Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why does not dark matter gather and form celestial bodies? since the only thing we know about dark matter that it "attracts" and affect our Baryonic matter's momentum and speed, which means that it does have mass of a sort.
so why didn't we witness a darkmatter-darkmatter interactions in form of collisions of celestial... | The standard answer is that dark matter does not seem to interact strongly with itself (although self-interacting dark matter is an active research topic), and does not emit electromagnetic radiation. The latter property means that a clump of dark matter cannot lose energy by radiating it away, and will remain a diffus... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/471226",
"timestamp": "2023-03-29T00:00:00",
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Why is Earth's gravitational acceleration $9.8 \frac{m}{s^2}$? How was the value of $g$ determined as 9.8 $\frac{m}{s^2}$?
I am not requesting the derivation but the factors/parameters that influence this value.
| One thing I'd like to add to these excellent answers is that although you didn't ask for a derivation, I think it is necessary in understanding the $g = \frac{GM}{r^2}$ equation.
The force due to gravity between two masses is given by Newton's law of universal gravitation;
$F=G\frac{m_{1} m_2}{r^2}$, where;
$F$ = Force... | {
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Why is normal force at the bottom dependent on normal force on top?
Why does the normal force on bottom of the track have anything to do with the normal force on top of the track? Why isn't the normal force at the bottom simply $mg$?
| The connection is that the centripetal force that keeps the car going in a circle is the same at the top of the track as at the bottom (because the car is travelling at a constant speed). If this centripetal force is $F$ then at the top of the track we have
$F = N_{top} + mg$
where $N_{top}$ is the normal force at the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/471561",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Potential by Assembling Charges For finding electric potential energy of a uniformly charged sphere, we can assemble the sphere by brining charges from infinity to that point. So to make a uniformly charged sphere of radius $R$ and total charge $Q$, at some instant, charge will be assembled up to a certain radius $x$. ... | Approach 2 is wrong. You didn't take into account the corresponding limits for potential. Potential at centre of sphere is not zero!! The expression is V(x)-V(0) instead of V(x).... Find potential at surface by integrating for electric field outside sphere from X to infinity V(infinity)=0. So Then if you wish you can f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/471655",
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Why was M87 targeted for the Event Horizon Telescope instead of Sagittarius A*? The first image of a black hole has been released today, April 10th, 2019. The team targeted the black hole at the center of the M87 galaxy.
Why didn't the team target Sagittarius A* at the center of our own galaxy? Intuitively, it would se... | Of course they targeted Sgr A* as well.
I think though that this is a more difficult target to get good images of.
The black hole is about 1500 times less massive than in M87, but is about 2000 times closer. So the angular scale of the event horizons should be similar. However Sgr A* is a fairly dormant black hole and ... | {
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Why can infinite planes be approximated as Gaussian surfaces? A little background: I'm an undergraduate studying Electrodynamics, currently in Chapter 8 of Griffiths.
A question I came across (8.4 part a for those curious) asks for a calculation of the force exerted by one point particle on another point particle of eq... | Imagine the infinite plane orthogonally intersected by a cylindrical Gaussian pillbox of area $A$. Force lines are normal to the infinite plane, therefore the totality of force lines exiting the cylinder are through the ends of the cylinder. If the charge density of the infinite plane is $\sigma$, and the integral onl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/471907",
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Proving that $dS$ is an exact differential mathematically OK...so I hope this is not too dumb a question:
We know that we can express $dS$ as $$dS=\frac{dQ}{T}=\frac{C_v}{T}dT+\frac{R}{V}dV,$$
where $C_v$ is the thermal capacity at constant volume and $R$ is the gas constant.
However, I recall that for a differential o... | For a perfect gas, once one arrives at an expression for $dS$, the integrability condition is a trivial check.
$C_v=\alpha R$ with alpha constant. Thus, $C_v/T$ does not depend on $V$, while $R/V$ does not depend on $T$ and the condition for integrability is trivially satisfied.
A little less trivial (but not too dif... | {
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Why was the imaging of M87 black hole easier than imaging the Milky way's Sagittarius A*? In the recent EHT press release of the image of the super massive black hole at M87, I am curious to know why the super massive black hole at the centre of milky way has not been imaged yet.
| The EHT needs a long exposure time. M87* is rather stable, so while SgrA* is apparently quite variable even during exposure time. The team is busy de blurring the SgrA* image. See this link and practice your Dutch at the same time: https://www.astroblogs.nl/2019/04/10/een-opzienbarend-eht-middagje-in-brussel/amp/
| {
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Stress-Energy Tensor and Conformal Invariance in String Theory Since the Euler-Lagrange Equations corresponding to the Polyakov Action implies no dependance on the auxillary metric we arrive at the constraint $T_{ab}=0$. We then change to lightcone coordinates $++$ and $--$ and write $T_{++}$, $T_{+-}$, $T_{-+}$, and $... | The stress-energy-momentum (SEM) tensor $T_{ab}$ doesn't vanish as an operator identity/off-shell. The Virasoro constraints $T_{ab}\approx 0$ are on-shell equations that hold in quantum average $\langle T_{ab}\rangle=0.$
If there is no Weyl-anomaly, we may consistently impose off-shell
*
*Dilation symmetry $\Right... | {
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Why is there no jet visible in the M87* black hole radio image? M87 is known to contain a jet that is likely created by the supermassive black hole at its center. The recently published radio image taken by the Event Horizon Telescope does not display any noticeable jet. I can think of a few reasons why, but lack knowl... | In fact if you see the two jets in the image M87. They are very weak and can not be clearly supported because of lack of resolution of the EHT. but if you are looking for a good quality image you can see that two jets come off in opposite directions.
| {
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What is frequency entanglement? If frequency (or energy) is regarded as a quantum property, can one generate a pair of photons with frequency entanglement? What would be the uses of this type of entangelment in say, sensing? How would you describe it mathematically? And would you be able to give a bit of intuition?
| We are basically talking about time-energy entangled photons. This is used for quantum communication. The real term is frequency bin entanglement.
First, a monochromatic laser pump produces frequency entangled photons, where the frequency of each photon is uncertain, but the sum of their frequencies is well defined.
TH... | {
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What causes the color difference of lightning flashes? Some flashes of lightning are seen in a blue shade while some have a yellowish/orange appearance .What is the possible cause of colour difference?
| Lighting produces light by ionising the air. For different proportions of gases in the atmosphere, you get different colours emitted during lightning. Learning from the comments, the following are the likely factors that affect the colour of lightning.
*
*Atmospheric composition varies with the place of interest. M... | {
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Magnesium has no unpaired electrons then why is it paramagnetic? Paramagnetism is often associated with presence of unpaired electrons in atomic orbitals of atoms of the element.But magnesium has no unpaired electrons in it's atomic orbitals but still is paramagnetic.Why?Please explain.
| Often, but not always. In metals the free electrons contribute to the magnetic properties and this contribution is not related to atomic orbitals. See "Pauli paramagnetism" for example. The free electrons have a diamagnetic component too (Landau diamagnetism). The balance between all the contribution will determine the... | {
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Why does a heavier element have a low specific heat capacity? Lead has 207 amu and 125j/kg/c while copper has 63 amu and 376 j/kg/c, why is that? So if energy is stored in the motion of the particles, heavier particles should move slower and therefore wouldn't this means that it require more energy to increase the temp... | I think you mean to say that they have a different number of particles- 1kg of lead and 1kg of copper surely have the same mass.
