Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Time dependent canonical transformations (a problem in Arnold's classical mechanics textbook) I am stuck on a problem on page 242 of Arnold's book "Mathematical Methods of Classical Mechanics". The problem statement is as follows:
Let $g(t): \mathbb{R}^{2 n} \rightarrow \mathbb{R}^{2 n}$ be a canonical transformation ... | It seems like it is an error, it is corrected in the second edition:
However, for some reason some of the chapters of the second edition on the Springer site (https://link.springer.com/book/10.1007/978-1-4757-2063-1) such as Chapter 9 are those of the first edition. I found the full second edition at https://loshijosd... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/686307",
"timestamp": "2023-03-29T00:00:00",
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De Broglie relations use which frequency or frequencies of a wave packet? The Wikipedia article about matter waves lists the De Broglie relation for the frequency $f$ of a matter wave as
$$ E = hf = \hbar\omega $$
with Planck constant $h$, total energy $E$ and angular frequency $\omega$.
The article also explains phase... | The answer to your question is that the frequency that appears in the De Broglie relations is the function $\omega(k)$. Note that the Wikipedia article on group velocity that you quote says:
If the wavepacket has a relatively large frequency spread, or if the dispersion ω(k) has sharp variations (such as due to a reso... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/686442",
"timestamp": "2023-03-29T00:00:00",
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If diverging rays never meet, why do parallel rays meet at infinity? I've seen that in the case of concave mirrors if the object is between focus and the pole - the reflected rays diverge and never meet.
But if the object is at the focus, it's defined to be meeting at infinity. Why is it so?
| The natural home for the geometry of plane curves is the projective plane, where everything is really much simpler. For example, a curve of degree $n$ and a curve of degree $m$ always meet in exactly $mn$ points in the projective plane (with a few provisos about exactly how to count), which turns out to be extremely c... | {
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Why do we multiply in the total wave function but add in the LCAO method? If to particles with wave functions $\psi_a$ and $\psi_b$ are „combined“ their total wave function is given by:
$$\psi(r_1,r_2)= A[\psi_a(r_1)\psi_b(r_2) \pm \psi_b(r_1)\psi_a(r_2)]$$
(+ for bosons and - for fermions, $A$ is a constant, here I‘m ... | These formulae do different things. The first one takes 2 (or more) single-particle wavefunctions and gives you a multiple-particle wavefunction that can be interpreted as having one particle in one state and another particle in another state. The second one instead produces a single-particle wavefunction that can be i... | {
"language": "en",
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Is energy really Conserved in rolling motion? Energy is conserved in pure rolling motion. Then why does the ball stops its motion after some time. I think it's not the case of air drag only. Does all work gets Transferred to surrounding in the form of heat?
| If the energy were indeed conserved, the ball would roll without stopping. The reason why it stops is Rolling friction, which results in converting some of the mechanical energy into heat. Note that this is a type of friction that is different from more familiar static friction, which is also present in case of an obje... | {
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What mechanism will force mechanical watch to tick slower when go fast, due to relativistic effects? To make mechanical watch tick slower, watch tick rate must be changed, oscialtion of balance wheel must be SOMEHOW changed, how would speed change oscialtion of balance wheel, due to relativistic effects?
I dont unders... | It is a very common mistake to assume that moving watches slow down, one that is no doubt due to the ambiguous phrase 'moving clocks run slow.' What time dilation actually means is that the time interval between two events occurring in the same place in one frame is shorter than the time interval between the same two e... | {
"language": "en",
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What is the potential difference between these two points in the given uniform electric field? So I have been given a uniform electric field $\vec{E}=20 V/m$ in the direction as show in the image. I have been told to calculate the potential difference $VC - VA$. According to the teacher (on YouTube) the potential diffe... | If 1m is the measure of each side of the square, you are right and they are wrong, $\Delta V=-20V$
To give an interpretation to their answer, one has to assume that 1m is the length of the diagonal AC of the square.
In that case, indeed $\Delta V=-(20)(1)cos(45)$ where the (1) is the length of AC and then the factor $c... | {
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Why same force acts on two different strings? Let us take two different strings and arrange them vertically. The first string is attached to the ceiling and connected in series with the second string and a mass $m$ is connected at the bottom of the second string. Why does the same force $mg$ act in both strings?If we ... | Tension is a contact force so on mass tension due to that string only will act which is in contact with it. This is something like on a particular bogie of a train forces due to only those bogies will act which are in contact with it.
| {
"language": "en",
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Deformation/Fracture from Impact What equations predict the deformation from two objects colliding? Such as dropping a heavy ball onto a plate of metal. Source references would help, I havent found much anything yet.
|
What equations predict the deformation from two objects colliding?
There are two possible types of deformation: Elastic and inelastic. For a perfectly elastic collision, the deformations of the two objects are totally recoverable so that the total kinetic energy before and and after the collision is the same. For sou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/687543",
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What causes this frost pattern on my windshield? I was walking back to my car yesterday when I noticed the frost on the back windshield formed these long "straight" lines:
The temperature was about -10C and I was wondering what the mechanism behind these lines was (the horizontal lines I can guess have to do with the ... | The following is pure speculation, but who knows... Maybe the car glass was at the ambient freezing temperature, but there was also rain falling, and drops continued moving in straight lines after hitting the glass and leaving a trace of water, which would freeze fast on the glass.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/687971",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What will happen if both electrons and positive charges got ability to move inside the conductor? Let's consider a conductor which has a potential difference across its ends.
And let's say that the electrons which already have tendency to move inside the conductor, by all of a sudden if positive charges (not protons be... | If there were free positive charges (with properties similar to the free electrons) in addition to the free electrons, then then the resistance would be lower and the Hall effect voltages would be lower (or reversed).
| {
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What is the direction of angular momentum? Are Torque and angular momentum same? I just started learning in my class 11 physics book, where I find Torque and angular momentum. After reading the definition, I am confused about are Torque and angular momentum are same? If not what is the difference between them? Lastly w... | I am going to try to answer plainly and avoid using vector algebra and concepts like the cross product.
I assume you are familiar with the concept of torque as a force at a distance. If not, read about torque as the moment of force with the example of balancing a see-saw. The main takeaway here is that the perpendicul... | {
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Is self-energy $\mathrm{Im}\Sigma^r<0$ always true? Consider a one-particle retarded Green's function $$G^r(\alpha)=[\omega+i\eta-\varepsilon(\alpha)-\Sigma^r(\alpha)]^{-1}$$ with self-energy $\Sigma^r(\alpha)$ for some quantum number $\alpha$. It is argued that $-\mathrm{Im}\Sigma^r>0$ always holds as it signifies the... | Let us consider the following:
*
*$\Sigma^r$ is a retarded self-energy, i.e., it is given by expressions like
$$\Sigma^r(\omega)=\sum_k |V_k|^2G^r(\omega).$$
Here $V_k$ might be replace by vortex parts with more complex structure, but the rpesence of the retarged Green's function, $\Im \left[G^r\right]<0$ suggests th... | {
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Separable Hamiltonian systems in quantum mechanics Why is it that in separable Hamiltonian problems the total eigenfunction is equal to the product of the individual eigenfunctions, but the individual Hamiltonians must commute?
