Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Is true black possible? Black is the absence of light because it absorbs light, but when we create black paint or black objects, light is always reflected, either in all directions in matte or smoothly in shiny black objects, making it never a true black. Would it be possible to use polarization to create an object tha... | The problem with the suggestion of using polarization is that you now have the reflections off the polarizers to contend with.
I think the short answer is "it depends on how 'black' you want it to be". "Truly black" = reflectance of 0. I am quite sure that is impossible - there will always be some probability of light... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/183473",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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How to calculate the period of the movement from a potential? I have an assignment, where I have an object moving in 1-D with a given mass and energy, and the potential V(x), and I'm supposed to calculate the period of the movement as a function of the energy
$$
V(x)=\begin{cases}\infty &x < -a \\
0... | It seems, based on the comments above, that you have figured it out. Just for closure, I am writing the steps out.
If you had just a parabolic potential well, $V(x) = \alpha x^2$, you could get the period quite easily - for a given mass $m$, the frequency would be
$$\omega = \sqrt{\frac{2\alpha}{m}}\\
T = \frac{2\pi}{\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/183645",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Polarisation by Reflection - oscillation direction I'm currently studying polarisation by reflection, and have come across two pieces of information from the same source, which I can't seem to understand on how they differ.
*
*The oscillation direction of the field polarised in the plane of incidence is parallel to ... | I have a site which also explains this phenomenon clearly here.
In short here you would find that when an unpolarised light hit at the interface of the two medium the reflected light will be generated such that only that component of electric field is oscillating, which is perpendicular to the direction from point of i... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Notation of vectors It's very common to see $\text{F} = 30 \text{ N}$ when the problem is unidimensional. Yet, force is a vector. Shouldn't I write $|\overrightarrow{F}| = 30 \text{ N}$? Because if I write $\overrightarrow{F} = 30 \text{ N}$ I'm saying that the vector is equal to an scalar. On the other hand, I rarely ... | Force is indeed a vector. Technically you should write $|\overrightarrow{F}| = 30N$, however there is usually context given that let you omit this.
If you are working in one dimension, then the vector-like direction is all encapsulated in the sign once you've defined your coordinate system (e.g. -30N is 30N downwards.)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/183856",
"timestamp": "2023-03-29T00:00:00",
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Is there a major difference between neutron-neutron collisions compared to proton-proton collisions? For the sake of argument, assume the LHC was able to accelerate / focus / collide neutron beams, with the same energy levels it runs at for p-p collision.
Would the collisions produce any major differences vs the p-p co... | Major differences no, because what really collides are constituents of the protons (called partons): the valence quarks, the quarks and anti-quark due to quantum fluctuation and the gluons. The same thing happen with neutron.
However, since in proton $u$ quarks carry more momentum than $d$ quarks (because proton contai... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Explain relationship between angular diameter distance and luminosity distance, Etherington Theorem I have a question relating to the Etherington Theorem.
The luminosity distance is defined by the equation for flux, i.e.
$F=\frac{L}{4\pi D_L^2}$
where flux is in units energy per unit time (luminosity) per unit area.
T... | See D. Hogg's Distance measures in cosmology, 2000
http://arxiv.org/abs/astro-ph/9905116
Section 7, Luminosity Distance, p. 6
$D_L=(1+z)^2 D_A$
follows because the surface brightness of a receding object is reduced by a factor $(1+z)^{−4}$, and the angular area goes down as $D^{-2}_A$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/184115",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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How electrons move so fast in a electric circuit? Whenever we switch on a bulb......it takes almost no time to glow up.....But we know that the atoms of a solid are tightly packed and there is a very little space between them.
So how the electrons travel through them irrespective of so much blockages in the conductor??... | In fact, electron's speed is not so fast that light bulb glows up immediately. It is the electromagnetic field which travels in the circuit at near the speed of light that is resposible for it.
After turn on the light, electron only acquires a little speed in addition its thermal speed. The thermal speed of electron c... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Entanglement of Tripartite States Is there any simple algorithm to determine the entanglement of a tri-partite state?
In particular, what is the proof for entanglement of $ |GHZ\rangle $ and $ |W\rangle $ states?
$ |GHZ\rangle =\frac{1}{\sqrt{2}}(|000\rangle+|111\rangle) $
$ |W\rangle =\frac{1}{\sqrt{3}}(|001\rangle+|0... | You can calculate the density matrix of the state $$\rho = |\varphi\rangle\langle\varphi|$$ And then, the reduced density matrix for one of the particles taking the partial trace $$ \rho_A = \textrm{tr}_{B,C}(\rho)$$ The state is entangled if and only if the reduced matrix is a mixed state. This can be checked, for exa... | {
"language": "en",
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Why is the electric field inside a charged conductor zero in the electrostatic case? I am trying to understand the idea (or the fact) that most books introduce which is about the electric field inside a charged solid conductor.
Books tell that the field has to be zero everywhere inside solid conductor, otherwise charge... | You have ignored the mobile charges in the conductor. In your plot the field lines are not perpendicular to the surface, particularly near the charges. That will cause the conduction electrons to move. The positive charges will attract electrons until the field inside the conductor is zero. This means that the whol... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/184606",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Simple generalization of the Feynman rules for QFT to thermal QFT? Assuming that one knows Feynman rules for QFT, what is the simplest way to generalize them for $T \neq 0$ case? What is the main difference? Can we just read them off from Lagrangian the same way as in QFT?
Since the partition function $Z$ in thermal qu... | Finite temperature Feynman rules are simply zero temperature Feynman rules for Euclidean ($t\to i\tau$) QFT in periodic imaginary time. So instead of continuous values for the momenta, you will have a discrete spectrum for the timelike moments (such as in the infinite potential well in basic quantum mechanics). It's ca... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/184722",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Calculating voltage in piezoelectric material The piezoelectric constitutive law is defined by the two equations:
$$S=s T+dE\\
D=d T+\epsilon E$$
$S$: Strain. $T$: Stress. $E$: Electric field. $D$: electric charge-density displacement. $\epsilon$: Permittivity (evaluated at constant stress). $d$: piezoelectric strain c... | If the material is not connected to a circuit and doesn't have any external charges added then $D =0$ so you can use
$$
D= dT + \epsilon E = 0
$$
along with the known stress $T$ to obtain $E$. Then use $V=EL$ to obtain the voltage $V$.
Here's a screenshot from Learnpiezo.org video series Lecture 3 Part F which covers t... | {
"language": "en",
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Does General Relativity imply loops in space? Everyone who has been interested in modern science has heard explanations (certainly simplifications) of general relativity, mostly that space is curved. The analogy with a rubber sheet is popular. In such an analogy, orbiting planets are said to be naturally following "a s... | "Straight lines" in curved space are geodesics. But the geodesics that define particle paths are in the pseudo-Riemannian manifold of space-time, they are not geodesics in space!
