Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Einstein Field Equations and Electromagnetic Stress-Energy Tensor My question is: if we write Einstein field equations in this form:
$$R_{\mu\nu} - \dfrac{1}{2}g_{\mu\nu}R=8\pi \dfrac{G}{c^4}T_{\mu\nu}$$
Then the left hand side is one statement about the geometry of space-time and the right hand side is one statment ab... | Yes. It does in fact mean that electromagnetic fields can also change the geometry of spacetime. Anything with energy and/or momentum affects the geometry of spacetime because, as you point out, the gravitational field equations exhibit a coupling of spacetime geometry to energy-momentum.
For more info in the case of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/55660",
"timestamp": "2023-03-29T00:00:00",
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Schrodinger's cat experiment What's wrong in taking the cat as an observer in Schrodinger's experiment? Plz kindly elaborate! And if possible also describe about possible logics if the question bears the answer No.
| The experiment is intended to highlight the problem of quantum superposition applied to macroscopic objects.
It's not inconceivable that a radioactive nucleus can be in a superposition of states. When you interact the nucleus with the detector, hammer and glass of poison, the wavefunction that describes these items bec... | {
"language": "en",
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Why can't we store light in the form of light? We can store cold (ice), heat (i.e. hot water bag) and electrical charge (batteries). We can even "store" a magnetic field in a magnet. We can convert light into energy and then, if we want, back to light. But we can't store light in form of light in significant amounts. ... | The answer by John Rennie and subsequent comments reminded me of this TEDtalk about energy storage from light.
I don't know the details, but this is what I understand they did: they've studied the electronic and absorption properties of foils made of nanotubes, in particular when combined with the result of some impres... | {
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What causes insects to cast large shadows from where their feet are? I recently stumbled upon this interesting image of a wasp, floating on water:
Assuming this isn't photoshopped, I have a couple of questions:
*
*Why do you see its image like that (what's the physical explanation; I'm sure there is an interesting ... | This is a great example of how nice it can be to reason about refraction stuff using Fermat's principle.
Let's reduce all this to 2 dimensions. The surface tension produces something like this:
Now if we want to know where a light “ray” needs to go to get from some light source, we just need to find the way that takes ... | {
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"url": "https://physics.stackexchange.com/questions/55833",
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Newton's third law of motion: An apple resting on the surface of earth My friend asked me a question which was:
For an apple resting on the floor, what is the action and reaction force pair?
I said that the Earth exerts a gravitational force on the apple and the apple also pulls on the earth and both these forces are... | You are basically correct. The apple and the earth exert equal but opposite forces on each other but, as they are in contact, neither of them can move. The forces are balanced by the internal pressure in the apple and in the floor.
Consider the case where the apple is not resting on the floor. In that case the apple wi... | {
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Do the proton PDFs change much with Q? Specifically, the second moments, do they change much from say 100 to 1000 GeV? Why or why not?
| You can check directly yourself using the Durham HEPData page, which lets you plot PDFs as a function of $x$ or $Q^2$.
At large $x = 0.1$, they're fairly constant over a range of $Q^2$.
But at small $x = 10^{-4}$, they rise quickly with $Q^2$:
This is an illustration of Bjorken scaling at large $x$ and its breaking a... | {
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distance of electron from proton An electron is projected, with an initial speed of $1.10 \times 10^5 \text{m/s}$, directly towards a proton that is essentially at rest. If the electron is initially a great distance from the proton, at what distance from the proton is its speed instantaneously equal to twice its init... | The potential energy due to the electrostatic interaction between two particles of charges $q_1$ and $q_2$ is
$$
U = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r}
$$
where $r$ is the distance between them.
| {
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Influence of charged particle's own electric field on itself I read this in my textbook: A charged particle or object is not affected by its own electric field.
Since I find this completely unintuitive and my mind is yelling "wrong! wrong! how could a particle even distinguish between its own field and the external fie... | The self force is the result of the radiated field created because of the force caused by another particle but it's not a force caused only by the particle to itself.
If we consider a particle with an extension and a charge density, there is no Coulomb force caused by a point of the particle over the rest of the point.... | {
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Why is electrical energy so difficult to store? Does anyone know a general answer to these questions? (I've asked them together because they're all pretty related, it seems.)
*
*Why is it that we find electrical energy so difficult to store? Do we just find energy difficult to store generally? (...surely not, we can... | A general answer which is not of any particular use is that electrical energy, and the forms in which we store it, are typically very low entropy systems. The lower the entropy the more they "want" to dissipate and the harder it is to stop that tendency to turn into (ultimately) heat. Same way that it is a lot easier t... | {
"language": "en",
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How to determine the direction of a wave propagation? In the textbook, it said a wave in the form $y(x, t) = A\cos(\omega t + \beta x + \varphi)$ propagates along negative $x$ direction and $y(x, t) = A\cos(\omega t - \beta x + \varphi)$ propagates along positive $x$ direction. This statement looks really confusing bec... | First the assumption/definition is that $\omega$ and $\beta$ are positive constants.
Next you are asking about the phase velocity ie the velocity of a crest, a trough, any fixed point on wave profile.
This means that $\omega t \pm \beta x + \phi$, which can be called the phase of the wave, is a constant.
If you differe... | {
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Hamiltonian of a simple graph I have a spin system:
As shown in the picture, there are two spins S1 and S2, and a pair of interactions between them. One is a ferromagnetic interaction and the other is anti ferromagnetic interaction. I am trying to calculate the Hamiltonian of this system.
The Hamiltonian of the syste... | The Hamiltonian of this system lives in a 4-dimensional Hilbert space since you have two spin $1/2$. Therefore, you should represent the spin matrix in this four dimensional space like this:
$S_1^z=\begin{pmatrix}
-0.5 & 0 &0 &0 \\
0&-0.5 &0 &0 \\
0 &0 &0.5 &0 \\
0 &0 &0 &0.5
\end{pmatrix}$ , $S_2^z=\begin... | {
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Does the collapse of the wave function increase entropy of the atomic system itself? Does wave-function collapse cause the entropy of the atom (ie. the sub-atomic particle system that makes up the atom) to increase?
| Disclaimer. I'm not sure it even makes sense to talk about changes in entropy of systems that undergo wavefunction collapse unless one also includes the measuring apparatus as part of the system. Having said this, here are my two cents that I hope are informative:
The (von-Neumann) entropy of a quantum system prepared... | {
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Are two waves being in phase the same as saying that the two waves are coherent? If two waves are coherent, is it the same as them being in phase? Please correct if I'm wrong.
| I believe that "in phase" means that the phase difference of the two waves is zero (and out-of-phase means that this difference is equal to pi). But more general if the phase difference of two waves remains the same during a time that is called "Coherence time", the fields are coherent during that time.
