Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Suppose infinite 3D space is filled with matter except a spherical cavity. Will a particle in the cavity experience force? Suppose infinite 3D Euclidean space is uniformly filled with dense matter except a spherical cavity. Will a particle in this cavity experience gravitational acceleration towards the nearest wall?
| Well, after reading other answers, I say different. Point me out where I am wrong and I would be glad to understand my mistake.
Suppose the entire region was filled with matter. So, using any kind of symmetry, there would be no force any particle. Now we remove a sphere, which contains that particle that we're observin... | {
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Difference between energy and coulombic efficiency of perfect battery I have been trying to reconcile coulombic and energy efficiency for a perfect battery, but failed. Where have I gone wrong?
a coulomb is a unit of charge. Equal to lots of electrons.
a battery has a fixed amount of chemicals which react and need a fi... | An ideal battery has the capability of driving a certain amount of charge around a circuit that being 200 Ah or 720 kC in your example. This represents 12 $\times$ 720,000 = 8.64 MJ of energy stored in the battery.
That is about it for an ideal battery other than actually giving it an infinite capacity, a constant term... | {
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Massless particles in a universe with compact extra-dimensions One common idea behind many extensions to the Standard Model (such as String Theory or Kaluza-Klein Theory) are small or hidden "Extra-Dimensions", that are compactified.
According to my understanding of Quantum Physics, this would result in each particle's... |
The string tension Tstring is the energy per unit length of the string. If the string is wound w times around a circular dimension with radius R, then the energy Ew stored in the tension of the wound string is
The mass of an excited string depends on the number of oscillator modes N and Ñ excited in the two directi... | {
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Determinant as a fermionic path integral I understand that the determinant of a matrix can be written in terms of a fermionic path integral. The expression is:
$$Z = \int D\bar{\psi}D\psi e^{-\iint d^4x' d^4x \bar{\psi}(x')B(x',x)\psi(x)}\tag{1}$$
The proof proceeds by rewriting the complex Grassmann fields in terms of... | there is a quick and dirty way of proving
$$\mathcal{D}\psi\mathcal{D}\bar{\psi} = \prod_n dc_nd\bar{c}{}_n,$$
although i admit that the method used is still subject of research.
First, we have to see how the integral $\mathcal{D}\psi$ is defined. You can find yourself that,
$$\mathcal{D}\psi = \prod_x d\psi(x)$$
so,... | {
"language": "en",
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Is an electron attracted to one of the magnetic poles ...? I noted the question above had been posted. And I wanted to comment, but nay, it was locked out. However, what of the old 'CRT' tubes, in which magnetic fields are used to steer the electron stream ? Now I know the 'Electron's' do not get attracted, or repul... | The electron has an intrinsic magnetic dipole moment $\mu$ related to its spin. Therefore,in addition to the Lorentz force, it should also experience a net magnetic force in the gradient of a magnetic field and move in or against its direction depending on its spin orientation.Therefore, an electron should indeed be at... | {
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Calculating height of a ball formula based on bounce I'm trying to figure out a formula for the new height of a ball, up until it stops bouncing.
The time iteration between each could be for example one second; and gravity of course would be 9.8
I've tried doing research at different websites such as physics @ illinois... | Excluding drag the equation for the height at time $t$ is
\begin{equation}h(t) = h_0 - \frac{1}{2}g(t-t_0)^2\end{equation}
This is zero (ie at the ground) when $t = \pm\sqrt{\frac{2h_0}{g}}+t_0$. In this case, $h_0$ is the height from which it is dropped, and $t_0$ is the time when it is dropped. So assume $h_0 = h$ is... | {
"language": "en",
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Can an object *immediately* start moving at a high velocity? What I mean is, suppose a ball is fired from a cannon. Suppose the ball is moving at 100 m/s in the first second. Would the ball have started from 1m/s to 2m/s and gradually arrived at 100m/s? And is the change so fast that we are not able to conceive it? Or ... | Nothing propagates instantly
For starters, any real object has a non-zero size. If you apply force to one side of a cannonball, it will start moving before the other side of the cannonball can be affected by that force. The time will be very small ("so fast that we are not able to conceive it") but nonzero. The cannonb... | {
"language": "en",
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Does spin state matters during interaction? I'm asking whether the interaction between a pair of spin-up or spin-down electrons be any different from the interaction between a pair of electrons that comprises of opposite spin state? I think since the dipole moment is a physical property then I can assume spin-up and sp... | I guess that the question is about the electromagnetic interaction. For simplicity, forget the magnetic part and consider only the electrostatic interaction. The electrostatic potential energy
$$V(\vec r_1,\vec r_2)={e^2\over 4\pi\varepsilon_0||\vec r_1-\vec r_2||}$$
depends only on the position of the electrons an... | {
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Torque of the contact forces about the centre of mass A person leans in the opposite direction when he or she lifts a heavy load in one hand.
I read a reason for the same in a book.
According to the book, if a body is placed on a horizontal surface, the torque of the contact forces about the centre of mass should be ze... | The person does not have to lean. When carrying a heavy load you should keep the load close to the vertical line through your centre of mass (CM). For stability, the combined CM (you plus load) must be between your feet. For heavy loads (eg a suitcase) you may need to lean slightly to achieve this, even when carrying c... | {
"language": "en",
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Finding intensity/noise measurement of hysteresis loop I'm hoping I could get some help from the experimentalists on some data analysis.
I have a number of hysteresis loops taken at different angles around extinction of a polarizer on a photodiode. I want to find the loop (and by proxy the angle) with the optimal sign... | You can use the symmetry properties of hysteresis loops to separate half of the noise from the signal. Let's say your signal is $U$, which is proportional to the magnetization, and you apply a field $H$. Even in the presence of exchange bias there is a point $(H_0,U_0)$ with respect to which the signal is antisymmetric... | {
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Does a trumpet operate using an open air column or a closed air column Just as the title states. I could not find a coherent answer online.
Many thanks in advance
| The issue is slightly complicated, due to the ambiguity of the terms "open pipe" vs "closed pipe" used to classify wind instruments.
Some authors use it to refer to the boundary conditions on the ends of the instrument. If the pressure of the standing waves in a pipe must be continuous with the outside pressure on bot... | {
"language": "en",
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How to derive the formula for angular velocity in three dimensions? The formula for the velocity of a point $\vec {r}$ with angular velocity $\vec{\omega}$ is given by $\vec{v}=\vec{\omega} \times \vec{r}$.
