Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why does the potential energy of the system decrease when two charge balls are connected using a connecting wire I am confused because I've seen in textbooks and online solutions to questions that when connected,the potential energy of a system of two charged spheres decreases.But according to law of conservation of en... | The energy is lost as heat through the wire resistance. Basically when you connect two conductors at different potentials through a wire they will exchange charge until they have the same potential. Energy is lost in this process but charge is conserved. This will become more clear once you learn about capacitors and c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/519563",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Quantum field theory, interpretation of commutation relation Let $\phi$ be the quantum field
$$
\phi(x) = \int \frac{d^3\mathbf{p}}{(2\pi)^3} \frac{1}{\sqrt{2E_\mathbf{p}}} \Big[ b_\mathbf{p}e^{-ip\cdot x} + c_\mathbf{p}^\dagger e^{ip\cdot x} \Big]
$$
with commutation relations
$$
[b_\mathbf{p}, b_\mathbf{q}^\dagger] =... | One interpretation is as follows: $[Q,\phi(\vec{x})] = \phi(\vec{x})$ means that $Q\phi(\vec{x}) = \phi(\vec{x})(Q + 1)$. Thus, if $\vert q \rangle$ is a charge eigenstate with eigenvalue $q$ (i.e. $Q\vert q \rangle = q\vert q \rangle$) then
$$ Q \phi(\vec{x}) \vert q \rangle = \phi(\vec{x}) (Q + 1) \vert q \rangle = (... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/519668",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 0
} |
Is it possible to conserve the total kinetic energy of a system, but not its momentum? It is possible to conserve momentum without conserving kinetic energy, as in inelastic
collisions. Is it possible to conserve the total kinetic energy of a system, but not its momentum? How?
To clarify, I am not necessarily talking a... | Yes, it is possible to conserve the total kinetic energy of the system but not the momentum.
Let me give you an intuitive explanation.
*
*Suppose we have two charges, in which one is fixed and other is free to move and then they are released at some distance. In this case since one charge is fixed so the net extern... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/520161",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "30",
"answer_count": 5,
"answer_id": 4
} |
How to understand transfer of momentum between motorcycle seat and rider? I have an app that samples acceleration at a motorbike seat. I want to be able to compare how comfortable these accelerations feel for two different motorcycles.
Let's say I have the following scenarios:
*
*A 75 kg rider on 300 kg motorcycle ... | The mass of the motorcycle is irrelevant. If the motorcycle (and hence rider) is experiencing the same acceleration, then they will "feel" the same thing. The rider will have the same momentum in either case.
The difference just comes into how much force is needed from the motor for the same acceleration. More mass mea... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/520365",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Calculating the Hamiltonian of complex scalar field I am working on the Peskin's QFT problems, and i'm finding difficulties in calculating the Hamiltonian of complex scalar field. The Hamiltonian read:
$$H = \int d^3x (\pi^*\pi+\nabla\phi^*\nabla\phi+m^2\phi^*\phi)$$
Then I substitute the expression of $\phi$ and $\ph... | The other answer can't be correct because it doesn't have units of energy $\omega_k$. Making an expansion using
$$ \phi(x) = \int \frac{d^3 k}{(2 \pi)^3 \sqrt{2 \omega_k}} \ \big(a_{\vec{k}} e^{-ik\cdot x} + b^{\dagger}_{\vec{k}} e^{ik\cdot x} \big )$$
I found (after neglecting the infinite constant)
$$ H = \int \frac{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/520514",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
How could the baseline of atmospheric neutrinos be as much as $10^7$ meters while exosphere (outer part of atmosphere) is at most 8e5 meters? Atmospheric neutrinos correspond to neutrinos produced by the interaction of cosmic rays in the Earth atmosphere. The Earth atmosphere is at most $800$ km=$8 \cdot 10^5$ meters.
... | Neutrinos produced in Earth's atmosphere have two opportunities to interact with detectors on Earth's surface: once on their way down from the sky, and again when they emerge unscathed on the other side of the planet. So the baseline is more like the diameter of Earth, which is about $12.7×10^6$ meters.
Famously, the I... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/520773",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why is simple harmonic motion considered to be a sinusoidal function? Motion of a pendulum is said to be an harmonic motion. What do we exactly mean by harmonic and why is that the displacement and velocity etc. Represented by a sine function?
| They result from physical systems with a peculiar type of restoring force: the acceleration is proportional to the displacement, but directed to the opposite side.
$x^{(2)}(t) = -k^2x(t)$
One way to examine what types of function have that property is testing as a solution a generic function expanded in a Taylor series... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/520999",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Why is the normal contact force horizontal on an inclined ladder?
There is only one force acting on the ladder which is its weight and it acts vertically downwards. Then why does the normal contact force from the vertical wall act horizontally on the ladder? There must be a horizontal force acting on the wall to exert... | Actually if you see the diagram , body is in rotational inertia, and rod is not perfectly vertical or horizontal, thing which work here is frictional force between rod and surfaces, friction always try to maintain the inertia, here the friction which acts is static friction.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/521221",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 6,
"answer_id": 5
} |
Why is there a "blue hour" after the "golden hour"? There's a great story about why the sky is blue during the day, and turns golden during sunsets:
Rayleigh scattering affects blue light more. During the day, blue light from the Sun is scattered towards us from all directions, causing a blue sky. During the sunset, t... | The reason is the same as in rainbow; different colours (wavelenghts)bends differently (sorry my language).
This Blue hour is the sunlight which arrives below the horizon. The reason why other light doesn't is on their wavelength. The Blue light can bend the most, and thus it can still reaches the Earth surface an hou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/521541",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
"answer_count": 3,
"answer_id": 2
} |
Dimensionless expression for differential equation I am working through Nonlinear Dynamics and Chaos by Steven H Strogatz. In chapter 3.5 (overdampened beads on a rotating hoop), a differential equation is converted into a dimensionless form. I am trying to work out which dimensions the initial equations had, and why t... | You substitute $\dot{\phi} = \frac{1}{T} \frac{d\phi}{d\tau}$. Now let's consider the dimensions
\begin{align}
[\dot{\phi}] &= [\frac{d\phi}{dt}] = \frac{rad}{s}\\
[\dot{\phi}] &= [\frac{1}{T} \frac{d\phi}{d\tau}] = \frac{1}{s} \cdot [\frac{d\phi}{d\tau}] \\
\Rightarrow [\frac{d\phi}{d\tau}] &= rad
\end{align}
and a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/521952",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Precise definition of the vertex factor Just a short question about the vertex factor in QFT. When I have an interaction Lagrangian
$$\mathcal{L}_{\mathrm{int}}=-\frac{\lambda}{3!}\phi^3$$
with a real scalar field $\phi$, is the vertex factor given by $-i\lambda$ or $-i\frac{\lambda}{3!}$?
Because as far as I learnt, ... | It seems that OP is not questioning the standard convention to divide each term in the Lagrangian with its symmetry factor, e.g., $${\cal L}~=~-\frac{1}{2}\partial^{\mu}\phi\partial_{\mu}\phi -\frac{1}{2}m^2\phi^2 - \frac{\lambda}{3!}\phi^3.$$
Rather OP is assuming the above standard convention, and asks if the vertex ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/522154",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Is Young's modulus a measure of stiffness or elasticity? Young's modulus seems like a modulus of stiffness. It tells us how difficult is it (how much stress is required) to produce longitudinal strain in a solid. It does not tell anything about how an object will react when the deforming force is removed.