In reality the ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What fraction of peak horsepower do typical 4 door passenger vehicles use? I was surprised when I looked at the power rating of the engine used on a Humvee. It's only ~190 horsepower, which is exceeded by many sedan engines.
So an obvious question is why doesn't my Camry SE burn more gas than a Humvee and I think it's ... | At normal highway speeds of 75, or less, about 20 percent based how auto makers are gearing the transmissions in most cars.
| {
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What Pauli matrices should I use for this two spin system? Consider the Hamiltonian $H = -J_\text{F}S^{(1)}_zS^{(2)}_z + J_{AF}S^{(1)}_zS^{(2)}_z$, describing the graph
Here, F means ferromagnetic and AF means antiferromagnetic interactions. I am having problem with the value of $S^{(1)}_zS^{(2)}_z$.Someone suggested ... | Essentialy $S^{(1)}_{z}.S^{(2)}_{z}=\sigma_{z}^{1}\otimes\sigma_{z}^{2}$ and you can easily check that $\sigma_{z}^{1}\otimes\sigma_{z}^{2}=\sigma_{z}^{1}\otimes I_{2\times 2}. I_{2\times 2}\otimes\sigma_{z}^{2}$. And $\Sigma_{z}=\sigma_{z}\otimes I_{2\times2}+I_{2\times2}\otimes\sigma_{z}$.
| {
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Why planets are orbiting only in one plane? Since gravity is three dimensional why planets are orbiting only in one plane around sun.
| The planets generally are traveling in a plane. The Sun's axis is tilted about 30 degrees to this plane. Pluto's orbit is roughly 17 degrees off of the Earth's orbit. Eris is 44 degrees. There is a distribution of smaller bodies at all inclinations.
http://en.wikipedia.org/wiki/Invariable_plane
http://en.wikipedia.org... | {
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"timestamp": "2023-03-29T00:00:00",
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How to describe heat transfer between two solid materials? A general equation for dealing with heat transfer between one material and a region of insulating material. I've seen basic heat transfer equations for one material, but I'd love to see an explanation of how to do two.
| Basically you can use Fourier's Law
$$
q = -k\frac{dT}{dx}
$$
with the appropriate boundary conditions between the two materials. The basic issue is that at the interface between the two materials, there is a jump discontinuity in the value of the thermal conductivity, and you have to take this into account in solvi... | {
"language": "en",
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How is parity relevant to determining angular momentum? Question:
Particle A, whose spin $\mathbf{J}$ is less than 2, decays into two identical spin-1/2 particles of type B.
What are the allowed values of the orbital angular momentum $\mathbf{L}$, the combined spin $\mathbf{S} = \mathbf{s}_1+\mathbf{s}_2$ (where $\mat... | Hmmm, an old question without a satisfactory answer. I'll have a go.
The spins of the two $B$ may combine as
\begin{align}
\text{singlet}\quad|s_1s_2\rangle &= \frac{\left|\uparrow\downarrow\right> - \left|\uparrow\downarrow\right\rangle}{\sqrt2},
&
\text{or triplet}\quad|s_1s_2\rangle &= \frac{\left|\uparrow\downarro... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Place each foot on a scale: can you add the two to find your weight? I frequent a blog from a British psychologist, and every Friday he likes to pose an interesting puzzle or riddle. The Monday after that he posts the answer. They're good fun, and IANAP but this week's answer made my it-might-not-be-quite-as-simple-as-... | Well, It would work, but only with the condition that your weight doesn't shift around between the time you look at the first reading and the next. But either way, the sum of the readings on the scales always equals "more than twenty stone" however much that specific weight may be, as long as the body in question is in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/57225",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Where are we : On level ground or on a ramp - moving in a train? Let's say we are traveling in a train. The path has two parts: one at ground-level and the other moving up on the ramp. The ramp has an inclination of $\arctan\frac{a}{g}$ with the horizontal, where $a$ is the acceleration of the train on level ground and... | Although the gravitational/inertial force causing the pendulum to tilt in the same way in both cases (see Equivalence principle link of @zhermes) thus not allowing you to see whether you are on accelerating or on the slope, you will probably be able to feel the difference.
The reason is that although the force parallel... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/57283",
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"source": "stackexchange",
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How does the solar sailing concept work? Wikipedia describes solar sailing as
a form of spacecraft propulsion using a combination of light and high speed ejected gasses from a star to push large ultra-thin mirrors to high speeds.
I understand the part where ejected gasses bump into the sail pushing the spacecraft. O... | I think you are really asking "how can light deliver an impulse to the sail". The answer is that although light has no mass it does carry momentum. When light is reflected off the sail, conservation of momentum requires that the sail changes momentum by twice the momentum of the light. The extra kinetic energy of the s... | {
"language": "en",
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Capacitance of a capacitor Why does the capacitance of a capacitor increase if the distance between the two plates of a parallel plate capacitor is decreased? I think, with decreasing distance between the two plates, the force of attraction between the charges on the two plates will increase, and as a result more charg... | A capacitor has a capacitance depending on the maximum voltage sustained across the plates $C_{\text{max}}=\frac Q{\Delta V_{\text{max}}}$.
The voltage sustained between the plates depends on field strength between the plates. The strength of the electric field between the plates is equal to the voltage sustained bet... | {
"language": "en",
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Can we change frame of reference twice in a single problem? My question has an inclined plane of mass $M$ and simple block kept on it, of mass $m$ (Both on a table). All surfaces are friction-less. Both of the objects would move, block down the incline and inclined plane parallel to the table, somewhat opposite to the ... | I'd recommend that you stick to one frame, otherwise you'll have to make coordinate transformations to make your equations consistent and that's significantly more work than it's worth.
Also, be careful that if the inclined plane accelerates (which it will if I understand your setup correctly) then you have to introduc... | {
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What does it mean that an inspiral is 'adiabatic'? Binary systems emit gravitational radiation. This causes the system to lose energy, which results in a shrinking of the semi-major axis. I have read on countless occasions that this 'inspiral' is adiabatic (here for example). What does this mean that the shrinking is a... | The $Q=0$ is just a convenient definition for thermodynamics. The key to adiabacity is that the process is approximately in an equilibrium state at every step. In thermodynamics, this means that you want the process to be reversible, which means that you want the entropy change during the process to be zero, and sinc... | {
"language": "en",
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Relating generalized momentum, generalized velocity, and kinetic energy: $2T~=~\sum_i p_{i}\dot{q}^{i}$ According to equation (6) on the first page of some lecture notes online, the above equation is used to prove the virial theorem. For rectangular coordinates, the relation
$$
2T~=~\sum_i p_{i}\dot{q}^{i}
$$
is obviou... | Your answer looks complicated and I feel it misses the point. The fact that $2T=\sum_l p_l \dot{q}_l$ is fundamentally due to Euler's homogeneous function theorem. This states that
$$
\text{if }f(\alpha \mathbf{x})=\alpha^k f( \mathbf{x})\text{, then } \mathbf{x}\cdot\nabla f(\mathbf{x})=kf(\mathbf{x}).