But, how can we derive the formula $\vec{\omega}=\frac{\vec{r} \times \vec{v}}{|\vec{r}|^2}$ from the above formu... | Use the identity (see this)
$$
{\bf v} = \left({\bf v} \bullet \hat{\bf r}\right) \hat{\bf r} + \left(\hat{\bf r} \times {\bf v}\right) \times \hat{\bf r}
$$
and the fact that ${\bf v} \bullet \hat{\bf r} = \left(\omega \times {\bf r}\right) \bullet \hat{\bf r} = 0$.
| {
"language": "en",
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Why is nuclear waste more dangerous than the original nuclear fuel? I know the spent fuel is still radioactive. But it has to be more stable than what was put in and thus safer than the uranium that we started with. That is to say, is storage of the waste such a big deal? If I mine the uranium, use it, and then bury th... |
But it has to be more stable
That's where you're wrong. Most of the decay products are much more radioactive than the $\rm U^{235}$ that was used in the reactor. Uranium is not very dangerous at all. I have held a uranium rod in my hand. Admittedly it was a) coated in nickel and b) $\rm U^{238}$ which is less radioac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/292958",
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Why is silver the best conductor of electricity? I've been wondering why silver is the best conductor of electricity for a while now, and I've observed that in Group 11 transition metals where silver is located, copper and gold too are also one the best conductors of electricity (Cu, Ag, Au are all in Group 11). I beli... | Electron-electron scattering is lower in silver. Conduction in the coinage metals is in the $sp$-band that are wide and quite free-electron-like. But there is scattering with the $d$-electrons. This is least important in silver where the $4d$-electrons are about 4 eV away from the Fermi-level (which is also why silver ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/293019",
"timestamp": "2023-03-29T00:00:00",
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Shape of water in rotating bucket I need to show that the surface of water in a bucket rotating with constant angular velocity will have parabolic shape. I'm quite confused by this problem, but here's what I did:
$$\vec{F}_{cf} + \vec{F}_{grav} = -\vec{\nabla} U = m(\vec{\Omega}\times\vec{r})-mg\hat{z}$$ where $F_{cf}$... | I'm pretty late to the question but I think I know a simpler way. You can solve this really easily with conservation of energy, the kinetic energy of a circle of water at a constant radius is $\frac{m r^2 \Omega^2}{2}$, in a idealised system the energy has nowhere else to go but increasing the waters gravitational pote... | {
"language": "en",
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Path of light rays in uniform velocity elevator I have been told that light rays seen from inside an accelerated elevator will seen as following a curved path, parabola. Like the image below. But what happens when a pulse of light entered into a non accelerating but uniformly going upward. It seemed to me that like the... | Your picture is used to help visualize a thought experiment where the speed could be constant or accelerating depending on the statement. In reality you would only see a light spot on the right wall. If the elevator was moving at normal speeds, the spot would be directly across from the opening whether moving at consta... | {
"language": "en",
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Mass falling onto a spring from an inclined plane I was studying for my AP Physics test when I came across the following problem, which seemed to confuse me:
The ramp is frictionless, and the spring is initially at it's relaxed length, and the angle is $\theta = 45^{\circ}$.
I worked through this by considering the po... | The motion of the box along the slope is dictated by two forces which act parallel to the slope.
The component of the weight of the box down the slope which acts all the time and the force up the slope due to the spring which acts only when the box is in contact with the spring.
As long as there is a net force down t... | {
"language": "en",
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What is the role of pillars in bridges?
As I can see in the picture, there are so many pillars which are holding the bridge. This picture gave a question to me that what are these pillars doing below the bridge?? An appripriate answer could be "these are providing support to bridge".
I tried to get the answer as foll... | The number of the pillars does not depend by the load that each one of them can carry.
Mainly the number of the pillars is selected in order to reduce the distance between them and so to minimize the moments and so the stresses produced and act on the beams that holds the bridge's deck, as very nicely @valerio92 answer... | {
"language": "en",
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Hermitian properties of the gamma matrices The gamma matrices $\gamma^{\mu}$ are defined by
$$\{\gamma^{\mu},\gamma^{\nu}\}=2g^{\mu\nu}.$$
There exist representations of the gamma matrices such as the Dirac basis and the Weyl basis.
Is it possible to prove the relation
$$(\gamma^{\mu})^{\dagger}\gamma^{0}=\gamma^{0}\... | Not exactly, one can choose gamma-matrices that satisfy the anti-commutation conditions, but do not satisfy the hermiticity conditions.
EDIT: (11/19/2016) However, one can argue that the hermiticity condition for gamma-matrices can be derived from hermiticity of the Dirac Hamiltonian (https://arxiv.org/pdf/physics/0703... | {
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Proton - neutron fusion? In reviewing some problems in an elementary book, I ran across a reference to the reaction $p+n\rightarrow d$ + "energy".
Is that possible? I don't see any reason why not, but I don't find any mention of this reaction at all using Google. It seems to me that the "energy" would have to be a co... | Small mistake in my answer
"This means that 1,4e-6 grams of uranium, 0,05e-6 grams of beryllium and 0.0059e-6 grams of hydrogen"
And i would add, that this cold nuclear fusion induced by radioactive decay will not result in a nuclear catastrophe. It is not a self-reinforcing process. In nuclear power, the more nuclei t... | {
"language": "en",
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How does an object undergoing circular motion increase its tangential velocity? I completely understand the concepts behind uniform circular motion. But let's say you are spinning a ball connected by a string to a motor in a horizontal circle. When increasing the angular velocity of the spinning motor, I can't see how ... | There must be tangential acceleration, from a component of the force parallel to the velocity.
Note that if your center-pointing force is different from the magic value $F_\text{centripetal} = mv^2/r$ for uniform circular motion, the radius of your circular motion will change, and the tangential velocity will change as... | {
"language": "en",
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Wave nature of matter in bonds We say that electrons are probability waves. Then if two or more elements form bonds by overlapping of orbitals then what happens to the wave function of the electrons? Is it possible that during bonding, these electrons still behave as waves and interfere?
|
Is it possible that during bonding, these electrons still behave as waves and interfere?
Of course. This has been confirmed experimentally.
The unequivocal experimental proof of the wave (frequency) nature of matter is the electron image recorded in 2007. This image was recorded by a team of Swedish scientists from t... | {
"language": "en",
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Exact solution to electron-electron scattering? One of the first results seen in elementary quantum mechanics is the closed form solution to the bound states of the hydrogen atom. In the usual approach, scattering theory is placed on the opposite side of spectrum; exclusively though of as a perturbative process. I am i... | To solve this problem, it is better to use the relativistic equation M2.
$$\Delta \Psi -\frac{1}{\hbar^{2}}\left [ \frac{m^{4}c^{6}}{\left ( E-U\left ( \overrightarrow{r}\right ) \right )^{2}}-m^{2}c^{2} \right ]\Psi =0$$
The problem is analogous to the hydrogen atom. It is necessary in the equation for the hydrogen a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/294109",
"timestamp": "2023-03-29T00:00:00",
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Effect of Change of Potential Difference applied to an X-Ray tube I am a high school student, so I know only the basics of X-Rays. I simply know about continuous X-rays, cutoff wavelength and threshold wavelength.
Now if I increase the potential applied to the X-ray tube, I am certain that the minimum wavelength of emi... | For a typical x-ray tube used in medical imaging, the radiation output (as measured in mGy/mAs) changes roughly with the square of the ratio of the ${kV_p}$
$$
y_1/y_2 = ({kV_p}_1/{kV_p}_2)^2
$$
where $y_n$ is the radiation output in mGy/mAs at ${kV_p}_n$
So if you measure the output of an imaging tube at 70 kVp and th... | {
"language": "en",
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Strange quark decay into two down quarks and an anti-down quark I saw that a $\Sigma^+$ can decay into $n+\pi^+$, which means that the $s$-quark must decay into $dd\bar{d}$. However, is there a Feynman diagram to represent this? I cannot find one for either the $\Sigma^+$ decay or the $s$-quark decay. I have only just ... | One possibility for this decay is as follows. Note that the initial quark content is $uus$ while the final quark content is $udd+u\bar{d}$.
