Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why electron do not eject out even when there is photon of less threshold energy with increasing in time When photon having certain energy less than threshold energy strikes on the electron of metallic plate. Electron do not eject out. But my question is when photon are falling continuously then electron must gain the... | This is just a matter of statistics. The number of atoms is typically many orders of magnitude greater than the number of photons. Therefore the mean time between excitations of the same atom is very long -- much longer than the time required for the atom's excitation energy to be thermalized.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why does the opposing force differ in when falling on concrete vs on water in spite of Newton's third law? If a person jumps from the first floor of a building and lands on a concrete surface, they will suffer serious injury because of Newton's third law.
If the same person jumps the same distance and lands in swimming... |
But the person in both case lands with same amount of force. Then why doesn't water offer the same amount of force in return as concrete does?
This is not correct: the force that the person applies to concrete/water is the same as the force that the concrete/water applies to the person (Newton's third law). The force... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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Why does this fan with one blade missing rotates counterclockwise while running? Video: Fan with one blade missing rotates while running.
The fan worked just fine until my friend tried to stop the spinning blades with her finger and knocked one off. Now it always rotates counterclockwise when running. Can someone expl... | From the video, it looks like that the axis of the fan rotor is not orthogonal to the vertical direction.
When a motor-driven rotor spins in a direction, a torque acts on it due to aerodynamic drag in the opposite direction, i.e. the torque can be represented by a vector orthogonal to the plane of the rotor, that can b... | {
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Why is it easier to raise AC current to high voltage than DC? In my country (and maybe all around the world I don't know) once electricity has been generated, it is then raised to 200k Volts for transportation.
I know this is to reduce the loss. Given $P=U.I$ and $P=I^2.R$, raising U will lower I and so limit the loss ... | You are absolutely right, the higher voltage, the less energy loss due to Joule heating.
The main reason why electricity is generated and transported in AC is that the generated electricity from electromagnetic motor due to mechanisms of electric induction is in fact in AC. So it would require a rectifier for convertin... | {
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"url": "https://physics.stackexchange.com/questions/724715",
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"source": "stackexchange",
"question_score": "9",
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The current in an $LR$ circuit I am trying to understand $LR$ circuits better. I am under the impression that inductors are resistant to change in current.
So, the premise here is that the circuit was switched to side 1 for a long time and switched on to side 2.
What I thought was the 4H inductor would be "okay" with ... | The problem is not with you. This is an example where the assumption of ideal circuit behavior leads to inconsistencies.
Assuming ideal inductors, immediately after switching the current in the 1 H inductor has to be zero, as it was before switching, while the current in the 4 H inductor in series with it has to be 5 A... | {
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Nature of tangential friction force When a ball rolls down a ruff slope the frictional force acts tangent to the ball and causes the angular acceleration of the ball but at the same time the frictional force is acting to reduce the translational acceleration of the ball. How is this possible when the frictional force i... | Forces don't need to act through the center of mass to produce translational acceleration. Consider a rod lying on a horizontal frictionless surface - applying a force at one end of the rod perpendicular to its axis will cause the rod to both spin and move translationally. Or, consider a rolling object placed on a rug ... | {
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Question Regarding The Movement of Charges We know that two electrons repel each other since they have like charges, which means they move in opposite directions. But how can they move if they exert equal and opposite charges, aren't the forces balanced which means there is no movement?
| As a motivational example, consider your air-table puck experiment from highschool. If you have a pair of pucks at rest, and this one pushes that one, then the two of them will move off in opposite directions. If they are equal mass then they move with equal speeds. The total momentum is therefore zero, since this one ... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Illuminance Formula This page says illuminance is
$$E=\frac{I}{L^2} cos \space \alpha$$
This page does something similar, but it ignores the $cos \space \alpha$ factor. Which is the correct formula?
Note: I don't have a physics background. I was looking at optimization problems in Calculus (which is why I came across t... | A physical formula always applies to a given situation, and it is important to first check whether your situation matches the one this formula is meant for.
The formula without the $\cos \alpha$ term is meant for a situation where the light hits the surface in a right angle. It's a special case of the more general form... | {
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Why does a rocket engine that produces a constant thrust over a set period of time have less energy if it has more mass? (Zero-$g$) A rocket engine with the thrust of 1N working for 10 seconds will add more kinetic energy to the rocket if it is attached to a 10kg rocket and less if it is attached to a 20kg rocket. The ... | Even if you assume that the change of the mass of the rocket, due to fuel consumption is negligible, the answer is that the heavier the rocket the smaller the variation of the kinetic energy. Details follow.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What reason/evidence do we have to think that the Planck length is the smallest length possible? From what I've gathered, Planck length is the smallest measurable length, though we do not know whether it is the smallest length physically possible. The Planck temperature is called the theoretically highest temperature, ... | I'ts only a reference that came from the universal constants, as far as I know there is no theoretical limit
| {
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Why do diffraction limits exist? My question does not deal with standard derivations of diffraction. I have no doubt that I can follow standard derivations for diffraction phenomena. Actually, I have probably been shown these before, it's just been so long that I forget them.