$$
When stated ... | {
"language": "en",
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"source": "stackexchange",
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Alternative methods to derive the static potential in the NR limit of QED In QED, one can relate the two-particle scattering amplitude to a static potential in the non-relativistic limit using the Born approximation. E.g. in Peskin and Schroeder pg. 125, the tree-level scattering amplitude for electron-electron scatter... | If you set $c\to \infty$ in the QED Hamiltonian you obtain a non-relativistic Hamiltonian whose potential only includes a pseudo-Coulomb term $(1/r)$, because this is the only term of order $c^0$ in the QED interaction. No further calculation is needed to obtain the potential.
| {
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Path integral with boundary and bulk terms I was wondering if their is a general strategy for computing path integrals with a mix of boundary and bulk integral actions. Do people use divergence theorem to convert the action into bulk integrals, or is there some other trick?
| The usual Feynman rules may still be derived. If there are both boundary fields and bulk fields, one needs to include the bulk-to-boundary propagators, too. The same problem has to be solved in the AdS/CFT correspodence. Search for "Witten diagrams" to see how the Feynman diagrams are ultimately done in this context.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Hamiltonians, density of state, BECs When working with Bose-Einstein condensates trapped in potentials, how can one tell what the density of state of a system of identical bosons given the Hamiltonian, $H$? (I have been told that it is possible.)
Suppose the Hamiltonian is some 2D harmonic oscillator -- so $$H=p^2/2m+(... | This is definitely possible. A good resource is this statistical physics script. The density of states for an electron gas is calculated explicitly there, check out eqn. (5.21) and following. Then, some BEC calculations are made explicitly, starting on page 119. V is the (physical) volume of the system you look at.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/58108",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 1,
"answer_id": 0
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Eye sensitivity & Danger signal Why are danger signal in red, when the eye is most sensitive to yellow-green?
You can check luminosity function for more details...
| Yes, It's true...
We know that our eyes have three types of cone cells - S (short), M (medium) & L (large). The naming is done in order to differentiate the cells from "which cell absorbs which color". S to Blue, M to Green and L to red. The peak wavelength of L is 564 nm, yellowish-green. The peak of M is 534 nm, blui... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/58166",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 7,
"answer_id": 1
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What happens when a compact fluorescent lamp implodes? When a incandescent lamp implodes, the filament burns up and the current is interrupted.
Yesterday, a compact fluorescent lamp imploded and blew all the switches / fuses. I'm not sure if the same would happen with ordinary fluorescent lamps.
Can it be that the char... | It very much depends on the control gear, there are a variety of designs for circuits for starting and running fluorescent tubes. I don't think any of them involve capacitors but there is likely to be an inductor that might cause a voltage spike when the circuit is broken. Normally, an implosion of the tube would not b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/59405",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What is the speed of acceleration of the inflation of the universe? Is the inflation speed of the universe accelerating or is it a constant speed of expansion proportional to distance between objects.
| *
*When we talk about universe inflation we should have in mind that the four cosmic forces did not appear yet, because at inflation no elements were formed yet.
*scientists say that at 0.03 second the inflation reached four light-years, also said that if it had continued at the same rate, it would have been disappea... | {
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Direction of the Area Vector (with regards to magnetic dipole) I'm learning about torque on a conductive coil in a magnetic field. I have been taught that $\vec\tau = \vec\mu \times \vec{B}$, where $\vec\mu$ is the magnetic dipole moment. Also, $\mu = I\vec{A}$, where $\vec A$ is the area vector of the loop.
To find ... | As far as I know, the area vector is a purely mathematical object whose definition is related to the orientability of the surface (in this case, a disk). This is a property of surfaces embedded in an Euclidean space that allows to choose surface normal vector to the surface at every point. For an oriented surface, this... | {
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Proof that a spherical lens is stigmatic In geometric optics, we generally allow that, for example in the case of a convex lens, rays coming from a particular point get refracted towards another particular point on the opposite side of the lens.
How is this proven from Snell-Descartes' law? Do we need to use the paraxi... | Usual spherical lenses are only approximately stigmatics, that is to say the image of a source-point is itself a point. You need paraxial approximation to ensure approximate stigmatism and avoid spherical aberration.
You can see it by playing around with just a plane interface between two different transparent media li... | {
"language": "en",
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How old is SUN ☉? How do we know/calculate the exact age of sun ☉ ? ie. 4.57 billion years. What is the way to calculate it?
| We do know that the solar system has formed along with the sun (being a third generation star). There are some isotopes distributed (though rarely) throughout the solar system. In Earth, we can do a radio dating for such decaying elements, which can be found in rocks, meteorite locations, etc..
For confirmation, we can... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/59670",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Galaxies moving away at the speed of light As an arts student, I really find those cosmological questions hard to understand and hence come here to seek your kind help.
The Hubble constant $H_0$ is estimated to be about 65 km/s/Mpc, where 1 Mpc (megaparsec) is around 3.26 million light-years. At what distance would gal... | The Hubble sphere is the locus of points where the Hubble flow is equal to c. The Hubble sphere is not an event horizon.
All observed objects with a redshift greater than about 1.46 are outside the Hubble sphere. In other words, these objects are receding superluminally. Furthermore, these objects were outside of the H... | {
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The rule breaker, emissivity + reflectivity = 1 If emissivity and reflectivity are inversely proportionate, why does glass have a high emissivity of around 0.95-0.97 as well as being very reflective for IR Radiation?
normally it works but not with glass!
Can anyone explain this?
| To me the problem is not linked to the reflectance, but to the surface finish.
Picking up an image of a reflection in the visible part of the spectrum is possible even on a black carbon surface if that surface is polished well enough. To convince yourself of this, simply pick a dark material with a well polished surfa... | {
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Is lattice enthalpy positive or negative? I've learnt that the lattice enthalpy (defined as the energy change from a solid ionic lattice to separate gaseous ions) is always positive, obviously. However, I've seen it explained as the opposite other places, so it's negative.
What is correct?
| Lattice energy is defined as when 1 mole of cation and 1 mole of anion combined to form 1 mole of solid crystal, energy is released. The energy released is known as lattice energy because we know anion and cation has highewr energy than crystal lattice therefore when bond is formed between cation and anion energy is re... | {
"language": "en",
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How does the freezing temperature of water vary with respect to pressure? I know when the pressure is reduced, the boiling temperature of water is reduced as well. But how does the pressure affect the freezing point of water?
In a low-pressure environment, is water's freezing temperature higher or lower than $0\sideset... | What happens when water becomes ice - it expands.