How can one o... | In physics elasticity is defined as the ability of a material to resist a distorting influence and return to its original size and shape when the distorting influence is removed (source Wikipedia).
Young’s Modulus is the ratio of applied stress to resulting strain in the linear elastic region of behavior. Therefore, th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/522296",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Internal force disintegrating a solid body? Let $M$ be a block on a frictionless surface. Now let us mentally divide (not physically) the block into 2:1 ration (i.e $1/3$ of the left be called $M_1$ and $2/3$ right be called $M_2$). So $M_1$ applies force $F_1$ on $M_2$ and $M_2$ applies force $F_2$ on $M_1$ and by 3rd... | If the body is isolated, then $a=0$ and the internal forces are $0$. This is a trivial case where there is no longer a contradiction or possibility of the body being torn apart. Therefore, let's consider the scenario of a body that has external forces acting on it.
You are forgetting about external forces being applied... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/522514",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 0
} |
Why does the second law of thermodynamics prevent 100% efficiency? So far in my thermodynamics lecture course, my understanding of the laws of thermodynamics is that the first law is about the conservation of energy, the second law says entropy must always increase or stay the same which apparently results in the fact ... | If you can convert all of the heat to work, you're reducing entropy by definition ($\Delta S = \frac{Q}{T}$ , If $Q<0$ then $\Delta S < 0$).
If you allow yourself to let some heat flow into somewhere cold (heating something up instead of using all of the heat to work) you raise the entropy in the cold substance enough... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/522878",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 4,
"answer_id": 0
} |
Usually, how much does a phonon travel without scattering? Phonons propagate without problems in a lattice, until they scatter on something, like a defect, an electron, or another phonon. But in a typical solid at room temperature, how much (or how long) is the mean free path of a phonon? I know that depending on the t... | That depends strongly on many factors. The reason for the decrease in thermal conductivity at high temperature is that the mean free path goes down because of phonon-phonon scattering (interaction with the lattice). At some point the phonons do not propagate much further than a lattice period and the lattice melts. So ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/522988",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
Path integral for fermions on circle and background gauge fields This question is continuation of Path integral for fermion on circle.
I'm reading Witten article Anomaly Inflow and the $\eta$-Invariant and wanna to understand some technical details.
In section 4.1 authors consider even number $n$ of Majorana fermions:... | This can be calculated by rotating to the Cartan subalgebra of the gauge symmetry group (which is why the matrices turned out diagonal) and then computing the functional determinants.
See, for example,
*
*https://arxiv.org/abs/1607.04230
which is part of the list of references I gave on your other question on the w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/523095",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
On the derivation of the north-south aberration angle In A.P. French's Special relativity, page $39$, the author said the north-south aberration angle $\alpha$ below, in figure (b), is equal to $v\sin(\theta_{0})/{c}$, where $\theta_{0}$ is the angle when the earth is stationary (no aberration).
How did $v\sin(\theta_... |
If you construct the right-angle triangle as shown in red on fig. (b) then it is easy to see that $\sin\alpha = \text{something}/c$. And by breaking $v$ into components you can see (from the doodle on the right) that the something is equal to $v\sin\theta_0$.
Then, as mentioned in my comment, all that's left is to say... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/523210",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Could speed of light be variable and time be absolute? I get my "demonstration" of time dilation from the textbook thought experiment.
A laser is mounted on a cart with a reflective ceiling. At $t=0$ the cart starts moving and the laser is fired. When the laser is reflected back at the starting point the (thought) expe... | No. You're neglecting that time dilation is only one effect explained by relativity. You'd also need to take into account length contraction or, more generally, Lorentz invariance. Your "absolute time" is not going to capture the fact that there are properties of spacetime (not just time) at play here.
In light of t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/523485",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
"answer_count": 7,
"answer_id": 4
} |
Is Griffiths simply wrong here? (Electrostatic Boundary Conditions)
In the above illustration, shouldn't $E_{above}$ and $E_{below}$ be in opposite directions? If not, how did Griffiths end up the following equation? From the above directions, shouldn't the flux add up?
| The illustration and the equation may be confusing. It corresponds to a situation with an external field pointing upward that is larger than that due to $\sigma$. However the two arrows are of the same length, so if this were intended then $\sigma=0$. If there is no such field then $E_{above}$ and $E_{below}$ point in ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/523620",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 1
} |
Conservation of Angular Momentum for Rigid Bodies I have question about Conservation of Angular Momentum of Rigid Bodies. I've been doing some examples from Hibbeler's book, and noticed that in this chapter about Conservation of Angular Momentum of Rigid Bodies, there are some examples where we sum all the angular mome... | Finding the rotational inertia of the disk about point A would involve a complex integration. Instead, they use the parallel axis theorem. The disk is treated like a point mass revolving about point A, but then you have to add its resistance to also rotating about its own center. Either approach would work for the rod... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/523898",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
How did early radar determine range/ distance precisely? Wikipedia talks about precise timing of the returned radar pulse, with an animation of a clock.
But they didn't have atomic clocks and such before or during WWII.
So how did they determine distances and (possibly) velocities back rhen?
| Early radar uses analog signals and displays.
For example, the WWII Chain Home system would send each pulse at the same instant that an electron beam started across a CRT. The beam would be deflected by any received signal, and the left-right offset gave the distance from the return time:
Chain Home display showing ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/524109",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
D'Alembert's principle and the work done by constraint forces in Atwood's machine From what I understand, constraint forces do no work because they are perpendicular to the allowed virtual displacements of the system. However, if you consider an unbalanced Atwood machine, in which both masses are accelerating in opposi... | Gravity is pulling the weights down, the cable provides a directly opposing restraint, to keep the weights from accelerating downwards at 9.8 meters per second per second. The actual work is done by using the heavier weight's gravitational potential.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/524222",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 5,
"answer_id": 4
} |
Postulate of constancy of speed of light in vacuum I'm not of course questioning the constancy of the speed of light, just the way the postulate about it is worded. It is often stated that the speed of light is independent of the motion of the source. Einstein himself said "and also introduce another postulate, which i... | The doppler effect in classical physics works just as well if you are moving towards or away from the source or if the source is moving towards or away from you. Relative motion is what matters.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/524364",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
Why does the rope fly up from the nail against gravity?
Why does the rope fly up from the nail against gravity? As shown in the picture, the blue arrow is the nail fixed on the wall, the yellow arrow is the rope, and the green arrow is the iron block. The rope on the right side of the nail moves downward under the act... | According to @weeeeliam's answers to the following questions:
What is the formula for calculating the tension of the rope section?
There is a circle of rope that rotates at a uniform angular velocity $ω$. What is the formula for calculating the tension of the rope section? Without gravity, the density of the rope is $ρ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/524670",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How does light speed in a medium affect refraction? Light rays hit a convex lens and converge at a focal point after passing through as shown by the diagram below:
It is obvious by looking here that the light rays travel different distances to the focal point but they arrive at the same time. Photons travelling along... | Ray optics is a simplification tool useful for making calculations but not very useful for understanding light behavior. If you want to understand why light bends when it changes medium, you need to consider light as a wave, not as a particle.