As a planets path is not closed in space-time (but some kind of spiral), massive bodies do not induce loops in the topology of the space-time... | {
"language": "en",
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When does light reach a shell observer in Schwarzschild metric? I am trying to simulate the trajectory of light in the Schwarzschild metric (as seen by a far away observer) with fixed $\theta = \pi/2$. According to my source (Chapter 18, section 18.5) the trajectory is then governed by:
$$\frac{dr}{dt} = \dot{r}$$
$$\f... | The way the equations are presented seems unnecessarily obscure, as there are only two equations that matter:
$$ \frac{d^2r}{dt^2} = \frac{-4M^2+2Mr+(r-5M)r^3}{r^3}\,\dot{\phi}^2 $$
$$ \frac{d^2\phi}{dt^2} = \frac{2(-3M+r)}{(2M-r)r} \, \dot{r}\dot{\phi} $$
These come from the geodesic equation expressed using coordinat... | {
"language": "en",
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Where does the majority of the mass of the usual matter come from? I apologize in advance to experts for the naivety of the question. It should be a duplicate but I didn't find any satifying question or answer about that.
The proton is composed by two up quarks and one down quark.
mass(proton) $\sim 940 \ MeV/c^2 ... | The three quarks you talk about are usually called the valence quarks of the proton, and their contribution to the mass of the proton is not it. In particle accelerators, when we hit protons with high energy beams, we discover that protons are made of a cluster of smaller constituents (like quarks and gluons, which con... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Crane Balancing, Center of mass I am working on the ICPC 2014 Problem C "Crane Balancing"
The initial idea was to calculate the center of mass of the polygon, which I did via this equation:
Where the Area A:
Now, the solution is to binary search over the mass and look for th e maximum mass M where the crane is still... | You have to find mass center of the whole system polygon - added mass and ensure that this center is located above polygon bottom base (without going over the extreme points)
CommonCenter.X=(PolyCenter.X*Poly.Mass + AddedMass.X*AddedMass.Mass)/(Poly.Mass+AddedMass.Mass)
CommonCenter.Y=(PolyCenter.Y*Poly.Mass + AddedMas... | {
"language": "en",
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What is the lowest level things have temperatures? Something can be cold. If you split it in half, it will still be cold, keep doing that and it will still be cold. My question is, what is the lowest level things can have temperature? Do atoms have temperatures? Do quarks?
| One definition of temperature is that it is the parameter which determines the distribution of velocities of an ensemble of particles. Note that I refer to an ensemble (a group) of particles. If you truly continue breaking down into smaller and smaller pieces, you no longer have the concept of a distribution and things... | {
"language": "en",
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Why did the electric potential energy fall in this situation? Suppose you have two capacitors configured as shown in the image below. One of them has charge $q$ and the other one is uncharged. Then, you close the switch, allowing charges to flow. After everything stabilizes, we now have another charge distribution, as ... | The rest of the energy is basically emitted as heat energy.
Why?
You have two capacitors in the circuit, and the connecting wires offer negligible resistance.
Hence, when electrons flow from the charged capacitor to the uncharged one, the electrons basically face no resistance, and they collide with high speed with th... | {
"language": "en",
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Confusion about two forms of connection coefficients I am new to GR. In one book I found that the connection coefficient expression is given by
$$ \Gamma^\mu_{\nu\lambda} = -\frac{1}{2} g^{\mu\rho} (\partial_\nu g_{\lambda\rho} + \partial_\lambda g_{\rho\nu} - \partial_\rho g_{\nu\lambda}). $$
In another book I found
$... | Since $\rho$ is already a summed-over dummy index in the first equation, we can't introduce it again. Instead, multiply both sides of the first equation by $g_{\sigma\mu}$:
\begin{align}
g_{\sigma\mu} \Gamma^\mu_{\nu\lambda} & = -\frac{1}{2} g_{\sigma\mu} g^{\mu\rho} (\partial_\nu g_{\lambda\rho} + \partial_\lambda g_{... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is an event horizon absolute to all observers? Recently I had discussion whether the event horizon of a black hole is absolute or relative to different (outside) observers. Does someone just 1m above the horizon (disregarding effects of tidal forces, stability of orbits etc.) perceive it at the same depth as someone at... | The event horizon is not absolute. It all depends on the observer. THAT is relativity. Space/time is relative to the observer. An event horizon is the consequence of space and time curving to a degree that light cannot escape relative to an observer at a certain point in space/time. An observer close enough to the blac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/185692",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Is the Planck length the smallest length that exists in the universe or is it the smallest length that can be observed? I have heard both that Planck length is the smallest length that there is in the universe (whatever this means) and that it is the smallest thing that can be observed because if we wanted to observe s... | None of the above. Though there are many speculations about the significance of the Planck length, none is proven in any currently accepted theory.
It is expected, though, that quantum gravity effects become definitely non-neglegible at the energy/distance scale set by the Planck length, so it provides a heuristic scal... | {
"language": "en",
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"source": "stackexchange",
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Meniscus attached to an inclined plate To be more specific, suppose a hydrophilic infinite plate is stuck into a semi-infinite region of water, above the water is a semi-infinite region of air, when the plate is stuck into the water vertically, the contact angle is $\alpha$, as shown in the figure below:
Needless to s... | To answer the question in your comment:
Yes the contact angle remains constant. The contact angle is determined by surface energies of the three materials and microscopic surface roughness, neither of which depend on the direction of gravity so tipping the plane will not effect that.
The height of the meniscus (distanc... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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If the speed of light is constant in all reference frames, why does the mirror clock experiment show light travelling on an angle? I was recently looking for answers as to why time slows down the faster you travel and regularly came across the mirror clock experiment. This experiment has a beam of light bouncing betwee... | The point of that experiment is not that the light goes slower but that the light has a longer distance. This means that a single bounce of the light off the mirror takes longer for the observer's point of view. This is due to time dilation. So it is not because the light is slower, but it is because the light has to t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/186189",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Causality and how it fits in with relativity I was talking to my teacher the other day about Einstein's spacetime and there's one thing he couldn't explain about the nature of Cause. I may be being stupid or just unable to comprehend, thanks for any replies.
According to Einstein and relativity, two observers will agre... | It's a bit more complicated than that. Given any two events, there is a quantity, called the interval (also 'spacetime interval' or 'invariant interval'), denoted $\Delta s^2$, and which equals $\Delta s^2=c^2\Delta t^2-\Delta \mathbf r^2$, which determines how the two events can relate to each other causally.
*
*If... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/186296",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Are spherical coordinates distances or angles? I've become confused about spherical coordinates when dealing with electric fields.
The way I always understood spherical coordinates is something like the below picture. To define a vector, you give it a distance outwards (r), and two angles to get a final position. Below... | You can't take the root mean square of the spherical coordinate parameters because they aren't all the same units (one is a length measurement while the other two are angle values). Well you can, but the output is meaningless.
To convert spherical parameters to Cartesian coordinates, you use simple trig:
\begin{align}E... | {
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"timestamp": "2023-03-29T00:00:00",
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Obtaining a copy of Hawking's Ph.D thesis - Properties of Expanding Universes Due to its popularity, I am interested to know the 4 chapter titles and topics covered in S.W. Hawking Ph.D, Properties of Expanding Universes. I also ask this because that thesis is hardly available.
| It seems it went online at last! It went global and public, and it collapsed the wave-function! Here https://www.repository.cam.ac.uk/handle/1810/251038
From this, the chapter titles are...
