partial ^2 y}{\partial t^2} = \frac{|\mathbf T|}{\rho} \frac{\partial ^2 y}{\partial x^2}$$
$$\frac{\partial ^2 x}{\partial t^2} = \frac{1}{\rho} \frac{\partial T}{\partial x}$$
The first one is the transverse wa... | {
"language": "en",
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Do elementary particles last forever? I have heard that not even black holes last forever, because of Hawking radiation. But what about elementary particles? Will an electron, for example, exist for all time?
| Even the so-called stable elementary particles might not last forever,
when there are other particles around.
Take for example electrons:
*
*Electron-positron annihilation:
The electron may be hit by a positron, both disappear, and 2 photons will appear.
$$e^- + e^+ \to \gamma + \gamma$$
*Electron capture:
The elect... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/576567",
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Can rockets fly without burning any fuel with the help of gases under extreme pressure only? Why is it necessary to burn the hydrogen fuel coming out of the engine for the lift of rockets?
If it is done to create a greater reaction force on the rocket then why can't we get the same lift with just adjusting the speed of... | Cold gas thrusters, generally using compressed nitrogen, are sometimes used for control, such as adjusting orientation in orbit.
In that case the low thrust is, if anything, an advantage, as it makes precise control easier.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/576645",
"timestamp": "2023-03-29T00:00:00",
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How to derive this relation? According to A relativist's toolkit by Poisson, the expansion of null radial geodetic in the Schwarzschild spacetime is $$\theta=\dfrac{2}{r}$$
How to derive this expression?
The expansion is defined as $$\theta=k^\alpha_{\phantom{\alpha};\alpha} = \dfrac{1}{\sqrt{-g}} \left( \sqrt{-g}k^\al... | You probably made some trivial error. For example, did you forget to raise the index on $k$?
$$k_\alpha=\left(-1,\frac{1}{1-2m/r},0,0\right)\tag1$$
$$k^\alpha=\left(\frac{1}{1-2m/r},1,0,0\right)\tag2$$
$$\sqrt{-g}=r^2\sin\theta\tag3$$
In the calculation of $\Theta$, only the $\alpha=r$ term contributes:
$$\Theta=\frac{... | {
"language": "en",
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Rutherford scattering experiment, part 1 Around 1906-1914 several classical experiments on scattering of $\alpha$-particles on gold and platinum foils have been performed by Rutherford, Geiger, and Marsden. In standard literature on the subject it is tacitly assumed that the atoms of gold and platinum remained at rest... | First, while your textbook may assume that the target atoms remained at rest (it makes the math easier), Rutherford, Geiger, and Marsden knew how to do the full kinematics problem and did not assume that. For gold and platinum it makes almost no difference in the analysis since those elements are ~50x more massive than... | {
"language": "en",
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Infinite Coulomb force when charges contact The Coulomb force between charged particles is inversely proportional to the square of the distance. Yet, why don't we observe the infinite force when the distance approaches zero? Say we can bring two positively charged glass rods and make them touch each other. We don't obs... | A similar statement can be made about the gravitational force. Thus when we take two point particles of mass $m$ and $m'$ arbitrarily close to each other the gravitational force between goes to infinity.
Thus either one of three things can happen:
*
*Either the gravitational inverse square law must be modified on ver... | {
"language": "en",
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How does the Sun generate its energy? We all know that the sun generates its energy from nuclear fusion in the core. The electromagnetic radiation produced slowly travels upwards, while constantly being absorbed and re-emitted by the charged ions, until it reaches the photosphere, where it can basically travel freely (... | The sun light received at earth, is approximately fitted with the black body curve:
Solar irradiance spectrum above atmosphere and at surface. Extreme UV and X-rays are produced (at left of wavelength range shown) but comprise very small amounts of the Sun's total output power.
That the law used the surface area for... | {
"language": "en",
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"source": "stackexchange",
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Are distributions of position and momentum assumed to be independent in quantum mechanics? Given a wave-function of a single particle we can calculate probability density for positions. We can also calculate probability density for momenta. Are these probability densities assumed to be always independent?
Or, in other ... | To say that position and momentum are not independent random variables in QM really undersells the point. It is not that we cannot measure them independently, the Heisenberg uncertainty principle states that we cannot measure both quantities simultaneously at all.