The Huygens–Fresnel principle will explain the rest.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/524782",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Why does a weather vane arrow point in the direction of the wind? It seems that a weather vane will rotate in order to minimize energy and thus orient itself parallel to the wind.
What I do not understand is why it is implied that the weather vane arrow should point in the direction of the wind.
I do not understand wh... | The vane has to be designed so that it has a preference to point in the right direction. In the example that you included, this is implemented by the flag at the back providing a broader cross section than the arrow head and also by the rooster standing slightly to the back half of the arrow.
You are correct that if th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/524846",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "38",
"answer_count": 5,
"answer_id": 2
} |
Are the muon/tau neutrinos produced in the Sun? If not, then where? I was reading about Solar Neutrinos, and apparently they are all Electron Neutrinos.
However, there are two other types of neutrinos, the Muon and Tau Neutrinos. Does the Sun produce them? If not, are they produced naturally anywhere in the universe?
| The neutrino creating reactions (fusions, decays, and fissions) that take place in the core of the sun are all low enough in energy that they can only produce electron neutrinos.
However, neutrinos mix (because they propogate in mass states which do not correspond to the flavor states in which they are produced and det... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/524948",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
What happens to matter when it is converted into energy? According to Einstein’s equation
$$E=mc^2$$
Matter can be converted into Energy. An example of this is a nuclear reaction. What happens to the matter in the process? Do the atoms/subatomic particles just vanish? Any insights into this process are appreciated.
| Not to take away from other more detailed answers, I think there's something that might be more to your point.
Matter is not converted into energy.
Mass is converted into energy.
This can be observed in, for example, nuclear fusion of hidrogen, resulting in a helium nucleus. With two protons (of, let's say, mass=1) you... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/525047",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "35",
"answer_count": 6,
"answer_id": 5
} |
Modified quantum harmonic oscillator: hamiltonians unitarily equivalent and energy spectrum Here is my Hamiltonian:
$H_{\alpha, \beta} (q,p) = \frac{p^2}{2m} + \frac{1}{2}m \omega ^2q^2 + \alpha q + \frac{\beta}{2}(pq^2 + q^2p) + m \frac{\beta^2}{2}q^4$.
How can I prove that $H_{\alpha, \beta}$ and $H_{\alpha, \beta‘}$... | The hamiltonian can be put in the form $H_{\alpha \beta} = \frac{1}{2m}(p + \beta m q^2)^2 + \frac{m \omega^2}{2}\left(q + \frac{\alpha}{m \omega^2}\right)^2 - \frac{\alpha^2}{m^2 \omega^4}$. Now define $P = p + \beta m q^2$ and $Q = q + \frac{\alpha}{m \omega^2}$. Since $[p,q] = -i \hbar$, it is easy to prove that als... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/525179",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Reducing the Aerodynamic loss of a Flywheel in Air I have a hypothetical flywheel spinning at 3000rpm. The steel flywheel is around 800mm in diameter with a "Smooth" finish. I was wondering whether it would be beneficial to implement golf ball dimples on the flywheel surface to reduce the laminar drag. There are many s... | Ideally, the flywheel would run in a vacuum.
In air, its surface should be as smooth as possible. With aircraft surfaces you have a stagnating point where air "hits" the aircraft straight on and then a flow path with a clear end at the trailing edge. The length of this flow path is used for calculating the Reynolds num... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/525268",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Is the capacitance of all types of capacitors increased by a factor of dielectric constant like parallel plate capacitors? I've learnt that the capacitance $C$ of a parallel plate capacitor is given by:
$$C=\frac{A\epsilon_0}{d}$$
where, $A$ is the area of cross section of the plates and $d$ is the separation between t... |
. . . . the capacitance of a spherical capacitor is given by $C=\dfrac{4\pi\epsilon_0 r_1 r_2}{r_2-r_1} . . . .$
If $r_2 - r_1 = d$ and $d\ll r_1$ and $r_2$ then $4\pi r_1r_2$ is approximately equal to the surface area of a sphere $A$.
The capacitance of a spherical capacitor with these characteristics can now be ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/525477",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Effective mass as a consequence of energy band structure The Wikipedia article on effective mass defines it as follows:
In solid state physics, a particle's effective mass (often denoted ${\textstyle m^{*}}$) is the mass that it seems to have when responding to forces, or the mass that it seems to have when interactin... | So what is illustrated in this figure is the energy band structure, these represent the dispersion, i.e. the energy $E$ in function of the wave vector $k$. Now, you can find in standard textbooks on solid state physics that the effective mass is defined as $$(m^*)^{-1} =\frac{1}{\hbar^2}\frac{\partial^2 E}{\partial k^2... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/525546",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How does water vapour replace air molecules? I know that density of moist air is less than density of dry air becuase water molecules replace air molecules, and hence as the average molecular mass of water is less than that of air, the density decreases.
Now my doubt is why do the water molecules replace air molecules,... | The volume of the Earth’s atmosphere isn’t fixed. It can vary slightly for a number of different reasons, including a slight increase due to water evaporation and So locally, dry air molecules can move out of the way to make room for gaseous water molecules during vaporization and evaporation.
Hope this helps
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/526026",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Origin of terms in the Nernst-Planck equation We know the Nernst Planck equation is
$$ \frac{\partial c}{\partial t} = - \nabla \cdot J \quad | \quad J = -\left[ D \nabla c - u c + \frac{Dze}{k_\mathrm{B} T}c\left(\nabla \phi+\frac{\partial \mathbf A}{\partial t}\right) \right] $$ $$\iff\frac{\partial c}{\partial t} = ... | The Nernst-Planck equation assumes an ideal thermodynamic behavior of ions, i.e., unit activity coefficients. Additionally, it uses self diffusivities, $D$, to describe the response of ions to an applied electric field.
This interpretation is at best valid for dilute electrolytes.
A generalized treatment of ion motion ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/526206",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Why is work defined as $W=Fd$? I am trying to understand what work really means in physics. I seem to be missing the conceptual link. Every resource says that $W=Fd$ but that does not make sense to me.
If, say, an elastic object suspended in space where there is no drag or resisting force of any kind is pushed by a for... |
I am trying to understand what work really means in physics. I seem to
be missing the conceptual link.
The short answer is work in physics is a means of energy transfer between objects that is the result of the action of a net force on an object through a distance. A differential amount of work is $dW=F.ds$. (The o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/526337",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 3
} |
Confused about what a wave is When a wave of something, let's say light or some electromagnetic wave is given, I am confused because I do not understand if shape of a wave represents projectile of it or some value that possess at certain positions. I researched a lot but I have no idea what a wave really is.
My questi... | The “shape” of the wave is exactly what a wave is. It is a “shape” formed in a medium in which it moves while maintaining the shape (ideally). The shape formed is a property of the medium and of the object that caused the shape to form in the medium.
For example think of the medium as water in a pond and the object as... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/526448",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 3
} |
Constructing W-algebras I am following the algorithm in W-algebras with two and three generators, in order to construct consistent (anti-)commutator relations for a particular W-algebra.
I am considering $W(2,4,4)$ where both dimension four operators are fermionic. I have two questions related to the method introduced ... | As it turns out, even though the authors of the paper I linked claim there are benefits to working with the commutators rather than the OPEs, I found using the OPEs much simpler, and didn't need the machinery provided in the algorithm in the paper.