*
*Title: Properties of expanding universes.
*Abstract.
*Introduction.
*Acknowledgements.
*Chapter 1. The Hoyle-Narlikar th... | {
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What about a surface determines its color? Light falls on a surface. Some wavelengths get absorbed. The other are reflected. The reflected ones are the colors that we perceive to be of the surface.
What is the property that determines, what wavelengths are reflected and what are absorbed? Is it electronic configuration... | A material displays a color when light is reflected off a surface.
When a certain wavelength reaches a surface, if the energy $E=\frac{hc}{\lambda}$ of the photon correspond to the difference between two electronic states then it has a certain probability to be absorbed. The probability of being absorbed depends on th... | {
"language": "en",
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"source": "stackexchange",
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Is there any tension in a massless spring that connects two free falling bodies in different horizontal planes? Two bodies A and B of same mass $m$ are attached with a massless spring and are hanging from a ceiling with a massless rope. They are in same vertical plane but not in same horizontal plane.
Now the string t... | There is tension in the spring. It it extended and hence there is tension! It is the centre of mass that falls with acceleration $g$ rather then each individual mass. So the equation $$mg-T=mg$$ is invalid. As the two masses fall they will oscillate (getting closer and further away) and the tension will cycle.
Let us... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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The Fermi Surface of the Free Electron Model for T>0K For the Free electron model, we can easily describe the Fermi surface at T=0 due to the uniqueness of the Fermi-Dirac Distribution at T=0; below the Fermi-level, a state is definitely filled, above, the state is not filled. So due to the this, the Energy contours ar... | The Fermi surface is a $T = 0$ property. But as the Fermi energies in metals are on the order of a few electron volts (that is a few $10^4\,\mathrm{K}$), it is a good concept for approximately discussing matters at $T > 0$ (where the sharp surface will not be present, but there will only be excitations states close to ... | {
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Calculating Dipole Magnetic Moment Given Magnetic Field Strength I am trying to figure out how to solve the following:
The Earth's magnetic field can be represented, in a first approximation, by a magnetic dipole placed in the Earth's center, at least up to
distances of a few Earth radii ($R_E$)·
Using the fact that... | Indeed, we can approximate the Earth's magnetic field as a dipole and apply:
$
\vec{B} = \frac{\mu_0}{4\pi r^3}(3(\vec{\mu}\cdot \hat{r})\hat{r}-\vec{\mu})
$
Where we know via the problem statement what the magnetic field strength at the North pole is, $|B_{N_{pole}}|$, and that the radius at the pole will be one eart... | {
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On energy levels and emission of photons This is a very basic question but I cannot seem to find the answer anywhere.
Say we have an atom in ground state. Its first energy level is 2 eV. An incoming photon of energy 2.5 eV hits an electron in the atom (with the lowest energy level) which is excited and moves up one en... |
An incoming photon of energy 2.5 eV hits an electron in the atom (with the lowest energy level) which is excited and moves up one enery level.
In most cases, this won't happen. The incoming energy must match the transition that is being excited.
It's possible for a 2.5 eV photon to excite a 2 eV transition, but only ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/187196",
"timestamp": "2023-03-29T00:00:00",
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How can the D'Alembertian of a field be interpreted intuitively? The D'Alembertian operator is defined as
$$
\Box = g^{\nu\mu}\nabla_\nu\nabla_\mu
$$
For the Minkowski metric in Cartesian coordinates that is
$$
\Box=\frac{1}{c^2}\frac{\partial^2}{\partial t^2} - \frac{\partial^2}{\partial x^2} - \frac{\partial^2}{\par... | The operator is just $\partial_t^2-\nabla^2$. So it is the difference between a "temporal laplacian" and a "spatial laplacian". Since laplacian measures curvature, this is basically telling you the difference in curvature between the spatial and temporal variation of the field.
One reason this comes up in physics is in... | {
"language": "en",
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Are Fluted Barrels More Rigid Than Standard Ones? This seems to be quite a debated topic in the shooting community and is something I'm not sure about.
A fluted barrel is a barrel that has grooves milled into it to reduce weight, help it cool faster and supposedly to make it less flexible (see picture below)
I don't s... | If you have the same mass, then the fluted beam will be more rigid because the second moment of area is larger - in the same way that an $\mathrm{I}$ beam is more rigid than a circular rod of the same mass.
In the case of a gun barrel, lighter weight helps in a number of ways - portability, ability to hold the gun stil... | {
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"url": "https://physics.stackexchange.com/questions/187370",
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Is entanglement a consequence of the uncertainty principle? I am an aspiring physicist and once, I asked my professor on what triggers quantum entanglement and he graciously remarked "The great uncertainty principle!" - I was slightly confused and didn't say anything but pondered about it quite heavily on my way to hom... | As far as I understand, it is not.
Entanglement is a consquence of the Hilbert space structure of composite systems in quantum mechanics.
When you postulate that if you have system A (with Hilbert space $H_A$) and system B (with Hilbert sapce $H_B$) then the Hilbert space of both systems together (i.e., when they inter... | {
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Turning points of particle
A particle of mass $m$ and energy $E<0$ moves in a one-dimensional Morse potential:
$$V(x)=V_0(e^{-2ax}-2e^{-ax}),\qquad V_0,a>0,\qquad E>-V_0.$$
Determine the turning points of the movement and the period of the oscillation of the particle.
I have started learning for my exam and... | Energy conservation dictates
$$ E = \frac{1}{2}m\dot{x}^2 + V(x) = \text{const}$$
With some arithmetic it follows
$$ \dot{x} = \frac{dx}{dt} = \sqrt{2m^{-1}(E-V(x))}$$
This ODE can be solved via separation of variables,
yielding
$$ \int_{t_1}^{t_2}dt = \int_{x_1}^{x_2} \frac{dx}{\sqrt{2m^{-1}(E-V(x))}}$$
The integral o... | {
"language": "en",
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Force of an ideal spring Suppose you have an ideal spring (constant of the spring $k$) attached to a uniform disc of radius $R$ as in the picture below:
The force $F$ in red is from the spring.
My question is the following:
How should I decompose the force $F$ into its $x$ and $y$ components??
My intuition would tell ... | If $S$ is de distance from $C$ to de $y$ axis, then $S=|r|\cos(\theta)$ where $r$ is the position of $C$ with respect to the origin and $\theta$ is the angle between the spring and the $x$ axis. However if you want to write $F_y$ then you would have $F_y=-k|r|\sin(\theta)u_y$. So you were correct in thinking in the dec... | {
"language": "en",
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conservation of angular momentum/conservation of energy? Perhaps a dumb question to ask, but
I was given the following problem to solve:
A 10 g bullet traveling at 400 m/s strikes a 10 kg, 1.0-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the a... | In any situation, momentum (linear or rotational) is conserved. So if there are no external forces, you can use that.