The $s$-quark can emit a $W^-$ and so turn into a $u$-quark, and this $W^-$ can then be absorbed by one of the initial $u$ quarks turning it into a $d$-quark. We then have quark c... | {
"language": "en",
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Fetter & Walecka's derivation of second-quantised kinetic term in many-particle systems On page 9 of Quantum theory of many-particle systems by Alexander L. Fetter and John Dirk Walecka, during the derivation of the second-quantised kinetic term, there is an equality equation below:
\begin{align}
\sum_{k=1}^{N} \sum_{... | The coefficient $C(E_1, E_2, \dots, E_k, \dots, E_N, t)$ corresponds to the configuration:
$1^{st}$ particle in state $E_1$, $2^{nd}$ particle in state $E_2$, $\dots,$ $k^{th}$ particle in state $E_k$, $\dots,$ $N^{th}$ particle in state $E_N$.
Say, this corresponds to the following occupation numbers:
$n_1$ particles ... | {
"language": "en",
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Quantizing a complex Klein-Gordon Field: Why are there two types of excitations? In most references I've seen (see, for example, Peskin and Schroeder problem 2.2, or section 2.5 here), one constructs the field operator $\hat{\phi}$ for the complex Klein-Gordon field as follows:
First, you take the Lagrangian density fo... | There is a conceptually simple (but fiddly) way of relating this expansion to the usual Fourier expansion. TL;DR: Requiring $\phi$ to satisfy the Klein-Gordon equation divides the nonzero Fourier components into two classes, corresponding to particles and antiparticles.
For a general complex scalar field defined on spa... | {
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"Unaccounted for" vertices in certain Feynman diagrams? I'm looking to understand where certain "unexplained" vertices in some Feynman diagrams come from, in a physical sense. For example, in the top figure (Aaij et al. 2015), in diagram (b), there is an "unaccounted for" $u\bar{u}$ pair that seems to come from nowhere... | Once you have quarks in a Feynman diagram, the strong interaction enters, and note, the strong, it means Quantum Chronodynamics . It means from that point on the usual perturbative expansion with the nice fixed rules for calculating the total integral with electromagnetic and weak interactions can only be used with app... | {
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Can we tell that we're in a flat space time? Or just in reference to other objects? If you are sitting in space, far from any planet or large gravitational object, can you be sure that you're in a flat spacetime? Is it possible that some very distant object is heavily warping spacetime, but because it's so far away, i... | Not an expert, but if think we are comfortable with 3d space. It is easier to visualize flat space time. Please correct my notion if at all possible and not a violation of the rules. I am just here to learn
| {
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How are we stardust? I am a layperson and certainly not a physics student, though I'm sure that is palpably obvious. I have a strong appreciation for people like Carl Sagan, Lawrence Krauss, and Sean Carrol.
I'm often challenged by creationists over the claim that we are all "starstuff" or "stardust". I can understan... | Well, people are made out of a bunch of elements, none of which are created on Earth: they all got here from somewhere else.
There are two sources for elements:
*
*Hydrogen, some Helium, some isotopes of them and I think some Lithium were made by 'primordial nucleosynthesis' within a few minutes after the big bang;
... | {
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What is the definition of "Complexity" in physics? Is it quantifiable? I don't know much about the discipline of "Complex systems studies" but I know in the field of "Statistical mechanics" there is much talk about the "Complexity of the system". Like "...the state of this system is more complex..." or "...as we see th... | As others have said, complexity is still a notion that does not have one and only one definition. However, you did ask for a quantitative definition, so one example of complexity of a quantum field (or even a quantum lattice system) I've seen in the context of quantum gravity is:
"the minimum number of quantum gates ne... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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One-loop Higgs mass in the Standard Model I cannot reproduce the one-loop Higgs mass expression with a cutoff regularization.
The standard result found in literature is (which leads to the so-called Veltman condition):
\begin{equation}\delta m_h^2 = \frac{3\Lambda^2}{16\pi^2 v^2}(m_h^2+m_Z^2+2m_W^2-4m_t^2)\end{equation... | One should actually (obviously..) add the Goldstone contributions. The Feynman rules are (consistent with my previous conventions):
\begin{equation}
hh\phi_+\phi_-: -2i\lambda , \ \ hh\phi_0 \phi_0: -2i\lambda
\end{equation}
Since the diagram involving the neutral Goldstone has a symmetry factor of 1/2, the total contr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/296139",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Rubbing of a fur - can the electrons in a fur be ever ran out? As we all know, if we rub ebonite rod with a fur, the rod becomes negatively charged(electrons get passed from fur to rod). But what happens if we will do that many times with the same fur but each time with another ebonite rub? I mean, is it possible that ... | The ebonite rod is a good conductor, so electrons will be floating on every part of it's orbit having sufficient electrons on it's highest energy level. The fur is just like the carbon atom that is a solid but a non metal, chemically the carbon atom has 2 inner electrons and 4 valence outer electrons which it really do... | {
"language": "en",
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Why is bench pressing your bodyweight harder than doing a pushup? Why does bench pressing your own bodyweight feel so much harder than doing a push-up?
I have my own theories about the weight being distributed over multiple points (like in a push-up) but would just like to get a definite answer.
| Consider leverage. Assume as in @Michael's comment that the centre of mass is somewhere near the middle. Further assume that the toes are fixed to the floor. If the torso and legs are rigid the centre of mass does not lift as far as the shoulders (at which the pressing force is exerted), so you've got leverage in you... | {
"language": "en",
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spacelike and timelike event or interval? Just a short question:
Is it valid to say that some event is space/time-like or is this term reserved for the distance between two events (the space-time interval) and four vectors?
| The terms spacelike, timelike, and lightlike refer to space time intervals only. They are used when discussing the sign of the distance between two different events. Mathematically, this comes from the sign of the metric tensor acting on two different four-vectors, $g(\mathbf{x},\mathbf{y}) = g_{ij}x^i y^j$. The metric... | {
"language": "en",
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Dark matter annihilation cross section What is the meaning of upper limit of annihilation cross section? Sometimes I have seen that $\langle\sigma v\rangle = 3.0 \times 10^{-26}\,{\rm cm}^{3}\,{\rm s}^{-1}$ or $2.0 \times 10^{-25}\,{\rm cm}^{3}\,{\rm s}^{-1}$.
Which is the better value and why?
| By "which is better" I assume that you mean "which is most constraining".