With a pressure change apply Le Châtelier's principle - "If a system at equilibrium is subjected to a change in pressure . . . . . . . then the equilibrium shifts in such a way so as to undo the effect of the change".
So in the case of the volume of ice being bigger tha... | {
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Higher order covariant Lagrangian I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at Klein-Gordon-Lagrangian) or non-covariant (e.g. KdV) ones. Also some pointers to the literature... | I) As user Vibert mentions in a comment, the Euler-Lagrange equations are not modified$^1$ by adding total divergence terms to the Lagrangian density
$$ \tag{1} {\cal L} ~ \longrightarrow ~{\cal L} +d_{\mu}F^{\mu}. $$
Adding total divergence terms leads to an inexhaustible source of higher-order Lagrangians.
II) Gen... | {
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How does the wavelength change in relativistic limit? In the text, it reads that the momentum of a particle will change if it is moving at speed close to light speed. In the general case, the wavelength is given as
$$
\lambda = \frac{h}{p}
$$
and
$$p = \frac{mv}{\sqrt{1-v^2/c^2}}$$
when $v \to c$, $p\to\infty$, so ... | Lorentz contraction! The measured de Broglie wavelength in the direction of propagation vanishes because that's what special relativity says happens. The wavelength has to go as $h/p$ as you wrote, so why does it surprise you that when $p$ gets large the wavelength gets small?
| {
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$\beta^+$ decay We've been discussing radioactive decay at school, and I grasped everything except for $\beta +$ decay. When I googled radioactive decay, I immediately found out they dumbed down radioactive decay for us, which is probably why they didn't care to explain what they did, they just showed some calculations... | Neutron mass ~ mass of proton + 2 electrons.
Beta- decay, by Einstein's formula, the remaining mass is converted into kinetic energy, the speed of the proton and electron.
Beta- is an exothermic reaction; it gives off energy.
Beta+ is endothermic; it needs energy to happen, the kind of energy that is available inside ... | {
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How do you tell if a metric is curved? I was reading up on the Kerr metric (from Sean Carroll's book) and something that he said confused me.
To start with, the Kerr metric is pretty messy, but importantly, it contains two constants - $M$ and $a$. $M$ is identified as some mass, and $a$ is identified as angular moment... | You tell if a space (or spacetime) is curved or not by calculating its curvature tensor. Or more unambiguously one of the curvature scalars (e.g. Ricci, or Kretschmann) since these don't depend on the coordinate system, but all of the information in the scalars is also contained in the Riemann tensor.
It is not necessa... | {
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Why the chemical potential of massless boson is zero? In Bose-Einstein condensation, the chemical potential is less than the ground state energy of the system($\mu<\epsilon_g$). But why does the massless boson such as photon have zero chemichal potential($\mu=0$)?
| The chemical potential is a complementary variable to $N$, the number of particles (of a certain kind), and they get combined in the same sense as $-\beta,H$ and similar pairs. The chemical potential "punishes" too high or too low number of particles in grand canonical and similar distributions such as
$$\exp(-\beta(H-... | {
"language": "en",
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Is it possible to "add cold" or to "add heat" to systems?
Amanda just poured herself a cup of hot coffee to get her day started.
She took her first sip and nearly burned her tongue. Since she didn't
have much time to sit and wait for it to cool down, she put an ice
cube in her coffee and stirred it with a metal... | I definitely disagree.
Cold is a relative feeling, cant be added;
Coffee will release temperature to equalize the temp.
| {
"language": "en",
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Towing of asteroid I recently studied that NASA has planned to tow and place it in the orbit of the moon.
My doubt is when asteroid is placed in the orbit near moon.since the gravitational field of earth is very high.what will it revolve around the moon or the earth.
Can anyone clarify my doubt ??
| The setup is just like this: Earth around Sun, Moon around Earth and finally asteroid around Moon. Here's a phrase I've got from Nat Geo (assuming this is the news you've studied)
NASA wants to identify an interesting asteroid flying around deep space, figure out a way to capture the spinning and hard-to-grab orb, nud... | {
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Dimensional Regularization involving $\epsilon^{\mu\nu\alpha\beta}$ Is it possible to dimensionally regularize an amplitude which contains the totally antisymmetric Levi-Civita tensor $\epsilon^{\mu\nu\alpha\beta}$?
I don't know if it's possible to define
$\epsilon^{\mu\nu\alpha\beta}$ in e.g. $$d-\eta$$-dimensions w... | This problem was already mentioned in the original 't Hooft-Veltman article and solved by Breitenlohner and Maison. This solution is known by the name "HVBM scheme" (after 't Hooft, Veltman, Breitenlohner and Maison).
A clear description of this regularization procedure is given for example in the following dissertatio... | {
"language": "en",
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How can I prevent my son building up static on his trampoline? Whenever my three year old son plays on his trampoline, it doesn't take very long for him to start building up a significant amount of static electricity. His hair stands on end (which is quite amusing), but when I help him down we both get a nasty static ... | Dryer sheets rubbed on you before you both get on there, works great for us!
| {
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If photons can be absorbed by electrons, wouldn't that mean light has a charge? I am a biochemistry and molecular biology major. If photons can be absorbed by electrons, wouldn't that mean light has a charge? Electrons only attract positive charges. Isn't it?
| No. Photons (of electromagnetic radiation) are produced by accelerating electric charges. This means that an excited electron (at a higher energy state) emits energy in the form of electromagnetic radiation proportional to the difference between the two energy levels (orbitals) between which the transition of electron ... | {
"language": "en",
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Physical Interpretation of the Integrand of the Feynman Path Integral In quantum mechanics, we think of the Feynman Path Integral
$\int{D[x] e^{\frac{i}{\hbar}S}}$ (where $S$ is the classical action)
as a probability amplitude (propagator) for getting from $x_1$ to $x_2$ in some time $T$. We interpret the expression $... | One of the the numerical values of the weight $\exp{\frac{i S}{\hbar}}$ is going to have a maximum contribution to the Feynman path integral. You've probably seen a probability density plot in 2D or 1D. The classical path is going to be the one that minimizes the action. Think of it as a maximum probability density mov... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/61139",
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"source": "stackexchange",
"question_score": "12",
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Does Earth produce metallic elements in its core? Does Earth produce metallic elements in its core?
| The densest elements (metals) in the Earth fall to the center, due to the gravitational force. The densest elements are radioactive, Earths core is radioactive, Uranium-238 is one radioactive species at the center of the earth.