But energy is only conserved in certain situations (such as elastic collisions). The deformation of the door by the bullet is inelastic. You can consider it similar to energy losses from friction. I... | {
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Why do our ears pop? Have you ever been on a train going through a tunnel or plane and your ears pop?I was wondering why this happens and I know it relates to pressure but don't know exactly the reason
| Part of your question is about human physiology; that's true. And that part is simple. Air pressure outside your eardrums needs to equalize with air pressure inside your eardrums, and this happens when the Eustachian tubes open up a little to let some air into the cavity behind your eardrums.
The physics parts of you... | {
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Can change in temperature cause a change in mass of an object? If a gold bar is heated to say 200 degree Celsius then will it have the same mass at say 10 degree Celsius. Does energy has mass? If so then does this increased 'heat energy' cause an increase in the mass of an object
| In the modern way of viewing things, no, (rest) mass is invariant. What happens is that the energy content of the body changes and some people still interpret this as a change in mass (which is an old point of view that, unfortunately, is fairly common).
A nice discussion about this can be found here:
http://profmatts... | {
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How can there be entropy change in this system? How can there be an entropy change in this system?
Suppose if I have a system consisting of liquid water, $1\, \mathrm{kg}$ at $290\,\mathrm{K}$, I stir it, and do say, $10\, \mathrm{J}$ of work on it, I can calculate the temperature change of the system given that:
$$U =... | The formula
$$
dS = dQ/T
$$
only applies to thermodynamic processes that can be described by a path in thermodynamic state space (representing a quasi-static process, where the system is in thermodynamic equilibrium at all stages). Only for such processes it is meaningful to talk about continuous change of thermodynami... | {
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Explanation of Michelson Interferometer Fringe Shift I have been working on an experiment where 2 glass microscope slides are pinched together at one end (so that there is a "wedge" of air between them) and placed in the path of a laser in one leg of a Michelson interferometer. When I move the glass slides (fractions o... | This is speculating - but if your slides are of non-uniform thickness, or they are bent as a result of the pinching, they will present a different path length in one leg of the interferometer (and therefore give rise to a shift in the fringe pattern). This may become clear by looking at this diagram:
In the diagram on... | {
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What was the largest object/particle tunneling observed? What is a current record? Reference to that would be nice. and what can be expected in near future? what are the theoretical limits?
| In some sense, there is some kind of classical tunneling. For example, a high jumper, if (s)he bends her/his body over the bar, can pass over the bar in such a way that its center of gravity is always below the bar, and his kinetic + potential energy is always less than mgh, where m is her/his mass and h is the height ... | {
"language": "en",
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Is this definition of orthohelium and parahelium incorrect?
"One electron is presumed to be in the ground state, the 1s state. An electron in an upper state can have spin antiparallel to the ground state electron ($S=0$, singlet state, parahelium) or parallel to the ground state electron ($S=1$, triplet state, orthohe... | The spins are not antiparallel in this state as @my2cts answer correctly states (as demonstrated by $\vec S_1 \cdot \vec S_2$ having a positive eigenvalue).
I was confused by this at first too, especially the argument, that the measurements of $S_{1z}$ and $S_{2z}$ will point to opposite directions due to entanglement ... | {
"language": "en",
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Different signatures I was working out the christoffel symbols, once where the metric that I am using has (+---) signature and another time where it has (-+++) signature because two books had different signatures and I had to check for any inconsistencies. I had the christoffel symbols the same for both but the curvatu... | The signature is one convention (both in special relativity and in general relativity).
But in general relativity there are many different conventions besides just the signature. The front inside cover of Misner Thorne and Wheeler lists conventions for signature, for the Riemann Tensor, for the Einstein Tensor, and for... | {
"language": "en",
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Probability density for momentum in Quantum Mechanics In a Quantum mechanics book, I found the following equations:
$$ \Phi(k)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \Psi(x,0)e^{-ikx}dx $$
and
$$ \Psi(x,t)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \Phi(k)e^{ikx-\frac{\hbar k^2}{2m}t}dk $$
So, with $Ψ(x,t)$ I c... |
So, I suppose that $Φ(k)$ is the probability density of the momentum. Is this true?
Almost. $\Phi(k)$ is the probability amplitude for the momentum of the particle. The probability density is obtained as usual by squaring the amplitude, giving $|\Phi(k)|^2$.
For a free particle, all values of momentum are always allo... | {
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How is the Full Standard Model group representation displayed? I have often seen, on YouTube lectures and textbooks, the direct product gauge group representation listed below and it is often accompanied with a statement to the effect that "this is how we sum up the standard model":
$$SU(3) × SU(2) × U(1)$$
My questi... |
As the above only deals with the gauge boson side of things
This is a wrong assumption.
The format represents the total knowledge from innumerable data of particle physics that have been fitted with SU(3)xSU(2)xU(1) . The particles are slotted into representations of the groups and there are rules of how the interac... | {
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How fast does heat travel via conduction? I have read this question which seems to ask an identical question, but I'm not sure - it had far too many words I don't understand, let alone the equations. Perhaps someone can answer with a heat-for-dummies answer.
I understand that given thermal conductivity, and thermal mas... | At near the speed of light. The same maxwells equations that describe the conduction of electric discribe the conduction of thermal energy.
| {
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Why does a Yo-Yo sleep, and then awaken? What are the mathematics / mechanics principles behind a sleeping Yo-Yo,
and in particular, what changes with a wrist-snap flick that
causes it to "awaken" and return to your hand?
(Image from www.wikihow.com/Make-a-Yoyo-Sleep.)
There must be some s... | "Sleeping" is when the YoYo rotates in place because the string is freely rotating around the bar between the halves. If something is done to prevent the string from freely spinning then the energy that was driving the YoYo to rotate in place is now used to reel in the string. Flicking your wrist or otherwise jolting i... | {
"language": "en",
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"source": "stackexchange",
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Why is probability of finding the electron at a certain point when one of the slits is closed $|\Psi|^2 $ & not $|\Psi|^2 dx$? Let in a given physical condition, the wave-function to a particle be assigned as $|\Psi (x_i,0,0,t)|^2 dx$.
Now, at the double-slit experiment , the probability of finding the particle at an... | The square of the wavefunction, $|\Psi(x,t)|^2$, is the probability density function for finding the particle. This means that the probability of finding the particle in an interval of (infinitesimal) width $\mathrm dx$ at position $x$ equals $|\Psi(x,t)|^2\mathrm dx$. On occasion, however, authors will drop the $\math... | {
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How to interpret vector operators in quantum mechanics? To the point:
How should I think about the equation $$\hat{\mathbf{x}}\mid\mathbf{x'}\rangle = \mathbf{x'}\mid\mathbf{x'}\rangle~?$$
Is it a triple of equations
$\hat{x}\mid x'\rangle = x'\mid x'\rangle$
$\hat{y}\mid y'\rangle = y'\mid y'\rangle$
$\hat{z}\mid z'\r... | Your second option is correct.
It is a simultaneous eigenket of all three commuting operators. And that is how it should be interpreted. To be explicit, the equation $$\hat{\mathbf{x}}\mid\mathbf{x'}\rangle = \mathbf{x'}\mid\mathbf{x'}\rangle~?$$
Is a triple of equations
$\hat{x}\mid \mathbf x'\rangle = x'\mid \mathbf... | {
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How to find tangential/radial/angular velocity for motion in any curve? Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction? If so why?