First, $\langle\sigma v\rangle$ refers to the cross section per unit velocity. This is important because it is conjectured that dark matter scattering with a velocity independent cross section has several problems that it seems to be possible to ... | {
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Symmetry factor via Wick's theorem Consider the lagrangian of the real scalar field given by $$\mathcal L = \frac{1}{2} (\partial \phi)^2 - \frac{1}{2} m^2 \phi^2 - \frac{\lambda}{4!} \phi^4$$
Disregarding snail contributions, the only diagram contributing to $ \langle p_4 p_3 | T (\phi(y)^4 \phi(x)^4) | p_1 p_2 \rangl... | The diagram of interest (the $s$ channel dinosaur) is generated at second order in the Dyson expansion (alongside the $t$ and $u$ channel dinosaur diagrams and the snail $1 \text{PI}$ reducible diagrams) within the correlator $\langle p_4 p_3 | T( \mathcal L(y) \mathcal L(x)) | p_1 p_2 \rangle$. Using Wick's theorem,... | {
"language": "en",
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Lorentz force (equation) i have a question
When we consider the motion of a particle, then write
ordinary Lorentz force
Why do not we consider a charged particle's own field, because
it is known, is always much larger than the external field and the even formation
It becomes infinite at the point where the particle is... | You can't consider particle's own field because its module will be infinite and it is impossible to state in which direction it is directed. For that field, expressed in spherical coordinates for example, the point r=0 is a singular point and even the force will be infinite and without a definite direction.
| {
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Why faraday rotation is not effective in case of circular polariation? As in case of linear polarization the plane of polarization gets rotated. Why it's not happening with circular polarization?
| Circular polarization is rotated just as much as linear polarization.
The catch is that the circularly polarized wave is itself “rotating” about the same axis, so the only effect is to change the phase of the wave. It's like taking a spinning wheel and rotating it by 90° — it's still spinning, and you need some notion ... | {
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Human body calories consumption estimate based on physics approximation I was looking for references online about equations that relates human kinetics and calories consumption, and it seems there are no many engineers interested in weight lifting (go figure...). I think under the right assumptions it cannot be to comp... | The CN Tower in Toronto holds annual stair climbs for charity.
The record for climbing the $1776$ stairs is a little under $8$ minutes.
Data for physics calculations is surprisingly hard to find, but assuming an $80$ kg climber going up $1776$ steps, each $0.18$ m high in $480$ seconds, we come out with a power output ... | {
"language": "en",
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Sensation of atmospheric pressure Pressure is force divided by area, and force is mass times acceleration.
Now, the newton [N] is the force needed to accelerate 1 kg by 1 m/s, and the kilogram-force [kgf] is the force needed to accelerate 1 kg by g m/s, where g is the standard gravity.
The standard atmospheric pressure... | Missing from the picture is that all macroscopic bodies in fluid or solid state do not like being compressed. These macroscopic bodies can be thought of as made up of molecules or atoms which below some distances will always start to repel each other. This causes them to exert a force against being compressed, i.e., br... | {
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Can atomic orbitals of an isolated atom rotate relative to the nucleus? I am a beginner at orbitals. It seemed interesting to me while studying p orbitals that the texts don't suggest that the orbitals are rigid relative to the nucleus.
But I thought mathematically these rotations would not be possible to know because ... | Atomic p orbitals have angular momentum. The angular part of the wavefunction is described by the spherical harmonics $Y_{\ell,m}$ where $\ell=1$ and $m=-1,0,1$. When one multiplies this with the time-dependent part $e^{iEt/\hbar}$, the result is a rotating phase.
The $p_x$ and $p_y$ orbitals of chemical compounds are ... | {
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Why should the perturbation be small and in what sense? In time-independent perturbation theory, one writes $$\hat{H}=\hat{H}_0+\lambda \hat{H}^\prime$$ where $\lambda H^\prime$ is a "small" perturbation.
*
*Why should the perturbation be small for perturbation theory to work?
*Both $\hat{H}_0$ and $\hat{H}^\prime... | When one assumes the solution to the perturbed system is of the form
$$|\psi\rangle=\sum_{n=0}^\infty \lambda^n|\psi_n\rangle$$
where $|\psi_0\rangle$ is an eigenstate of $H_0$, one hopes that the expression is meaningful and that only the first few terms are significant which is to say that $|\psi\rangle$ is in some s... | {
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Car Power/Torque to Weight -- non linear? ( Hello, my first question ... )
Assume two cars, each with exactly the same body, but one a scaled down version of the other (hence, aerodynamics approach equality):
"junior car" - has an engine that delivers 200 ft-lbs of torque and weighs 3000 pounds
"base car" - has an eng... | In the real world, at constant speeds, coefficient of drag matters more than the weight of the vehicle, at least within the normal range of vehicle weights, else a vehicle weighing 2500 lbs. would get twice the gas mileage of one weighing 5000 lbs., and this isn't true. Loss from drivetrain friction and other areas wil... | {
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How to vary the current using batteries? I am making a door bell as a school assignment. It works by having a solenoid produce a magnetic field which attracts a pice of iron attached on a conductor. when the iron is attracted towards the solenoid the current is broken so it falls back, inducing the magnetic field again... | You can use potentiometer in series with the battery to vary the current.
| {
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Regarding Energy and Momentum in QM I've been trying to learn Quantum Mechanics for a few months now, and there's a pretty fundamental thing I never quite understand: What is energy and momentum in quantum mechanics?
I've been following MIT's QM course, and the instructor talked about the energy and momentum of light/w... | This is actually more of a comment than an answer but I don't have enough reputation to post a comment yet. Anywho, it's important to distinguish between classical dynamical definitions of dynamical properties and quantum mechanical definitions. First of all the definition you gave for momentum is that of linear moment... | {
"language": "en",
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use of static vs kinetic friction when orthogonal forces are applied Suppose I have a mass sitting on a surface with friction. Now I start pushing on the mass in one direction (call this direction the x direction). To get this mass accelerating, I have to push the mass with a force greater than $\mu_{s}mg$. Assuming th... | There doesn't seem to be a clear and obvious answer from first principles, but if the object is in motion, kinetic friction should be applied. It might be useful to consider the microscopic model - that the static form of friction is applied when there are molecular attractions between the object and the floor.
Howeve... | {
"language": "en",
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What does it mean to say that two optical systems are equivalent to each other? I am studying about Michelson interferometer from Pedrotti and they transformed a Michelson interferometer into an equivalent system consisting of light rays originating from two virtual images of the sources.
When can such conversions int... | The notion of "equivalent" in physics generally has many different uses and associated definitions. It is often a question of input/output. Two systems would be said to be equivalent if they have the same output for the same input. This is how the concept is used in circuit theory, for example.
In optics it is easy to... | {
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Inconsistency in Vertex Factor in Scalar QCD I'm trying to find the vertex factor for the scalar-scalar-gluon-gluon interaction. The diagram is
This corresponds to the term $g^2 \phi^{\dagger}A_{\mu}^a\left(T^aT^b\right)_{ij}A_{\mu}^b\phi_j$ in the Lagrangian density. Naively, I expect the factor to be
$$
-ig^2\left(... | Since $A^a_\mu A^b_\nu g^{\mu\nu}$ is symmetric in $a$ and $b$, only symmetric part of $T_aT_b$, i.e. $\frac{1}{2}(T_aT_b + T_bT_a)$ should contribute to the vertex. Also, since the term is quadratic in gauge potential, you get a combinatoric factor of 2.