There are $~2.91\times10^{24}$ atoms in a kg of lead, and $~9.45\times10^{24}$ atoms in a kg of copper. Heat (more accurately, thermal energy) is "stored" in the particular degrees of freedo... | {
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If a satellite speeds up, does that make it move farther away or closer? If a satellite is in a stable circular orbit and goes about 41% faster (escape velocity) then it leaves its host forever. I get that. However, what if it speeds up by less than 41%?
Intuitively, it would seem to make the satellite move farther awa... | Since the stable velocity v for a given orbital radius $R$ is given by $v = \sqrt\frac{GM}{R}$, I would assume that the satellite spirals outwards at an accelerating rate. Since its velocity is greater than the stable velocity for that orbit, it will start to increase the radius of that orbit. As the radius increases,... | {
"language": "en",
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Calculating refraction between numerous media Last year, our teacher made us an exam to check our knowledge in light reflection and refraction. I don't perfectly remember it, but I know that one of the exercises included a ray with its angle of incidence, and let's say 7 media with their respective indexes of refractio... | Yes, you are right, except for that it is not the division of $\theta$, but $\sin\theta$. However, the real reason what you said is true can be seen by a bit of observation.
$$n_i\sin(\theta_i) = constant$$
Because:
$$\frac{n_2}{n_1} = \frac{\sin\theta_1}{\sin\theta_2}$$
And for the ray going to the third medium fro... | {
"language": "en",
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Show two Lagrangians are equivalent I need to show that these two Lagrangians are equivalent:
\begin{align}
L(\dot{x},\dot{y},x,y)&=\dot x^2+\dot y + x^2-y ,\\
\tilde{L}(\dot x, \dot y, x, y)&=\dot x^2+\dot y -2y^3.
\end{align}
It is the case iff they differ for a total derivation like $\frac{dF}{dt}(x,y)$.
In this cas... | I leave it to OP and the reader to prove that OP's two Lagrangians are indeed classically inequivalent, but let me make the following general remarks:
*
*Two Lagrangians $L_1$ and $L_2$ are classical equivalent iff they give the same Euler-Lagrange (EL) equations.
*A sufficient condition is that the difference $L_2... | {
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What had Feynman meant when he told nobody understands Quantum mechanics? What do we mean by understanding Quantum mechanics? What had Feynman meant when he told nobody understands Quantum mechanics?
What do we mean by understanding Quantum mechanics?
| I read the two existing answers (Anna; Valter Moretti) and I judge that whereas they are saying some correct things, they are not identifying correctly the issue which Feynman was pointing out.
The situation is that with quantum theory we have a very well-defined and detailed prescription for calculating, correctly and... | {
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Why does my baby's feeding bottle get smashed in fewer pieces when fuller? After and after again my baby has tossed in the air his glass made feeding bottle and get it smashed on the floor, I realized that the more the milk the bottle has the fewer fragments I had to collect...
This makes me curious enough but as my l... | When the bottle is in the air it has a potential energy of $(m_b+m_m)gh$. As you mentioned in the comment, more the bottle is filled more will be the potential energy. But in collisions it is not necessary for all the kinetic energy of the bottle to be converted to kinetic energy of the pieces. The energy is converted... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/475922",
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Why does nature favour the Laplacian? The three-dimensional Laplacian can be defined as $$\nabla^2=\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}.$$ Expressed in spherical coordinates, it does not have such a nice form. But I could define a different operator (let's call... | This is a question that hunted me for years, so I'll share with you my view about the Laplace equation, which is the most elemental equation you can write with the laplacian.
If you force the Laplacian of some quantity to 0, you are writing a differential equation that says "let's take the average value of the surroun... | {
"language": "en",
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What happens when a the volume of a perfect vacuum (0 psi) is increased? I'm an engineer working on a design in which a "plunger" will be pulled out of a sealed vessel, where the starting volume of the vessel is essentially zero and I need to know what will happen to the surrounding structure. If I'm asking this in the... | Suppose the plunger is 1 square inch in diameter. The work you do to pull it out is 14.7 pounds (force) times the distance you pull it out. Where's the energy? It's potential energy you got by lifting a 1 square inch column of air that distance. Let go of it, and that column of air will fall back, converting potential ... | {
"language": "en",
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Why is radiation dangerous? From Wikipedia:
Exposure to radiation causes damage to living tissue; high doses result in Acute radiation syndrome (ARS), with skin burns, hair loss, internal organ failure and death, while any dose may result in an increased chance of cancer and genetic damage
Why exactly is radiation da... | @David White is correct. This is a very broad question.
Radiation, or more specifically, electromagnetic radiation, covers a broad range from very low frequency long wavelength radio waves that pass right through you with no interaction to very high frequency short wavelength radiation that can cause severe biological ... | {
"language": "en",
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How is the relative force of the fundamental forces measured? My physics textbook includes the following table:
My question is about the fourth row, where it compares the relative strengths of the fundamental interactions. How are these determined? Is the ratio of electromagnetic and gravitational simply the ratio of ... | Of course anna v's answer is right, here are a few things I would like to add:
*
*EM force strength is measured from experimental data
*weak force strength is measured from experimental data
*gravitational force strength is not measured, but is only theoretically predicted
*strong force strength is theoretically ... | {
"language": "en",
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What should be the independent variable in a resistance experiment? I was asked a question by a student today and I have been pondering about it for a while now. In an experiment to measure resistance of a conductor, should we vary voltage across the conductor and measure the current or should we vary current flowing i... | In principle it doesn't matter so long as you measure both the voltage and the current accurately (don't just trust that the value of the independent parameter is whatever you set the source to). You ideally want to use Kelvin sense connections to be able to measure the two operating parameters independently.
You also ... | {
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Intrpretting questions on Fickian diffusion I am considering the Zimm model for polymer dynamics, and have come across a question
Find an expression for the time it takes for the polymer to diffuse a distance equal to its contour length $L=Nb$, if the drag coefficient for the polymer is $\gamma = N\beta b$ where the ... | I guess that should be that easy; you may swap $L$ with any other length... the only thing that could be bit fishy for me is that $\sqrt {\langle R^2 \rangle}$ (the position variance) is not necessarily equal to $\langle \vert R \vert \rangle$ (the average diffusion distance). But usually I use them interchangeably.
| {
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Wigner phase space operator correspondence: how to order? According to Gardiner-Zoller (Quantum Noise), operators acting on the density matrix can be mapped via e.g. (I'm taking Wigner space as an example, but the same holds for P and Q)
$$a\rho\leftrightarrow\left(\alpha+\frac{1}{2}\frac{\partial}{\partial\alpha^*}\ri... | $$a\rho\leftrightarrow\left(\alpha+\frac{1}{2}\frac{\partial}{\partial\alpha^*}\right)W( \alpha,\alpha^*)\equiv D W( \alpha,\alpha^*),$$
$$\rho a^\dagger\leftrightarrow\left(\alpha^*+\frac{1}{2}\frac{\partial}{\partial \alpha}\right) W(\alpha,\alpha^*)\equiv D^* W( \alpha,\alpha^*).$$
You proved $[D,D^*]=0$, and, of co... | {
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Why can I throw a larger stone farther than a smaller stone? Recently I was throwing stones(don't ask me why) when I noticed that there seems to be an optimum weight of stone so that it travels the farthest.