Please try to give a different explanation than saying that the radial velocity points in t... | You would be pretty accurate in saying: "the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction"
Why?
Consider each case individually:
1) An object has only "radial velocity" that is, it points directly away (or towards) the observer... | {
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What are the symmetry criteria for continuous phase transitions in Landau theory? My understanding is that within Landau theory, a continuous phase transition is only possible if certain symmetry rules are satisfied. (These rules represent necessary but not sufficient conditions for a continuous phase transition.) One ... | This "criteria" is neither sufficient nor necessary.
There are many symmetry-breaking transitions which are not continuous. For example, it is well-known that $n$-state Potts model has a thermal symmetry-breaking phase transition, and when $n>4$ it is first order. For a more realistic one, I think melting transition i... | {
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If Coulomb and Esu have different dimensions, why can we convert simply by 1C= 3*10e9 esu? I was always told in school we cannot convert an apple into a potato, so we have to have the same dimensions on both sides.
When converting coulomb to esu, we do not seem to bother with dimensions. Why is it still possible?
| An important point here is that you don't just convert from Coulombs to ESU. You also change the units of various constants that appear in the expressions of electromagnetism.
The most obvious example is, Coulomb's Law
$$\begin{align*}
F_{SI} &= \left (8,99 \times 10^9 \,\mathrm{N \, m^2/C^2}\right)
\frac{q_{1, C} \, q... | {
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Friction in Rolling Motion My understanding of rolling motion:
When a body rolls, at every instant, there is just one point of contact between the body and the plane and this point has no motion relative to the plane.
Now if there is no motion relative to the plane, then how does the rolling friction came into being?... | Your first quote is correct for an idealised model. There is no rolling friction then. Both wheel and surface are considered completely rigid.
Ideal model - no rolling friction
Non-ideal/more realistic model - rolling friction comes into the picture
These pictures are from this link that gives a very good graphic vie... | {
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Radius of curvature I have come across a question that asked me to find the radius of curvature of a projectile.
As far as I know, the path of a projectile is a parabola and I have found mention of the radius of curvature referring to lenses and mirrors. But in optics, the lens and mirrors were assumed to be part of a ... | We can draw a tangent (Call it 't') at any point (call it 'p')on a curve. We can also draw a circle to which 't' is a tangent. The radius of this circle is the radius of curvature to the given curve at the point 'p'.
An analogy from motion of a body along a curved path may help easier understanding.
When a body moves a... | {
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What is "forward peaking"? In "Research and Development for a Gadolinium Doped Water Cherenkov Detector" the phrase "forward peaking" is used to describe a signal. This comes up in lots of other contexts too, but I still can't work out what's meant by it. The sentence in question is;
"But due to a strong forward peakin... | It means that when the neutrinos hit electrons, the electrons are moving preferentially in the same directions that the neutrinos were moving. So when we are building a water Cherenkov detector for solar neutrinos, the Cherenkov signal will be coming from the direction of the sun. This is very advantageous to suppress ... | {
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"Center of a black hole is a time" $\newcommand{\d}[1]{\mathrm{d} #1}$In one lecture (around 1:33:15) of the series of lectures "Theoretical Minimum" of Prof. Susskind he talks about black holes and the Schwarzschild metric:
$$\d \tau^2=\left(1-\frac{r_s}{r}\right)\d t^2 - \left( \cfrac{1}{1-\frac{r_s}{r}} \right) \d r... | The Schwarzschild metric as you've written it is only one particular coordinate system and the fact that $r$ and $t$ switch roles at the event horizon is an artifact of that coordinate system. There are other coordinate systems which make certain properties of the metric more intuitive. The ones that might be most usef... | {
"language": "en",
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Can we find actual rest mass of things on Earth Earth moves around the Sun and the Sun moves around the galaxy and the galaxy moves with unknown speed and direction. We have speed so the mass of us all altered.
Can we know the real rest mass? If so, can we deduce our speed in the universe?
| The rest mass of an object, by definition is the total energy of an object as measured by an inertial observer who is at rest relative to the object. If the object is not moving uniformly, then you can measure its rest mass from a momentarily co-moving freefall frame. This rest mass is also the constant in Newton's law... | {
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Phase on Aharonov-Bohm effect doubts How I show that $$\Lambda(\textbf{x}')=\frac{q}{\hbar}\int \mathbf{A} \cdot d\mathbf{x'}$$ on $$
\tilde{\psi}(\textbf{x}',t)=e^{[\frac{iq\Lambda(\textbf{x}')}{\hbar c}]}\psi(\textbf{x}',t)$$ for Aharonov-Bohm effect? I don't know about path integral formulation, that was suggested o... | You should be able to show by direct substitution that your proposed wave function $\tilde{\psi}(\mathbf{x},t)$ solves the Schroedinger equation, where the vector potential is included via the minimal coupling prescription
$$ \mathbf{p} \to \mathbf{p} - \mathrm{i} q \mathbf{A}(\mathbf{x})$$
(up to a sign convention for... | {
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Galaxy bias and baryon acoustic oscillations (BAO) I have a doubt with the concept of galaxy bias and how it affects baryon acoustic oscillations, it is supposed to mean that by measuring the distribution of galaxies we are not measuring the actual distribution of dark matter (I imagine this is due to processes of gala... | You are correct about the bias factor - because the dark matter distribution is not measured directly, but via tracers (galaxies), there may be some bias in the tracers. This is put into the analysis as an unknown bias parameter $b$ that needs to be fit.
Now the second part of your question - why do we care about the d... | {
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Is it possible for man to break Earth into 2 parts? Many countries have extreme devastating nuclear weapons. Also they have weapons in very large numbers.
I want to ask that
Is it possible for man to break earth into 2 parts with the help powerful weapons like nuclear weapons or any other technology?
|
break earth into 2 parts in which each part is nearly equal to half of volume of the earth
Yes and no.
No, as in you can't neatly split the planet in half. Most of the earth is liquid and will re-form once the cutting device has passed through it. Much like cutting pudding.
Yes, if you want 2 half-earth balls when yo... | {
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Why is the introduction of a quantization volume necessary for quantization of the EM field I have been working through the quantization of the electromagnetic field, and every source I find introduces a quantization volume with periodic boundary conditions in the process, in which we fit the general solution of $A(\bo... | Quantizing in a finite volume is not specific to the electromagnetic field, and it is not a necessity, neither for the electromagnetic field nor for any other.
It is generally more well-behaved to quantize in a finite volume because no infrared-like divergences appear from allowing arbitrarily low momenta (since no arb... | {
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What is the meaning of coherent decay rate and population decay rate? In quantum optics, especially the part when talking about atom-light interaction, there are two different kinds of decay rate, coherent decay rate $\gamma_{ij}$ where $i$ and $j$ are atomic energy states, and population decay rate $\Gamma_{ij}$.
I do... | I am not a specialist of quantum optics but I am familiar with laser and classical optics.