In my case, the two fermionic generators carry an $\mathfrak{sl}(2)$ ch... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/526692",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Irreversible, Compression and expansion work for a piston with ideal gas How can we calculate the work done by the piston or on the piston by including the internal pressure of the piston and not the external one. Because if the external pressure is doing work, the internal pressure might be too in the opposite directi... | It is important to be aware that, in an irreversible expansion or compression of an ideal gas, the gas does not satisfy the ideal gas law. The ideal gas law applies only to a gas in thermodynamic equilibrium, or, in the case of a reversible process, a gas passing through a continuous sequence of thermodynamic equilibr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/526791",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why are lasers more useful for cutting and similar tasks than non-coherent light? I'm working a lot with lasers the last few years, and trying to understand the basics. So some of what I say next may be wrong or partially correct - if I find that out, that will be valuable.
As I understand it, a laser is a light source... | The acronym LASER is short for "light amplification by stimulated emission of radiation". The stimulation part is important, because this way we are able to obtain high energy densities. In contrast to a light bulb or a LED, the laser beam is also rather directional. This enables us to focus the beam onto "small" spot ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/526896",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Using the uncertainty principle to estimate energies in ground states Suppose, for example, that we want to find the minimum energy of a particle undergoing simple harmonic motion. In classical mechanics, the energy is:
$$E = \frac{p^2_x}{2m} + \frac{1}{2} m \omega_0^2x^2$$
where $m$ is the mass of the particle and $x$... | I totally agree: This "derivation" is mathematically improper.
The energy of the system under consideration is given by
$E = \frac{p^2}{2m} + \frac{m\omega^2 x^2}{2}$. However, as you know this is not true, because the energy levels would not posses any uncertainty. Thus, we should interpret this relationship by assumi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/527112",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Is the equation $g=GM_Em/R_E^2$ in Tipler incorrect? I was reading my textbook (Tipler et al.), and I am unsure of one of the expressions they used. On page 374, it says (near Figure 11-10) that $g = GM_Em/{R_E}^2$. Is this even dimensionally correct? I got a units of $m/s^2$ on the left hand side and Newtons on the l... | Yes it is incorrect. Most probably it is a typo.
It can either be
$$F_g =G \frac {M_E m}{R_E^2}$$
Here they might have misprinted $F_g$ as $g$.
Or
$$g = G \frac {M_E}{R_E^2}$$
Here they probably mistyped the $m$ over there.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/527219",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Gauge ghosts & unphysical states in gauge theory I have a general question about a statement from Wikipedia about ghost states as occuring in gauge theory:
"In the terminology of quantum field theory, a ghost, ghost field, or gauge ghost is an unphysical state in a gauge theory."
I learned gauge theory up to now wi... | TL;DR: Ghost states do not belong to the physical Hilbert space.
This begs OP's next question: What exactly is the physical Hilbert space in a gauge theory?
If we transcribe the gauge symmetry into a BRST symmetry, we can give a precise technical definition: The physical Hilbert space is given by the BRST-cohomology o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/527340",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 0
} |
Entropy change in the free expansion of a gas Consider the adiabatic free expansion of a gas since there is no external Pressure hence Work done on the system is 0 and since the walls are insulated (hence adiabatic) the heat absorbed is 0. However since this is a irreversible process then entropy change > 0 hence dQ > ... | The equality $dS=dQ/T$ is only valid for reversible processes, so it does not apply in a free expansion.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/527438",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 4,
"answer_id": 0
} |
Understanding Electrostatic Work $$W=-\int_\infty^\textbf{r}\textbf{F}\cdot\textbf{dl}
=-Q\int_\infty^\textbf{r}\textbf{E}\cdot\textbf{dl}
= Q(V(\textbf{r})-V(\infty))
=QV(\textbf{r})$$
I'm trying to understand how this definition of work turns into a positive
$$W=QV(\textbf{r}).$$
The integration of $-Q\int_\infty^r ... | Keep in mind that electric field is negative gradient of potential.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/527555",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Two-Dimensional Lorentz Velocity Transformation Problem
Two spaceships A and B are approaching along perpendicular directions, as seen from earth.
If A is observed by a stationary Earth observer to have velocity $_$ = -0.90c and B to have
velocity $_$ = +0.90c, determine the speed of ship A as measured by the pil... | As mentioned by @G.Smith, your second equation is not correct. According to the velocity addition formula, we have:
$$u'_x=\frac{u_x-v}{1-\frac{vu_x}{c^2}}=\frac{0-v}{1-\frac{0}{c^2}}=-v=-0.9c$$
Remember that the velocity of $B$ shall be considered as $v$ in the above link. $(u_x=v=0.9c)$ Therefore, we can write:
$$u'_... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/527804",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
If a ball is thrown to a person standing on a frictionless surface, is the impulse of the thrower equal to that of the catcher? If a person throws a ball, exerting a given impulse does the person that catches the ball receive the same impulse assuming that the catcher moves. Is the impulse that the catcher receives les... | Let both the men have a mass of M and the ball have a mass of m. Now, let's say the first man throws the ball at an angle $\theta$ and velocity v towards the second man.
Now, just after he has thrown the ball we will see this:
The velocity of the first man will be $\frac{mv \cos{\theta}}{M}$ in the opposite direction... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/528162",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 2
} |
Left and right Weyl representations are inequivalent representations We introduce the two-component spinors in the following representations:
$$
\psi_\alpha \rightarrow\psi'_\alpha=\mathcal{M}_\alpha^\beta\psi_\beta$$
$$
\bar\psi_\dot{\alpha}\rightarrow\bar\psi_\dot{\alpha}'=\mathcal{M^*}_\dot{\alpha}^\dot{\beta}\bar{\... | This is the claim that left-handed Weyl spinors and right-handed Weyl spinors are not the same.
*
*An abstract way to see that there cannot be such a matrix is to first show that the two representations correspond to $(1/2,0)$ and $(0,1/2)$ in the usual parlance of expressing representations of the complexification ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/528389",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Given fluids expand non-linearly, how were physicists able to make a linear temperature scale? Materials expand with increase in temperature. As far as I know this property for fluids was put in use to make initial thermometers. We know that expansion of fluid is given by the following formula (at a given pressure) (Wi... | Physicists were using gas-based thermometers, where linear range is looking like -150 to 2000 Celsius. They were quite lucky that gases are not very easy to liquify in XVII century.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/528463",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "26",
"answer_count": 8,
"answer_id": 7
} |
What does the arbitrary constant in cosine equation of displacement in S.H.M say? The phase and phase constant in a displacement time equation show from where the particle has started.