If I generate the same amount of force each time(and assuming all other variables like air resistance, angle of ... | Doriano Brogioli has pointed out correctly the important role of air resistance. However, I would like to flesh out one of the details in his answer.
If I generate the same amount of force each time...
In reality, your muscles can apply more force when they are moving more slowly. This is called the "force-velocity r... | {
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Why are there rings (halos) around street lights? Especially when it's foggy I was in a car that was turned off last night for some time and the windows became foggy via condensation (moisture droplets building up on one side of window). Looking outside, I could see that street lights which were near me had a halo or a... | The very fine droplets on the window act as a diffraction grating. In principle, a single droplet would produce (very faintly) something called an "Airy's disk" pattern. If they are all the same size, and the light is monochromatic, these will add constructively to make a clear ring. But in reality the droplets are man... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/477273",
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What is the definition of beam energy in particle physics? For example, the proton beams in the LHC collider have 7 TeV energy. Does this mean that the individual protons in the beam have 7 TeV energy or that the energy of all the protons in the beam add up to 7 TeV?
| Collision experiments are done to create particles that can not be studied under normal circumstances. Energy and momentum conservation as well as the famous Einstein equation $E=mc^2$ tell us that a heavier particle can not just "pop out of thin air". But if we let two particles with enough energy collide, they can cr... | {
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Is curved spacetime a real thing or just math? I was curious if the curving of spacetime by mass/energy was actually a real thing or is it just a mathematical construct, a way of visualizing the force of gravity and explaining it and that there is not truly a "fabric of spacetime" and this fabric doesn't actually curve... | Spacetime is curved by gravity, this is a very useful model, but this model of curved spacetime is not compatible with quantum mechanics. However, gravity may also be represented in the form of gravitational time dilation in flat, uncurved space.
This may be shown easily for the Schwarzschild metric:
$$ ds^2 = -(1 - \f... | {
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Current in the inductor at $t=0$ $L_1 = 5H, L_2=0.2H, M=0.5H, R_0=10 Ω$, and $i_g=e^{-10t}-10 A$. I need to find $i_2$.
I've started with DE
$$i_2R_0+L_2(di_2/dt)+M(di_g/dt)=0$$
and solved it for $i_2$, so $$i_2=0.625e^{-10t}+Ce^{-50t}A,$$
where C is constant.
I can't find C because I don't understand how to obtain... | The key is opened at t=0. Before that a steady current was flowing in the first network.
So, before t= o, change in current is zero. Thus, $\frac{di}{dt} = 0$.
Thus the induced current in the second network is zero at the instant t=0, i.e, $i_2(0) = 0$
| {
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Magnetic field at boundary of electromagnet iron core Assume you have an iron core in the interior of the solenoid. It is well known that the strength of the field should increase by a factor of several hundred inside the solenoid as a result of the iron core.
However, at the boundary between the iron core and the sur... | At the boundary of air and iron core, the following relations hold:
$$\vec {n}\cdot(\vec {B_1}-\vec {B_2})=0,\quad [\vec {n},\vec {H_1}-\vec {H_2}]=0$$
$\vec {n}$ is normal to the surface of the core. The surface-normal induction component is continuous. The tangential component of the magnetic field is also continuou... | {
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Griffiths Electrodynamics Problem 9.39: How can $\sin(\theta_T)$ be greater than one? When an electromagnetic wave strikes an interface between two linear media, Snell's law states that $\frac{\sin(\theta_T)}{\cos(\theta_I)} = \frac{n_1}{n_2}$ where $\theta_I$ is the angle of incidence, $\theta_T$ is the angle of trans... | Using Euler's formula
$$e^{ix}=\cos{x}+i\sin{x}$$
one can write
$$\cos{x} = \frac{e^{ix}+e^{-ix}}{2}$$
If $x$ is real, then $\cos{x}$ is real. However if you allow complex numbers $x=u+iv$ then
$$\cos{(u+iv)} = \frac{e^{iu-v}+e^{-iu+v}}{2}$$
and you see that the cosine (and sine as well) can be complex valued and grea... | {
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Shape of orbitals in atoms with multiple electrons I found this statement when browsing the Wikipedia article for atomic orbitals:
"Orbitals of multi-electron atoms are qualitatively similar to those of hydrogen."
Is this true? Googling around I could only found this article where in page 50 it seems to address how to ... | An approximation that seems to work well for the multi-electron case is the Hartree-Fock method.
In Hartree-Fock, we assume the mean-field approximation. Each electron feels the repulsion from other electrons based on their average, not instantaneous, positions. (This assumption prevents Hartree-Fock from predicting v... | {
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Can you change the wavelength of light keeping frequency constant and can you do the opposite as well? Can you change the wavelength of light keeping frequency constant and can you do the opposite as well?
I understood the basics but please don't hesitate to go deeper into the concept. Also, If you happened to have an ... | Wavelength times frequency gives the speed of a wave: $\lambda \nu=v$. The speed of light in a vacuum is a constant, but light can move more slowly in media (for example in water). For a photon of fixed energy, the frequency is fixed, so the wavelength of light should change when it goes into a medium in which the spee... | {
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Pauli Exclusion and Black Holes Pauli exclusion principle states that 2 identical electrons cannot be in the same state, where state includes a spacial component.
I have heard that, in order to avoid being in the same state, in a white dwarf, the De Broglie wave length of the electrons becomes shorter and shorter, mea... |
My question is, by applying more and more pressure, can we confine more and more identical neutrons/ other fermions in an arbitrarily small space, eventually forming a black hole? Or, at some point, fermions must be converted into bosons?
Black holes are classical entities.Fermions and bosons are quantum mechanical ... | {
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Why hydrogen lines are less visible in the Sun spectrum than in supernovae clouds? Supernovae clouds are very colorful, and if I trust documentaries I watched, the colors are due to excitation of elements, as in fireworks. Since the Sun is mostly made of hydrogen, I suppose those lines should be very apparent but they ... | The difference is that in the Nebulae you have black background for your hydrogen lines emission, and you can observe this easily with very simple imaging techniques (typically, 3.5-8nm pass-band filters do just fine).
On the sun you have "white" background - black body emission from deep levels of the sun. Hydrogen l... | {
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Why wavefunction becomes exponentially smaller during quantum tunneling? I am interested in quantum tunneling and I am wondering why the wavefunction of a particle would becomes smaller so that there is a slight possibility of finding it at the other side of a big energy barrier? Is there any interaction otherwise how ... | Wavefunctions are solutions of quantum mechanical differential equations, with given boundary conditions for the problem at hand, i.e. tunneling:
Is there any interaction otherwise how can the wavefunction knows there is a barrier?