I would say that coherent decay is stimulated emission and population decay rate is simply spontaneous emission.
When atoms/electrons are interacting with light they have a certain probability of absorbing photons to get into hi... | {
"language": "en",
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Kinematics of Euler angles relative to a rotating frame I have a rotating body $B$ and a rotating frame $F$ whose orientations are described by the quaternions $q_B$ and $q_F$ respectively. I also have the angular velocity vectors $\omega_B$ and $\omega_F$.
I'm then interested in the Euler angles (extrinsic x-y-z) of B... | First Thought (probably not the fastest)
Let us assume you have a vector space in $R^{3}$ with a quaternion defined as:
$$
\mathbf{q} = q_{F}^{*} \ q_{B} \\
= a + b \hat{\mathbf{x}} + c \hat{\mathbf{y}} + d \hat{\mathbf{z}}
$$
where $(a, b, c, d)$ are the Euler parameters and $(\hat{\mathbf{x}}, \hat{\mathbf{y}}, \hat... | {
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Why do elements on the Binding Energy per Nuclear Molecule after Iron (most stable) even form? So I was reading about the stability of elements based on Nuclear Binding Energy, and I saw that the 'Iron group' of elements were most tightly bound and hence most stable, and that is why the graph peaks there. Why do elemen... | There are a couple of related questions:
*
*What elements can be created in the fusion process of different types of stars?
*What is the heaviest element possible produced in a supernova?
though surprisingly I can't find an exact duplicate (which probably just means I didn't look hard enough).
Iron is the most stab... | {
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Cylindrical capacitor in an electric circuit I've come across a tricky question and would appreciate some hints or explanations as to why the given solution is the way it is. The question reads as follows:
A coaxial cable consists of a wire with radius $a$ (the core of the cable), which is wrapped with insulating mate... | There is only one connection to the wrapper, at the power supply end. One can read the problem to imply that the resistor at the other end is connected to the wrapper, but you shouldn't. If there were a connection there, the resistor would be shorted out. As the wrapper has only one connection, at long $t$ it will h... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/191424",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Field expansion in Peskin & Schroeder Peskin and Schroeder state something which I'm not fully understanding. More specificially I think it's just phrased in a way I'm not understanding.
In the Schrodinger picture we can expand the real scalar field $\phi(x)$ which satisfies the Klein-Gordon equation as
$$\phi(\textb... | The upshot is that we need one condition to specify how the operators in the Schrödinger and Heisenberg picture are connected. This is usually done by declaring that the two pictures agree at some fixed instant $t_0$.
To summarize: The Schrödinger operator $\phi(\textbf{x},t_0)$ does not depend on time $t$, while the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/191625",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is magnetic reconnection reconcilable with magnetic field lines neither starting nor ending? According to Maxwell's equations, magnetic fields are divergence-free: $\nabla \cdot \mathbf{B} = 0$. If I understand this correctly, this means that magnetic field lines do not start or end. How can we reconcile this with magn... | $\nabla\cdot\mathbf B=0$ does indicate that there are no magnetic monopoles, so there isn't a "starting" or "ending" point for field lines is mostly correct. So this must mean that magnetic field lines either
*
*form closed loops
*extend to infinity
*intersect the domain boundary (wall, stellar surface, et... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/191942",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Clarifying some notation, the square of a vector derivative I'm reading a text which asserts that, if $\vec{F}(\vec{x})=-\nabla V(\vec{x})$ then we define
$$E = \frac{m}{2} \left( \frac{d\vec{x}}{dt}\right)^2-V(\vec{x}) \, .$$
However, I don't understand how you can square $d\vec{x}/dt$ since this is a vector function.... | The kinetic energy of a particle whose motion is described by $\textbf{r}(t) = \left(x(t),\,y(t),\, z(t)\right)$ is, at the point $(x,y,z)\in\mathbb{R}^3$, defined as
$$
T(x,y,z) = \frac{1}{2}m\left(\dot{x}^2 + \dot{y}^2 + \dot{z}^2\right) =
\frac{1}{2}m\,\textbf{v}\cdot\textbf{v}
$$
and yes, the square of a vector mea... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Raychauduri equation for Milne universe I am trying to solve this kind of problem:
Consider the Milne model, i.e., the empty $ \kappa = −1 $ Friedmann model. Verify by a direct calculation that the expansion $ \Theta $ of the unit normal to the $ \tau = \mathrm{const}$ hypersurfaces satisfies
$$
\dot{\Theta} + \Thet... | It can be shown that $\omega_{ab} = 0 \Leftrightarrow \omega^a \equiv \epsilon^{abcd}u_b \nabla_c u_d = 0$. The latter quantity is known as the twist (or vorticity). In a local inertial frame it is easy to see that $\vec{\omega} \sim \vec{\nabla}\times \vec{v}$ where $\vec{v}$ is the 3-velocity field of the flow.
This... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/192118",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is UV catastrophe same as IR catastrophe? I am currently studying quantum physics from Serwey-jewet. Where in the topic of Planck's law, infrared catastrophe is alternatively used for UV catastrophe while explaining how Plancks constant explains Rayleigh jeans law and UV catastrophe. Is it the same thing or it is an er... | It has to be an error. Rayleigh-Jeans theory fails at high frequency, but it's a good approximation for low frequency.
Infrared catastrophe has nothing to do with the black body radiation problem. Only at high frequencies it was evident that Rayleigh-Jeans model failed.
In the following plot you can see how at low freq... | {
"language": "en",
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Help recognizing partial differential equation I would be very grateful if someone could tell me something about the following partial differential equation:
$$
\frac{\partial U}{\partial t} = K * (\frac{\partial^2 U}{\partial r^2} + (1/r)\frac{\partial U}{\partial r}).
$$
A friend told me that the equation models the... | That is the heat equation in polar coordinates with axial symmetry. The (isotropic) heat equation without sources or sinks is
$$
\frac{\partial U}{\partial t} - K\nabla^2U =0.
$$
If you look up the Laplacian operator in cylindrical coordinates, you will find that your expression matches this exactly.
| {
"language": "en",
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Simple Harmonic Motion in Special Relativity I was trying to see what results I would get if I were to incorporate relativistic corrections into the case of a harmonic oscillator in one dimension. I thought that if the maximum velocity of the oscillating body were to approach relativistic velocities, the measurement of... | You can get an exact solution for $t(p)$, although it involves a rather nasty integral that I'm not sure can be written in closed form. Here's how:
The equations of motion are
$$
\frac{dp}{dt} = -kx \qquad \frac{dx}{dt} = \frac{1}{m} \frac{p}{\sqrt{1 + p^2/m^2 c^2}}.
$$
This second equation can be obtained by taking t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Will a bullet travel the same after going through 2 substances (in different orders)? This may seem like a trivial question, however I am a little curious as to whether 'order matters' in the case of this system, or whether you would be able to treat any object as a 'black box' with given input and output.