My question deals with thinking about diffr... | It’s all fields, forget particles. Particles is a misnomer. What are called particles in quantum field theory are actually quantized excitations in quantum fields. The quantized fields obey wave equations and diffractions limits follow from wave equations.
| {
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Friedmann equation I've seen in literature
$$\dot{H} + H^2=\ldots$$
Source: https://en.wikipedia.org/wiki/Friedmann_equations
Defining the LHS. Since
$$H = \frac{\dot{a}}{a}$$
And that
$$\left(\frac{\dot{a}}{a}\right)^2 = \frac{8\pi G}{3}(\rho + 3P)$$
Then replacing gives
$$H^2 = \frac{8\pi G}{3}(\rho + 3P)$$
So my que... | The forth equation you wrote, being
\begin{equation}
H^2=\frac{8\pi G}{3}(\rho+3P)
\end{equation}
is incorrect. The first Friedmann equation is given by
\begin{equation}
H^2=\frac{8\pi G}{3}\rho.
\end{equation}
Now, taking a time derivative in both sides, we find:
\begin{equation}
2H\dot{H}=\frac{8\pi G}{3}\dot{\rho}.
... | {
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What makes a photon a photon? As i understand photons are excitation of the electromagnetic field. Therefore charged particles are affected by this excitation. But what if we have (highly theoretically) a particle that has the exact same properties like a photon (spin 1, no electric charge, no color charge, no mass etc... | Simple answer: Yes. It's possible to have 2 different types of photon where only one type interacts with the electron and the other type doesn't. In our universe, however, there doesn't seem to be this other type of photon.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why is current finite for point charges? If an electron passes through a flat plane, then there will only be a single point in its entire path which lies on the plane,i.e the entire charge of an electron passes through in an instant (as it is a point charge), then why isn’t the current infinite at that instant and zer... | WARNING: there are many paradoxes that arise by treating an electron as a classical point particle. You are best off to avoid this concept entirely. Electrons are not classical point particles, they are particles as defined by quantum electrodynamics.
If you are still reading then you have ignored the warning, like man... | {
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What are the significant digits, when the standard deviation is larger than the value? Let's say I have some quantity $a = 1.234\,a.u.$ with a standard deviation of $\sigma = 123.4\,a.u.$. How do I express the uncertainty in this case?
*
*$a = (1.2\pm 123.4)\,a.u.$
*$a = (0.0\pm1.2)\times10^2\,a.u.$
*$a = (0\pm120)... | The official recommendations can be found in section 7 of the BIPM's "Guide to the expression of uncertainty in measurement"
https://www.bipm.org/documents/20126/2071204/JCGM_100_2008_E.pdf/cb0ef43f-baa5-11cf-3f85-4dcd86f77bd6
It recommends to avoid the use of the ± symbol entirely unless you are reporting a confidence... | {
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Shouldn't the velocity of the wave associated with a particle be equal to the velocity of the particle? If a free particle of mass $m$ is moving with a velocity $v$, then it's kinetic energy is $\frac{mv^2}{2}$, therefore its frequency is $\nu = \frac{E}{h} = \frac{mv^2}{2h}$ where $h$ is Planck's constant, and it's wa... | The velocity you're talking about is the phase velocity $v_p$
$v_p$ is defined as $v_p = \frac{\omega}{k}$ or more commonly as $v_p=\lambda \nu$
The problem with the phase velocity is that it is only defined for purely sinusoïdal waves.
When we deal with wavepackets (made of a continuous sum of purely sinusoïdal waves)... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Does the earth’s rotational angular velocity change? This is what is written in The Feynman Lectures on Physics, Vol. 1 (ch.5)
We now believe that, for various reasons, some days are longer than others, some days are shorter, and on the average the period of the earth becomes a little longer as the centuries pass.
Wh... | To add to @gandalf61's answer: You can also look up solar time.
Due to the orbit around the Sun, the Earth has to rotate a bit more than 360° for the sun to get back to the same apparent position in the sky. Then, since the orbit around the sun is elliptical, the Earth moves around the sun at different speeds depending... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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If reference frames are equally valid, then why do teachers say the geocentric view is wrong? If all reference frames are valid, then why is the geocentric model taught as "wrong" in schools?