You can also compute functional derivative of the action, $\frac... | {
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Why do electrons move from amber to wool during static electricity charging? We know our word for electron comes from the Greek word for amber, since the ancient Greeks experimented with static electricity by rubbing amber on wool.
We know that a static charge is built up by the electrons in the amber moving to the woo... | Electrons, like gas molecules, will diffuse. So, a material with
a high concentration of surface electrons will lose some to any material
nearby that has a lower concentration.
The diffusion halts when buildup of
charge creates sufficient voltage drop to reach equilibrium between
ohmic (field-driven) current and d... | {
"language": "en",
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Orthogonality of the particle in a box model I found that for the particle in the box model, since the solutions represent the wave functions $\psi_n=A\sin{\frac{n\pi x}{L}}$ and $\psi_{n+k}=A\sin{\frac{\left(n+k\right)\pi x}{L}}$, hence the integral shown below $$\int_{-\infty}^{+\infty}A^2\sin{\frac{n\pi x}{L}}\sin{\... | To calculate electronic transition you need to have some time dependent potential then at least to first order the probability of transition between eigenstates is $|\int dt <\psi_k|V(t)|\psi_{k'}>e^{iE_k -E_{k'}t}|^2$ this is very different from $\int \psi_k^*\psi_{k'}dx$.
| {
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Do unstable equilibria lead to a violation of Liouville's theorem? Liouville's theorem says that the flow in phase space is like an incompressible fluid. One implication of this is that if two systems start at different points in phase space their phase-space trajectories cannot merge. But for a potential with an unsta... | A few comments on the question you are asking:
*
*The Liouville equation describes not a single particle, but an ensemble of states that evolve according to the laws of mechanics. The Liouville equation says that the entropy of the system stays constant at all times, which is to say that this equation describes isent... | {
"language": "en",
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Is the universe non-linear? First of all, I've read this other question Is the universe linear? If so, why? and I'm aiming at a different kind of answer.
Theories like General Relativity or QFT, which are believed to be quite fundamental, are strongly non-linear. However, in the end, both theories must be just low ener... | The obvious example is hydrodynamics.
The interactions in a fluid all originate from the interactions between atoms and molecules that are described by quantum mechnics, and QM is as far as we know linear. However the Navier-Stokes equations are (scarily) non-linear and produce all sorts of weird behaviour.
It's an int... | {
"language": "en",
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If the ground's normal force cancels gravity, how does a person keep rotating with the Earth? When I am on earth, the weight of my body is countered by the reaction of the ground. So, there is no net force acting on me.
But I am spinning with earth. But if there is no centripetal force then why am I spinning? And the e... | It is easier to consider you standing on the Equator.
Assume that the gravitational field strength at the Equator is $g$. This would be the acceleration of free fall at the Equator with no air resistance if the Earth was not spinning.
If the reaction of the Earth is $N$ then assuming down is positive and using N2L, ... | {
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Perturbation Theory for a ring in an Electric Field
A particle of mass $m$ move on a circular ring of radius $a$. The only variable of the system is the azimuthal angle, which we will call $\varphi$. The state of the system is described by a wave function $\psi(\varphi)$ that must be periodic,
$\psi(\varphi + 2\pi)... | This is a simple exercise in properly applying time-independent perturbation theory to the eigenvalue equation
$$
\frac{d^2\psi_n}{d\varphi^2} +\frac{2E_n ma^2}{\hbar^2} \psi_n(\varphi) =-\epsilon\frac{2 m a^3 q}{\hbar^2} (\cos \varphi ) \psi_n(\varphi).
$$
All you have to do is substitute 1st order approximations to... | {
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How varying length of loop affects induced emf
*
*What is happening when delta x of this loop increases? Give me a theoretical idea and how is emf increasing? I know that flux is changing but I think that the rails on which conductor rod is moving is not contributing that much to induced emf
*What is induced emf a... | The induced emf blv is called motional emf. thus we are able to produce induced emf by moving a conductor instead of varying magnetic field that is, by changing the magnetic flux enclosed by the circuit.
it is possible to explain the motional emf expression by invokin the lorentz force actin on the free charge carries... | {
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Can we measure the exact value of the Fermi Level in semiconductor? Or is it always measured relatively to the Conduction/Valence Band energy level? From the books that I read, the discussion and the formulas related to the Fermi Level are always relative to the energy level of Conduction/Valence Band, or Fermi Level i... | Fermi level characterizes the filling of the energy levels, e.g., the concentration of electrons is given by
$$n = \int dE D(E)\frac{1}{1 + e^{-\beta(E-\mu)}},$$
where $D(E)$ is the density-of-states and $\mu$ is the Fermi level. As you see from this equation, shifting the Fermi level will make the occupations of all t... | {
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Is there a standard, coded table of physical units? I am a programmer in the medical/biosignals area, and I want to represent physical units in a database table. Ideally, I would like to have a code that uniquely identifies a given physical quantity.
As an example, ISO defines strings to represent languages, such as "e... | That would be the International System of Units by the Bureau International des Poids et Mesures, as seen here.
| {
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Concept of negative mass in solving problems I have searched a lot on the internet regarding negative mass. And in the meantime, I came across this question.
The question states:
Consider two spherical empty regions (C1 and C2) in an otherwise
uniform and essentially infinite intergalactic gas cloud of density
$\r... | As my previous answer was not understood and the wrong one was chosen as correct, I'll try to present a clearer answer.
The integrals in forky's answer are fine, but the bubbles repel!
Imagine that in stead of completely empty bubbles you have balls of styrofoam, with $\rho'= (1/10000)\rho$, or any other density, as sm... | {
"language": "en",
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Thermodynamics: What is the entropy change of an electrical resistance taken as system? Consider a system consisting only of an electrical resistor through which a constant current is flowing. Simultaneously, it is rejecting heat such that its temperature is constant throughout the process. With this much of informatio... | (I am assuming that temperature is constant in the resistor. If you want, think about it as a quasi-1D object)
If we assume the system to be stationary, then all the thermodynamic parameters in the resistance will be constant. Therefore, since entropy is a state function, the entropy change in any given time interval w... | {
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What is the upper limit on gravitational time dilation? First, please forgive me: I'm not versed enough in mathematics to even approach working this out for myself.
Now, the question: how much "slower" could time pass for a person around a supermassive black hole (such as S5 0014+81)? Would this increase indefinitely w... | The time dilation becomes infinite at the event horizon. That is, an observer watching from far away would see the rate that a clock runs slow to zero as the clock approaches the event horizon. This is not directly related to the mass of the black hole. The mass determines where the event horizon is, but it's the dista... | {
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How to choose origin in rotational problems to calculate torque? We know that $\text{Torque} = r \times F$ and $r$ is the position vector. But the position vector depends on the choice of the coordinate system and in turn on the choice of origin. So, where should we take the origin?
Also, do torque, angular velocity an... | It says the torque about the axis is the same irrespective of where you take the origin. Because the moment arm will always be the same.