The boundary condition of a barrier defines the wavefunction by construction. It has... | {
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Does kinetic energy warp spacetime? My interpretation of GR leads me to think that energy (namely kinetic) also adds to the curvature of space-time. Which, has raised a thought experiment. If a $10000$ kg ship closely passed a $1$ kg glass ball at $0.8c$ relative to the glass ball, would the glass ball be moved in the ... | Kinetic energy is part of the time-time component of the stress energy tensor, so by the Einstein field equations it does influence the curvature. However, the relationship is too complicated to justify a straightforward assertion that it adds to the curvature.
First, the curvature is a rank 4 tensor, not a scalar. So... | {
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How did Maxwell figure out the speed of light? The Wiki article is about 2 graduate years of physics beyond my understanding. What is a good high-school rendition of his thought process: regarding his use of the "distributed capacitance and inductance of the vacuum" to reach his conclusion?"
| The speed of light has been accurately measured by Foucault in 1862. See http://www.speed-light.info/measurement.htm for a historical overview of deyermi actions of the speed of light.
Maxwell unified electromagnetism and one of the consequences of his equations was that electromagnetic fields could propagate at the s... | {
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Is light affected by space warping or time warping? Gravity, according to the General Theory of Relativity, is simply the curvature of space-time. Objects in the universe move through space-time in geodesic paths. Also, the most interesting part is that it is impossible to curve/ warp space without having an effect on ... | Light is affected by both effects of gravity, you can count for time dilation and curvature too, this is the Shapiro effect.
When light passes next to the Sun, its speed measured from Earth will be less then c because:
*
*it moves in curved spacetime
*clocks near the Sun tick slower (compared to clocks on Earth)
Pl... | {
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Factorising a 4D Dirac delta function in a rest frame I'm working through a QFT problem and at one stage in the solutions we have this step:
$$\delta^{(4)}(p - q_1 - q_2) = \delta(E_1 +E_2 - M)\delta^{(3)}(\bf{q_1} - \bf{q_2}).$$
We are working in the rest frame of a meson with mass $M$ and the process is a decay to a... | Always
$$
\delta^4 (k) = \delta^1(k_0) \delta^1(k_1) \delta^1(k_2) \delta^1(k_3)
$$
If the momenta in your question are on-shell, then $\vec p=0$ because of the frame chosen,and $p^0=E_{p}=M$ , $q_j^0=E_j$, for the "on-shellness". Putting everything together you get your equality
| {
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What will happen to atmospheres of very large planets? Our earth can hold our atmosphere whereas Mars cannot. So the atmosphere retention mass must be between the masses of Mars and Earth, but if mass is to be considered then can an iron ball having the same mass of the earth hold an atmosphere of its own?
Also since l... | One reason Mars lost its atmosphere is that it lost its magnetic field. Without a magnetic field to protect it, the upper atmosphere is gradually blown away by the charged particles in the solar wind.
| {
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Why aren't satellites disintegrated even though they orbit earth within earth's Roche Limits? I was wondering about the Roche limit and its effects on satellites.
Why aren't artificial satellites ripped apart by gravitational tidal forces of the earth?
I think it's due to the satellites being stronger than rocks?
Is th... | When I was a kid I also wondered why artificial satellites within the Roche Limit were not pulled apart by tidal forces.
When I was a kid I also wondered, if any body within the Roche Limit would be pulled apart by tidal forces, and since the surface of the Earth is deep within the Roche limit, why aren't all objects o... | {
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Why can't a low solidity wind turbine be used in high torque applications through gearing? From my understanding, low solidity wind turbines (such as the three blade type) are more efficient due to a higher tip speed ratio, giving a higher coefficient of performance. However, they are not well suited to high torque ap... | High speed turbines have higher blade stresses, more stringent balancing requirements, and more design issues with the rotordynamics of flexible blades.
By comparison, a low speed turbine that works can be cobbled together with any sort of crude technology - it might not be very efficient, but it can do a useful amount... | {
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How are atoms supported on each other in a material? Suppose we have a ball made up of iron. There are a "lot" of atoms in the ball.
My question is "how" are the atoms supported on top of each other?
And, is it due to the repulsion of electrons the atoms maintain distance between themselves?
| Atoms in a solid are held in position by bonds which form between the atoms. Those bonds consist of either 1) electrons which are simultaneously shared by two atoms, yielding a covalent bond, 2) electrostatic forces of attraction which arise when one atom donates an electron to another, yielding an ionic bond, or 3) th... | {
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Physical intuition behind torque converter A torque converter (also here) is a device used in some cars. It uses several "fans" coupled through a liquid (transmission fluid) in order to perform the function of a clutch, but more importantly it acts as a liquid gear in the sense that it multiplies the torque going from ... | To me, this is by far the most understandable video that explains this mechanism:
https://www.youtube.com/watch?v=bRcDvCj_JPs&feature=emb_rel_pause
To summarize, the torque multiplication is the result of the reactor that helps the pump increase the oil pressure. When the difference of speed between the pump and the tu... | {
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Which side is convex in my plano convex lens? So, I am building an optical system and have got a Thorlabs plano-convex lens (part # LA1172-C) with a 400mm focal length. This makes the convex side of the lens so flat that it is difficult for me to discern (by naked eye) which side is convex on the lens. I need to know w... | If you are not concerned that it would damage the lens, you can put the lens on a smooth and flat surface and try pushing from the edges. I suppose you should be able to detect a small movement if the convex side is at the bottom.
As for an optical solution? I am not sure. As planar-convex lenses are non-ideal, you cou... | {
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Why does the potential difference across a type of parallel circuit not act like a potential divider?
Image credit (Q3)
In this attached circuit, when $R_1=0\Omega$, I am failing to understand how the two cells affect the potential difference across the central resistor R3. I understand that potential difference is co... | First, when $R_1 = 0\Omega$, resistor $R_3$ is in parallel with the source $V_1$ (a zero ohm resistor is identical to an ideal wire). Parallel connected circuit elements have identical voltage across and so $V_{R_3} = V_1 = 10\,\mbox{V}$.
But, as an exercise, you should work out the general solution for $V_{R_3}$ when... | {
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Liouville's integrability theorem: action-angle variables For classical dynamical systems, let $I_{\alpha}$ stand for independent constants of motion which commute with each other. 'Remark 11.12' on pg 443 of Fasano-Marmi's 'Analytical Mechanics' suggest that $I_{\alpha}$s can be taken as canonical coordinates.
For a c... | *
*Given $n$ functionally independent, Poisson-commuting, globally defined functions $(I_1, \ldots, I_n)$, so that the Hamiltonian $H$ is a function of $(I_1, \ldots, I_n)$ with $\mathrm{d}H\neq 0$, there certainly exist locally defined coordinate transformations:
$$ (I_1, I_2,\ldots, I_n)\qquad \longrightarrow \qqua... | {
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Information content in black holes Bekenstein-Hawking formula for entropy of a black hole tells us that information content in a black hole is proportional to its area which is in fact proportional to the mass^2 of the black hole. The information content before the formation of the black hole can be different which has... | Infomation Content in Black Holes
Your question is essentially (if i interpret it right) can stars with differing sets of initial detailed information--and thus differing information entropy-- converge to identical black holes?