I've checked many websites but none of them clear the issue. Wiki says that in relativity, any object could be regarded as the c... | Sean Carroll wrote a blog post about this exact queston years ago: https://www.preposterousuniverse.com/blog/2005/10/03/does-the-earth-move-around-the-sun/.
As Sean E. Lake says, it's perfectly true that the Sun goes around the Earth ... in some reference frame. And that reference frame is actually a quite convenient o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/728129",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "21",
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Why Is Capacitance Not Measured in Coulombs? I understand that the simplest equation used to describe capacitance is $C = \frac{Q}{V}$. While I understand this doesn't provide a very intuitive explanation, and a more apt equation would be one that relates charge to area of the plates and distance between them, I'm havi... | An analogy here would be to a pressure vessel and asking what mass of air will fit inside.
While the tank has a fixed volume, the amount of air that will go inside depends on the pressure you that you use to force it in. For quite a while the relationship is linear. At double the pressure, you have double the mass of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/728239",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "20",
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Brewster's angle for Metal? As metal has a high refraction index, it is possible to have Brewster's Angle for Metal when the light incident from the air? Is it possible to derive from any formula?
| So there is pseudo-Brewster angle for metals (Citation: Journal of Applied Physics 78, 4799 (1995); doi: 10.1063/1.359763):
It is a subject of textbooks that the reflectivity of metals is a
function of the angle of incidence and that it has a minimum for a
given wavelength at the pseudo-Brewster angle. Consequently, t... | {
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Is the kind of physics proposed for "warp drive" related to the way that space really is expanding? As I understand, some parts of Universe really are moving faster than light -- is this expansion something we think we can create artificially?
And if we can do this artificially, could it be done a on very small scale i... | At the current moment, we don't even know what dark energy is which is the reason the universe expands faster than the speed of light. There is not really a way we could recreate it per se but there are talks about how we can create an effect similar to dark energy which has some kind of "negative energy effect".
There... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does temperature depend on the frame of reference? The way I understand it, temperature is the average kinetic energy of the particles of a system. However, kinetic energy depends on the velocity of the particles, which is relative. If a cup of coffee were traveling at 99% the speed of light relative to an observer, it... | Well let's take the case of you in your spaceship with a cup of hot water in your hand, and a thermometer in the cup registering "90 Celsius". You speed up to 99% of the speed of light and go zooming right past the rest of us who are watching nearby. As this occurs you hold the cup up to a porthole so we can read the t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/729183",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 2,
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Explain Heisenberg's uncertainty principle There was one homework question that asks what Heisenberg uncertainty tell us about the energy of an electron in an infinite square well when the length of the well decreases. The correct answer is that the energy decreases when length increases. I know that the energy should ... | At first, uncertainty principle tells us not about how accurate measurement can be, but how accurate a state of particle can be regardless of any measurement devices used for measuring anti-commutating operators. Second, when you decrease length of well, then particle position becomes more accurate, hence by Heisenberg... | {
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Peskin and Schroeder's QFT book page 289 On Peskin and Schroeder's QFT book page 289, the book is trying to derive the functional formalism of $\phi^4$ theory in first three paragraphs. But the book omits many details (I thought), so I have some troubles here.
For the free Klein-Gordon theory to $\phi^4$ theory:
$$ \ma... | In the path integral formalism, $\phi$ is not an operator, it is an integration variable. In other words, inside the integral $\int D\phi$, $\phi$ is just an ordinary classical field. So there’s no need to worry about Baker-Campbell-Hausdorff and such.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Isentropic fluid: cross product of gradients is zero, why? In the vorticity equation we have the baroclinic term of the form: $$\frac{ {\nabla}\rho}{\rho}\times\frac{ {\nabla}{P} }{\rho}.$$
Why does it go to zero for isentropic flow?