U-238 decays to Thorium via alpha emission, due to the electric force
$$^{238}_{92}\text U_... | {
"language": "en",
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Invariance, covariance and symmetry Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from field theory?
| The definitions of these terms are somewhat context-dependent. In general, however, invariance in physics refers to when a certain quantity remains the same under a transformation of things out of which it is built, while covariance refers to when equations "retain the same form" after the objects in the equations are... | {
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What would happen to the Moon if Earth is turned into a black hole? Assume that all of sudden the Earth is turned into a black hole. And the moon revolves around the Earth (before turning into a black hole). What would happen to the Moon after earth changes to black hole will it be sucked to the black hole or continue ... | $F= (GMm)/r^2$ where $M$ is mass of earth and $m$ is mass of moon and all factors are constant hence $F$ does not changes . As earth now has an infinite density hence only when moon hits the event horizon it would experience a greater $F$. So unless it happens moon would retain its orbit.
| {
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Is a black hole a perfect black body? A black body absorbs all light/radiation in its reach. According to basic laws of physics, the more energy a body absorbs the more it can emit. Therefore, a black body absorbs all energy directed at it and also emits all energy that's been absorbed.
A black hole is known to absorb... | Yes, black holes are supposedly near-perfect black bodies. They emit thermal radiation called Hawking radiation, which, however, does not originate from beyond the event horizon, but is a consequence of the interaction of the strong gravitational field outside the horizon with the vacuum.
The process is sometimes descr... | {
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What is Anderson localization? Could someone give an example worked out in detail? What is Anderson localization, for someone with no previous knowledge on the subject?
I tried to read Anderson's original paper, but it was too terse for me. I have seen a couple of intuitive explanations, e.g. 50 years of Anderson local... | A nice example due to Michael Berry is to look at a stack of transparency sheets. Collectively the stack makes an excellent reflector precisely because of the randomness of the gaps between the individual sheets. If the gaps were constant you would just have a photonic band gap. Finite 1D systems require finite rando... | {
"language": "en",
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Bose-Einstein condensate for general interacting systems There is Bose-Einstein condensate (BEC) for non-interacting boson systems. Can we prove the existence of BEC for interacting systems?
| Bogoliubov proved long, long ago that the condensate is stable against weak interactions. The interactions scatter some fraction of bosons out of the lowest-energy single-particle state ("depleting" the condensate), but off-diagonal long range order remains. For a nice introduction to Bogoliubov's theory see Ben Simon'... | {
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Electric field near a conducting surface vs. sheet of charge I know perfectly well how to derive the magnitude of the electric field near a conductor,
$$E = \frac{\sigma}{\varepsilon_0}$$ and near a sheet of charge, $$ E = \frac{\sigma}{2\varepsilon_0} .$$
In fact, I can explain with clarity each step of the derivatio... | The answer is simple. It is all in the definition of sigma. In the case of a non-conducting sheet sigma means entire charge in a given area of the sheet meaning both surfaces and everything between them. In the conducting case it is just easier to think of sigma as being the charge on one surface not the sum of both as... | {
"language": "en",
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How long does a supernova last? Is a supernova over instantaneously? Or, does the (for want of a better word) explosion continue for a while? What is/are the order of timescales involved? What is the duration for which the supernova continues to release copious amounts of energy?
| Supernovae can take well over a week to reach maximum luminosity, and they stay rather bright for months after the peak. This just goes to show how much energy is involved in these event.
I was going to assemble a collage of light curves from my own research, but then I realized this has already been done at Wikimedia ... | {
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What is the fastest a spacecraft can get using gravity-assist? Assuming normal spacecraft and space objects (no neutron stars, black holes, etc). To what speed can a spacecraft accelerate using gravity-assist?
For example, if a spacecraft is moving at relativistic speeds, it probably won't get seriously sped up by norm... | There are other answers there, but I wanted to give an answer in terms of the velocity of the spacecraft, the velocity of the planet, and the surface gravity of the planet.
TL;DR The largest increase in speed possible in a gravity assist is
$$ \frac{2sgr}{gr + s^2} $$
where $s$ is the initial speed of the spacecraft re... | {
"language": "en",
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Parabolic motion (experiment) We performed a laboratory, performing six releases of a sphere with angles $15^\circ,30^\circ,45^\circ,60^\circ,75^\circ,40^\circ$ a parabolic movement, took five distances for each angle, the initial velocity was calculated $3.025~\text{m/s}$.
Then doing 5 tosses of the sphere with an an... | I can think of two or three things.
*
*The whole experiment can be divided into two parts. In one part you calculate the initial speed by measuring distance. In the other part you calculate speed by measuring time. Assuming that your calculations are correct, that would suggest that there might be a difference in th... | {
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Can the effects of a person's mass upon the local gravitational field be detected and measured remotely? As the title suggests, Can the effects of a person's mass upon the local gravitational field be detected and measured remotely?
I am aware any mass produces and effects gravity but couldn't find anything in my searc... | The gravitational field of small objects can be measured. In fact as far back as 1797 Henry Cavendish measured the gravitational field from lead spheres. He used pairs of spheres of mass 158kg and 0.73kg, so for a person weighing say 70kg the same method is in principle possible, although in practice people are an inco... | {
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When does Thevenin's theorem not apply (modelling a power source with a ohmic internal resistance) Most physics text books say that a power source can be modelled as an EMF with a internal resistance. This is also know as Thevenin's theorem or Norton's theorem. However I have read in some sources that this is not alway... |
When does this model not apply/break down and for what reasons?
Thevenin's theorem assumes linearity. So, if your circuit is non-linear, the theorem doesn't apply. However, one can linearize the circuit about an operating point and find a small-signal Thevenin equivalent circuit.
To find the Thevenin equivalent of ... | {
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Is light red shifted in optical tweezers? This is a question I put to my supervisor during my PhD many years ago, and never really got a satisfactory answer to.
In an optical tweezers, assume that a beam of light is used to move a glass bead. My question is whether the outgoing light is red-shifted. If it is not I can... | Sure - the relativistic doppler effect means that light which is scattered off a moving object can be redshifted or blueshifted. And there can be more redshifted photons than blueshifted photons, or vice-versa, depending on where the object is, and how it's moving, relative to the center of the trap.
But since the obje... | {
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Voltage of open circuit
A battery with emf $\varepsilon$ and internal resistance $r$ is connected
with a resistor $R$ in the following open circuit. What is the voltage $V_{ab}=V_a-V_b$?
The answer is $- \varepsilon$. "No current. There is no voltage change across R and r.". But I don't really understand why ... I... | Think of the open as infinite resistance. Your current will be $I = E/(R+\infty) = 0$. Now, voltage dropping across every resistor is proportional to the current and resistance: $V(r) = I * r$. Since infinite resistance is infinitely larger than R, all $E$ will drop across $\infty$ and 0v is left to R. Particluarly, $V... | {
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Forces as One-Forms and Magnetism Well, some time ago I've asked here if we should consider representing forces by one-forms. Indeed the idea as, we work with a manifold $M$ and we represent a force by some one-form $F \in \Omega^1(M)$. It sounded really natural, because if $v \in TM$ then $F(v)$ would be the work done... | I think the point is that the force of an EM Field acting on a particle is not just defined by the forms itself but more by the Lorzenz Force
$F= q(E +i_v B)$
Where $E$ is a one form, $B$ a two form where we insert the tangential vector of the particles curve with the inner derivative. Here you can see that the magnet... | {
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How can anything be hotter than the Sun? I've heard that if a space shuttle enters the atmosphere from a bad angle its surface will become so hot that it will be hotter than the surface of the Sun.