Another way view it is $rsin\theta$. The more away you take the origin, the greater the $r$ and hence smaller the $\theta$. However you take it the $risn\theta$ will result same reg... | {
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Reversible process in General Physics Usually, for christmas , I have lunch with my family and a couple of other families. Most of the people got a Phd on chemistry, or molecular biology, and are high academics (they're in they 50-70). On the other side, i'm the only one who studies physics there, and 2 years ago, in t... | Never-the-less, there is the law of entropy, which chemical re-actions follow, which has an irreversibility of direction to it. probably that is behind the comment. A chemist might not have picked up how that law applies in other areas (or maybe I should say at other scales/levels) if they have specialised, I suppose.
| {
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Solution of Dirac equation-Positive and Negative energy For particles defined with positive energy, we use $$\phi=
\begin{pmatrix}
1 \\
0 \\
\end{pmatrix}
$$ or $$
\begin{pmatrix}
0 \\
1 \\
\end{pmatrix}
$$
while for particles defined with negative energy, we use this ... | I don't understand is why is the 4-spinor split into two components, one for the positive energy and the other for the negative energy. It did not say anything here.
You are misinterpreting the large and small components of the Dirac 4-spinor for the positive and negative energy solutions (a common mistake). Each Dira... | {
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Why can't the Klein-Gordon equation explain the hydrogen atom but the Dirac equation does? Why can't the Klein-Gordon equation with a Couloumb potential describe the hydrogen atom?
Why can the first order Dirac equation explain it?
What are the failures?
| The application of the Klein-Gordon equation for the hydrogen atom leads to logical contradictions.
Allowance for relativism in the Klein-Gordon equation should lead to more accurate solutions for the hydrogen atom compared with the Schrodinger equation. However, on the contrary, solutions became increasingly worse wit... | {
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"timestamp": "2023-03-29T00:00:00",
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After measuring momentum, it seems like the particle's position could be literally anywhere? Once measuring momentum, the wavefunction "collapses" into something that looks like this
If you were to then measure the position, couldn't it be literally anywhere? What am I missing? Is it even possible to measure momentum ... | Each observable corresponds to a mathematical operator in Hilbert Space. There are pairs of observables which are called conjugate variables, these cannot both be known accurately at the same time. The measurement of one immediately makes the measurment of the other impossible. Position and momentum are such a pair. It... | {
"language": "en",
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Deviation in refraction related question Why in refraction incident ray remain undeviated when incident angle is 0°? Please give the molecular interpretation.
| Refraction is explained by the wave nature of light. What happens is that the incident light wave wavefront is slowed down by the optically denser material (glass slab, lens etc.). If the angle of incidence is more than 0 degrees, the parts of wavefront are slowed down as soon as they interact with the denser material ... | {
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Thermodynamics Question: Does measuring the temperature of an object change its temperature? Suppose that I want to measure the temperature of an object, such as a pot of hot water. When I stick the thermometer into the pot, I know that the temperature measured by the thermometer is its own temperature when it reaches ... | Yes the thermometer affects the temperature of the body that you are measuring. The change in temperature can be found doing some simple calorimetry (so you have to know the temperature, mass, and specific heat of the thermometer before you use it). And the change in temperature might be significant (but typically isn... | {
"language": "en",
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Projectile Motion - $V_f = V_i + at$ - Divide by zero If I have a projectile that is thrown at some horizontal velocity at some height, and horizontal acceleration is zero, can't I use the equation $v = v_0 + at$? The problem is when I use it since $v$ will equal $v_0$ (acceleration is zero so velocity won't change) I ... | Resolve the vertical component until it h=0, it hits the ground. Use this time t in the horizontal $s=ut+(1/2)at^2$ where a is 0. Because horizontal acceleration is zero.
| {
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Why is the circumference of a circle drawn on a sphere less than the circumference of the circle of same radius drawn on a flat surface? Why is the circumference of a circle drawn on a sphere less than the circumference of the circle of same radius drawn on a flat surface? This is an extract from the book "The Elegant ... | I think the crucial ingredient to this is that the difference arises because one assumes that this is from the perspective of "sphere-people" who live confined to the surface of the sphere. They cannot see, hear or reach points interior or exterior to the sphere. The surface of the sphere is their whole world and exi... | {
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How does a small object move with constant velocity when drag force is equal to its weight? When drag force ($bV$) equals to object's weight (mg) then upward and downward force becomes equal. As a result the object comes to rest. If this is true, how is a body moving with constant velocity?
| When opposing forces are equal the object does come to arrest. Just try standing on a scale. As for a car traveling down the highway it matches the wind and road resistance with more throttle until an equilibrium is reached at whatever speed you desire.
| {
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Light clock with 1 m ticks A standard light clock has two mirrors, say one metre apart, and a light pulse. When the clock is stationary the light path is perpendicular. When moving, diagonal. The clock ticks over each time the light hits the mirrors. The light takes longer to travel the diagonal path, so the clock take... |
Is one metre the same in both frames? It has to be, it is the distance the mirrors are apart in both frames.
No, a one meter light path is most assuredly not the same in both frames. If the mirrors are 1 m apart then in one frame the pulse of light travels 1 m but in another frame the same pulse of light travels more... | {
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What are Hamilton's equations with respect to a nonstandard symplectic form? Hamilton's equations for a Hamiltonian $H(q,p)$ w.r.t. to a standard symplectic from $\omega = dq \wedge dp$ are $$\dot{q} = \partial H_{p}, \quad \dot{p} = - \partial H_{q}$$
How do Hamilton's equations write w.r.t. a nonstandard symplectic ... | A Hamiltonian $H:M\rightarrow \mathbb{R}$ defines a vector field $X_H$ through the equation
\begin{equation}
\omega(X_H,\cdot)=dH.
\end{equation}
For $\omega=F(q,p)dq\wedge dp$ and substituting the components $X_H=X_{Hq}\partial_q+X_{Hp}\partial_p$ we get
\begin{equation}
F(q,p)(X_{Hq}dp-X_{Hp}dq)=(\partial_qH)dq+... | {
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Apparent weight in circular motion Here's a diagram below. From my understanding, the apparent weight is the weight that you feel > which is the upward force on you > which is the normal force.
I can clearly see how you'd weigh more in the bottom of the circle, because the net force is directed up, and so that would me... | It would be helpful if the meaning of the vector symbols n & w can be defined. it looks like w is gravity, and N is centrifugal acceleration. In the case N will be smaller at the top as the v is lower.
F seems to be confusing, it seems to be labelled in two places as the overall resultant force, but it would be differe... | {
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Scattering, 4 point correlator, #distinct Feynman diagrams
In order to compute the scattering probability that two particles of type 1 (associated to $\phi_1(x)$) which come from the far past with the momenta $p_1$ and $p_2$, to scatter and evolve into two particles of type 2 (associated to $\phi_2(x)$) with the mom... | Without knowing the text you are referencing, it's possible that they are only considering amputated diagrams, since the third diagram is a self-energy correction to the 4-point contact diagram. If you consider amputated diagrams, you only look at the diagrams close to the interaction vertex, and you effectively discar... | {
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Why is the speed of light said to be constant when we know it slows down in a medium? If we ask someone what the speed of light is, they will say that it is constant and its value is $3\times 10^{8}\ \mathrm{m/s}$.