I understand that, if the flow is barotropic, the above term vanishes. However, an ise... | Write pressure as a function of density and specific entropy, $P(\rho, s)$, so that its differential reads
$dP = \left( \dfrac{\partial P}{\partial \rho}\right)_s d \rho + \left( \dfrac{\partial P}{\partial s}\right)_{\rho} d s$
and its gradient
$\nabla P = \left( \dfrac{\partial P}{\partial \rho}\right)_s \nabla \rho ... | {
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Low temperature behavior for ferromagnets: theoretical and experimental discrepancies This is in reference to page 326, 327 of introduction to solid state physics, 8th edition by Charles Kittel
The mean field theory does not give a good description of the variation of $M$ at low temperature. For $T<<T_{c}$ the argumen... | Start from the definition of $\tanh x$ in terms of exponentials
\begin{align}
\tanh x &= \frac{e^x -e^{-x}}{e^x +e^{-x}}\\
&= \frac{1 - e^{-2x}}{1 + e^{-2x}}\\
&=(1 - e^{-2x})\left(1 - e^{-2x} + O(e^{-4x})\right)\\
&=1 - 2e^{-2x} + O(e^{-4x})\;,
\end{align}
where in the second last line we have Taylor expanded in power... | {
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I'm having trouble understanding the intuition behind why $a(x) = v\frac{\mathrm{d}v}{\mathrm{d}x}$ I was shown
\begin{align}
a(x) &= \frac{\mathrm{d}v}{\mathrm{d}t}\\
&= \frac{\mathrm{d}v}{\mathrm{d}x}\underbrace{\frac{\mathrm{d}x}{\mathrm{d}t}}_{v}\\
&= v\frac{\mathrm{d}v}{\mathrm{d}x}
\end{align}
However, this feels... | This intuition is for one dimensional motion: Consider a particle moving in a line. At any time $t$, its velocity is $v(t)$, its acceleration is $a(t)$. The change in velocity after a small time $dt$ will be $a(t)dt$. The change in position will be $dx=v(t)dt$
The identity you wrote is expressing the fact that $vdv=adx... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Thermal Equilibrium and adiabatic walls - Zemansky In Zemansky's "Heat and Thermodynamics" it is stated that:
A thermodynamic system is in thermal equilibrium with its sorroundings iff it is in mechanical and chemical equilibria with its sorroundings, it is delimited by diathermic walls and its macroscopic coordinates... | As I understand it:
Mechanical equilibrium: Equal pressures (forces).
Chemical equilibrium: Equal chemical potentials (fugacities)
Thermal equilibrium: Equal temperatures
Thermodynamic equilibrium: The state in which all three types of equilibria are satisfied.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/731227",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How to derive the $vx/c^2$ term from first principles? In Lorentz transforms, the formula for time transformation is
$$t' = \gamma \left( t - \frac{v x}{c^2} \right)$$
I understand that the term $\frac{v x}{c^2}$ represents "time delay" seen by a stationary observer but I don't understand how to derive it from first pr... | One route (explained broadly) is as follows:
Once you've written down $x'(x,t)$ as a length contraction, (which itself follows from time dilation), then it follows from the first postulate there exists a mode of description for $x(x', t')$ in terms of $-v$. Writing both sides equal to $\gamma$ (which is with the square... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is there a known closed-form expression for the susceptibility of the 2-D Ising model at $B = 0$? The Onsager solution for the 2-D Ising model allows us to find (among other things) complicated expressions for the internal energy of the system (in the thermodynamic limit and in zero magnetic field):
$$
u \equiv \frac{U... | As far as I know, there is no closed form for the partition function in the presence of a field. Therefore there is no closed form for the susceptibility.
The closest I know of can be found here. Below are some screenshots of the relevant part of the paper. If you cannot get your hands on it, give me your email, I will... | {
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Could you feel your weight falling through the a tube drilled through the center of the earth? Suppose you drill a hole through the center of the earth (assume the earth is uniform and no air resistance) and you jump in. Would you be "weightless" throughout the entire fall?
The reason I ask is that if you jump off a cl... | You would experience the feeling of weightlessness throughout the entire vibration as you move back and forth through the Earth. You hint at this in your question when you make reference to astronauts training for weightlessness in aircraft. The aircraft in this case is not simply moving down (and horizontally) but r... | {
"language": "en",
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Correlation of the strength of the Balmer lines with the age of a galaxy I don't understand why a strong absorption line H$\delta$ indicates a young star population.
First of all, a strong H$\delta$ line just means that I have more A-type stars, doesn't it? Where is the connection to the age of a galaxy?
| A-stars have a main sequence lifetime of < a billion years and are much more numerous in a burst of star formation than the higher mass, and much more luminous O/B stars. The Balmer lines, particularly H$\delta$ are particularly prominent in A-stars compared with both hotter and cooler stars.
Lots of H$\delta$ tells yo... | {
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Regarding Lenz's Law presented in hyperphycsics The following diagram is presented in hyperphysics as an introduction of Faraday's Law and Lenz's Law.
If the red arrows represent the direction of current, then what do the positive and negative poles across the resistor means? From my understanding, resistors do not pro... |
From my understanding, resistors do not produce a potential difference
Whenever there is a current $I$ through a resistor with resistance $R$, there is a potential drop $V$ across the resistor equal to $V=IR$. The potential gradient is always opposite the direction of the (conventional) current. This is why in the di... | {
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Does a random number generator have real entropy? In thermodynamics, entropy is defined for gases. Of course, my laptop is not a gas. However, it contains a random number generator and I have seen the word ‘entropy’ being used in this context. Is this the same entropy? How can this entropy be linked to the definitions ... | The answer is simply that a random number generator's entropy and Thermodynamic entropy are not the same things.