How can that be? It seems to an uneducated mind that Sun is really really hot, how could something seemingly minor such as... | As for the question of whether anything can be hotter than the sun. The Sun is composed of plasma, an energetic phase of matter in which electrons get ripped off of atoms, and electrons and ions coexist in something that might best be described as an ionized gas.
According to this wiki page, the so-called Z machine ha... | {
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How can Ohm's law be correct if superconductors have 0 resistivity? Ohm's law states that the relationship between current ( I ) voltage ( V ) and resistance ( R ) is
$$I = \frac{V}{R}$$
However superconductors cause the resistance of a material to go to zero, and as I understand it, as $R \to 0$, $I \to \infty$. Does ... | In superconductivity we have current without voltage, and in Josephson effect we have a current without voltage. These are quantum systems where bizarre behavior is anticipated. The resistivity of the superconductor is given by $\rho=\mu_0\hbar/(2m_e)$, where the constants are understood.
| {
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Polarization of sound Sound can't be polarized because the vibration of such type can't be polarized i.e, it can't be limited or controlled by any barriers and so polarization is not possible in them.
This is what my teacher answered me when i asked the question. But i didn't understand what did he mean by "the vibrati... | I am not sure exactly what your teacher meant, but to me the simple explanation is simply that sound is a pressure wave. Pressure has no direction, only a single value (scalar) and sound waves are fast periodic modulations of the pressure.
A wave on a string can have polarization because the string can be distorted in ... | {
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Why does the quantum eraser seem to violate energy and momentum conservation? In the literature of the quantum eraser experiment it is argued that the change in statistics of the system from non-interference to interference is due to the erasing of "distinguishing information". The preparation of the experiment almost ... | In the quantum eraser experiment, the interference is re-created logically, not physically. It is re-created by conditioning on some observable which is measured after the interference pattern has failed to appear on the detector. This doesn't require any energy.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/62828",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
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Is it possible to have topological degeneracy in 1D ? I mean to have q-fold degenerate ground states on a ring which could not be lifted by local perturbation.
If the answer is no, then what is the physical (or mathematical) reason against having such a state in 1D ?
| This may not be how people generally think about topological degeneracy, but if you define it to be any degeneracy or asymptotic degeneracy in the thermodynamic limit with the following two properties:
(1) it cannot be lifted by local perturbative Hamiltonians that respect the symmetry;
(2) it cannot be attributed to s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/62900",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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measure higher frequencies then half of Planck-frequency? The maximum frequency is defined by the Planck frequency $\omega_P$. Also there is the Shannon theorem which tells us that to lossless capture a signal, you have to sample it with minimum of the double frequency.
That states that you cannot measure frequencies ... | The Nyquist-Shannon sampling theorem is about continuously sampling a waveform. This really matters when a waveform is a mix of many different frequencies. The theorem says you must sample at a rate double the highest frequency. With light you only need to take one "sample" (the energy of the photon or its momentum)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/62965",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Probability of position in linear shm? The problem that got me thinking goes like this:-
Find $dp/dx$ where $p$ is the probability of finding a body at a random instant of time undergoing linear shm according to $x=a\sin(\omega t)$. Plot the probability versus displacement graph. $x$=Displacement from mean.
My wo... | The differential $dp(x)$ is the probability of finding the body in an interval of length $dx$ centered at $x$. The quantity $p$ you are looking for is the cumulative distribution function,
$$P(x)=\int_{-\infty}^x \frac{dp}{dx}(x) dx,$$
which is the probability that the particle will be to the left of the point $x$. Sin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/63022",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Is there a relativity-compatible thermodynamics? I am just wondering that laws in thermodynamics are not Lorentz invariant, it only involves the $T^{00}$ component. Tolman gave a formalism in his book. For example, the first law is replaced by the conservation of energy-momentum tensor. But what will be the physical me... | I don't know a definitive answer to your (really good) question, but here is a quote from an old textbook I have by Christian Moller ("The Theory of Relativity"):
Shortly after the advent of the relativity theory, Planck, Hassenoerl,
Einstein and others advanced separately a formulation of the
thermodynamical laws... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How to determine the direction of medium's displacement vectors of a standing wave? Consider the following problem taken from a problem booklet. My questions are:
*
*What is displacement vector?
*And how to determine the direction of displacement vector at a certain point?
*Where is the position with zero displace... | A standing wave is a wave that has nodes. The points of the wave go up and down in some places, and remain at zero at others (the nodes). The general form of a standing wave is a sine curve that remains at a fixed position, but its amplitude changes in time between $+A_0$ and $-A_0$. Specifially, there is a time where ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Definition of electric charge and proper explanation Is there a definition of electric charge and proper explanation of it?
It is said "Electric charge is the physical property of matter that causes it to experience a force when close to other electrically charged matter." How is it though that matter can get charged?... | I think every fundamental definition is kind of going in circle.
I would say an electric charge is something that obeys Maxwell's laws.
But to write those laws, you have to know $\vec{E}$ and $\vec{B}$ which need a definition of an electric charge.
At the end you just group things that look/react alike and named them. ... | {
"language": "en",
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"source": "stackexchange",
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Evolution principle of the physical laws I wanted to know if there is a physical theory that considers that the laws of physics undergo an evolutionary process. That see the law of physics or the absence of them, as something dynamic, and that with time they slowly converge to something we know today. A kind of simulat... | The reason why the "evolution of physical laws" is not popular is because we can make sense of observations from a long time in the past with the laws we know (star formation and evolution comes to mind). One can of course consider an change in physics with time, but this would only add complications to a thoery that w... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 5,
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Finding surface tension of water at certain temperature and pressure The question is:
Using the Young-Laplace Equation (if applicable), find the surface tension (dynes/cm) for water at 20
degrees Celsius with 2.5 psi. Round to the nearest tenth.
Well, I didn't use the Young-Laplace equation, not sure ... |
Using the Young-Laplace Equation (if applicable)
Basically a trick question trying to get you to equate the pressure in the question with $\Delta P$ in the Young-Laplace equation.
The actually pressure dependence of water's surface tension is given in On the Evaluation of the Surface Tension-Pressure Coefficient fo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/63568",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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} |
Recommendation for a physics history/non-fiction book I know that there are a lot theses being published on lives of physicists. Is there a history/non-fiction book that tracks the development of a problem chronologically? Like pieces of a puzzle.