The short answer is Yes --provided the no hair hypothesis is correct.
The longer answer has... | {
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Does light take the path of least time because it travels in straight lines or vice versa? My question is which of these two feats is a consequence of the other?
Light travels in straight lines, mostly. Does it do that as a result of Fermat's principle of least time? and if so, is there a reason as to why it follows th... | Light travels in straight lines because it takes the path of least time. The reason it takes the path of least time is because this is the path where the phase, which is proportional to the time, is a minimum. Since it is minimum, its derivative is zero with respect to small changes in the path. Thus, decomposing the l... | {
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Confused concept of " force" in ordinary language versus precise concepts in physics I'd like to be able ( for philosophical purposes) to illustrate this general idea : " science makes clear and precise concepts that are confused in ordinary/prescientific thought".
I think that a good example could be the concept of ... | Best example I can think of is from the original Star Wars movie, in which Darth Vader intones: "Never underestimate the power of THE FORCE". What he should have said (to make the units come out right) was:
"Never underestimate the power of THE FORCE times distance divided by time".
| {
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Is motion smooth? It's obvious that for every particle velocity is smooth i.e it cannot undergo sudden finite change in its position in infinitisiminal time.
Similarly any particle's velocity cannot undergo a change instantaneously (Infinite acceleration can't happen, intuitively).
Does this pattern apply to higher tim... | In order for jerk to be non-zero, the acceleration $a=\frac{\mathbf{d}v}{\mathbf{dt}}$ must be time-dependent:
$$a=\frac{\mathbf{d}v}{\mathbf{dt}}=f(t)\tag{1}$$
That's because the derivative of any number, no matter how large, is always zero.
But if $(1)$ applies the jerk becomes:
$$j=\frac{\mathbf{d}a}{\mathbf{dt}}=f'... | {
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Why haven't we yet tried accelerating a space station with people inside to a near light speed? Is that something we could do if we use ion or nuclear thrusters?
Wouldn't people in the station reach 0.99993 speed of light in just 5 years accelerating at 1g and effectively travel into the future by 83.7 years?
That wou... | I'm no physicist, but, just to add to the list of insurmountable problems with this idea, I've always thought the hardest problem was the "air resistance" in space.
The density of interstellar space is about 1 atom per cubic centimeter. If your spaceship is 1 meter cubed, and travels at c for 1 second, you have travell... | {
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Does pair production happen even when the photon is around a neutron? In order for a photon to decay into a pair of $e^+ e^-$, it must have at least $E_{\gamma}=1.022$ MeV and must be near a nucleus in order to satisfy the conservation of energy-momentum.
But would this happen even if the photon is near a neutron and n... | Quantum mechanics says that everything that is not forbidden is compulsory. Any process that doesn't violate a conservation law will happen, with some rate or cross-section. However, this general principle doesn't tell you what the rate is. For example, it's theoretically possible for 124Te to decay into two 62Ni nucle... | {
"language": "en",
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"source": "stackexchange",
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Can someone explain how magnetic potential energy can exist even though the field is non-conservative? $U=-B\cdot \mu$ is defined to be the magnetic potential energy, I saw this in my lecture notes, but we had already talked about the fact that since the work done to move a charge there is path dependant, there can not... | The problem you're having is that your confusing a field's scalar "potential" with potential energy. The concepts are related, but in a particular way. Say I have a vector field $\mathbf{V}(\mathbf{x})$. There is a mathematical theorem that I can break this field down into two two parts
$$\mathbf{V}(\mathbf{x}) = -\nab... | {
"language": "en",
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Flight Tme of Neutrinos between Emission & Absorbtion At a rough estimate,how long could a neutrino travel before striking a particle which would absorb it,& are there any neutrinos from the early days of the universe still wandering about?
|
i.e.
So this estimate of mean free path is more than a light year of lead! A fairly common qualitative statement in physics texts is that the mean free path of a neutrino is about a light-year of lead. Griffiths makes the statement "a neutrino of moderate energy could easily penetrate a thousand light-years(!) of le... | {
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If an object is travelling near light speed, would it's actions seem to be in slow motion? Hypothetically if we were observing a clock travelling near light speed relative to us, we would see the clock ticking at a much slower speed than us. If that is true, then would all actions that are at rest relative to the clock... | From our point of view (our reference frame) - we, who observe a clock traveling near light speed relative to us - all events are much slower - so the clock explosion is much slower, too. It's a fact.
(The only problem is how to observe this wonderful slow clock explosion in an object passing us with so enormous speed.... | {
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Can a wire having a $610$-$670$ THz (frequency of blue light) AC frequency supply, generate blue light? We know that when we give alternating current across a wire then it will generate an electromagnetic wave which propagates outward.
But if we have a supply which can generate 610 to 670 terahertz of alternating curre... | I second this Emilio Pisanty's point: the power supply you are
envisioning is a light source. Now the question that remains is: can
you propagate this light through a wire, just like you would do with a
regular low-frequency electric signal?
To get a hint of the answer, look at how people use wires to transport
high fr... | {
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Does rotation happen throughout the whole x axis of an object simultaneously? For example, if I draw a line on the side of a pencil top to bottom, then snap one end of it as in launching it due to the pressure of my fingers. Anyways, if I record the pencil launch in slow motion (perhaps it’s my phone that has to do wit... | Your question is a bit difficult to understand,but what you seem to be saying is that if you launch your pencil like a dart & give it some spin as you launch it,will the rotation manifest itself instantaneously along the whole length of the pencil? No,it won't. No signal can travel faster than light,so the rotation imp... | {
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Difference continous - discrete symmetry I am trying to understand the difference between the two types of symmetries.Wiki
Wikipedia says that
*
*Translation in time : $t \rightarrow t + a$
is a $\textbf{continuous}$ symmetry, for any real $t,a$
but
*Time reversal: $t \rightarrow -t$ is a $\textbf{discrete}$ symm... | In a nutshell, $a$ is an arbitrary but fixed 1-parameter, while $t$ is a running time coordinate. One cannot consistently put a fixed parameter equal to a running coordinate. Phrased differently, $a$ is here not allowed to depend on $t$.