But if we recall refraction of light, we say that when the light travels from a rarer medium to a denser ... | Speed of light is a constant. That is $3\times10^8$ m/s.
Now the question is why it is thought to be a fundamental constant.
Let's say there is a ball moving with 3 m/s speed and you are moving towards ball with speed 2 m/s, what is the relative velocity of ball for you , that is 5 m/s.
Now apply same logic for ligh... | {
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Using Delta Dirac function as a mathematical tool in Green's functions So, I was studying green's functions and in general I understood that if I have an operator $\mathscr{O}$ that acts of a function $h_1(\vec{r})$ such that
$$\mathscr{O}h_1(\vec{r})=h_2(\vec{r})$$ Then all I need to do is to find the function, $g(\v... | *
*Calculate the Laplacian of $1/r$ using spherical coordinates, you get that it is zero where $r \neq 0$.
*Use Green's Theorem to calculate the volume integral of $\nabla^2(1/r)$ in a sphere (of arbitrary radius) about 0, the value of this integral is $-4\pi$ (regardless of the radius of the sphere chosen).
Since ... | {
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Why do we get tired after walking While we were studying pure rolling of bodies in the chapter rotation we were told that energy conservation holds if a body is purely rolling ( The point of contact between the rolling body and ground is stationary w.r.t. ground ). Considering a person to be system. Whenever the person... | You are, unfortunately, missing out on two crucial mechanisms of energy dissipation: kinetic friction in our joints (and other internal and external parts, like clothes) and the inefficiency of converting chemical energy into motion. As we walk, our muscles exert forces constantly in various directions; in order to do ... | {
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Would it be possible to use light to transfer physical object (nanoparticle) from one place to another? I know that light has momentum and it has been used to pick up nanoparticles. But I am thinking, is it possible for us make a pouch of light to carry a very small object from one place to another. The transfer should... | I do not understand what you mean by a "pouch" of light. However, yes it is possible to move very small objects using light.
Light can be used to manipulate micron-sized particles by a technique known as Optical Tweezers.
Light is refracted as it passes through a transparent or translucent object. Light carries moment... | {
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In deriving the heat transfer equation, why do we use heat capacity at constant pressure? I have seen many derivations of the heat transfer equation. It always has a form something like the following:
$$\rho C_{P} \frac{\partial T}{\partial t}-\nabla\cdot(k\nabla T)=\dot{q}_{V}$$
No matter how you write it, there is al... | In the derivations you are referring to, the fluid is assumed to be incompressible. in the limit of an incompressible fluid, the heat capacity and internal energy are functions only of temperature. So it doesn't matter whether you call it Cp or Cv or just C.
| {
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Magnetization currents (amperian currents): how to show that they are always zero in total from the definition? For magnetic field in matter the two following amperian current densities are defined:
*
*Surface currents: u.m. $[\frac{A}{m}]$
$$J_{A,s}= \bf{M} \times \hat{n}$$
*Volume currents: u.m. $[\frac{A}{m^2}... | If you're comfortable with delta functions etc., you can prove that the surface current formula is a special case of the volume current formula (the special case where M goes sharply to zero across a boundary). So we really only need the volume current case.
Kelvin-Stokes theorem says
$$\oint_\Gamma \mathbf{M}\, \cdot\... | {
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Getting thermal comfort by cooling just one point of body? Can I get thermal comfort by cooling or heating just one point of body like wrist or foot?
As far as I know, Wrist and foot are the most thermally sensitive points of body. I saw that wrapping a wet cloth in the wrist can give someone thermal comfort during sum... | yes, there are products such as wrist bracelets that use the fact that your blood vessels are close to the surface on the wrist.
Search for "wrist cooling device"
They seem to be active, using e.g. Peltier effect.
There was an article about a device that uses a closed water circuit and was at least tested for tennis pl... | {
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Phase Transitions and Bubble Nucleation The potential for a first order phase transition is shown below
The phase transition occurs from the spontaneous formation of bubbles. Inside the bubbles the field value is at the "true vacuum" and outside the bubble the field value is at the "false vacuum". In many texts, a se... | I think nucleation is only relevant to first order phase transitions. This is because only a first-order phase transition has an entropy curve $S(U)$ which leads to the possibility of metastable phases (e.g. supercooled vapour or superheated liquid).
| {
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Why does torque produce a force on the axis of rotation? If a door is rotated about its fixed axis in (outer) space, a force parallel to the door on the hinges will arise due to centripetal force on the centre of mass and conservation of momentum (Newton's third law).
But any torque on the door will create a force on ... | It is only due to the hinges that that when the door is pushed ,that it doesn't translate along the line of action of force applied and the hinges changes the velocity of the door and thus a force is necessary for that.This force is variable , changing its direction every instant
| {
"language": "en",
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Is there a difference between observation and entanglement? I have very basic knowledge about quantum mechanic. I started wondering if there is any difference theoretically between observation and entanglement between subject and object.
I.e. if we simplify an observer state to q-bit and initial state of second is $\al... | The observer you model here is Wigner's friend as seen by Wigner: he may have observed something, but for Wigner he is now in a superposed state.
You are right that entanglement is the proper relationship between a quantum system and an observer, when both are described as a larger quantum system, but upon measurement ... | {
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What did the big bang "look like"? I've been reading here for a while now and something I always see is people saying "the big bang happened everywhere" or "the center of the universe is where you are", explaning that the big bang didn't happen from a single point, but everywhere at once.
The problem is that I am unabl... | It probably is not possible for humans to get a physical picture of that time, because to do so would involve comparing it to something in the world around you today. But the Big Bang was almost certainly so completely different in it's "appearance", that we do not have words, past experiences or even intuition to help... | {
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Relationship between Coordinate Time and Proper Time While I was reading Ta-Pei Cheng's book on relativity, I was unable to derive the correct relationship between coordinate time $dt$ (the book defined it as the time measured by a clock located at $r=\infty$ from the source of gravity) and proper time $d\tau$ from the... | The answer provided by Rumplestillskin is correct
$$d\tau = \sqrt{1-\frac{r_g}{r}} dt$$
but it is only valid for the clock statically residing in the gravity at coordinate distance $r$ from the center. For moving clocks in the Schwarzschild coordinates, for example in radial free fall, the relation between the proper ... | {
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How is the isospin quantum number calculated? $$\Lambda^+_c$$ and $$\Sigma_c^+$$ are both made up of the same quarks, and have the same I_3, but have different isospin quantum numbers. How is the isospin quantum number determined? Also is the isospin quantum number indicated by the greek letter used?
| From Wikipedia (excluding the anti-quarks for now to keep it simple):
In the modern formulation, isospin (I) is defined as a vector quantity
in which up and down quarks have a value of $I = 1/2$, with the
3rd-component ($I_3$) being 1/2 for up quarks, and -1/2 for down
quarks, while all other quarks have $I=0$. ... | {
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Why don't humans burn up while parachuting, whereas rockets do on reentry? I guess it has something to do with their being both a high horizontal and a vertical velocity components during re-entry. But again, wouldn that mean there is a better reentry maneuver that the one in use?
| Re-entry velocity from LEO is $~7,800 \frac m s$, from lunar space it is as high as $~11,000 \frac m s$ [1].