In my school textbook, first the displacement equation was given as :-
$$x= A\sin(\omega t+\phi)$$
where $\phi$ i... | At $t=0$ the displacement $x$ is not necessarily $0$:
$$
x(0)=A\sin(\phi) \tag{1}
$$
In addition, the velocity at $t=0$
$$
\dot{x}(0)=\omega A \cos(\phi) \tag{2}
$$
(1) and (2) are two equations for your 2 unknowns $A$ and $\phi$. Thus, as you alluded to
$$
\frac{x(0)}{\dot x(0)}= \omega\tan(\phi)
$$
from which you c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/528699",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
On the "spectrum" of an operator in quantum mechanics Very simple question, I'm new to this. I'm reading Griffiths book on QM and have a question about the "spectrum" of an observable operator. Does the spectrum of an operator require specification of a particular system? Or is the spectrum of an operator just every po... | Each operator has it's own spectrum. For the hamiltonian the spectrum is the set of allowed energy levels. This depends on masses and potentials.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/528816",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Commutator of $B$, $C$ vanishes if $A$, $B$, $C$, $AB$, $AC$ are Hermitian
Suppose 3 operators $A$, $B$, $C$ are Hermitian operators. Assume $A$ has a non-degenerate spectrum, and $AB$ and $AC$ are also Hermitian. Show that $$[B,C] = 0$$
From the conditions $A$, $B$, $C$, $AB$ and $AC$ are Hermitian operators, one ca... | You are nearly there. If $A$ commutes with $B$ it means that they can be diagonalized simultaneously. Now use the fact the the eigenvalues of $A$ are non-degenerate. This means that also $B$ is diagonal in the same basis. Repeat with $C$ and you are done.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/528943",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
$V$-$I$ characteristic of a solar cell please explain the VI characteristics of a solar cell. The characteristics is given in my book without any explanation. How can the Voltage decrease on increasing current shouldn't it be opposite.
Solar Cell I-V characteristics
(Image from Electrical 4 U - Characteristics of a S... | A simple (but sufficient) model is to consider the sunlight as a stream of photons, each with their own energy depending on the colors in the sunlight. Each photon can give its energy to a single electron.
If you try to get out a small current from the solar cell, there are more than enough photons, but you can't chang... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529053",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 2
} |
How do the unit vectors in spherical coordinates combine to result in a generic vector? I might be missing the obvious, but I can't figure out how the unit vectors in spherical coordinates combine to result in a generic vector. In cartesian coordinates, we would have for example $ \mathbf{r} = x \mathbf{\hat{i}} + y \m... | I think the problem comes from confusing the radial unit vector for spherical coordinates and a trajectory vector. They are different, to build the second one you can use the $\hat{r}$ only if the path is radial, but it can have another components if the trayectory is not.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529113",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 7,
"answer_id": 5
} |
How does the current remain the same in a circuit? I understand when we say current, we mean charge (protons/electrons) passing past a point per second. And the charges have energy due to the e.m.f. of the power supply.
Now tell me, if a lamp has resistance and you hook it in the circuit, how will the current stay the ... | Ok , so I think that confusion lies in the concept of current. When we apply potential difference through a circuit having resistance, a single electron does not move from one end to the other. What actually happens is that it replaces electron next to it which in turn replaces the electron next to it and this happens ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529224",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 9,
"answer_id": 3
} |
Feynman Propagator for fermionic field $S_F(x-x)=0$ When doing some calculations in my QED course, my tutor used that for
$$S_F(x-y)= - \int \frac{d^4p}{(2\pi)^4}\frac{i( \gamma_{\mu}p^{\mu}+m)}{p^2-m^2+i\epsilon}e^{-ip(x-y)}$$
the Feynman Propagator of a fermionic field,
$$S_F(x-x) =0.$$
He shortly mentioned some sy... | This is not true. See section 3 of this article where the full analytic expression is derived. For finite mass, we can write the $x^2\rightarrow 0^+$ fermionic propagator (the $x^2\rightarrow 0^-$ limit gives the same answer, but with Bessel instead of Hankel functions when $x^2\neq 0$):
$$
\begin{align}
S_F(x)&=(i\gam... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529340",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
To what extent is standard quantum mechanics actually non-relativistic? I often hear that while QFT is a relativistic theory, standard quantum mechanics is not. But fields aren't inherently relativistic, you can easily construct non-relativistic QFTs, a relativistic QFT is one with a Lorentz invariant Lagrangian.
In t... | The Klein Gordon equation , the Dirac equation were developed partially to give quantum mechanical equations that were also Lorenz invariant, to replace the Schrodinger one. Maxwell's equation when used for the photons as a quantized equation is of course Lorentz invariant.
QFT depends on the plane wave solutions of t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529497",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 4,
"answer_id": 1
} |
Normalization of the action in Special Relativity The action for a massive point particle in Special Relativity is given as
$$A =-mc^2\int d\tau,$$
Where $\tau$ represents the proper time, and $m$ represents the (rest) mass. From what I could understand, the Action must not change with respect to the reference frame, a... | For a single particle, it does not matter what prefactor you use, the equations of motion and everything else stays the same. The factors only start to matter when you couple different systems to each other. For example, consider a charged particle in an electromagnetic field described by a vector potential $A_\mu$. Th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529682",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 4,
"answer_id": 1
} |
Definition of reducible representation A reducible representation of a group $g \rightarrow D(g)$ is one which leaves a subspace $U$ invariant, i.e. $D(g)|u\rangle \in U, \space \forall |u\rangle \in U$.A completely reducible representation is one that can be broken down into a direct sum of irreducible representations... | *
*Leaving a subspace invariant means that $D(g)u\in U$ for all $g\in G, u\in U$. Since $P_U v \in U$ for the projector $P_U$ onto $U$ and any $v\in V$, you have that $D(g)P_U v \in U$ for all $v\in V$. So applying $P_U$ again to $D(g)P_U v$ does nothing, since the latter is already in $U$, there is nothing to project... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529829",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
The Calculation of work in different frames Say there is a man running on a road. Friction is applying a force hence he is accelerating, but the friction is static hence does no work. We know that the change in kinetic energy is due to internal work done by his muscles.
Now say that the same man is running on a wooden... |
Thus work is frame dependent.
Is my conclusion correct?
Yes. Work is frame dependent. This can be easily seen by noting that distance is frame dependent and since $W=F\cdot d$ then work is also frame variant.
Note that the plank frame that you describe is non inertial. So energy is not trivial and is actually not ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529918",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
If magnetic field lines don't exist, what are these iron filings doing around a magnet? Obviously the iron filings can be seen aligning themselves along the virtual magnetic field lines produced by the permanent magnet, the virtual magnetic field line is made of electromagnetic field due to the alignment of electrons i... |
That does look like there are real lines, doesn't it?
It's because each iron filing becomes its own magnet which affects the others.
Notice how they're all crowded together close to the ends of the magnet, and then there's a region where they're thin, and then they get closer together farther away?
I think that's beca... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530030",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "56",
"answer_count": 7,
"answer_id": 4
} |
Boyle's Law and hot air balloon A bit dumb question because it is really difficult to imagine it. :-
Pressure is force per area. Talking about gases, the pressure is said to be the force molecules exert on walls of let's say a balloon.
Usually in examples of Boyle's law, our teachers mention hot air balloon, that the s... | Like you said, pressure arises from the force exerted by the molecules on stuff. In case of the balloon whose pressure inside is higher than the pressure outside, the number of collisions per second of the molecules outside the balloon is lower than that of the ones inside. Thus the balloon feels a net force that is ou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530129",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Explicit calculation of spin connection through Cartan's first structure equation Given the metric
$$
ds^2 = F(r)^2dr^2 + r^2d\theta^2 + r^2 \sin^2(\theta)\, d\phi^2,
$$
I'm trying to find the corresponding spin connections $\omega^a_{\ b}$ using the first structure equation:
$$
de + \omega e = 0.
$$
I found the vi... | There is also an explicit procedure that is often better if the vielbein is simple.