In mathematics, when the method of separating variables is used, for example for some PDEs, ... | I think this is a mistake on the language of the textbook. The important part is that the Hamiltonian splits into a radial and angular part $H=H_r+H_\Omega$ in a way such that for separable wavefunctions $\psi(r,\Omega)=F(\Omega)R(r)$
$$H_r(\psi)=FH_r(R)\text{ and } H_\Omega(\psi)=H_\Omega(F)R.$$
In particular, this im... | {
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What is the connection between mechanics and electrodynamics that makes it necessary for both of these to obey the same principle of relativity? Mechanics obeyed Newtonian relativity (faithful to Galilean transformations) before Einstein.
Einstein formulated Special relativity (faithful to Lorentz transformations), and... | The common denominator is that both electromagnetic and mechanical phenomena occur in space and time. Special relativity accounts for the unvarying speed of light by explaining that the geometry of space and time is not Euclidian, so all processes in physics which involve functions of space and time will be affected by... | {
"language": "en",
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Is formation of a black hole thermodynamically favourable? Isn't it like that the black hole is just swallowing suns and other parts of cosmos, and thus continuously absorbing matter. I know that it emits radiations also, which should be negligible in terms of the absorbed matter and thus energy. If the net internal en... | On the contrary, black holes are the objects in the universe with the highest entropy. According to the Hawking-Bekenstein formula, the entropy $S$ of a black hole is proportional to its surface $A$ which is by swallowing matter constantly increasing as does entropy:
$$ S= \frac{k_BA c^3 }{4 G\hbar }$$
using the usual... | {
"language": "en",
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Why displacement is not used to calculate average potential energy in SHM? We know that the average potential energy of a body executing simple harmonic motion (SHM) is
$$\frac{1}{4}KA^2$$
where $K$ is the spring force constant and $A$ is oscillation amplitude. This was derived using potential energy as a function of t... | One calculation averages over $t$, the other over $x$. When $|x|$ is small, more energy is kinetic, so $\dot{x}$ is greater. Therefore, these two averages are inequivalent. They're both well-defined notions of "average", as are any number of alternatives to taking an arithmetic mean. However, the time-average is usuall... | {
"language": "en",
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If gravity can accelerate a photon by bending its trajectory why doesn't it slow down a photon? If gravity can accelerate a photon by bending its trajectory why doesn't it slow down a photon? This looks like magnetism effects on particles(changes direction but not magnitude of the velocity) ...
| In everyday language "accelerate" implies making the photons go faster, but in physics parlance, it suffices to change the direction. In other words, if you change the direction but not the magnitude of a velocity, you still have an acceleration, but the object neither speeds up nor slows down.
That's what gravity does... | {
"language": "en",
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The location of the exact center of the observable universe If simultaneously in every direction, I were to precisely measure the distance to the edge of the observable universe (not: the physical universe), then would I find myself exactly in the center with zero error tolerance? Would it make a difference if I were a... | If the universe is infinite in extent then there can be no centre of the observable region from Earth nor a centre of the entire universe.
If the universe is finite, spherical and expanding equally in all directions then there can theoretically be a centre of the entire universe but not a centre of the observable regio... | {
"language": "en",
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Gravitational forces of a building In trying to understand the gravitational forces of a building, I have devised a thought experiment:
A building is floating in space. The building's mass is asymmetrically distributed. Inside it also has a large concentrated mass, not aligned to the center of gravity of the building a... | The dust would float around evenly distributed, because the gravitational forces inside the building cancel each other out.
B: The dust collect around its nearest walls and ceilings, i.e. the local masses inside the system.
C: All particles are attracted towards the center of mass of the building as a whole, i.e. the g... | {
"language": "en",
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What do $R(r)$ , $R^2(r)$ & $4\pi r^2 R^2(r) $ represent in accordance to schrodinger's wave equation? What do $R(r)$ , $R^2(r)$ & $4\pi r^2 R^2(r) $ represent in accordance to schrodinger's wave equation?
Being a JEE aspirant I haven't been taught to properly interpret the Schrodinger's wave equation. We have just bee... | The Schrodinger wave equation is the first quantum mechanical equation discovered, a differential equation where the potential between two quantum particles can be inserted and a solution found.
It is called a wave equation because the main solutions are functions of sine and cosine , and the equations were used in ... | {
"language": "en",
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Can the conduction band get completely filled? I have just started studying basic solid state physics and I got to know that filled or empty bands do not conduct. Is this only the case for valence band or also conduction band.
Is there any case that I can excite so many electrons to the conduction band that it becomes ... | Yes and no. The point is that any conductor has its own "breakpoint". Just consider a fuse. The conductivity is limited by its resistance, after that the material starts to melt or lose energy in some way.
So, yes it stops conducting. But just because it broke up.
| {
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What exactly is mass? I was looking for a definition of mass and most of the time what I got was that "it is the amount of matter". Now that is very vague. And the way we define matter is "anything that has "mass" and occupies space". so... what exactly is mass?
Can you please answer it to the level where a highschool ... | Mass is the property of an object, that
*
*resists acceleration by requiring a force (inertial mass, $m_i$)
*attracts another object (gravitational mass, $m_g$)
Once you start quantifying these observations, you arrive, respectively, at
*
*$F = m_ia$
*$F = G m_{g1} m_{g2} / r^2$
It was a deep insight that these ... | {
"language": "en",
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What does the arrow of time and entropy say about the universe and repetition? This question What is the relationship between how time is viewed in thermodynamics and how time is viewed in general relativity? is close to what I was wondering, but it didn't get into repetition specifically.
I'm not a physicist, my Scien... | The arrow of time and the second law of thermodynamics are the same thing. They are just different ways to look at it. We basically associate increases in entropy with forward time. If you were to see a system whose entropy was decreasing, you would perceive time to be flowing backwards (think of coffee and creamer sud... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/691425",
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Boundary conditions in Gaussian path integral The $N$-dimensional Gaussian integral
$$\int \mathrm{d}^N x \, \mathrm{e}^{-\frac{1}{2}\boldsymbol{x}^\mathrm{T}A\boldsymbol{x}+\boldsymbol{b}^\text{T}\boldsymbol{x}}=\left(\frac{(2\pi)^N}{\det A}\right)^\frac{1}{2}e^{\frac{1}{2}\boldsymbol{b}^\text{T} A^{-1}\boldsymbol{b}}... | You can decompose the functions by expanding them in terms of the eigenfunctions of $A$. The eigenfunctions depend on the BC's imposed on the $f$'s and so the BC's, such as being periodic, are automatically incorporated.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/691698",
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Sources for emission spectra I'm currently looking at a spectrum from a balmer lamp with clear lines for H-alpha through H-gamma.