In particular, the 1-parameter family $(\mathbb{R}\ni t\mapsto t+a\in\mathbb{R})_... | {
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Initial speed is zero and so is power? If I want to accelerate something from standstill to max speed, with a constant force (acceleration and mass don't change), the equation P = F * v would say that in the beginning we use 0 W power. How is that possible? Since power is the rate of transference of energy to the body ... | If you want to accelerate a body from $v$ to $v+\Delta v$, the associated change in energy is
$$\Delta E=E\left(v+\Delta v\right)-E\left(v\right)=\dfrac{1}{2}m\left(v+\Delta v\right)^{2}-\dfrac{1}{2}mv^{2}\approx mv \Delta v$$
You can see that for larger $v$ it costs more energy for the same increment $\Delta v$. Essen... | {
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Unorthodox way of solving Einstein field equations Usually when we solve field equations, we start with a stress energy tensor and then solve for the Einstein tensor and then eventually the metric. What if we specify a desired geometry first? That is, write down a metric and then solve for the resulting stress energy t... | This is sometimes jokingly called Synge's method. Here's an excerpt from Ingemar Bengtsson's A Second Relativity Course describing it (see Chapter 5):
We would now like to see a solution describing a physical system that approaches (in some sense) the Schwarzschild solution as it evolves. This can be obtained by mean... | {
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Is my understanding of vectors correct? I recently learned that a vector in mathematics (an element of vector space) is not necessarily a vector in physics. In physics, we also need that the components of the vector on a coordinate transformation as the components of the displacement vector change. So, if my understand... |
I recently learned that a vector in mathematics (an element of vector space) is not necessarily a vector in physics
A vector in "physics" is exactly the same thing as you have defined it in "mathematics".
Any vector space contains a basis $e_i$ upon which each element can be expanded as
$$
v = \sum_k v^k e_k.
$$
By ... | {
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What is a Material Called that Translates the Image of a Touching Object's Surface? What is the name of a material that moves light through it in such a way that it appears that the surface of an object has translated through the material? Also, what is an example of this type of material?
From very distant memory, I ... | From en.wikipedia.org/wiki/Ulexite:
The light transmits.
An example found in nature is Ulexite.
| {
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Why does the Schrödinger equation work so well for the hydrogen atom despite the relativistic boundary at the nucleus? I have been taught that the boundary conditions are just as important as the differential equation itself when solving real, physical problems.
When the Schrödinger equation is applied to the idealized... | The boundary condition at r=0 is that the wave function should be finite. The Schrödinger equation for hydrogen UC atoms and likely all atoms has solutions with negative $\cal l$, which are rejected because they diverge at r=0. See for example Schiff's textbook on quantum mechanics.
As for relativistic effects, you ma... | {
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Can Hydraulic System work on a Moon Robot? Since the Moon has no atmosphere and the temperatures reach maximum 123 C and min minus 153 C, how feasible is it to use hydraulic actuators to move the Robot legs?
Since my assistant Professor insists on going forward with the idea of building a smaller scaled model using the... | Yes, hydraulics will work - as long as you use a fluid that has a working range relevant to the ambient conditions.
Skydrol is used on aircraft as it has the properties deemed necessary... not the nicest stuff if you get it on skin etc...
| {
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Can I contract index in this expression? I'm reading Carrol text on general relativity, on page 96 they arrive to the term
\begin{equation}
\frac{\partial x^{\mu}}{\partial x^{\mu '}}\frac{\partial x^{\lambda}}{\partial x^{\lambda '}}\frac{\partial^2 x^{\nu '}}{\partial x^{\mu}\partial x^{\lambda}}.\tag{1}
\end{equatio... | The chain rule (3) is correct, but expression (1) is only 1 out of 2 terms in expression (2)
$$ \frac{\partial^2 x^{\nu ^\prime}}{\partial x^{\mu ^\prime}\partial x^{\lambda ^\prime}}~=~ \frac{\partial x^{\mu}}{\partial x^{\mu ^\prime}} \frac{\partial}{\partial x^{\mu}}\left( \frac{\partial x^{\lambda}}{\partial x^{\la... | {
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Is plane altitude limited by engine power and if so does air density cause this? I notice that, for example, human-powered flight operates at low altitudes. This might of course be due to safety but I wonder if in fact the delta in air pressure is greater at lower altitudes and this prevents low-powered aircraft from r... | Here's what happens when airplanes go to higher altitudes.
First, there's less oxygen, so they have to have ways to get enough, like turbo-charging. Jet engines have built-in turbo-charging, and supersonic engines also use ram effect.
Second, since the air is less dense, they need to go faster to get the same lift. Tha... | {
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Why choosing for prime numbers eliminates vibration? I have read that the spokes of a car wheel are usually five because, besides other substantial reasons, five being a prime number helps to reduce vibrations.
The same also happens with the numbers of turbine blades and the way a microwave grill is spaced. Prime numbe... | Gears should have (co)prime number of teeth to provide even wear (https://en.wikipedia.org/wiki/Prime_number#Computational_methods), but I don't see why a wheel needs to have a prime number of spokes. On the other hand, it seems that an odd number of spokes might be preferable for manufacturing (https://www.quora.com/W... | {
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What makes a atom more likely to become a cation (lose electron) What makes an atom more likely to lose an electron and become a cation?
Does the exact location of the electrons maybe influence that? I know that you can't know the exact position of an electron until you measure it. This would prevent such experiments f... | The environment of the atom plays a role. An isolated atom is likely to lose its electron due to ever-present background EM radiation, even if weak. When many other atoms are nearby, they help prevent loss of the electron, but for an isolated atom it is much more probable that the electron is free of the nucleus than b... | {
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Pauli matrices acting on creation operators in the second quantization formalism I'm looking at some lecture notes for electron scattering taking place at a ferromagnet-superconductor junction. The idea is to start from a tight binding model, and eventually obtain the BdG equation.
However, I have some problem with the... | I strongly suspect you are merely looking at quadratic forms of Dirc oscillators, tallied in garbled aspirational notation.
In the conventional basis of Pauli matrices,
$$
\vec M \cdot \vec \sigma = \begin{pmatrix} \cos\theta & e^{-i\phi}\sin\theta \\ e^{i\phi}\sin\theta &-\cos\theta \end{pmatrix}.
$$
In this basis,... | {
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What is the definition of functions of Grassmann numbers? I understand there are some relevant questions, but none of them solves my issue.
From Atland and Simons (Condensed Matter Field Theory), the definition of functions of Grassmann numbers are defined by Taylor expansion. However, I do not understand the exact mea... | *
*The main point when dealing with non-commutative objects [like Grassmann-odd numbers, which anticommute rather than commute], apart from, say, Taylor coefficients, we also need to specify an order of objects: The function/symbol itself does not amount to a full characterization.
A similar issue arises when we want ... | {
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Is there a way to add lenses together to shorten their focal length? I need to know if there is a way to put lenses in front of each other to make their focal length shorter. I tried putting them directly in front of on another, but I wasn't sure if there was a better way. I don't know anything about lens physics. Than... | If you put the lenses very close together and if the thin lens approximation also holds, then their dioptric strengths (inverse of the focal lengths) are approximately additive. If they're not very close together, then in general the combination will not show behavior that's equivalent to that of any simple lens.
| {
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Problem with Sudden Approximation in quantum mechanics If the Hamiltonian of a system changes abruptly (over a very short time interval) from one form to another, we would expect the wave function not to change much, yet its expansion in terms of the eigenfunctions of the initial and final Hamiltonians may be different... | Leaving aside the a-physical approximation of a mathematically infinite potential, the validity of the sudden approximation relies on the alteration of the Hamiltonian imposing sufficiently small changes on the state of the system, and that really isn't the case when you push the boundary far into the original space in... | {
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If the pressure inside and outside a balloon balance, then why does air leave when it pops? Sorry for the primitive question but when we inflate a rubber balloon and tie the end, its volume increases until its inner pressure equals atmospheric pressure.