What this means is that the distribution of momentum de... | {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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Weird projectile motion question The question is as follows:
A ball is thrown from a point $O$ towards a vertical wall in such a way that, after rebounding from the wall, it returns to $O$ without striking the ground. The ball’s initial velocity has magnitude $U$ and is at an angle $θ$ above the horizontal. When the b... | I'm not sure I understand the problem exactly, so do let me know if this doesn't answer your question:
If you've solved the first part, you should be convinced that the particle returns to $O$ when it's projected at a value of $\theta$ that satisfies the following equation: $$\sin{2\theta} = \frac{3 g b}{U^2}.$$ It can... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/577448",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Time transfer from proper to coordinate: apparent Special / General Relativity mismatching in theory In SR we've learned that the time dilation for an observer moving clock w.r.t one fixed in a frame at rest is
$$\tau = \gamma \tau_0 = \frac{\tau_0}{\left(1-v^2/c^2\right)^{1/2}}$$
ref: "Special Relativity - A.P. French... |
Can anyone clarify this (apparent) contradiction?
It's just different nomenclature. There is no contradiction.
French's equation 4-5 is
$$\tau = \gamma \tau_0 = \frac {\tau_0} {\left(1-v^2/c^2\right)^{1/2}}$$
Note that French's equation 4-5 uses two taus, $\tau$ and $\tau_0$, to represent the time difference between ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Intuition for the Ricci tensor of a Reissner-Nordström black hole The Reissner-Nordström metric is given by $$g = -h(r)\,{\rm d}t^2 + h(r)^{-1}\,{\rm d}r^2 + r^2\,{\rm d}\Omega^2,$$where ${\rm d}\Omega^2$ is the round metric on a unit sphere $\Bbb S^2$ and $h(r) = 1-2mr^{-1}+qr^{-2}$, where $m\geq 0$ is a mass and $q\i... | Actually, the Reissner-Nordström metric has
$$h(r)=1-2m/r+q^2/r^2\tag1.$$
(The charge is squared.)
The Ricci tensor is diagonal with
$$R_{tt}=-\frac{q^2}{r^4}g_{tt}\tag{2a},$$
$$R_{rr}=-\frac{q^2}{r^4}g_{rr}\tag{2b},$$
$$R_{\theta\theta}=\frac{q^2}{r^4}g_{\theta\theta}\tag{2c},$$
$$R_{\phi\phi}=\frac{q^2}{r^4}g_{\phi\p... | {
"language": "en",
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Why can we see light further than it shines? This is a question I’ve been thinking about for a while. If I’m standing in the middle of a straight road, during night, I can see a car coming towards me because of its lights even if it is kilometers away. Notwithstanding, the driver can not see me because the car will bri... | I have never seen such a load of unnecessary verbage in answer to a question!
We see the light from stars millions of light years away from us but only a complete dum-dum would expect an observer on a planet orbiting a distant star to see that star's light reflected off say an astronaut doing an EVA in Earth orbit.
The... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/577954",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "32",
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Electronic band structures I am looking for step-by-step, clear, detailed and rigorous explanations of methodologies to calculate electronic bands of semiconductor, GaAs as an example, by solving the Schrödinger equation with the k.p method. Everything I could find so far assumes some degree of prerequisite knowledge. ... | People often get annoyed when somebody cites wikipedia, but I would like to point out its less known feature: articles have references, which are often worth exploring. Though here, predictably, one of the main references is the Kittel's book. I suppose that there are more in depth treatments devoted to this subject, b... | {
"language": "en",
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In Charles' law how to change volume in order to observe the change in temperature? At constant pressure,
$$ V\propto T$$
Letting the piston freely moving fixes the pressure of the gas to the atmospheric;
then heating the gas causes the $T$ to increase,
this causes the $V$ to increase by the same factor.
However, in th... |
However, in the other direction, how can one maintain the pressure
constant while changing volume? Feels it is impossible to change
volume and maintain the pressure constant at the same time
Think about it this way. The pressure against the walls of the vessel is proportional to the rate at which the gas molecules co... | {
"language": "en",
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Will a plastic feel less heavy when I put it in a bucket of water and carry it? If I'm carrying a bucket of water in one hand and a piece of plastic in the other, and then I decide to keep the plastic in the bucket of water (it floats). Will it feel less heavy in the second case?