But there are additional, non-hydrogen lines at 774 nm and 842 nm. I assume that they are oxygen lines ("water vapour filling" of the tube), but I have a very hard time to find data about ox... | It may be that the lines you are seeing are molecular rather than atomic lines. For example, see Figure 1 of the paper attached here. The horizontal axis is plotted in a unit that is basically $1/\lambda$, so the features around 13,000 wavenumbers correspond to $\lambda \approx 770$ nm and the features around 11,700 wa... | {
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What is exactly mean by wavelength in De Broglie equation? I'm wondering what exactly is meant by the wavelength in De Broglie formula $p=\frac{h}{\lambda}$, where $p$ is the momentum of a particle and $\lambda$ is the wavelength. I know that a wave function might very well be messy without a defined wavelength.
Can so... | You might have heard about the wave-particle duality: depending on how you look at it, matter can behave as being made of particles, or it can behave as being made of waves.
That all depends on the kind of experiment you are performing: roughly speaking, if the typical lengths of your experiment are large enough you wi... | {
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Double slit formula derivation. Why not $I_{\theta} = 4 I_m (\cos \beta)^2 \left( \frac{\sin{\alpha}}\alpha \right)^2$? The intensity of the double slits is given by
$$I_{\theta} = I_m (\cos \beta)^2 \left( \frac{\sin{\alpha}}\alpha \right)^2$$
where
$$\alpha = \frac{\pi a}{\lambda}\sin \theta$$
$$\beta = \frac{\pi d}{... | Here's one of many explanations (emphasis mine) .
If one of the slits in the double-slit experiment is covered, what
will be the new intensity? Please explain.
If only one slit is open the intensity (= rate of arrival of photons
somewhere) becomes evenly distributed (no fringes) and at one quarter
of the peak intensit... | {
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h-bar limits measurement precision. What limit arises for h-bar itself? The question is simple.
h-bar, or $\hbar$, limits the precision of every measurement, books tell us.
For example, length measurements are limited by the Compton wavelength.
What limit for the measurement of h-bar itself arises? Or is there no such ... | There is no uncertainty at all in the value of $\hbar$. In the 2019 revision of SI units, Planck's constant was defined to be exactly $6.62607015 \times 10^{-34}$ Joule seconds.
| {
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"url": "https://physics.stackexchange.com/questions/692836",
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Resistance-capacitance (RC) circuit
My textbook says: "This continues until the voltage across the capacitor matches the emf of the battery"
If I were to have a resistor in series with a capacitor, would the voltage across the capacitor still be equal to the emf of the battery?
My thinking process: The voltage across ... | If you set up a circuit like this, with reasonably high values for the resistor and the capacitor, a measurable current will flow for at least a few seconds. Initially the current is quite high, but as the charge and voltage on the capacitor increase, the voltage across the resistor decreases and so the current decreas... | {
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Speed of heat through an object According to the Heat equation (the PDE), heat can travel infinitely fast, which doesn't seem right to me. So I was wondering, at what speed does heat actually propogate through an object?
For example, if I have a really long iron rod at a constant temperature (say 0 Celsius), and one en... | Heat equation for a $1D$ bar:
$$T_t=\alpha T_{xx}\tag{1}$$
Note that heat losses like radiation or convection are excluded from this analysis.
Boundary conditions (BC, chosen)
$$T(0,t)=0$$
$$T(L,t)=0$$
Initial condition (chosen)
$$T(x,0)=f(x)$$
We're looking for a function:
$$T(x,t)$$
Which we believe can be represente... | {
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"source": "stackexchange",
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$I$ proportional to $V$ or vice versa? I am confused whether Voltage depends on current or the vice versa. I always thought that the vice versa was correct. I tried to find the answers of some of my other conceptual doubts on the web but I was not able to understand the answers as people were saying things beyond schoo... | They both depend on each other.If you have the IV diagram of a circuit element you can find the current for some voltage across the element and you can find the voltage for some current through the element.
| {
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Expectation value of $r^{-3}$ for $\ell=0$ I'm trying to calculate the hyperfine structure energy for Hydrogen. From Jackson's Electrodynamics book eq. 5.73 we have:
$$H_{HFS}=\dfrac{\mu_{0}}{4\pi}\left[\dfrac{-8\pi}{3}\mu_{N}.\mu_{e}\delta(r)+\dfrac{1}{r^3}\left(\mu_{N}.\mu_{e}-3\dfrac{(r.\mu_{N})(r.\mu_{e})}{r^2}\rig... | The angular part of the integral vanishes for $\ell = 0$. (The proof is left as an exercise to the reader; it helps to choose coordinates such that $\vec{\mu}_N = \mu_N \hat{z}$ and $\vec{\mu}_e = \mu_e (\cos \alpha \hat{z} + \sin \alpha \hat{x})$.)
So if we "do the angular integral first", the expectation value of th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693354",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Finding deflection of an electron through 2 charged plates when given initial velocity I've been trying to relate the initial velocity of an electron to the deflection created based on the electric field between 1 pair of plates. The 2nd half of page 3 of this pdf is what I'm concerned with. Now, I was trying to derive... | I think that I need to write another answer to explain my original answer in more detail and to agree with the comments that @CottonHeadedNinnymuggins made with regard to the answer @josephh produced which I believe to be erroneous as it assumes a constant acceleration in the $y$ direction both inside and outside the e... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Are there any slow neutrinos? Since we now know that neutrinos have a rest-mass, we ought to be able to observe relatively slow-moving neutrinos. Have we seen any?
| The energy of neutrinos depends on the process that formed them (more energetic reactions create more energetic neutrinos). Since neutrinos have no charge, there is no way to use electric fields to accelerate them (we can do that with charged particles in colliders).
We may see neutrinos of the Cosmic neutrino backgrou... | {
"language": "en",
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What would happen if you left Earth and then it was destroyed? (Potential energy and thermodynamics) So I did some research on magnetic generators and what kind of energy magnets loose when they move something. Turns out magnets loose potential energy (you need to expend energy to get the object moved closer to or furt... | You might be interested in the shell theorem
This way, with a thin shell and an opening, you could quickly and sharply change applied gravitational force on your space ship by going through the opening in the shell.
| {
"language": "en",
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"source": "stackexchange",
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Can two waves be considered in phase if the phase angle is a multiple of 2$\pi$? Question is essentially what the title states. Wavefront is defined as the locus of points that are in phase. So I wanted to know if the locus would be the points of only a single circle or multiple circles whose points all have the same d... | In phase means that the oscillations are at the same stage in their cycle at the same time. So if, at a given instant, the phase angle – for example $2\pi\left(\frac tT-\frac r{\lambda}-\text{constant}\right)$ – differs by $2\pi n$ for $n=0, ±1, ±2...$ at two points in the path of the wave, the oscillations are in phas... | {
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How Does Neutron Absorption Cause Nuclear Fission? "In the case of neutron-induced fission reactions, an incident neutron provides additional energy to a target nucleus in the form of kinetic energy and nuclear binding energy. Neutrons have the principal advantage, and they do not need to overcome the coulomb forces as... | In the case of fission, a neutron is a convenient way of delivering a punch to a marginally stable nucleus, perturbing it from a more-or-less spherical shape in the process of either scattering off the nucleus or getting captured.