But after that equality is obtained why does the air goes out when... | I had the same doubt.
But what i think as an answer is the pressure inside balloon is higher because not the atmosphere pressure is same as pressurein balloon, but because effective force is same.
Let me explain
Suppose a normal balloon, now you blow it what actuallyyou are doing is creating high pressure in balloon ... | {
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What was the vertical beam of light in Chernobyl? In the HBO miniseries Chernobyl after the initial explosion we see a clear bright light shooting vertically up from the plant. I presume this was a thing that actually happened and not some creative license they took.
What was the cause of this light and what are the me... | There are 2 sources:
*
*Ionized-air glow, caused by gamma radiation from the core (more bluish color). While gamma radiation is emitted in all directions, it is shielded on the sides , and escape to air directly only in the vertical direction.
*Just light scattering (like in regular projectors), where core is a br... | {
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Would setting the ideal gas constant to $1$ yield an attractive natural temperature scale? In this recent question, there was a comment 'The "zero point" of Kelvin is natural, but the scale is not'. This led me to wonder whether setting $R = 1$ in the ideal gas law would be an attractive and more natural temperature s... | In natural units Boltzmann's constant, $k$, is normally set to one, rather than $R$. They differ by a factor of Avogadro's number; a mole is an arbitrarily defined unit based on the kilogram and is not "natural".
At least in my experience of high energy physics choosing $k = 1$ is common practice; I'm sure it occurs in... | {
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Bernoulli's equation's contradiction Using Bernoulli's equation
P Pressure
p density
V velocity of fluid
$$P_1+ \rho gy_1+\frac{1}{2}\rho V_1^2
= P_2+\rho gy_2+\frac{1}{2}\rho V_2^2$$
$$V_1^2-V_2^2 =\left(2g(y_2-y_1) +\frac{2(P_2-P_1)}{p}\right)$$
$$V_1^2-V_2^2 =K$$ (1)
Where K is constant
Using equation of ... | The relation is true for A1=A2 only, in essence a varying area must lead in varying a pressure, there you assumed that the change in all external pressures is zero whereas area has changed, which is wrong.
Addendum:
the relation is also true for V1,V2=0 where no change in external pressure causes no flow, any fluid mov... | {
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Does the second-order correction to degenerate perturbation theory vanish? Consider a degenerate two-state system with states denoted by $|1\rangle$ and $|2\rangle$. If we apply a perturbation $H^\prime$, the first order correction to the energy is obtained by choosing two linear combinations of $|1\rangle$ and $|2\ran... | According to Sakurai, once you have the first order energy shifts, you no longer deal with a degenerate case and you can use the non-degenerate perturbation formulas to calculate higher order corrections.
So, I suppose for the second order you need to use the new energy levels in the denominator and not the unperturbe... | {
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How do phone loudspeakers work? From what i understand, loudspeakers require AC signals to cause an electromagnet to oscillate due to changes in current direction, thus force direction. How can this happen with a phone's battery/cell? shouldn't the battery only be capable of producing direct current?
|
How can this happen with a phone's battery/cell? shouldn't the battery
only be capable of producing direct current?
First, let's address what is meant here by direct current since the term has different meanings according to context.
Direct current may mean unidirectional current which may be constant or time varyi... | {
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Which particle mediates the Aharonov-Bohm effect? BACKGROUND
The Aharonov-Bohm (AB) effect induces phase shifts between the two paths that an electron could take around an enclosed magnetic field. In radial coordinates, assume that the magnetic field is localized around the origin and that the two paths traced by the e... | It is the electromagnetic field disturbance. You may have static magnetic field enclosed in the solenoid, but it is not possible for dynamic field. $\mathbf{\dot{B}}=-\boldsymbol{\nabla}\times\mathbf{E}$
So a switching on of the solenoid will produce a spreading wave
AB-effect is purely electromagnetic (and quantum)
| {
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Why isn't my calculation that we should be able to see the sun well beyond the observable universe valid? I recently read an interesting article that states that a human being can perceive a flash of as few as 5 or so photons, and the human eye itself can perceive even a single photon. The brain will filter this out, h... | Although I don't understand even the tiniest bit of the equations, and I am by no means a physicist, there is one additional factor: The atmosphere of our planet partially filters out what we can see beyond it.
| {
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Berry connection in a solid I am having troubles to understand an equation-sign for the Berry connection in a solid.
The general formula reads
\begin{equation}
\vec{A}(\vec{R}) = \mathrm{i} \langle \Psi(\vec{R}) \, | \nabla_{\vec{R}} \, | \, \Psi(\vec{R}) \rangle \text{.}
\end{equation}
Now assuming that
\begin{equat... | $\mathbf{k}$ is not a parameter of the Hamiltonian $H_0$ for the eigensystem of your second equation. For the general definition of Berry connection, the Hamiltonian $H(\mathbf{R})$ depends on the parameter $\mathbf{R}$. So for Bloch states, one should use $u_{n\mathbf{k}}$ for the eigensystem $H_{\mathbf{k}}u_{n\math... | {
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Difference between 'white light' and spectral light for rings of Newton In my book of waves and optics, there's a chapter about the rings of Newton and as a question there is: how is the interference pattern when we use white light, considering me it's : there are rings in different color, the ring with the smallest di... | "Spectral light" is a fairly weird phrasing, but presumably it means monochromatic light of well-defined wavelength. This will produce a well-defined set of rings.
White light, by comparison, is formed by multiple wavelengths, all of which will create rings at different diameters, overlapping with each other. At the ve... | {
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Baker-Hausdorff for normal ordering exponential Let $A=A^+ +A^-$ where $A^+,A^-$ denote the creation and annihilation portion of the field. Then in Eduardo Fradkin, Field Theories of Condensed Matter Physics, equation (5.284), it states that
$$
:e^A::e^B: ~=~ e^{[A^+,B^-]}:e^{A+B}:\tag{5.284}
$$
where $::$ denotes norm... | Ref. 1 contains several$^1$ typos, e.g. the aforementioned eq. (5.284) if we use$^1$ the definition above eq. (5.262):
Let $\phi^+(x)$ ($\phi^-(x)$) denote the piece of $\phi(x)$ which depends on the creation (annihilation) operators only,
$$\phi(x) ~=~\phi^+(x)+\phi^-(x).\tag{5.262}$$
The corrected eq. (5.284) is d... | {
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Why is the drag force proportional to $v^2$ and defined with a factor of $1/2$? $$Drag = \frac{1}{2}C_d \rho Av^2$$
I understand that the strength of the drag depends on the density of the fluid the body passes through, the reference area of the body, the drag coefficient, and the velocity of the object.
I don't, howev... | Adding just a bit to the previous answer, I believe that the drag coefficient definition is based on the dynamic pressure term in Bernoulli's equation, $\frac{1}{2}\rho v^2$. Thus dependence on velocity squared is expected, and is often observed. However, fluid flow is complicated, and $C_d$ determined empirically in m... | {
"language": "en",
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Is the velocity of the spinning rod constant after it's hit? Say we've got a rod floating around in space, with two masses of $m_0$, one attached at each end. Let's say the rod has a length of $l$.