We have $$ \mathrm d e^a=-\frac{1}{2}C^a_{bc}e^b\wedge e^c, $$ where the $C^a_{bc}$ are the vielbein commutators. We can invert the first structure equation explicitly as $$ 0=\mathrm de^a+\omega^a_{\ b}\wedge e^b \\ =-\frac{1}{2}C^a_{b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530257",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
What would the surface temperature of the Earth be without the Sun? If the Sun would not heat the earth, and never had heated it in the past,
its surface would only be heated from the inside.
What would be the current temperature of the surface?
| 57 degrees Fahrenheit
And without sunlight, the Earth would get very, very cold. Earth's surface temperature now averages about 57 degrees Fahrenheit, but by the end of the first week without the sun, the average surface temperature would be below the freezing point.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530715",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
If sound passes through material, vibration is produced. So are electromagnetic waves produced too? Sound means vibration of molecules and vibration produces electromagnetic waves. So, this means that sound produces electromagnetic waves directly.
Is this possible?
| Motions of neutral atoms do not radiate
@Cyclone's answer provides very useful insight, but is ultimately irrelevant. As long as the medium that is vibrating is neutral, no energy is radiated. The EM waves emitted by the protons in the air interfere destructively with those emitted by the electrons and cancel out.
Put... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530863",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
"answer_count": 7,
"answer_id": 2
} |
Entanglement between what? According to the standard definition of "Entropy of Entanglement"
https://en.wikipedia.org/wiki/Entropy_of_entanglement
one starts from the density matrix of a pure state
$$
\rho=|\psi\rangle\langle\psi|,
$$
then divides the system into two parts, $A$ and $B$, traces away the degrees of ... | Indeed, the definition is pointless without a choice of partition of the underlying space. It is true that sometimes this is not made explicit. For example, people often talk about "entangled particles", but they should be really talking about specific properties of the particles being entangled, not the particles them... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531000",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
How to visualize newtonian objects in term of harmonic oscillators? From the group $U(1)$ in QED, via group representation we get the harmonic oscillators. However, I still have a hard time to imagine newtonian objects (computer, headphone, etc) as a combination of oscillators. I have take a look at classical limit but... | Suppose the object comprises $n$ degrees of freedom, and we work in a Cartesian coordinate system for these degrees of freedom, so each coordinate $q_i$ is $0$ at a stable equilibrium. The kinetic energy is of the form $\sum_i\frac12m_i\dot{q}_i^2$; the potential energy is of the form $\sum_i\frac12k_iq_i^2$, plus high... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531122",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Torque and force Does the force due to torque on the edge of a wheel depend on the mass of the the wheel or is it always $\tau / R$?
| Yes, it does depend on wheel mass, but indirectly. Here is how =>
By definition torque is:
$$ \tau = r\,F_\perp $$
And Newton second law expressed for rotation is :
$$ \tau=I\,\alpha $$
where $I$ is moment of inertia and $\alpha$ is angular acceleration. Putting these equations together and solving for a force gives
$$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531249",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 3
} |
Why does the same proportion of a radioactive substance decay per time period? (half life) Just wondering, if decay is random, why does the activity half every half life, as in, why does it have to reduce by the same proportion in the same time period?
| An example that might help:
Start with a big pile of coins. Flip them. Remove the heads. About half remain.
Take the remainder and flip them. Remove the heads. About half remain.
Take the remainder and flip them. Remove the heads. About half remain.
The analogy: An atom has a 50% chance of decaying in some particula... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531441",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "65",
"answer_count": 5,
"answer_id": 2
} |
How fast does a particle need to go to have a significant probability to quantum tunnel through a star? According to this answer tunneling probability depends, among other things I don't know, on the length of the barrier.
Due to length contraction when going at relativistic speeds, it seems it should be theoretically ... | For quantum tunnelling density and velocity is arbitrary. Tunnelling might be the wrong word as it involves a spherical "wave" starting at the particle extending to infinity, the Schrodinger wave. It is the probability of the particle existing at any point on the wave. The wave-function "collapses" when someone observ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531582",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why is Newton's First Law not considered a vacuous statement? How did Newton come to postulate the law of inertia when every inertial body that he was considering was (by his own other hypotheses) being acted on by the force of universal gravitation.
In other words, he simultaneously posits the law of Inertia and then... | Physics from the time of Newton to now is the discipline where mathematical differential equations are used , whose solutions fit the experimental data points and are predictive of new data. In order to do this , a subset of the possible mathematical solutions of the differential equations is picked by use of postulat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531760",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Double slit for electrons (two beams or one)? I understand the double slit for waves but for electrons do we have a beam for each slit so each beam is responsible le to shoot electrons through its own slit.
Or do we have just one beam? Which slit do we place the beam to? If it’s in the middle, wouldn’t all the electro... | In the Copenhagen interpretation, the principle is that there is a wave and that wave difracts through the holes like any other wave. The electron as a particle then appears at the screen with a probability that depends on the square magnitude of the wave. In this context, it is not suggested that the electron definite... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532009",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 5,
"answer_id": 4
} |
Clarification on a statement Bernevig's textbook on Topological insulators On page 11 of the aforementioned book Bernevig claims after doing some calculation that the integral of Berry curvature over a sphere containing a monopole is $2\pi$. Now my question is the following: the berry curvature is defined as the curl o... | It hinges on the fact that the berry connection is not globally defined on the sphere. For Stokes' theorem(or Divergence theorem as you stated) to work, you need a vector field ${A}$ defined on the whole manifold.
But if you choose a coordinate system on the sphere (e.g. spherical coordinate) and express the berry conn... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532423",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Travelling to the future while seemingly standing still? Some time ago I thought about this possibility, knowing about the time dilation from general relativity. What would theoretically happen if I travelled at near the speed of light in a circle that has such a small radius so that my brain and the people around me w... | That's funny, I had the exact same thought while I was first taught special relativity. This can definitely work, though you would require enormous amounts of energy. An example would be a satellite in orbit around Earth. Given high enough speed, the people inside the satellite could undergo significant time dilation(e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532560",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
How is a 25-year-old can of soda now empty without having been opened or poked? I just discovered in my parents' basement a Sprite can from 1995* and also a Coca-Cola can probably from the same year.
Both cans are unopened and have no visible damage or holes. The Coca-Cola can feels "normal", but the Sprite can is emp... | The more likely explanation of any of the described scenarios is probably in the realm of corrosion chemistry.
In time, the protective Al coating is penetrated in the presence of dissolved salts.