That nucleus can hold itself together only if it remains spherical. If it begins to wobbl... | {
"language": "en",
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How to make the Moon spiral into Earth? I recently watched a video of what would happen if the Moon spiraled into Earth. But the video is pretty sketchy on the physics of just what would have to happen for that to occur. At first I thought I understood (just slow the Moon down enough), but my rudimentary orbital mechan... | Using the parallel axis theorem:
$$L(moon)=mvr$$
The moon must either loose mass $m$ or tangential speed $v$ for some reasons, therefore loose angular momentum $L(moon)$ which is the only phenomenon it is holding it in orbit and not pulled down by Earths larger gravity.
The orbital angular momentum of the Moon is $2.9 ... | {
"language": "en",
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If force depends only on mass and acceleration, how come faster objects deal more damage? As we know from Newton's law, we have that $\mathbf{F} = m\cdot\mathbf{a}$. This means that as long as the mass stays constant, force depends solely on acceleration. But how does this agree with what we can observe in our day-to-d... | 2 main reasons.
Intuitively, the 2 objects e.g exert an electric force on eachother, due to its charge
For higher velocities, the charge 1 is going to get CLOSER to the charge 2 before being repelled away, meaning it exerts a higher force causing more work to be done on charge 2.
And also for higher relative velocitie... | {
"language": "en",
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Time constant versus half-life — when to use which? In some systems we use half-life (like in radioactivity) which gives us time until a quantity changes by 50% — while in other instances (like in RC circuits) we use time constants. In both cases the rate of change of a variable over time is proportional to the instan... | "What is a simple intuitive way to know the difference between the kind of systems where half-life is useful , versus systems where time constants are more meaningful."
For systems obeying an exponential decay relationship, either half life or time constant can be used. I think it's largely a matter of tradition that h... | {
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Differential equation of the free falling object with air resistance I'm puzzled by the result I get when I try to solve the differential equation for an object that is falling subject to air resistance. Suppose the $y$-axis is directed upwards, then $\vec{F_a}=bv \hat{y}$ and $\vec{P}=-mg\hat{y}$, where $b,v, g$ are p... |
Suppose the y-axis is directed upwards, then $F_a→=bv\hat{y}$ and $P=−mg\hat{y}$, where b,v,g are positive. This leads me to the following equation:
The bold part is where the entire problem lies. You decided to make the positive direction of y upwards, right? But you are describing a falling motion, this means that ... | {
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Is the retarded propagator exactly the Green's function? I am trying to prove that, for the real scalar field $\phi(x)$, the retarded propagator, which is defined as
$$
D_{R}(x-y)=\theta(x^0-y^0)\langle 0 |[\phi(x),\phi(y)]|0\rangle
$$
is the Green's function for the Klein-Gordon operator; that is the function $G_R(x-y... | Retarded propagator is a Green's function, but a Green's function is not necessarily a propagator. There are two reasons why a green's function might not be a retarded propagator:
*
*Boundary conditions in time, which allow introducing retarded, advanced, time-ordered and anti-time-ordered Green's functions (one coul... | {
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Gauss law for magnetism on electromagnetic wave
While studying electromagnetic waves, I'm confused with Gauss law for magnetism.
Shouldn't magnetic flux be zero in shown surface? Or do I understand it wrong?
Edited image after Mauricio's answer
| The lines on your picture are not magnetic field lines. They are lines (with arrows) to represent the direction and strength of the magnetic field at each point along the z-axis at a fixed time.
The wave in your picture has a form something like
$$ {\bf B} = B_0 \sin (kz - \omega t) \hat{\bf j}\ ,$$
where $\hat{\bf j}$... | {
"language": "en",
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How do the fundamental quantum fields create particles? According to QFT, particles are excitation of their respective fields (electrons are the excited quanta of the electron field, photons for the electromagnetic field, etc). This excitement is due to the energy being placed in the field therefore raising the field o... | Good question! It was the superfast expansion of the universe that pulled them into real being. Like two photons can create a particle/antiparticle pair, or a particle/antiparticle pair can excite two photons, gravitons can do the same. This happened during inflation and in a sense all these particles are still virtual... | {
"language": "en",
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How are sidebands generated in an AM signal? I can't understand how sidebands get generated, even after reading this wikipedia page: https://en.wikipedia.org/wiki/Sideband#Amplitude_modulation
This is how I picture Amplitude Modulation in its simplest form.
There is a LC circuit. A an inductor plus a capacitor work tog... | Not all the frequencies are generated in LC circuit. Mixing process can also make some. To further clarify, you can plot an exaggerated modulation. If you look at the dark blue plot, $\sin(x) \sin(5x)$, you can see that the troughs and crests are not evenly spaced and are not coincide with the ones in unmodulated signa... | {
"language": "en",
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Why should the electron's energy knocked out be dependent on the intensity of the light? I know according to the photelectric effect this is not true , but the belief that it should be according to classical physics ? , could someone explain the approach of what classical physics 's hypothesis was ?
| The energy carried by the classical electromagnetic wave is given by the Poynting vector
Electromagnetic waves carry energy as they travel through empty space. There is an energy density associated with both the electric field E and the magnetic field B
This leads to the expression for the Poynting vector
The highe... | {
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Exclusion plots I am having issues in reading exclusion plots like the one in the picture below (It is a plot regarding WIMP searches). What does the lines from various experiments (such as CRESST or LUX) mean? I don't understand if the line excludes the region above or below. I know that the closed lines are regions w... | Cross sections above the lines are ruled out.
The vertical axis on this plot is "cross section", which is a measure for the interaction probability. Higher cross sections mean higher interaction probability. Experiments search for interactions, and if they don't find anything significant, they rule out that dark matte... | {
"language": "en",
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Why the generating function $F = q + Q$ form Hamiltonian with old coordinate dependence? In the book Analytical Mechanics by Louis N.Hand, chapter 6, Question 1, It is asked to use the generating function $$F = q + Q\tag{1}$$ to any Hamiltonian (I have used Harmonic oscillator). By doing so we get a new Hamiltonian wit... | *
*Note that $\frac{\partial F}{\partial t}=0$ means explicit time differentiation, not total time differentiation.
*However the real show-stopper are OP's equations (2) and (3), which are supposed to be 2 conditions on the 4 coordinates $(q,p,Q,P)$ that specify a canonical transformation $(q,p)\to (Q,P)$ of type 1,... | {
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Could we estimate the total energy of the universe? So I know that we do not know the sum of all energy in the universe, but why can we not just estimate with the following logic? (That I assume has some fatal flaw preventing anyone from guessing the total energy of the universe with it)
Since the universe is considere... | IF the universe is infinite, and it also satisfies approximately the homogeneous characteristic, THEN the sum of all energy is also INFINITE.
IF the universe is finite, and it also satisfies approximately the homogeneous characteristic, THEN the sum of all energy is UNKNOWN because the volume of the finite universe is ... | {
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Maxwell's equations not satisfied simultaneously? In an exercise in Electromagnetism, it is stated that $\vec{E}$ is uniform between the plates of a capacitor, and is given by
$$\vec{E} = \frac{Q_0}{\epsilon_0 S} \cos(\omega t) \cdot \hat{z}$$
Supposing that the media between the plates is non-conductive, $\sigma = 0$... | Yes, it is possible to interchange the time derivative with the curl (or rot) operator. This is just a consequence of Schwarz's theorem and the fact that the expression you gave is twice continuously differentiable.