I would like it to be mathematical and trying to get into the heads of ... | There is hardly a book covering all physics, but for particular subjects there is some. For example:
Jammer: The Conceptual Development of Quantum Mechanics.
Whittaker: A History of The Theories of Aether and Electricity.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/63753",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
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North and south of magnetic field
The current I is flowing upward in the wire in this figure. The direction of the magnetic filed due to the current can be determined by the right hand rule.
Can we determine the north and the south of the magnetic field produced by the current I by using a hand rule?
| You're right with the right hand rule. It's accepted because it agreed with the observations. Placing a magnetic needle (compass) in the influence of the (theorized) magnetic field lines, the compass deflects in the direction of the field indicating the curl. The direction how we twist our fingers show the direction of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/63820",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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"answer_id": 2
} |
Does relativistic mass have weight? If an object was sliding on an infinitely long friction-less floor on Earth with relativistic speeds (ignoring air resistance), would it exert more vertical weight force on the floor than when it's at rest?
| My previous answer proved to be wrong. Energy density ("relativistic mass") does contribute to gravity - and the fact that the object is moving at relativistic speeds does affect the space-time around it.
There is an interesting document that explains the problem in further context.
Besides, when we think about it, i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/63961",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "22",
"answer_count": 4,
"answer_id": 0
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How do you determine the heat transfer from a $p$-$V$ diagram? I doubt this question has been addressed properly before, but if there are similar answers, do direct them to me.
I am currently studying the First Law of Thermodynamics, which includes the p-V diagram and of course, $\Delta U = Q_{to} + W_{on}$.
My questio... | If you have a path on $p-V$ diagram that is $p=F(V)$, then using
$$
dU=\delta Q-pdV \implies \delta Q=dU+pdV
$$
NOTE MINUS SIGN as $pdV$ is work done BY the system. $Q$ is the total heat received by the system (it is negative if system releases heat). Assume we are dealing with an ideal gas with $f$ degrees of freedom... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Angular momentum conservation while internal frictional torque is present So this appears in a problem which looks simple enough in its context; It's something like this:
Two discs, A and B, are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and $2I$ respectively about the common axis. Dis... |
How can we apply angular momentum conservation when friction is present?
Why not? If we have a closed system, momentum and angular momentum are conserved. In this case, the full system is disk A and disk B, and there are no external forces, so the system is closed. There are internal forces, namely in this case, fric... | {
"language": "en",
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"source": "stackexchange",
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Donors/Acceptors in Metal Oxides Can anyone explain to me why most articles describe chromium as an acceptor in titanium dioxide? In TiO2, titanium has the charge state Ti$^{4+}$ and oxygen has the charge state O$^{2-}$. When Cr substitutes for Ti, it does so as Cr$^{3+}$. Now, at first glance, Cr has atomic number ... | A 3+ ion substituting for a 4+ ion is called p-type doping. Since it only contributes 3 electrons there is one missing, called a hole. This hole will readily accept an electron, so it is an acceptor. As you say this will also give an impurity band just above the valence band. That Cr gives fewer electrons to the lattic... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/64218",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 1,
"answer_id": 0
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Physical interpretation of Poisson bracket properties In classical Hamiltonian mechanics evolution of any observable (scalar function on a manifold in hand) is given as
$$\frac{dA}{dt} = \{A,H\}+\frac{\partial A}{\partial t}$$
So Poisson bracket is a binary, skew-symmetric operation
$$\{f,g\} = - \{f,g\}$$
which is bil... | The physical interpretation is integrability conditions being satisfied on the manifold. From the first equation, if you would take A not depending on 't' explicitly then dA/dt = [A,H]. The Poisson bracket contains in it the dynamics involved in canonically conjugate variables and in classical mechanics, we can measure... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/64421",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 3,
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Assuming space is infinite can our observable universe be an island amongst an archipelego? According to recent measurements our observable universe is roughly 93 billion light years in diameter; also it appears (according to WMAP measurements) that spacetime is flat.
Supposing space is infinite.
It seems to me that it... | As noted above in comments, I'm not competely sure I understand the question. But anyway, I'll give it a shot.
The answer is model-dependent. The standard cosmological model at the moment is the Lambda-CDM model. This model has various parameters. Depending on these parameters, the spatial curvature can be positive, ne... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/64502",
"timestamp": "2023-03-29T00:00:00",
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"question_score": "1",
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What do people actually mean by "rolling without slipping"? I have never understood what's the meaning of the sentence "rolling without slipping". Let me explain.
I'll give an example. Yesterday my mechanics professor introduced some concepts of rotational dynamics. When he came to talk about spinning wheels he said so... | watch the following video for a great explanation:
http://www.youtube.com/watch?v=xbXsSEtbkzU
and read this article for the interesting causes of rolling resistance/friction: //www.school-for-champions.com/science/friction_rolling.htm
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/64555",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "42",
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"answer_id": 11
} |
Why does increasing the temperature of a thermistor decrease it's resistance? Surely, upon an increase in temperature, the atoms within the thermistor would vibrate with more energy and therefore more vigorously, hence making the electrons flowing through the electric circuit more likely to collide with one of the atom... | Using your playground example....
Imagine if you had to pass a message (electricity) across the playground, when cold you would have to stretch between each fixed person to pass this message. When hot, more people fill the gaps, the message is easier to pass.
Hope this helps :)
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/64627",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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Does inertia increase with speed? I have heard that when the speed of the object increase, the mass of the object also increase. (Why does an object with higher speed gain more (relativistic) mass?)
So inertia which is related to mass, increase with speed?
So, if I accelerate on a bus, my mass will increase and my iner... | It depends on how you define inertia. http://en.wikipedia.org/wiki/Inertia#Interpretations. The answer to your question is 'yes' if we interpret inertia as p=mv, and no if we interpret it as F=ma.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/64661",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 1
} |
How does an earthen pot keep water cool? I understand that evaporative cooling takes place thanks to small pores contained in the pot and that allow some water to go through and evaporate. However I couldn't understand clearly whether water inside the pot stays at its original temperature or would it cool further?
If i... | Imho, this process is driven not by energy considerations but by kinetic considerations. That should be why it naively seems weird that water absorbs heat from a cooler object and evaporates. Note: This is an explanation I came up with on-the-fly and have no references to back up with.
Since the earthen pot has small p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/64716",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 3,
"answer_id": 2
} |
Comparing Static Frictions In this figure, which of the static frictional forces will be more?
My aim isn't to solve this particular problem but to learn how is static friction distributed . Since each of the rough-surfaces are perfectly capable of providing the $-1N$ horizontal frictional force but why don't they ? T... | The contact forces with two blocks are $N_1 = m_1 g + m_2 g$ for the bottom block (to the floor) and $N_2 = m_2 g$ for the top block (to the 1st block).