My scenario ... | No - hitting the steel plate first will deform the bullet resulting in greater drag in the gel and lower penetration
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/192818",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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A misconception in an application of Newton's laws When a body is kept in ground, and is at rest, the downward gravitational pull is balanced exactly by the Normal Reaction if we assume the earth to be an inertial frame. But this would mean that any external force provided to that body would lead to its motion. if this... |
When a body is kept in ground, and is at rest, the downward gravitational pull is balanced exactly by the Normal Reaction if we assume the earth to be an inertial frame.
This is not correct. The normal force is a constraint force that acts in one direction (upward). Suppose you exert an upward force of five newtons o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/192963",
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Free fall into circular motion If I'm on a roller coaster free falling from height $h$ and then suddenly start going into horizontal motion with a radius $r$ of turn what is the $g$-force I experience?
I worked out the equation like this but am not sure if it is correct:
*
*(1) instant velocity of free-fall $v=\sqrt... | There are two accelerations involved: The gravitational acceleration $g$ that points down, and the centripetal acceleration $a_r = \frac{v^2}{r}$ that points along the radius vector of the curve. The component of the gravitational acceleration that is tangential to the curve does not contribute to the g-force as it acc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Must we test whether e.g. $A=B$ and $A=C$ implies $B=C$ by experiment? Chaper 10, conservation of momentum in "The Feynman Lectures on Physics" in the chapter entitled, the authors write that
Suppose we know from the foregoing experiment that two pieces of
matter, $A$ and $B$ (of copper and aluminum), have equal mas... | We know how real numbers (in the mathematical sense) behave. There is no a priori reason however to assume that masses of objects behave as real numbers. The proposed experiment can be seen as a check to see if masses actually can be modeled by (a subset of the) real numbers.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193266",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why are bandstructures plotted only along certain symmetry points? Why is it that bandstructures are usually represented along certain symmetry points ? What determines these symmetry points ?
| Here's an example bandstructure
(image from here). Each point on the horizontal axis is a point in k-space. Then the vertical axis shows the bands.
k-space is three dimensional. In a perfect world we would make a four-dimensional graph with k-space on three axes versus band energy on the fourth axis. Alas, we live in ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193347",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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With a machete, why is a diagonal cut more effective than a right angle one? When cutting back some thick growth in the garden a question that always nagged me. Why is cutting diagonally seemingly more effective than cutting at right angles? Part of the answer is obviously to do with the ease of cutting vertically as o... | The flexural rigidity of a vertical beam will be greater with a diagonal cut. This allows more of the force to be channeled into cutting the target as opposed to bending the target.
The determinants of flexural rigidity affected by a diagonal as opposed to a horizontal cut are the cross section of the beam and distanc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193455",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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drift velocity of gas needed to get into a pressurised vessel Would a gas entering a narrow tubular opening of an initially empty vessel at a given velocity, fill up the vessel to a definite pressure?
If so, how is the velocity of the gas related to the final pressure of the gas in the vessel?
If now, the gas is let o... | Preliminary:
Pressure is the driving (or source) term in Naiver-Stokes equation that governs fluid flows in continuum region, if we know pressure at inlet and outlet we can find the velocity for simple low speed flows.
This process is isentopic if there is no heat flow. That problem can be solved by Bernoulli equatio... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193527",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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A circuit that is net charged What differences would you measure if a circuit were significantly charged negatively? Would the resistance change? To be clear, I mean that excess electrons are added to the system. The circuit can be of any kind you can imagine.
| To do this experiment, you will need:
1> a grounded, sheilded cable, (to prevent magnetic interference)
2> an ability to apply a voltage from the cable to ground, (say a battery, or better a variable DC source, with the postive terminal grounded and the negative one attached to the cable) and
3> a sensitive ohm-meter. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193618",
"timestamp": "2023-03-29T00:00:00",
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Why are angles dimensionless and quantities such as length not? So my friend asked me why angles are dimensionless, to which I replied that it's because they can be expressed as the ratio of two quantities -- lengths.
Ok so far, so good.
Then came the question: "In that sense even length is a ratio. Of length of given... | "In that sense even length is a ratio. Of length of given thing by length of 1 metre. So are lengths dimensionless?"
No, if they where then where did the 1 meter come from, why wasn't it 1 feet, or 1 mile?
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193684",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "55",
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"answer_id": 6
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Are Cosmic Rays net neutral in charge? As I understand them, Cosmic rays mainly consist of high energy charged particles. I began to wonder if they would eventually net charge the Earth and then assumed that they must come in roughly equal amounts of charge. If they don't I suppose the charged Earth would deflect like... | The net charge of earth due to incoming CR particles may not be static and may vary over periods of time. Earth may have a semi-stable ferromagnetic core and transient peaks of positive or negative absolute-earth-charge may inductively contribute to earth’s magnetic pole reversal. Assuming CR particles with directed en... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193771",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do the waters of the different oceans of the world have different ratios of their H and O isotopes? I was reading about the Kelvin, then water, which defines it, so I ended up reading about the VSMOW. It's based on "average" ocean water.
From https://en.wikipedia.org/wiki/Vienna_Standard_Mean_Ocean_Water :
"VSMOW i... | The water in the Oceans is partly
1) the original water from their formation and this will have come into equilibrium with the underlying strata of earth. These strongly depend on location for the chemicals composing them and this will apply to the isotopes in these chemicals
2) Rain water which brings down whatever d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193950",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Ozone elimination I have a potential problem with airflow through a high voltage capacitively coupled RF discharge (in a tube) producing ozone. How can I remove ozone from the airflow? The use of liquids is not possible. Flow rate is quite low, in the mL per minute.
| The absolute cheapest thing could be to wire a variable resistor in series to try to get the discharge voltage down: it's possible that you could reach a regime where you're only ionizing some of the gases in the air, without melting the resistor.
Since ozone's "badness" comes from being hyper-reactive you might be abl... | {
"language": "en",
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If two objects have all the same conditions except different masses. Will their terminal velocity be different? I can't seem to find a straight forward answer to this. I really just want to know if changing mass of an object affects the terminal velocity. If two objects of the same dimensions except one had twice the m... | Imagine 3 objects. One is a flat piece of paper. The second is an identical piece of paper rolled into a ball. The third object is the exact same shape and size as the rolled up piece of paper but it's made of iron.
If you drop the flat paper and the rolled up paper at the same time, the rolled up paper hits first bec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194476",
"timestamp": "2023-03-29T00:00:00",
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Is double-slit experiment dependent on rate at which electrons are fired at slit? I am a mathematician and I am studying string theory. For this purpose I studied quantum theory. After reading Feynman's book in which he described the double-slit experiment (Young's experiment) I was wondering if I send one electron per... | Imagine that the sended electron interacts with the surface electrons from the slits edges. Together they form a quantized electric field. This field is not static in the sence that the position of the incoming electron is slightly different and the surface electrons are not standing still. The incoming electrons get d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194570",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does a magnet cause magnetic force and its magnitude/direction? Magnetic fields are created due to electron spin in the magnet. But how exactly does an electron "spinning" create forces around the magnet? Also, the magnetic force on a charge moving in the magnetic field is $qvB\sin\theta$, and its direction is perp... | Magnets are made from metals. Metals have crystalline structures and this means that the atoms somehow are fixed. Under the influence of an external magnetic field the magnetic dipole moments of the atoms get somehow aligned and sometimes could stay aligned after removal of the external field. The magnetic dipole momen... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194628",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Time evolution of scalar field Consider the quantized real scalar field acting on the vacuum state $\vert 0 \rangle $. We can interpret the state $\phi(\textbf{x})\vert 0 \rangle $ (defined in the Schrodinger picture at $t=0$) as a particle created at $(t=0,\textbf{x})$.