As for your paradox, the issue is with the hypothesis that $\vec{J} = \vec{0}$. Notice that for one to g... | {
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What is positive rotation direction of a pulley in the Atwood machine? In the Atwood machine the mass $m_1$ hangs on the left and $m_2$ hangs on the right, with $m_2 > m_1$. When released from rest the system accelerates clockwise which we define to be the positive direction.
The pulley has non-negligible mass and also... | There is no positive direction in Atwood machine problems, unlike most kinematical problems you might encounter where you assume right and up is positive while left and right is negative,in Atwood machines, you simple assume a flow, be it to the right or to the left, and then you assume any force acting in the directio... | {
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How to express $|m\rangle\langle n|$ in terms of ladder operators? Let us consider the Hamiltonian of a single harmonic oscillator, which is expressed in terms of creation/annihilation operators as
$H=\hbar \omega (a^{\dagger}a+1/2)$. The eigenstates of this Hamiltonian are the number states ($n\geq 0$)$$a^{\dagger}a|n... | From the properties of the creation operator, one can show that
$$| n \rangle = \frac{(a^\dagger)^n}{\sqrt{n!}} | 0 \rangle,$$
which I'm assuming here to be a well-known result. Taking the adjoint of this expression, we find that
$$\langle n | = \langle 0 |\frac{(a)^n}{\sqrt{n!}}.$$
Therefore,
\begin{align}
| n \rangle... | {
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"timestamp": "2023-03-29T00:00:00",
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Can sound waves deform (curl brake) like water waves? As far as I understand, both water waves and sound waves are mechanical waves, in the sense that both are created by the relative movement of particles in a certain medium. Sound is propagation of waves in air (relative movement of air molecules), and water waves pr... | Perhaps the difference for unconfined waves in gases is that sound waves are spherical whereas those in seas are close to linear.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How is electric field arising from photons? This question has nothing in common with the question it is proposed to be duplicate e.g about virtual photons. The question is about a real radiation field where is known that no virtual photons exist.
The electric field E moving up and down (in its value) as a sinusoidal w... | Photons in mainstream physics, are quantum mechanical entities which in great numbers build up the classical electromagnetic radiation, which is what you are describing with the changing fields.
This picture for circularly polarized light gives an intuition how the classical wave is built up from a quantum mechanical... | {
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Conservation of momentum + conservation of energy + Newton's second law = Contradiction? When a body with a mass of 1 kg moves at constant velocity of 1 m/s and collide (elastic collision) with a body with the same mass that's at rest, we know from conservation of momentum and conservation of energy that the first body... | The total energy of the system must be constant, and before and after the collision it is the kinetic energy of one of the bodies.
But during the very small $\delta t$ of what we call contact, the potential electrostatic energy between the atoms of the surface can not be neglected. It is exactly this potential energy t... | {
"language": "en",
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Can objects move during a collision-elastic collisions? Can two objects move together during an elastic collision before moving apart? Or would this be considered an inelastic collision since during the time in which the objects were stuck moving together, the kinetic energy was reduced.
| Total energy of the system: before and after the elastic collision: $E_b = E_{kb} = E_{ka} = E_a$
During the $\delta t$ of contact: $E = E_k + E_p$, where $E_p$ is the repulsive electrostatic potential energy. $E = E_b = E_a$.
It is not a temporary inelastic collision. What matters is the kinetic energy before and afte... | {
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LSZ formula for initial and final one particle states The LSZ formula for a real scalar field $\varphi$ is (Srednicki 5.24)
$$
\left<f|i\right>=i^{n+n'}\int d^4x_1e^{ik_1x_1}(-\partial_1^2+m^2)...\\
\quad d^4x'_1e^{ik'_1x'_1}(-\partial_{1'}^2+m^2)...\\
\quad \times \left<0|T\varphi(x_1)...\varphi(x_1')...|0\right>.\tag... | The LSZ theorem basically says that if you take the Fourier-transform of an $N$-point function $\langle \phi_1\phi_2...\rangle$ and send the momenta on-shell, you will see a product of simple poles $(p_i^2-m^2)^{-1}$ for each momenta, and that the residue of this pole will be the connected scattering amplitude for asym... | {
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"source": "stackexchange",
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Features of General Relativity applicable only to 3+1 dimensions? While studying general relativity, I noticed that much of the theory could easily be generalized from a $(3,1)$-dimensional spacetime to an $(n,1)$-dimensional spacetime without any changes. So, is this the case for all results that we can derive in gene... | Fun fact: The familiar 3+1 dimensions are the only number of dimensions in which stable planetary orbits exist.
| {
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"url": "https://physics.stackexchange.com/questions/699983",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can satellites change direction without any medium in space? How can satellites change direction without any medium in space? How do spaceships move in space if there is no medium?
How does Newton's third law of motion work in space?
|
How satellites can change direction without any medium in space? How do spaceships move in space if there is no medium?
It works by the principle of conservation of (linear) momentum which is derived directly from the third Newton's law of motion. Effectively, the rocket ejects fuel at high velocity in the opposite d... | {
"language": "en",
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What does it mean mathematically the position of the center of mass relative to other particles is the same? My understanding is that the center of mass of a system of particles is that an imaginary point that travels in space and has position vector $$\vec r = \frac{\sum_{i=1}^{n}m_i\vec r_i}{\sum_{i=1}^nm_i}.$$
My te... | The statement you are asking about is the following, I think.
Let's say we compare the positions measured in two different coordinate systems $A$ and $B$, i.e. $\vec{r}_{i,A},\,\vec{r}_A$ and $\vec{r}_{i,B},\,\vec{r}_B$. Now let's further say that coordinates in the two different coordinate systems are related by one o... | {
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Uncertainty Principle in 3 dimensions I'm trying to understand how to write Heisenberg uncertainty principle in 3 dimensions. What I mean by that is to prove something of the form $f(\Delta p_x,\Delta p_y,\Delta p_z,\Delta x,\Delta y,\Delta z) \geq A$.
This is what I got:
The unknown volume that a single particle can b... | The uncertainty relation holds for each direction in space-time, so $\Delta x_i \Delta p_i \geq \hbar/2$ for $i=0,1,2,3$ ($t,x,y,z$).
| {
"language": "en",
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Do the components of a force written for a purpose actually exist? On an inclined plane if you put a box, the force of gravity $mg$ is written as sum of two forces $mg\sin\theta$ and $mg\cos\theta$ where $\theta$ is the angle the incline is making with earths surface. Do these forces $mg\sinθ$ and $mg\cosθ$ actually wo... | What you are describing is called 'vector decomposition'. Your question is a bit philosophical in nature and there is no straight answer. It is the same as asking "if you are holding 5 apples, are you actually holding 3 apples and 2 apples?" Both statements are true: you are holding 5 apples and you are also holding 3 ... | {
"language": "en",
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What scale are Maxwell's Equations valid? Both Maxwell's equations and quantum mechanics are used to describe the behavior of electrons in circuits.