A couple of distinct features of thermodynamic entropy is the following.
*
*Every thermodynamic entropy depends on a variable corresponding to the thermodynamic energy of the system.
*Thermodynamic entrop... | {
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Laser safety of standard laser pointer diode I am thinking about designing vector display with standard pointer laser diodes. I would make display be diffuser of some sort like milky glass or paper, but I want to make it see through, rather than seeing dot on paper. Would that be okay or is it possible to mess up someh... | It is absolutely possible to mess up, but you can take measures to understand the consequences.
The most useful thing is to understand the classes of lasers. I'm a fan of this image from Laser Safety Facts.
I would recommend taking the second most conservative approach, and assuming that your diffuser fails completel... | {
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In an entangled system, what happens to Alice's wavefunction right after Bob makes a measurement? Suppose two entangled particles are far apart. One is with Alice and the other is with Bob. The relative velocity between Alice and Bob is zero (and spacetime is flat), so that we can define a notion of simultaneity that i... | If Bob observes "down", due to the wavefunction collapse the full system will be described by :
$$
\left|down,up\right\rangle
$$
There is indeed some sort of "spooky action at a distance", but this action cannot be used to transfer information.
When Bob observes "down", he will instantaneously know the state of the par... | {
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How do we prove that the 4-acceleration transforms as a 4-vector in Special Relativity? In order to define the acceleration of a body in its own frame, we need to first prove that the acceleration is a four-vector so that its dot product with itself can then be labeled as acceleration squared in the rest frame. For vel... | Since you accept that four-velocity is a four-vector, this is an argument that four-acceleration is a four-vector:
$$a^{\mu}=\lim _{h\rightarrow 0} \frac{v^{\mu}(\tau+h)-v^{\mu}(\tau)}{h}$$.
The path is parametrized by $\tau$, the proper time, which is a scalar because it's equal to the spacetime interval (upto maybe a... | {
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What is the entropy of the system, surroundings, and universe of a reversible adiabatic process? I had a homework question that confused me a little bit. We were told to find the change in entropy of the system and the universe of a process. This process is an adiabatic, reversible process. From what I understand, reve... | You are not missing anything.
The change in entropy of the system for a reversible adiabatic process is zero. There is no transfer of entropy to or from the system because there is no heat transfer to or from the system due to it being an adiabatic process. Likewise since only heat can transfer entropy to the surroundi... | {
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Why does a sensitive thermometer absorb little heat? In an experiment to measure the specific heat capacity of water I'm trying to make it as accurate as possible. And somewhere I read that a sensitive thermometer absorbs little heat. By "sensitive" I am referring to the amount of change in thermometric property for a ... | The sensitivity of a thermometer is defined as the smallest temperature change which can be measured, thus if you have two mercury in glass thermometers and the only difference between them is the size of the bulb, the one with the larger bulb will be more sensitive.
The thermometer with the smaller bulb will react fas... | {
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Why does using images that are not really formed work in ray optics? It's all in the title. For instance, if I have two lenses , I have been taught to first find the position of the image formed by the first lens, and then use that image to find the final image formed by the 2nd lens, if the first image is formed beynd... | Because the pattern of rays emerging from the first image is (more or less) the same as the pattern of rays that would emerge from a real object at that point.
| {
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Definition of momentum We say that momentum is the measure of how a body is moving or the quantity of movement inside a body
But what this definition really mean?
This terms are very vague
$p=mv$,why the movement inside the body depend on it's mass?
| The definition is simply $\mathbf{p} = m \mathbf{v}$.
In classical mechanics, this quantity is conserved in absence of an external net force, since the second principle of dynamics reads
$\dfrac{d \mathbf{p}}{dt} = \mathbf{F}^{ext}$,
and thus $\mathbf{p}(t) = \text{const.}$ if $\mathbf{F}^{ext} = \mathbf{0}$.
In order... | {
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Optical theorem Peskin and Schroeder I'm trying to understand the optical theorem of Peskin and Schroeder
$$\tag{7.50} \text{Im} M(k_1,k_2\rightarrow k_1,k_2)=2E_{cm}p_{cm}\sigma_{tot}(k_1,k_2\rightarrow\text{anything})$$
which Peskin and Schroeder says follows from
$$\tag{7.49} -i[M(a\rightarrow b)-M^\ast(b\rightarrow... | I am also reading the book, I may not provide an answer, as far as I can understand:
$-i[M(k_1,k_2\rightarrow k_1,k_2)-M^*(k_1,k_2\rightarrow k_1,k_2)]=2 Im (M(k_1,k_2\rightarrow k_1,k_2))$
In eqn (4.79), if we consider $(E_A,\vec{p_A})=(E_1,\vec{p_{cm}})$ and $(E_B,\vec{p_B})=(E_2,-\vec{p_{cm}})$ as two incoming parti... | {
"language": "en",
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What are the consequences of the tidal friction on the galaxy? In the Earth-Moon system tidal-friction slows down the rotation, so does it do the same for the galaxy?