The highly reactive exposed Aluminum will chemically react (even with the water content, not too mention any acids presence... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532731",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "33",
"answer_count": 7,
"answer_id": 4
} |
Age of Universe from Friedmann Equation - How to actually solve the integral? The Friedmann equation for a flat universe can be written as
$$
H(t)=\frac{\dot{a}}{a}=H_0\sqrt{\Omega_{m,0}\cdot a^{-3}+\Omega_{\Lambda,0}}=H(a)
$$
To calculate the age of the universe, many books jump directly to the result. But there shoul... | I found that Mathematica could deal with the integral in a minute or so, giving the result:
where I have used the notation $\Omega_{m,0} = m$ and $\Omega_{\Lambda, 0} = n$. Being a conditional expression, it depends upon these parameters being in certain bounds, but let's go ahead and assume that they do. Since the un... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532828",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 3,
"answer_id": 1
} |
Schrödinger equation on operated states I understand that we can apply the Schrödinger equation to any wavefunction. Now, my question is, can we apply it to states that are being operated upon? Because, when we apply an operator on a state, we get another state which might/might not be a linear multiple of the original... | If you start with $\psi$ that solves the Schrödinger equation:
$$
i\hbar \frac{\partial \psi}{\partial t} = \hat{H}\psi
$$
And acts $\hat{A}$ on $\psi$:
$$
i\hbar \frac{\partial (\hat{A}\psi) }{\partial t} = \hat{H}(\hat{A}\psi)
$$
Then because we work in the Schrödinger picture and if we assume that $\hat{A}$ doesn't ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532974",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
"answer_id": 0
} |
Cyclic invariance of trace of fermions Consider the Green's function of fermion operators with imaginary time,
$$\mathcal{G}(\nu, \nu', \tau) = - \langle T_\tau c_{\nu}(\tau) c_{\nu'}^\dagger(0)\rangle\tag{1}$$
To show it satisfies the periodicity,
$$\mathcal{G}(\nu, \nu', \tau) = - \mathcal{G}(\nu, \nu', \tau+ \beta) ... | I can see why you might be confused. If the trace were only over the spinor indices on a fermi field, $\psi_\alpha$ say, then there would be an additional minus sign. Here, however, the trace is over the entire many-body Hilbert space and the $c_\nu$'s are just like any other operator and so have a cyclic trace. This ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533078",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Ionizing radiation in thermal radiation According to the black-body radiation equation, the spectrum extends to infinitely high frequency (although its intensity gets small quickly towards high frequency).
(1) How do you roughly estimate the ionizing radiation power in common high power thermal sources like a 2KW heate... |
How to roughly estimate the ionizing radiation power in common high
power thermal source like 2KW heater without fan then make sure it is
safe considering it is used for years instead of 0.1 second/year in
case of DR Xray scan?
A common 2 kW resistance heater does not emit ionizing radiation. It's radiant heat ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533166",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 5,
"answer_id": 4
} |
Shape complexity of a substance and its effect on heat retention While cooking, I have noticed that a ball of boiled spinach retains its heat for a long time. I understand that spinach is 91% water. It is my hunch that the same volume of water would cool much faster. If 9% of spinach is attributable to other compounds,... | You may need to test your hunch to see if you are right. Water has a very high specific heat, so it is a very good reservoir of heat. A timer and a thermometer might say that it cools off just as slowly.
However, two things might make a "ball of water" cool off more quickly:
*
*Evaporation. If the whole surface o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533336",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Stability of plum pudding model My textbook says that the plum pudding model(Thomson's model) should be electrostatically unstable. Why is that so?
| Your textbook is wrong. Earnshaw's theorem does not apply to the plum pudding model: the pudding provides a non-zero divergence.
Actually Thomson was aware of the possible problem of stability, and this was one of the reasons for his choice of the model. In his 1904 paper, he was able to show that, for an increasing n... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533431",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Does Another Universe Where Time Runs Backwards Revive the Idea of a Cyclical Universe? https://www.pbs.org/wgbh/nova/article/big-bang-may-created-mirror-universe-time-runs-backwards/
This article talks about a new theory where the big bang happened in one direction for us and the other direction where time is going ba... | An interesting idea is that at the Big Bang positive matter went forwards, and negative matter went backwards, but time is circular, so we'll meet again.
Since most of space is pretty empty, a collision between the two universes would not wipe everything out instantly. Galaxies would, for the most part, collide with n... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533815",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 3
} |
Clarification of the concept "less resistance means less heating" in a wire So my textbook says that the reason cables that are suppose to carry high currents, are thicker that those that are meant to carry lesser current, is that "less resistance (of the wire) means less heating..."? Is this even true?
Isn't CURRENT ... | Well as far as i can i see, you cannot change the current passing through the wire. This is because they are "suppose to carry high current"(as per the question) . So the only possible way to reduce heat losses is to decrease resistance(heat loss is proprtional to resistance of wire).
That being said transmission cable... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533927",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 8,
"answer_id": 4
} |
Do black holes move through space? I know it was already asked here:
Does a black hole move through space? What happens to other things around it?
And it might be a very stupid question, but here it is:
From a relativistic perspective, do black holes move through space, or is it the space around them that is curved in... | Yes they can. Everything moves in space. If you're looking for proof they can move, the Standard Model says the galaxies (which have black holes) are moving away from us. That’s a lot of black holes moving.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534022",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 4,
"answer_id": 3
} |
Gravity, matter vs antimatter I have a simple question regarding matter-antimatter gravity interaction.
Consider the following though experiment:
If we imagine a mass $m$ and an antimass $m^-$, revolving around a large mass $M$
the potential energy of mass $m$ should be:
$$ U_1=-\frac{GmM}{R} $$
and the potential energ... | The short answer is that we don't know. While we have made some small amounts of anti-matter, it has not lasted long enough to measure the very weak force of gravity.
However, people have speculated. Here is a long article on Wikipedia about that, with arguments going both ways.
The introduction to that article states... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534289",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 4,
"answer_id": 0
} |
What if the net force provided for a circular motion is larger than the required centripetal force? Will an object be pulled towards the centre linearly if the net force provided for a circular motion is larger than the required centripetal force? And why?
For example, if the object in a circular motion which is connec... | When pulled harder towards the centre, it cannot start moving linearly towards the centre.
It already has a tangential speed (otherwise there would be no circular motion). In order to start moving linearly towards the centre, the tangential speed must be zero. If you pull directly inwards, then there is no force acting... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534748",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 0
} |
What does this notation for spin mean? $\mathbf{\frac 1 2}\otimes\mathbf{\frac 1 2}=\mathbf{1}\oplus\mathbf 0$ In my quantum mechanics courses I have come across this notation many times:
$$\mathbf{\frac 1 2}\otimes\mathbf{\frac 1 2}=\mathbf{1}\oplus\mathbf 0$$
but I feel like I've never fully understood what this nota... | The $\otimes$ sign denotes the tensor product. Given two matrices (let’s say $2\times 2$ although they can be $n\times n$ and $m\times m$) $A$ and $B$, then
$A\otimes B$ is the $4\times 4$ matrix
\begin{align}
A\otimes B =\left(
\begin{array}{cc}
A_{11}B&A_{12}B\\
A_{21}B&A_{22}B
\end{array}\right)= \left(\begin{arra... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534887",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 4,
"answer_id": 0
} |
Are the components of the curvature tensor defined by the Robertson-Walker metric constant? In the Robertson-Walker solution the curvature is uniform. However the space is "expanding" and so the matter density is decreasing over time (or not because it's modelled as a perfect fluid?). Does the expansion affect the comp... | I prefer to put the metric in the form
$$ ds^2 = dt^2 - a^2(t)\left[d\chi^2 + f^2(\chi) d\Omega^2 \right]$$
or alternatively
$$ ds^2 = a^2(\tau)\left[d\tau^2 - d\chi^2 - f^2(\chi) d\Omega^2 \right],$$
where
$$ f(\chi) = \sin\chi,\,\, \chi,\,\, \sinh\chi $$
for positive, zero and negative curvature, respectively. f is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535148",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Where does energy go in joining capacitors of different capacitance charged by different potential, hypothetically assuming no resistance in circuits? I don't understand why there is any change in initial and final energy since we have already assumed a perfectly conductive circuit. I mean, theoretically at least, ther... | When charges move due to an electric field (i.e. down the potential gradient) the electric potential energy of the system decreases. When you put in the second capacitor there is a brief moment where an electric field is present that causes excess charges to move to the other plates. Hence you have less energy stored. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535367",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
"answer_id": 1
} |
The quantization of the electromagnetic field in Peskin and Schroeder (Eq.9.52) I'm working on the quantization of the electromagnetic field in Peskin (page 294).