There's another mass, $m_1$, moving at some velocity $v$ towards one of the masses.
$m_1$ collides and sticks instantane... | The linear momentum is determined from the velocity of the center of mass, and uses the entire mass of the rod. The mass of the rod in total will not change, and thus we need the velocity to be constant as well. The center of mass in this case will lie somewhere closer to the heavier side of the rod, but when you are d... | {
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Why can't we take space as universal frame of reference? Suppose we have a ball filled half with water in space with nothing else around (nothing else in the whole space except the ball) and suddenly it accelerates for time t. obviously, there would be movement in water which will tell us that the ball underwent motion... | You are asking if we can take space as a universal reference frame. Now what we usually use as universal reference frame, is the CMB. But in SR and GR, there is no universal frame of reference in theory.
But let's disregard that, and say you want to move that bucket with water.
First of all, how would you say if the bu... | {
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What makes north pole of a magnet north pole in the first place? This question might seem absurd and illogical to many. But it just popped out in my mind while I was reading about magnetism.
-Like in case of charges, positive and negative charge on an atom means absence and presence of extra electrons respectively. So... | It is history, and it is worse than you think. North pole was defined as the pole that was attracted to the geological north of the earth. Compasses were very important to the sailors sailing the oceans.
A compass is a magnetic dipole, as magnetic monopoles do not exist as far as we know experimentally. This means that... | {
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Pion decay as a point-particle The $\pi^-$ meson is a composite particle of $\bar{u}d$ quarks, but for many practical purposes it can be treated as a point particle with an effective interaction. The vertex responsible for the $\pi^-(p)\rightarrow e^-(q_1)+\bar{\nu}_e(q_2)$ can be written as:
$$(-i)\sqrt{2}G_FV_{ud}f_{... | On the face of it, your expression looks fine, and the pion momentum is the only usable trace of the annihilated pion. So you must evaluate the pion momentum you wrote. In your conventions, you have conservation of momentum, so $p = q_1-q_2$, and you must proceed to apply the equations of motion on your spinors.
H... | {
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Mathematical form of distribution function with high energetic beam Maxwell Boltzmann distribution function (MBDF) has the form
$$f(v)=n(\frac{m}{2\pi k_BT})^{\frac{3}{2}} exp(-\frac{mv^2}{2k_BT})$$ [Basic Space Plasma Physics by Rudolf A. Treumann & Wolfgang Baumjohann]. The shifted MBDF has the form $$f(v)=n(\frac{m}... | Since the only plasmas where that bump-on-tail velocity distribution function (VDF) can exist are those that are either weakly collisional or collisionless, it is perfectly okay to add VDFs. That is, those plasmas are neither in thermodynamic or thermal equilibrium, so there is nothing wrong with adding two VDFs as th... | {
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Rising sea levels due to thermal expansion According to NASA, one of the main reasons for the rising of sea levels is the increase in ocean temperature. The increase was of $0.4^\circ \text{F}\sim 0.2^\circ C$ for waters with depth $\sim700\text{ m}$. The observed sea level rise in that period was of around $\sim 10\te... | The first source of error I noticed was the temperature difference. it's listed as approximately .2 - .4 degrees. This is not known very accurately and your equation is linear in the temp difference. Also, β is given for 17º C while the water was much colder. β could also depend on pressure which is much greater at 700... | {
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Why is effective mass a tensor? So I came across the effective mass concept for solids the other day. It was mentioned that the effective mass is a tensor and may have different values in different directions. However, this is stark contrast to ordinary mass which is direction independent (as far as I know). So how do ... | Effective mass $m_{\ast}$ is just a constant that shows up in the dispersion relation $\epsilon(\mathbf{k})$ of an energy band. Consider a one-dimensional band with dispersion $\epsilon(k)$. Expanding near a minimum of $\epsilon$
\begin{align}
\epsilon(k) \approx \epsilon_0 + \frac{\hbar^2 k^2}{2m_{\ast}}
\end{align}
I... | {
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What is dimension? What is the size of dimension? Recently I heard a TED talk by Brian Greene where he was speaking about String Theory working on $(10+1)$ dimensions. Plus he said that we live in only in $(3 +1)$ dimensions. So where are others?
He explains that it is crippled to small sizes which we cannot perceive.... | The number of dimensions of space is the number of coordinates required to specify a point in space. The space we see is three-dimensional because we can specify a point in it as $(x, y, z)$. If we needed $(x,y,z,v,w)$ there would be five dimensions.
Each dimension is different, independent direction in which we can mo... | {
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Gaussian path integral is equivalent to saddle-point? If we have a path integral involving many fields,
$$Z = \int \mathcal D \phi_1 \cdots \mathcal D \phi_n \exp(-S[\phi_1,\ldots, \phi_n]),$$
and $\phi_n$ occurs only quadratically-- i.e. the $\mathcal D \phi_n$ integral is Gaussian-- I've been told that integrating o... | Gaussian integration is a particularly simple case of the WKB expansion, cf. e.g. this Phys.SE post. Of course, the caveat is that the saddle point may be complex-valued. In other words, in the 1D case, the saddle point may lie in the complex plane, and one has to show that one can close the integration contour between... | {
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Idealization of Eletric Field at a point According to Jackson "Classical Electrodynamics", in the first chapter about electrostatics:
[...] point charges or electric fields at a point must be viewed as
mathematical constructs that permit a description of the phenomena at
the macroscopic level, but that may fail to... | We ususally talk about the EM field (as E and M together) as per QFT, and the electric and magnetic field are manifestations of the EM force.
Now you are asking why the EM field must be viewed as a mathematical construct. This means that the interaction of the EM field with other charges is mathematically modeled by vi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/488561",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Metric tensor in the comoving cordinate frame In the textbook "Gravitation" by Misner,Thorne and Wheeler (page 717), when the isotropy of the universe is considered, it is stated that in the comoving frame the metric tensor can be written as:
$g_{\alpha \beta} =\frac{\partial}{\partial x^\alpha}\frac{\partial}{\partial... | As Matt says in a comment, this is just a notation stating the definition of the metric. MTW notate it with a dot, to make it clear that the right-hand side is the inner product of two vectors. $\partial/\partial x^\alpha$ is a notation for the vector corresponding to a unit change in the coordinate $x^\alpha$. In this... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/488671",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why is it that when a chalk board gets cleaned, the area that used to have chalk is the cleanest? Why is it that when you erase a chalk board, the area where the chalk used to be becomes the cleanest? By that I mean that when you erase a chalk drawing, the board gets smeared with chalk dust, but the area where the draw... | When you press a chalk stick into the chalkboard to write on it, the chalk particles tend to clump up and stick to each other. Thus, when you erase, it's significantly easier to remove the big clumps of chalk particles together.
On the other hand, when you erase, you tend to leave chalk dusts behind. These chalk dusts ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/488780",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
"answer_count": 4,
"answer_id": 2
} |
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