*
*If not how come, and why it's different than on Earth?
*If so can this slow-down be the reason for collapse of the matter to quasars? If not why?
... | Tidal friction is caused by big objects that can "feel" gradient in the gravitational field of another object. It works for moon, because it's diameter is close to the distance from Earth to Moon. Moon deformation requires energy that goes from orbital rotation. But objects, orbiting galaxy has too small sizes to feel ... | {
"language": "en",
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Relation between velocity and mobility of electrons and holes I have been studying band theory and semiconductors in condensed matter physics and I am confused about the relation
between mobility and velocity of electrons and holes in semiconductors.
My standard text book reference, Introduction to Solid State Physics,... |
The velocity of a hole is equal to the velocity of the missing electron
The missing context: in the same band.
Typically we talk about "electrons" in the conduction band and "holes" in the valence band. But the quote is talking about electrons filling or leaving a vacancy in the valence band.
The velocity of the hole... | {
"language": "en",
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How does thermal motion tend to change the direction of electron spin? Purcell(3rd edition, Chap-11, p-548) in context of paramagnetism writes
Thermal agitation tends always to create a random distribution of
spin axis directions.
I have trouble understanding how do molecular collisions change the direction of electr... | A clue is already hidden in your question. You understand that the spin is influenced by the external magnetic field. If you replace spin with magnetic dipole, the phenomenon of thermal disturbance of the alignment of the spins becomes much clearer.
The disturbance occurs because an electron is not only an electric cha... | {
"language": "en",
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Does Proca's hypothesis make sense of giving mass to the photon in reference to special relativity? The Romanian physicist Proca formulated his famous Lagrangian to describe a hypothetical massive photon. From it we derive, as equations of motion, the relations that the electric and magnetic fields must obey (the analo... | Calling $c$, the parameter in Lorentz transformations, the speed of light is something of a misnomer. It should more properly be called speed of massless particles -- or as robphy suggested in the comments, '“maximum signal speed” (putting more emphasis on the causal structure).' Whether or not the photon is actually a... | {
"language": "en",
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Velocity in power calculations in different inertial frames In calculating power using the formula $\underline{F}\cdot\underline{v}$, what is the correct velocity to use? Does one use the velocity of the body on which the force is acting, or the velocity of the body providing the force? I always thought it was the form... |
Does one use the velocity of the body on which the force is acting, or the velocity of the body providing the force?
The velocity of the body on which the force is acting. More specifically, the mechanical power delivered to a system is $\vec F \cdot \vec v$ where $\vec v$ is the velocity of the material of the syste... | {
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Why is the mass of small elements taken as $∆m$ in center of mass of a continuous body? A continuous body has continuous distribution of mass. Doesn't $\Delta m$ mean $m_f - m_i$? But, is the mass Changing? If yes, how is the mass varying? Why is the mass of the small elements in a body taken as $\Delta m$? Why isn't i... | It's a good question.
Normally speaking, we consider a quantity written as $\Delta x$ to conceptually mean a "change in a quantity". For example a "tiny change in time" or a "tiny change in position".
However, the usage in case of center of mass calculation is in a different conceptual sense. We can think of chopping u... | {
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Connection between covariant derivative operators upon conformal compactification I'm having trouble determining the connection between two covariant derivative operators. These are: the one associated with the original space-time (and thus with the metric $ \tilde{g}_{ab}$) and the one associated with the non-physical... | I redid the calculations (and included them for future readers). The first $\Omega$ in your equations should be $\Omega^{-1}$, but despite that the last formula is correct (and I think the previous ones are as well).
The Christoffel symbol transforms as:
\begin{align*}
\widetilde\Gamma_{ab}^d
&=\frac{1}{2}\widetilde g^... | {
"language": "en",
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Why does high frequency have high energy? The electromagnetic spectrum's wavelengths all travel at the same speed, $c$. Also, the wavelength $\lambda$ and frequency $\nu$ are related by $c = \lambda \cdot \nu$. Since all moving particles here would have the same speed, why would higher frequencies have more energy?
| The relation just means that the wave can be decomposed (very roughly said) into quanta that have certain energy. For higher frequency waves the individual quanta have bigger energy than for the lower frequency waves. That is an experimental fact - many phenomena can only be explained by this. But the wave itself may ... | {
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Why does a small thermocol ball fall slower than a metal ball of the same volume and surface area (air resistance equal)? Suppose a thermocol ball and a metal ball of same volume and surface area (but different masses, obviously) are dropped from the same height from rest. The acceleration due to gravity is 'g' and the... | Let $R$ be the resistive force.