I am confused on the interlinking between the two and the dividing line between when you use one vs the other. When must you abandon Maxwell's equations and move to quantu... | Two of Maxwell's equations assume a "continuity" in electricity where there is in fact "quantization".
Gauss's Law
$$\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0}$$
and Ampere's Circuital Law with Maxwell's correction
$$\nabla \times \vec{B} = \mu_0 \left(\vec{J} + \varepsilon_0\frac{\partial\vec{E}}{\partial t}\ri... | {
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Will I get a shock holding a superconductive wire? Assume a current carrying superconductive wire is in front of me, with no voltage source attached.
If I hold it, will I get a shock? Forget for a minute that the superconducting wire will be too cold to touch.
My initial instinct was a maybe, for a second but ultimatel... | Let's say the superconductor you grab is one turn of N turns of a 1 meter diameter by 1 meter long solenoidal magnet with an internal B=1 Tesla. The current in this closed loop is flowing with no resistance as long as the temperature stays at 4 degK.
Out of boundless curiosity, you grab the superconductor with your ~30... | {
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Mathematical Definition of Point Source Wikipedia describes a mathematical definition of a point source as "a singularity from which flux or flow is emanating".
The usual definition in Physics describes it just as a source whose dimensions are negligible in comparison to another variable you're relating it to, which le... | None of the objects of mathematical geometry actually exist in the real world. However, they are useful as models of things in the real world. Use a point as a model when the physical object is small enough that its size isn't an important parameter of the problem.
| {
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Why is it more energy efficient to keep a certain temperature in my house (instead of stop heating)? Today I got this recommendation
German for:
Savings-tipp of the month: Turn down your heating on leaving the apartment. But never turn it off completely. Room temperature reduction is much more economic than the rehea... | I'm not at all convinced that a little condensation (if any) will change the heat flow thru walls significantly. Not to mention that heat flow thru walls depends a lot on what construction types, what insulation, etc.
Next: it is true that some heat pumps, under some delta-temperature regimes, work far less efficient... | {
"language": "en",
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If plutonium-238 (Pu-238) absorbs a neutron, does it become Pu-239? I am asking this simple question because I am always hearing about how thorium reactors are less perilous to the world because, unlike uranium reactors, they produce some Pu-238, which is not suitable for a bomb, rather than Pu-239, which is.
But can't... | According to [1],
Neutron absorption in Pu-238 that does not cause fission instead
generates Pu-239.
Let us, however. make it clear what specifically we are trying to compare. If it is Pu-238 and Pu-239, then one can use the latter in weapons directly, and the former needs to be used as a fuel in a nuclear reactor fi... | {
"language": "en",
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Rotated square during relativity I'm working with relativity and I can't seem to understand the following explanation for why a square with side length $L$ is perceived as rotated when travelling at a velocity $v$ (relativistic effect has to be taken into account):
I understand the first paragraph of 11.5. I also unde... | Points A and B are the top left and bottom left corners of the relativistically contracted square in Fig 11.49
If the observer had depth perception, they would see a parallelogram with near and far edges of length $L/\gamma = L \sqrt{1 - \beta^2}$ connected by 'slanted' edges of length $L \sqrt{1 + \beta^2}$. Fig 1.50 ... | {
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Why EM waves lose energy via the square of distance but the light will not? Does that mean that EM propagate forever in vacuum? today at some class at the university we were taught about the propagation of EM (electromagnetic) waves and that they lose energy proportional to the square of distance. Then someone asked: "... | Light is not inherently a particle or a wave, it simply what it is and the best we can do is construct models of it. Sometimes it is best to model it as a wave, sometime it is best model it as a particle. For macroscopic concerns, it is useful to model light as a wave, whose intensity decays with the square of the dist... | {
"language": "en",
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How can light produce electric and magnetic field when there are no accelerating charged particles? If we see light as a wave, especially in vaccum, there is nothing there, no particles, yet light has an electric and magnetic field. How can this be possible?
| Accelerating charged particles cause EM radiation, true. They don't cause all EM radiation. See Black-body and emission for two.
We mathematically describe light as wave-like (because that's how it behaves) but if one interprets "seeing" as the act of intercepting and interpreting light, we actually see [collections of... | {
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Has it been experimentally proven that energy causes gravity? I know that under general relativity energy and mass are equivalent under $E=mc^2$. But has it been experimentally proven that energy alone causes gravity, for example, does a nuclear reaction generate gravity independent of the mass of the reactor alone? I... |
But has it been experimentally proven that energy alone causes gravity, for example does a nuclear reaction generate gravity independent of the mass of the reactor alone?
Gravity and nuclear reactions cannot be tested in the laboratory, because gravity is a very very weak force. Only by fitting astrophysical observa... | {
"language": "en",
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Finding latitude of landing of projectile in Rotating Earth Assuming that the Earth is a uniform sphere of radius $R$, rotating about its axis with a uniform angular velocity $\omega$. A rocket is launched from the Equator in a direction due North. If it keeps on flying at a uniform speed $v$ (neglecting air resistance... | It's not too difficult to work out the problem in the general case. The highest latitude reached will just be the inclination of the orbit (or its supplementary angle if that's greater than $90^\circ$). If we consider an inertial frame (not rotating with the Earth), spherical trigonometry gives the relationship $\cos i... | {
"language": "en",
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Maxwell's eq-meaning of del's cross and dot product? In maxwell's eq there is del whose cross and dot products exist.
So what is del in cross vs dot product.
What's the difference when it's just a partial differential operator.
| You're used to the definitions$$U\cdot V=U_iV_i,\,(U\times V)_i:=\epsilon_{ijk}U_jV_k.$$(I've used Einstein notation without worrying about index heights.) Similarly,$$\nabla\cdot V=\partial_iV_i,\,(\nabla\times V)_i:=\epsilon_{ijk}\partial_jV_k.$$Since derivatives don't commute with functions, the consequences are sli... | {
"language": "en",
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Lagrangian first integral I want to extremize $$\int dt \frac{\sqrt{\dot x ^2 + \dot y ^2}}{y}.$$
I have thought that, since the Lagrangian $L(y, \dot y, \dot x)$ is $t$ dependent only implicitly, that i could use the fact that $$L(z,z') \implies L - z' \partial L / \partial z' = c.$$
So $$L - y' \partial L / \partial... | Hint: Noether's theorem yields that
$$\begin{align} L\text{ has no }&x\text{-dependence} \cr
\quad& \Downarrow&\quad\cr \text{momentum } &p_x \text{ is conserved}, \end{align} $$
and
$$\begin{align} L\text{ has no explicit }&t\text{-dependence} \cr
\quad& \Downarrow&\quad\cr \text{energy } p_x\dot{x}+p_y\dot{y}&-L\te... | {
"language": "en",
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What happens when you shake a coke bottle too hard? I've been thinking about this recently :
what happens when you shake a coke bottle too hard?