However, I'm confused about the Eq.(9.52). Peskin says Eq.(9.51) and Eq.(9.52) are equivalent, but why? Is Eq.(9.52) derived from Eq.(9.51)?
For a real scal... | The idea is that the quadratic part of the action should be invertible and the inverse gives the propagator of the field. Eq. 9.52 is trying to solve for the inverse $\tilde{D}^{\nu\rho}_F$, but you cannot because $-k^2g_{\mu\nu} + k_\mu k_\nu$ is singular. That's the exact same as saying that the quadratic action vani... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535447",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Geometry of Young's experiment for optical path length I am currently studying the textbook Modern Optical Engineering, fourth edition, by Warren Smith. When presenting the concept of optical path length, the author says the following:
With reference to Fig. 1.13, it can be seen that, to a first approximation, the pat... | Let us consider the following diagram:
When the distance $L$ between the slit plane and the screen is large compared to the distance $d$ between the slits, we can assume $S_1P$ and $S_2P$ are parallel to each other. And the $\delta$ in the image represents the optical path difference.
Now consider the light orange col... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535549",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
How to explain the Maxwell Boltzmann distribution graph (physically)? While studying the kinetic theory of gases, I came to the section: "The Distribution of Molecular Speed" of a book. The book first (without any explanation) proposes the Maxwell's speed distribution law as
$$P(v) = 4\pi \left ( \frac {M}{2\pi RT} \ri... | Spherical coordinates give R^2 sin
The difference between $$ dN/N \propto \exp(-v_x^2/s^2) dv_x $$ and $$dN/N \propto v^2 \exp(-v^2/c^2)dv$$ lies in the detail about correctly moving from $dv_x$ to $dv$. Consider the infinitesimal volume in cartesian and spherical coordinates $$dv_x dv_y dv_z \propto v^2 \sin\theta\, d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535849",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 5,
"answer_id": 4
} |
Can a system reach equilibrium using only reversible processes? Consider an isolated system. We know that it will reach equilibrium after enough time. According to what I have read so far, the system should undergo irreversible processes to reach equilibrium, but is there any counterexample to this statement? i.e a sys... | Assume an isolated system. Start from an equilibrium state $0$ and remove some internal constraint so that the system spontaneously moves to another equilibrium state $1$. The difference in entropy $\Delta S = S_1 - S_0$ between the entropies of the final $S_1$ and initial $S_0$ is never negative (2nd law), and it is p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536146",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why is the speed of light in vacuum a universal constant? While getting familiar with relativity, the second postulate has me stuck. "The speed of light is constant for all observers". why can't light slow down for an observer travelling the same direction as the light?
| The short answer is, because if we assume the speed of light is constant then our equations predict experimental outcomes with greater accuracy.
The electromagnetic answer is, because if you plug the measured permittivity and permeability of free space into Maxwell's equations, that is the speed you get.
The Relativist... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536432",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 7,
"answer_id": 3
} |
Can the real-time Green's function be written in the form of path integral on the real axis? In every textbook, the path integral of the Green's function is written in imaginary-time. I wonder whether we could write real-time green function in the path integral form.
| You mean the (equilibrium) statistical mechanics textbooks, which deal mainly with the statistical sum, and therefore need only the imaginary path integral.
The real-time path integral is usually derived in quantum mechanics textbooks, where it is sometimes also shown to be the direct solution of the Schrödinger equati... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536561",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
If work is a scalar measurement, why do we sometimes represent it as the product of force (a vector) and distance (scalar)? Consider an object being pushed 3/4 of the distance around a circular track. The work done on the object would be the distance of 3/4 the track’s circumference times the force applied to the objec... | The work is the dot product of the force and the displacement, and displacement is a vector; we have to take into account what direction it is pointing. If an object is traveling in a circle, then it has to have a centripetal force, so it doesn't have a constant force. It could have a constant magnitude force, though. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536688",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 4,
"answer_id": 3
} |
Why doesn't the orange light filter appear bluish if it transmitts orange and reflects or absorbs all other frequencies? I was going through the absorption and reflection phenomenon of light and this question struck my mind as I was walking through the light filters. Why does orange filter not appear bluish if it trans... | There are actually two major types of filters:
*
*Absorption filter
A piece of orange glass (like in a photo camera filter), for example, is an absorption filter. It absorbs higher frequency light, and doesn't absorb much the red-orange frequencies. The result is that due to the usual, Snell's reflection these are... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536827",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
What does "up to a total derivative" really mean and how should I know when to use it? I am a mathematician who is taking a quantum field theory course without much prior pyhsics. We have had the term "up to a total derivative" a few times, yet every time I asked what it meant I didn't really grasp it.
As an example, f... | Since the Lagrangian density (which is confusingly also referred as a Lagrangian) is defined as a function which is integrated on, we may always think the $\mathcal{L}$ in inside a 4D integral, since the action is defined via
$$
S = \exp \left( \int d^4x \mathcal{L} \right).
$$
Now, we may decompose the term to two id... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536941",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Conservation of energy of 2 identical Rolling Disks with and without friction My physics book claims that if two identical disks moving at the same velocity travel up nearly identical hills, with the second hill not having friction, then the disk rolling up the first hill will travel to a greater height. Given that the... |
Given that the disks started with the same kinetic energy while rolling at the base of the hill, shouldn't they reach the same height (i.e. same potential energy) as a result?
First, let's assume that no slipping occurs on the hill with friction and that both disks are rolling without slipping before they get to thei... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537088",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 5,
"answer_id": 2
} |
Confusion regarding properties of Poisson Brackets I have just started learning about Poisson Brackets, and came across the following property
$$\{q_i,q_j\}=0$$
And
$$\{p_i,p_j\}=0.$$
Where $p$ and $q$ are respectively the momentum and position coordinates i.e. phase space coordinates.
Now Poisson Brackets are defined ... | I think there is an misunderstanding on your side. $$\frac{\partial q_j}{\partial q_i} = \delta_{ij},$$ where $\delta_{ij}$ is the so-called Kronecker delta.
I hope this helps so far.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537275",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why can vector components not be resolved by Laws of Vector Addition? A vector at any angle can be thought of as resultant of two vector components (namely sin and cos).
But a vector can also be thought of resultant or sum of two vectors following Triangle Law of Addition or Parallelogram Law of Addition, as a vector ... | There are two main cases of separating into components: standard coordinates system, and separating into normal and parallel.
In a standard coordinate system, there is a set of coordinates, and points are given in terms of those coordinates. Not all coordinate systems are vector spaces; for instance, the longitude lati... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537550",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 7,
"answer_id": 3
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.