Different books give the terminal velocity of a skydiver as about $56 \frac m s$ or $75 \frac m s$ [2, 3]. The exact value isn't material, but the fact that it is two powers of ten smaller then re-entry velocity... | {
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Where does all the heat go during winter? I do not understand where actually the heat in our surroundings go during the winter season. Is it radiated out into space? I know it cannot coz global warming would not be a issue then. It might get absorbed but where? I tried figuring it myself but couldn't please help.
|
Where does all the heat go during winter?
There is less energy coming from the sun in the form of electromagnetic radiation impinging on the land during winter.
Depending on the latitude, in regions where there is winter , the difference is large.
The closer to the equator the smaller the effect of "winter".
So it ... | {
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How force exerted by spring is always opposite to the direction of displacement in Hooke's law Suppose a spring lying on a horizontal table, displaced from its equilibrium length by an external agent. The external agent is removed, the spring will head back to its equilibrium length. Here, the direction of spring force... | Imagine a spring which has a force $\vec F_{\rm sy}$ applied on it by you and this produces an extension $\vec x$.
You then have $F_{\rm sy}=k\vec x$
However it is usual to be interested in the force the spring exerts on you $F_{\rm ys}$.
Using Newton's third law $\vec F_{\rm sy}=-\vec F_{\rm ys }$ so $\vec F_{\rm ys}=... | {
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Does folding a paper towel help dry your hands faster by creating interstitial forces? The question is based on a TEDx video, where the speaker claims that folding a paper towel before using it creates interstitial forces which help dry your hands faster.
The question:
Does this effect actually occur? If it does, then ... | The speaker actually claims it works by "interstitial suspension". I think he is referring to capillary action, which you are aware is involved here. He does not claim this method is faster, only that it is more environment-friendly. Shaking before wiping is a crucial factor.
Folding has 2 advantages : it reduces exces... | {
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Pauli matrix for triplet state? Question is, what would be the result of applying the operator $\hat A = [3I + \vec\sigma_1 . \vec\sigma_2]$ on the |singlet$\rangle$ and |triplet$\rangle$ states ($\vec\sigma_1$ acts on the 1st particle and $\vec\sigma_2$ acts on the second particle ONLY), ie, $$\hat A|singlet\rangle=?|... | As @rob asked you to, you are meant to simply write down
$$
\hat{B}\equiv\vec{\sigma}_1\cdot\vec{\sigma}_2 = {\sigma}_1^x {\sigma}_2^x +{\sigma}_1^y {\sigma}_2^y+{\sigma}_1^z {\sigma}_2^z \\= ({\sigma}_1^x+i {\sigma}_1^y)({\sigma}_2^x -i{\sigma}_2^y )/2 +({\sigma}_1^x-i{\sigma}_1^y ) ({\sigma}_2^y +i{\sigma}_2^y)... | {
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Confusing working of lens Why do lens don't splits light into its seven constituent colors, like Prism?
*
*Why is lens left is correct, not right one?
*How does lens came to know that rays are coming from infinity or are at Focus and converge/diverge them at different point accordingly?
| Real lenses suffer from chromatic aberration due to the refractive index of glass varying with the wavelength of light.
All a lens does is to refract incoming rays of light.
It so happens that if rays of light close to and parallel to the principal axis of a lens cross at a point after refraction.
| {
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Why does water flow slower on butter? Last night I was in my bathroom conducting an experiment about the speed of water on butter.
The experiment went something like this:
*
*Cover half a sheet pan with butter and leave the other half untouched.
*Incline the sheet pan at an angle of roughly 50°.
*Start the stopwat... | adhesive forces of water particle are different with base of sheet and butter molecule
From your experiment results we can conclude water-butter molecule adhesive force is higher
pl. support your experiment with video if possible (- providing YouTube link ?)
if you pore honey instate of water it will end up in differ... | {
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Can I use Root-Mean-Square Speed to measure the average speed of particles in solids and liquids? Can I use the equation $v_{rms}= \sqrt{\frac{3RT}{M}}$ of Root Mean Square Speed to measure speed of particles in liquids and solids as well? I am doing a Javascript animation about molecular motion of solids, liquids and ... | Due to equipartition theorem, average kinetic energy of particles in a system of classical particles is
$$\langle K\rangle=\frac32k_BT=\frac{m\langle v\rangle^2}2.$$
This is true even if there are some interactions: for derivation see this answer. Thus we have
$$\langle v\rangle^2=\frac1m 3k_BT=\frac{N_A}M 3k_BT=\frac{... | {
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In determining sound beam steering angle, where does a constant of 0.514 come from? I've read in some sources (like this, among some other) that for determining sound beam steering angle in a phased-shift array system, it is using a formula of:
$$\theta = \arcsin (0.514 \lambda\mkern-6mu^{_-}\mkern-12mu^{_-} / e)$$
Whe... | It comes from point spread function theory in optics and 0.514 is the factor used for specifically considering the part of your beam that encircles half the power (-6 dB of peak). It is derived from the Airy Function
| {
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Scaling argument for friction force on a chain in shear flow In her paper entitled "Deformations of One Tethered Chain in Strong Flows", the author makes the argument that given a shear flow velocity $v_x(y)=sy$ in a solution of viscosity $\eta$, and a tethered particle in the flow of size $y$, then the friction force ... | In the continuum limit the body (i.e. aggregate of blobs) seems to become a cylinder, but with increasing radius along X direction. Area of elemental circular strip at distance $x$ will be (circumference of cylinder at $x)\times~dx$. But circumference is proportional to diameter $y(x)$. Therefore area of the elementary... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/305930",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Friction of a Car in Motion It is commonly known that friction opposes motion. For example, if a block is sliding down a wooden surface with no forces other than friction acting on it, friction acts in the direction opposite to the block's velocity.
Let's say a car is driving at constant speed along a perfectly circul... |
It is commonly known that friction opposes motion.
If that were so you would not be able to move from rest.
Friction opposes or tries to oppose the relative movement between two surfaces.
If you have two blocks on top of one another and at rest and apply a force on the bottom block what will happen?
The bottom blo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/306151",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 5,
"answer_id": 1
} |
Can an accelerating frame of reference be inertial? In physics problems, the earth is usually considered to be an inertial frame. The earth has a gravitational field and the second postulate of the general theory of relativity says:
In the vicinity of any point, a gravitational field is equivalent to
an accelerated ... | Accelerating frames are never truly inertial; however, in many situations the acceleration is sufficiently small that we can assume the accelerating frame to be inertial. It largely depends on the scale relevant to the problem.
For example, for purposes of projectile motion, we can consider the Earth to be an inertial ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/306303",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 0
} |
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