I know that shaking a coke bottle and opening it would release the coke. So if I tried it, what would happen : would the bottle explode to the chemical reaction, the lid to po... | Shaking the bottle doesn’t raise the pressure inside the bottle (you can test this with a can; the side pushes in the same before and after shaking)
Instead, shaking puts lots of little bubbles into the liquid. When you decrease the pressure by opening the top, those many bubbles can grow very quickly. That drives up t... | {
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Why the prongs of a tuning fork have different oscillation phases? I've been reading many questions about why tuning fork has two prongs. Many of them explain that each prong oscillates with opposite phases. As a consequence, the compression and decompression of air gets stronger and the oscillation on the stem is redu... | The centre of mass of the tuning fork does not move if the two prongs are moving $\pi\$ out of phase. The forks moving in phase would result in the centre of mass of the fork trying to move which would result in the damping of those oscillations.
Those two types of oscillation can be thought of as the normal modes for ... | {
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Electric displacement at the boundary of a dielectric and vaccum At the boundary of an infinite linear dielectric with constant $\kappa$ and a vacuum, a charge q is placed. In order to calculate the electric displacement$(\mathbf{D})$ we can use Gauss's law for dielectrics i.e. $\oint\mathbf{D}\cdot d\mathbf{a}=Q_{fenc... |
Now since the electric displacement vector does not depend on the dielectric
Careful -- ${\bf D}$ is affected by the presence of a dielectric, just not in an immediately obvious way. You need to use the properties of ${\bf E}$ and ${\bf D}$ fields at dielectric boundaries, specifically
\begin{align}
{\bf E}_{\parall... | {
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What gives particles mass? Also why are particles like photons considered massless when they have energy and momentum? Interested in knowing the quantum explanation for what gives particles mass, and why particles like photons are considered massless when they have energy and momentum.
| Mass is energy that a particle has when it is at rest. Photons are never at rest, and so don't have mass. A related fact is that in the limit that the photon's momentum goes to zero, its energy also goes to zero.
Fundamental particles like electrons, quarks, and the $W$ and $Z$ bosons receive mass by interacting with t... | {
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Space-time continuum expansion I still don't understand how the expansion of the universe works.
If the universe is made up of an infinite number of points that make up space-time, then how can space expand or stretch. Common sense dictates that in order for space to be stretched, the length between points must increas... |
But when we have an infinite number of points, changing the length between them simply does not make any sense.
It absolutely does make sense. Infinite sets need care. Many of the ideas that work for finite sets are changed for infinite sets.
Consider the set of real numbers from 0 to 1 and the set of real numbers fr... | {
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What frequency of cord shaking maintains the same vertical motion for a point on the cord after increasing the wave speed on the cord? I'm studying for my upcoming AP Physics 1 exam but can't figure out this problem
A student shakes a horizontally-stretched cord, creating waves. The graph above shows the vertical pos... | It's not specified which point on the cord we are focusing on. That is for good reason: different points behave the same way, just with a different phase offset, which is not relevant to the question.
As long as we are picking an arbitrary point, why not pick the end point in the hand of the student? The speed with whi... | {
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About a hypothetical universe Imagine a universe dominated by matter, but it is balanced with a cosmological constant $\Lambda=4\pi G\rho$ so the universe is static ($H=0$). However, what would happen if some of that matter turns into radiation?
I was trying to see the Friedmann Equations and found that $\dot{H}+H^2=-\... | You have the hubble constant, but you have to integrate that to get the cosmological parameter:
$$\begin{align}
\frac{\dot a}{a} &= - \sqrt{\beta}\tan \left(\sqrt{\beta}t\right)\\
\ln a &= \ln a_{0} + \ln \cos \left(\sqrt{\beta}t\right)\\
a &= a_{0}cos\left(\sqrt{\beta}t\right)\\
\end{align}$$
so, you have a big bang a... | {
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Why do we take $N = mg - mv^2/r$ opposed to $N = mg + mv^2/r$
So while solving this problem, the solution assumes the normal force to be $$N = mg - mv^2/r$$
But I've learnt that centripetal force isn't any new force and it's an already existing force acting towards the centre.
So shouldn't it be that
$$mg=mv^2/r$$
Why... | As you noted, "centripetal force isn't any new force and it's an already existing force acting towards the centre." The centripetal force just refers to the component of the net force in the centripetal direction (orthogonal to velocity). Since the speed is constant here, the centripetal force is equal to the net force... | {
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Definition of a wave packet In Shankar's QM book page 168, the author stated
a wave packet is any wave function with reasonably well-defined
position and momentum.
What does he mean by resonably well-defined position and momentum? What are some examples of well defined/ not well-defined position and momentum?
| For example, one can speak of a Gaussian wave packet:
$$
\psi(x,t)=\frac{1}{(2\pi\sigma_x^2)^{1/4}}e^{-\frac{(x-vt)^2}{4\sigma_x^2}},
$$
which has finite uncertainty in momentum and finite uncertainty in position (Which can be easily calculated as an exercise).
On the other hand, a plane wave is not a wave packet, as i... | {
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What is the Frauchiger-Renner experiment? Can it be described more simply? Several question on the Physics SE have mentioned a 2018 paper by D. Frauchiger and R. Renner with the title "Quantum theory cannot consistently describe the use of itself" (doi, arXiv). Slightly abridged abstract:
[...] [W]e propose a Gedanken... | I see that the question doesn't really need an answer anymore, so here goes a comment :) There is an accessible review paper (which I co-authored, feel free to ask here as well) on thought experiments in quantum mechanics, including the one by Frauchiger and Renner, and the criticisms surrounding them. It is in open ac... | {
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Nitro Brews and Sodas I feel pretty sure this is a mechanics question, so here goes. I just finished a Nitro Pepsi - Yum! (I know, 63 grams of sugar. I had to brush my teeth twice after drinking it!)
It is well known that "nitro" drinks, (Guinness beer is another example), which have nitrogen gas, rather than carbon... | You might consider that a nitrogen gas molecule is both lighter and smaller than a carbon dioxide molecule and this plays a part in the size difference between the two bubbles under the same conditions. The different solubilities of the two gases in solution may also play a role. I don't believe either gas is altering ... | {
"language": "en",
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Phonon, photon have chemical potential equal to zero Hi I know the chemical potential of the phonon and photon is equal to zero. And I know the reason is the number of these particle isn't conserved.
But I don't know why the number of the phonon isn't conserved? Isn't the number of phonons 3N?
Thanks for your help.
| $3N$ is the number of available vibrational modes, where $N$ is the number of atoms in the solid. Each mode can have a non-negative number of phonons, so the total number of phonons is not $3N$. In thermal equilibrium, the average number of phonons in each mode is given by Bose-Einstein distribution with zero chemical ... | {
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Is it possible to visualise red shift? If a picture of a star or galaxy hurtling away from Earth is taken, does it appear red despite it being a different colour? Would a blue coloured star moving away from us appear red to us or vice versa? If so how do scientists understand if say, the red colour of a star is due to ... | In order to get a visible (to the human eye) color change because of the Dopler redshift, an object has to:
*
*be moving at speeds at least ~5000km/s in regard to the human observer
*have a distinct color in the red-yellow-green range with rather high color saturation.