Applying Newton's second law $mg-R = ma$ where $a$ is the acceleration of the ball.
Thus $a= g-\frac Rm$.
Assuming that the density of the metal ball is greater than that of the thermocol (made of expanded polystyrene beads) ball then the mass of the metal ball is greater than that of th... | {
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Lorentz contraction using odometers? In principle, would cars moving between a pair of points at different speeds show different odometer readings due to Length contraction? When we use odometers to measure length between two points, what can we say of length contraction?
| Yes, in theory the odometer will measure a contracted length. To show that rigorously is quite a complicated matter, because the rotating wheel of the car is no longer circular in the frame of the car or of the road.
Relative to the road, the bottom of the wheel is stationary, the centre of the wheel is moving at the s... | {
"language": "en",
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What is the correct gravitational potential energy of a single particle in an $N$-body system? I am aware that the total gravitational potential energy of a system of $N$ particles is given by pairwise interactions, i.e., you start with a single particle in the system, and then calculate the work done (negative for an ... | The total potential energy of a system of $N$ particles interacting through Newton's gravitational force can always be written either as
$$U_{total}=-G\sum_{i=1}^{N-1}\sum_{j=i+1}^{N}\frac{m_im_j}{r_{ij}}\tag{1}$$
or as
$$U_{total}=-\frac{G}{2}\sum_{i=1}^{N}\sum_{j=1;j \neq i}^{N}\frac{m_im_j}{r_{ij}}\tag{2}.$$
In the ... | {
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Intuitive understanding of the unit $kg/s^3$ — the unit of sound volume I know that decibels are used to measure volume of sound, and they are basically a logarithm of $kg/s^3$. The best explanation that I have for the unit of $kg/s^3$ is that it is an alternate way of saying $W/m^2$, which measures intensity of sound.... | Not every combination of base units has a clear physical meaning. The best way to understand any quantity is to look at the equation that produces it. For instance in your case sound intensity $I$ is an expression of the power $P$ traveling through a perpendicular area $A$,
$$I=\frac P A$$
So you correctly stated tha... | {
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Second quantization: Hamiltonian in field operators vs Tight binding form Hamiltonian written in terms of field operators: The kinetic energy (KE) part of Hamiltonian is
$$
H=-\frac{\hbar^2}{2m}\int d\mathbf{r} \Psi^\dagger(\mathbf{r}) \nabla^2\Psi(\mathbf{r}) \tag{1}
$$
Hamiltonian written in tight-binding form:
One r... | The operator $\Psi^\dagger(\mathbf{r}_i)$ creates a particle at $\mathbf{r}_i$ which is infinitely localized (i.e. it has a delta-function wave function.) In contrast, $c_i^\dagger$ creates a particle which is localized at position $\mathbf{r}_i$, but has wavefunction $\phi_i(\mathbf{r})$. You should think of this as e... | {
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Does it matter when we measure the spin of the other entangled particle? Let's say, we have 2 entangled particles: A and B which are a light-year away from each other.
We know if we measure the spin of particle A, we can be certain the spin of particle B will be in the opposite direction.
My question is: does it matter... | No, it doesn't matter.
Say you have the entangled state:
\begin{equation}
|\psi_0\rangle=\frac{1}{\sqrt{2}}\left(|\uparrow\rangle_A|\downarrow\rangle_B + |\downarrow\rangle_A|\uparrow\rangle_B \right)
\end{equation}
If A makes a measurement and finds, say, spin up, then the state $|\psi_0\rangle$ collapses into:
\begin... | {
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How can the Joule be the unit of both work and energy?
Say a person applies 1 N to a box with a mass of 1 kg, displacing 1 m. This is one Joule of work
(1 N for 1 m).
Now say the person applies 1 N to a box with double the mass, displacing 1 m as well. This is still one Joule of work, despite the person having to push... | Work is a transfer of energy from one system to another (by any means other than heat). So it must have the same units as energy.
Similarly, if I transfer 5 EUR to your account then your account balance is 5 EUR larger. The transfer is work, and the balance is energy. They must be in the same units. It wouldn't make se... | {
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What is the difference between mechanics and analog? What is the difference and the relationship between mechanics and analog/analogue? I have noticed that mechanical things are often considered analog.