Peskin and Schroeder say that the state $\phi(x)... | This problem arises because you cannot compare states in the Heisenberg picture and states in the Schrödinger picture (except for $t=0$) because they are physically different objects.
The only thing that coincides and can be compared are matrix elements or expectation values. If you have a look at expectation values, y... | {
"language": "en",
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Coulomb's law with an $r^3$, not $r^2$, in the denominator I am reading an older physics book that my professor gave me. It is going over Coulomb's law and Gauss' theorem. However, the book gives both equations with an $r^3$, not $r^2$, in the denominator. Can somebody please explain why it is given as r^3? An image is... | It does give "Coulomb's law" with $\frac{1}{r^3}$, it gives it in its proper vectorial form
$$ \vec E \propto \frac{\vec r}{r^3}$$
which, when taking the absolute values, yields the form you are probably more familiar with
$$ E \propto \frac{1}{r^2}$$
since $\lvert \vec r \rvert = r$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194894",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Observations of erratic rotation of asteroids An asteroid generally has an irregular shape, therefore, one would expect its rotation is quite erratic in some sense. Are there any observational examples?
| Rigid bodies with three distinct moments of inertia have two stable rotation axes, the axes with the greatest and least moments of inertia (typically the shortest and longest axes). Non-rigid bodies have but one stable rotation axis, the axis with the greatest moment of inertia. The axis with the least moment of inerti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/195022",
"timestamp": "2023-03-29T00:00:00",
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The Makeup of the Pentaquark Why is it that when they have the artist's rendition of the Pentaquark it shows two downs, two ups, and one anti-strange quark? Is this or is this just for show? Follow up to this question: if this configuration is just for show, what is the Pentaquark truly made of?
| I suggest you to read my answer here for a quick look into exotic hadrons. These particles mostly(at least so far) are very unstable appears for a short time and decay into another particles, hadrons and mesons. Hadrons made of 3 quarks and mesons one quark and its anti-matter. These unstable particles(resonances) have... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/195310",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Engine fuel consumption vs power Something that has bothered me for a long time is why a 600 hp engine uses more fuel per kilometer than a 80 hp engine. Let pretend I have two equal cars (same shape same weight etc) except for the engine, one is 600 hp and other is 100 hp. If I manage the throttle to accelerate both wi... | To generate more power, an engine needs to be able to burn more fuel; laws of physics, chemistry and thermodynamics dictate this requires a larger displacement (bigger volume in which you burn the fuel).
Larger volume = larger area over which you generate friction, more more importantly, more air being pulled through p... | {
"language": "en",
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"source": "stackexchange",
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How is energy dissipated in a travelling em wave How is energy dissipated in a travelling em wave. Will there be any dissipation if it were to travel trough vaccum ?
| Individual photons will not lose any energy as long as they do not interact with any other particle. If you are referring to the intensity of the EM emission, that depends of the angle incidence from their source.
So basically, if you imagine a laser that could emit just a single photon in the vacuum of space, that pho... | {
"language": "en",
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Proof for Resistance is directly proportional to length and inversely proportional to the area of cross-section? I have heard that Resistance is directly proportional to length and inversely proportional to area of cross-section. Can someone give me a practical explanation for this?
| Well, I guess you could "derive" it in the Drude model (see my post here), where the proportionality of current density $\vec j$ and electric field $\vec E$ is the conductivity $\sigma$ or inverse resistivity $\rho$:
$~~~~~~\vec j = \cfrac{q^2}{m} \tau n \vec E = \sigma \vec E = \cfrac{1}{\rho} \vec E$
Using the curren... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/195725",
"timestamp": "2023-03-29T00:00:00",
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What happens to a radioactive element or isotope's electrons when it undergoes alpha decay? It seems to make sense that when an atom loses two protons, it would lose two electrons as well, but I don't actually know what happens.
| It is complicated and we ignore it, but your intuition is right. When the nucleus loses an alpha particle its charge decreases by two. The atomic physicists now claim their job is done and don't care. The solid state physicists don't consider radioactivity, so they don't care either. If it is an atom floating freel... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/195831",
"timestamp": "2023-03-29T00:00:00",
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Why do semiconductors remain neutral outside the depletion region? Why there is a sharp cut off of the charged region outside the depletion region, like on this image?
For example why don't electrons on the conduction band in the n-type side rush towards the positively charged area making the whole piece positively cha... | Look up the depletion region approximation. Which by the way is actually pretty good, especially when the junction is revered biased.
When it is forward biased, or one side is highly doped sometimes it is not as good and it would be better to work out the solution numerically. Then you could find that the edges are not... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/195928",
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How covalent bonding lower the energy of potential energy? Considering the potential energy of interacting particles, how does covalent bonding lower the energy of the system?
| They would not bond if it was not lower energy. Like I said look at it from the other direction - it takes energy to pull them apart. An O2 molecule is actually smaller than an oxygen atom. It is a tight orbitals that fill the orbitals. Like hudling (spooning) from the cold. S likes to fill (2) and then P likes ... | {
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Why is it difficult to hear when speaking in the presence of strong wind? We say that sound waves require medium for their propagation, but during heavy storms or strong wind we cannot hear sound properly. Even if wind is flowing towards specific direction and we speak in that direction we cannot hear it well. Why is i... | Sound waves in air are a series of high and low pressure areas moving through the elastic medium of the air. If the medium is being compressed and rarefied by other areas of high and low pressure, the integrity of the sound wave may be broken and may become unrecognizable through the background noise of the medium's t... | {
"language": "en",
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"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Is there some no-go theorem for $D=9$ Kaluza Klein QCD+EM? While QCD is a typical product of AdS/CFT and some other research trends in extra dimensions, I have never found in the literature an example producing the non-chiral part of the standard model, colour plus electromagnetism, or even color alone, from D=9 Kaluza... | While it is certainly possible to get an $SU(3) \times U(1)$ gauge group from the metric alone, if one started with a 9d theory, there are several issues with using Graviphotons as gauge bosons in a 4d theory.
Most prominently, in addition to vector bosons you will always create scalars in the adjoint from internal com... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/196610",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 2,
"answer_id": 0
} |
Is it true that spring has more force acting on it at its positive maximum amplitude than than at the negative one? Am I missing something?
It seems obvious to me that at $+A$ and $-A$, the spring has restorative forces equal in magnitude but opposite in direction.
But since gravity is always pulling it down, the spr... | The answer is no. The net force at the maximum elongation points has the same magnitude.
This is because the rest point of the spring is modified by the gravitational weight of the mass. The mass oscillates around this new rest point, and at the points of maximum amplitude the net force is the same. One can tell that t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/196718",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 2
} |
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