*be bright enough to be visible in color for t... | {
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Conservation of energy and work done by a torque Suppose you let a solid roll down an incline without slipping, from height $h$. My textbook gives the following conservation of energy relation
$$mgh = \frac{1}{2}mv_{cm}^2 + \frac{1}{2}I\omega^2.$$
Why do we not have to include the work done by the static friction (nonc... | The solid is assumed to be a rigid body. Friction causes rotation and does do rotational work with respect to the center of mass. But, for no slipping of a rigid body, the net work from friction is zero because the decrease in translational kinetic energy of the center of mass due to friction is exactly matched by the ... | {
"language": "en",
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Relativistic angular momentum confusing definition After reading Wikipedia, I'm confused by the relativistic angular momentum definition. OK for the 4-angular momentum tensor. But does it mean that the following more intuitive "angular momentum" will not be exactly conserved at high speeds in a reference frame at rest?... | For Minkowski or Schwartzschild spacetimes, the quantity $$m\left(X^i\frac{dX^j}{d\tau} - X^j\frac{dX^i}{d\tau}\right)$$ is conserved for masses following geodesic trajectories. It results from the existence of some Killing vectors.
In the Minkowski spacetime, the geodesics are straight lines, and it is the trivial fac... | {
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What happens when the universe runs out of fuel? After some X billion years, one would think the stars in the entire universe will run out of hydrogen. What would happen next? Is there any way to get hydrogen out of heavy metals (extreme fission)? Just curious.
| Star formation will die out long before all the hydrogen runs out. Much of it will be trapped in very low mass stars and lots more will be in the very sparse intergalactic medium (where $\sim 50$% of it is now).
In terms of possible production mechanisms, almost all the hydrogen that exists now comes from the big bang.... | {
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A question about the Dirac operator and zero modes in the book "Mirror Symmetry" by Clay Institute I have a question about the book "Mirror Symmetry" p.296~298.
Using the notations there, the Dirac operator and its conjugate are denoted as $D_z$ and $D_{\overline{z}}$. In p.297, the book assumes that $D_{\overline{z}}$... | I don't know exactly what the book is doing, but in calculating correlators of Fermi fields interacting with a dynamical background gauge or gravitational field the Green functions of the Fermions in a given backround field configuration have to be weighted by the Dirac determinant for that configuration. If there a... | {
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Why does applying the kinetic energy operator to a free particle result in a divergent integral? The wavefunction of a free particle is just
$$\psi = Ae^{i(kx-\omega t)}$$
and when you plug this into the Schrodinger equation you get the dispersion relation
$$E = \frac{\hbar^2 k^2}{2m}$$
However, using the kinetic energ... | The equation for the expectation value of an operator:
$$ \langle\hat A\rangle = \int \psi^* \hat A \psi ~ d^3x $$
assumes that the wavefunction $\psi$ is normalised. If it is not normalised you need to use:
$$ \langle\hat A\rangle = \frac{\int \psi^* \hat A \psi ~ d^3x}{\int \psi^* \psi ~ d^3x} $$
The problem is that ... | {
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EMF being equal through KVL
In the given figure,we connect three cells of different emf which are $V_1,V_2,V_3$ with a resistance $R$ in the first loop. Now suppose we emit current $I$ from $V_1$. $I$ gets divided into $I_1$ and $I_2$ with $I_1$ flowing through $V_2$ and $I_2$ through $V_3$.
Now if i apply KVL in the ... | This entire issue can be avoided given that we do not use the idealisation that the potential difference across an ideal wire is zero. This idealisation is not true. The presence of some "internal resistance" can be used to fix this, but a better way is to just accept there IS potential difference across an ideal wire... | {
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Failure of Newton's corpuscular theory and success of photon theory of light Corpuscular theory of light States that:
Light is made up of small discrete particles called "corpuscles" (little particles) which travel in a straight line with a finite velocity.
According to Einstein,
Light is composed of small particle ... | As an example, when using the corpuscular theory refraction of light and Snell’s Law is predicted using Newtonian Mechanics but a requirement of the theory is that the speed of light in glass is greater than that in air which is found by experiment not to be true. Theory related to photons have the speeds in different... | {
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How can light penetrate gold in an astronaut's visor? Astronaut visors use a thin gold layer to decrease intensity of IR radiation coming from the sun. The thing is, gold is a conductive surface, so how can it transmit light through it. Is this related to the skin effect, where an AC current running through a wire will... | Sufficiently thin gold films are not opaque but green:
This is near the percolation threshold at which clumps or islands of atoms join to form a continuous opaque film. See also Norrman et al. (1978). "Optical properties of discontinuous gold films," Phys Rev B 18, 674, and Turner, T. (1908). "Transparent silver and o... | {
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Does the standing wave equation proof require $\ell=Nλ$? Consider two identical sources $S_1$ and $S_2$ of waves, separated by a distance $\ell$ (as shown in the figure).
The sources produce waves in opposite directions(and towards each other). Now, suppose we wish to derive the equation for the standing wave produced... | The 'standard equation' that you quote arises from this superposition of progressive waves...
$$y=y_1+y_2=A\sin(\omega t-kx)+A\sin(\omega t+kx)$$
These 'component' waves are clearly in phase at $x=0$.
Your 'component' waves, $y_1=A\sin(\omega t-kx_1)$ and $y_2=A\sin(\omega t-kx_2)$ are not in phase at $x_1=0$ for an ar... | {
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How does one apply the phase change of $π$ on reflection at the rigid end of a string? Consider a string, with a free end $P$ and another end $Q$ which is rigidly fixed.
Now, we start oscillating the point $P$ (with $0$ initial phase difference) and a wave starts traveling(in the positive $x$ direction) towards $Q$. L... | The general solution to the time-harmonic wave equation on a string may be written as
$$y(x,t)=\sin(\omega t)\left[A\sin(kx) + B\cos(kx)\right].$$
The condition at $x=0$ is that $y(0,t)=A_0\sin(\omega t)$, and so we find that $B=A_0$. We further require that $y(L,t)=0$, where $L$ is the distance between $P$ and $Q$. ... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Does gravitation really exist at the particle level? As I understand, we usually talk about gravity at a macro scale, with "objects" and their "centre(s) of mass". However, since gravity is a property of mass generally (at least under the classical interpretation), it should therefore apply to individual mass-carrying ... | For the interaction of one small (atom scale) mass and one large mass, measurements of the Earth's atmosphere that anyone could do with a homemade barometer and a nearby mountain constitute direct experimental confirmation. We find more gas molecules at low altitudes than at high altitudes. Only gravity acting on each ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/709780",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "27",
"answer_count": 5,
"answer_id": 0
} |
Is vapor pressure conserved during an adiabatic ascent of an air parcel? Consider an air parcel with relative humidity $H$ and vapor pressure $e$ that experiments an adiabatic lifting process. Obviously the saturating vapor pressure is going to change since said process is going to lower the temperature of the system, ... | For the adiabatic ascent of a moist parcel of air there are two scenarios:
*
*if the parcel is not saturated it will just get colder and expand as it goes upwards. Parcel vapor pressure will remain constant as there are no condensation processes.
*once the parcel gets saturated (when it reaches its lifting condensa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/709932",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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