The available traction is $F^\star_1 = \mu_1 (m_1+m_2)\,g$ and $F^\star_2 = \mu_2 m_2\, g$ or
$$ \begin{pmatrix}F_1^\star\\F_2^\star\end{pmatrix} = \begin{bmatrix}1&-... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/64780",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Optics alignment of a confocal scanning microscope I am facing a challenge in my project regarding optical alignment.
See the figure:
The challenge is with the vertical optical system alignment. I considered placing a mirror and check back if the image and source coincide. But since the light is too low on power (less... | A low tech version of a point-like source at the stage plane is to use a pinhole (very small, depending on magnification of your objective, say 1um - 10um). Then illuminate the back side of the pinhole using a laser. You will get a quasi-point source, of course not good for determining PSFs but maybe enough for alignem... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/64865",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can a car's engine move the car? Newton's First Law of Motion states that an object at rest or uniform motion tends to stay in that state of motion unless an unbalanced, external force acts on it.
Say if I were in a car and I push it from the inside. It won't move. So how is the engine of a car capable of moving t... | The car's engine tries to make the wheels turn. However, the wheels encounter friction against the road so they cannot just spin. As the road has much higher inertia than the car, it will not move when the wheels want to turn. Instead, it is the car that moves.
The end effect is that the engine pushes against the road,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/65001",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 5,
"answer_id": 0
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Quantum Mechanical Operators in the argument of an exponential In Quantum Optics and Quantum Mechanics, the time evolution operator
$$U(t,t_i) = \exp\left[\frac{-i}{\hbar}H(t-t_i)\right]$$
is used quite a lot.
Suppose $t_i =0$ for simplicity, and say the eigenvalue and eigenvectors of the hamiltionian are $\lambda_i... | Starting with:
$$U(t,t_i) = e^{\frac{-i}{\hbar }H(t-t_i)}$$
If $t_i=0$:
$$U(t,0) = e^{\frac{-i}{\hbar }Ht}$$
Using the identity: $\sum\limits_i \left|\lambda_i\right>\left<\lambda_i\right|=\mathbb{I}$
$$U(t,0) = \sum\limits_i e^{\frac{-i}{\hbar }Ht}\left|\lambda_i\right>\left<\lambda_i\right|$$
Since the exponential ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/65041",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
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Why the magnetic flux is not zero? If $\vec{\mathbf B}=B\vec{\mathbf a}_z$, compute the magnetic flux passing through a hemisphere of radius $R$ centered at the origin and bounded by the plane $z=0$.
Solution
The hemisphere and the circular disc of radius $R$ form a closed surface, as illustrated in the figure; there... | According to Maxwell's equations the magnetic flux over a closed surface must be zero.
In this case the hemispherical surface in question is not a closed surface, it is an open surface.
If we consider the closed surface (the hemispherical section And the circular base)
the total flux passing through will be zero.
Using... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/65183",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 0
} |
Induced current using a reference system bound with a moving charge Suppose we have a charge moving at velocity $\mathbf{v}$ in the same plane of a square wire.
If I sit in a reference frame where the square wire is still, since the charge is moving with velocity $\textbf{v}$ in this coordinate system, I will see an... | In these type of questions, the following effects usually exist, but are usually missed:
*
*The electric potential(and ergo the electric field), that corresponding points of the wire feel, varies. This effect will polarize the wire which is always negligible, and we are going to ignore it as well.
*in a moving wire... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/65242",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 0
} |
Convergence of Light on the Retina So, I've learned about lens ray diagrams-but the problem I'm having is that when ray diagrams are drawn for a point of an image, they converge to another point, but there are two problems that I see with regards to our eyes:
1) In the simplest drawn case it's at least three rays conve... | Geometric optics can be confusing. On your first question: you have to keep in mind that the three rays one usually draws are just example rays highlighting the divergent cone of light emitted from a point and hitting the lens and subsequently being focused via a converging cone onto a unique point in the image plane. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/65300",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How does relativity explain gravity, without assuming gravity I have seen the "objects pull down on space-time" explanations, but they assume a "pull down" force themselves. Could anyone explain the space-time explanation without assuming gravity in the first place?
|
but they assume a "pull down" force themselves.
The images of flat sheets "pulled down" where the planets are do not reflect the fact that the curvature of spacetime is an intrinsic curvature that is measured by geodesic deviation.
What has been done, in order to help visualize the spatial curvature, is to take a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/65363",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 1
} |
Stable Nuclei - Deviation from equal protons and neutrons While studying the semi-empirical mass formula for nuclei, I came across an "asymmetry term" whose function, as far as I understand, is to build in the fact that nuclei "prefer" to have equal numbers of protons and neutrons. This is explained by the Pauli exclus... | Well, look at the other terms...in particular consider the Coulomb term as that one depends only on the proton number.
Walecka's book writes it as
$$ E_3 = \frac{3}{5} \frac{Z (Z-1)}{4\pi R_C} e^2 \approx a_3 \frac{Z^2}{A^{1/3}} \,.$$
This term is strictly positive and grows rapidly as the atomic number increases, whil... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/65415",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 2,
"answer_id": 0
} |
Why does sound move faster in solids? I know that the molecules are closer together in solids, and I know thicker springs also respond carry waves faster than thinner springs, but for some reasons I can't understand why.
The molecules will have a larger distance to move before colliding with another molecule, but in a... | The difference between solids and gases appears in the momentum conservation equation:
$\rho\frac{d\vec v}{dt}=\vec S$ where $\vec S$ is a source term that expresses the rate at which momentum is exchanged between neighboring volumes, a "restoring force".
In gases, $\vec S=-\vec \nabla p$, where the pressure $p$ relate... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/65580",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 3,
"answer_id": 1
} |
Tensor equations in General Relativity In the context of general relativity it is often stated that one of the main purposes of tensors is that of making equations frame-independent.
Question: why is this true?
I'm looking for a mathematical argument/proof about this fact.
|
In the context of general relativity it is often stated that one of the main purposes of tensors is that of making equations frame-independent. Question: why is this true?
Actually this isn't quite true. General relativity doesn't have frames of reference (except locally, which is trivially true because GR is the sam... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/65700",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 2,
"answer_id": 0
} |
Why are the magnetic moment and the angular moment related? Why are the magnetic moment and the angular moment related? I've always read everywhere that they are related but found nowhere a satisfactory explanation of the cause
| Magnetic moment, angular momentum, and charge are related, because the magnetic field is how the electromagnetic interaction carries angular momentum.
If there were an intrinsic relationship between magnetic moment and angular momentum, you would expect the neutrino to have a magnetic moment. The current PDG reports ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/65822",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 2
} |
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