I think it will feel the same because i... | Assuming the densities of the water in the bucket and the density of the plastic are constant, and that no water spills out of the bucket when the plastic is placed in the bucket, then
$$W_{Tot}=ρ_{w}V_{w}+ρ_{p}V_{p}$$
Where $W_{Tot}$ = Total weight of the combination of the water and plastic in the bucket (ignoring th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/578995",
"timestamp": "2023-03-29T00:00:00",
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How do Electrons in a Crystal Lattice form Pair bonds? How do electrons around adjacent atoms in a crystal lattice form pair bonds when they are both negative and should repel each other?
| Strictly speaking, the bonds are not formed between the electrons, but between atoms, which are electrically neutral, because they also contain positively charged nuclei. It is difficult to give a deeper answer, since there exist many types of chemical bonds and the answer is different for each of them. A good start co... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do aluminium sheets wrinkle easily but are hard to un-wrinkle? I notice when I buy aluminium sheets (the kind used for wrapping food) they come in straight, smooth rolls. Once I use them though, they become wrinkled, and they are impossible to un-wrinkle. Image of a wrinkled sheet:
Why is this the case? Only thing... | When aluminum is plastically deformed as during the wrinkling process, the aluminum right in the wrinkles gets stronger than the undeformed aluminum. This process is called strain hardening and is most easily demonstrated with a piece of aluminum wire. If you bend the wire into an angle and then try to unbend it again,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/579314",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can non-harmful eddy currents be used to heat water? I think after 'googling' some web sources that eddy currents are strictly localized in a volume of iron surraunded by a loaded inductive coil so can not cause an electric shock to a person while the person touches a point of that iron that is farther from the coil if... | yes you can. eddy current induction in hollow steel pipes is used to heat-treat the pipe and any liquid flowing through the pipe at the same time is going to get heated up by contact with the pipe's walls.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/579540",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why the inner core of planet Earth is not composed of the densest materials? I read on various sources the inner core of our planet is said to be mostly composed of a iron-nickel alloy, plus some lighter elements like silicon. On the other hand, I know that in general lighter elements go to the upper layers and heavier... | Two years on and Winston´s question is still not answered.
Osmium and iridium are distinctly heavier than all other elements and their natural alloy, osmiridium, should find its way (by hydrostatics over millions of years) to the centre of the Earth.
Cox estimates the abundance of Os at $10^{-4}$ ppm and Ir at $10^{-6}... | {
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Why do waves, specifically light, diffract through a slit? I've been wondering this for a while now, and have thus far only come across answers that seem to use an equation as an explanation. I've also looked at Huygens' principle (albeit not in-depth), but this doesn't make much logical sense to me.
I'd sincerely appr... | A plane wave, by construction, has all frequency components in the direction perpendicular to propagation. Now you let that impinge on a slit (or multiple slits) - you are now altering those frequency components, and what comes through the slit(s) is no longer a plane wave but the Fourier transform of the real space sl... | {
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"timestamp": "2023-03-29T00:00:00",
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Why are the capacitors in this circuit in parallel but not in series?
In the circuit, the capacitors are said to be connected in parallel. Why is that so?
Edit: The switch will be closed and C2 is fully charged by C1 and no more current will flow between C1 and C2. The question asks for the voltages and charges hold b... | This is a nice question, Consider this circuit first, that build from one resistor and battery,
We can apply kirchhoff's law and we can get that $$V_R=V$$ while $V$ is the battery voltage, thus we can say that the resistor is connected parallel to the battery.
Now check the following circuit,
We can see that applying... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Electric Potential Energy - How a charge can be brought from infinity to a point without accelerating it? Question:
My Book says:
ELECTRIC POTENTIAL ENERGY: Electric potential energy of a charge($q_o$) at a point(A) in the electric field due to any charge is given by the work done by an external force to displace $q_o... | Only because $q_0$ is very far away, it doesn't mean that it must be at rest with respect to the point $A$. I can suppose that no matter how far I imagine $q_0$, it has a radial velocity $v$ in direction to $A$.
Suppose the charges have opposed signals. Some control device attached to $q_0$ makes sure that the increasi... | {
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"url": "https://physics.stackexchange.com/questions/579974",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why we cannot use Gauss's Law to find the Electric Field of a finite charged sheet? I could not understand why we can't use Gauss's Law to find the Electric Field of a finite charged sheet?
| In order to calculate the electric field using only the Gauss law (rather than by solving the Poisson equation) one usually exploits the symmetry of the problem. In textbook cases this usually means that one can guess such a Gaussian surface, that the electric field has the same magnitude and direction in respect to th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/580186",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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