Note: The difference between digital and analog is clear to me.
| Originally the term "analog" came from computing, where mechanical computing machines implemented systems that were analogous to the physical systems they simulated. When electronic analog computers came about, a key component was the "operational amplifier". Because they were developed to support math, it turned out t... | {
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Linear transformation in $pV$ Say ideal gas is in a state $p_1$, $V_1$, $T_1$ (known). I compress this gas such as $\frac{dp}{dV}$ is a constant. I want to reach $T_2$>$T_1$ and I need the values for $\frac{dp}{dV}$. Would it be right to picture the problem like that: say I have a point $(p_1,V_1)$ in a $pV$ diagram, ... | It certainly is correct. You need to get to a point with $T_2$, so the endpoint lies somewhere on the $T_2$ isotherm. The condition $\frac{dp}{dV}=\text{const.}$ means that the curve connecting the startpoint with the endpoint is really just a line segment. And there you have it, this is exactly what you have said.
| {
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What is the state of an entangled photon after its twin is absorbed? Let's two photons are entangled in polarization after a laser beam passes through a Betha Barium Borate crystal. They take different paths and one of them (1) is absorbed in a black sheet. What is the state of the leftover photon (2)? Is it in superpo... | Take the initial state of the pair and project onto the outcome of the measurement.
| {
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How to calculate radioactivity concentration of components in reactor? I understand the reactor parts will become radioactivity because there are neutron flux in reactor. How should we calculate the reactivity of reactor parts? For example lets say there is a reactor core with thermal neutron flux of 1n/cm^2. If there ... | There are laws of activation (and deactivation) of materials. In a simple way, the activity is proportional to the number of target nuclei, to the flux of neutrons, to the cross section of activation.
In practice, these basic notions become very complex:
You must know the exact composition of the materials, take into a... | {
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Why are there hemispheres in Huygens principle? In the formulation of Huygens principle, it is said that the secondary waves are spheres but on the plots for determination of the wavefront there suddenly become hemispheres? What is the reason for this mismatch? Is there any physical explanation based on the momentum of... |
In the formulation of Huygens principle, it is said that the secondary
waves are spheres but on the plots for determination of the wavefront
there suddenly become hemispheres?
The whole sphere is often not shown as a convenience in creating the plot. Also, showing only half of the sphere avoids the issue of the backw... | {
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Paradox regarding Young-Laplace equation Recently I've been working with the Young-Laplace equation and came across the following physical paradox that I couldn't wrap my head around. It goes like this:
Imagine a spherical droplet (filled with water) in air. By the Young-Laplace equation, we know that the pressure in ... | The Young-Laplace equation you give is exactly the force balance you are looking for.
Because it is curved (with total curvature $2H=2/R$), the surface area element inside the fluid element exerts a certain portion of its surface tension, namely $2H\gamma = \frac{2\gamma}{R}$, in the radial direction (add up the vector... | {
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Generalized conjugate momenta and the generalized Fourier transform Let the Lagrangian be a functional of $\hat{\phi}$ and $\partial_{\mu}\hat{\phi}$, i.e. $\hat{L} = L(\hat{\phi},\partial_{\mu}\hat{\phi})$, where $\hat{\phi}$ is an operator.
The conjugate momenta is defined as $$\hat{\pi} = \frac{\delta \hat{L}}{\delt... | *
*Quantization of a theory starting from a classical Lagrangian density ${\cal L}(\phi,\partial\phi)$ is a non-trivial process. Let us assume that it is possible for OP's theory.
*There might be operator ordering issues when performing a Legendre transformation from the Lagrangian to the Hamiltonian formulation at ... | {
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Is energy "equal" to the curvature of spacetime? When you are solving the Einstein field equations (EFE), you basically have to input a stress–energy tensor and solve for the metric.
$$
R_{\mu \nu} - \frac{1}{2}R g_{\mu \nu} = 8 \pi T_{\mu \nu}
$$
For a vacuum solution we have:
$$
T_{\mu \nu} = 0
$$
This yields:
$$
R_... | The curvature of spacetime is proportional to energy.
Spacetime curves around that energy.
If you imagine a sphere with energy at its centre then the curvature is the same at every point on the surface of the sphere.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/740401",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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Is Hubbles law due to Gravity? Hubble's law states that Distance is proportional to Velocity. A ScienceDirect article states that Classical Hubble expansion is characterized by a proportional increase in the rate of expansion groups based on the distance from the main center of gravity
So is it due to gravity?
| No, Hubble's law is due to the expansion of the universe.
I can't say what the ScienceDirect article meant because you didn't link it, but the description of what it wrote does not sound sensible either.
Edit: from the link, the relevant quote is:
A special place in astrophysics is the effect of Hubble—expanding group... | {
"language": "en",
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Given a magnetic field how to find its vector potential? Is there an "inverse" curl operator? For a certain (divergenceless) $\vec{B}$ find $\vec{A} $ such that $\vec{B}= \nabla \times \vec{A} $.
Is there a general procedure to "invert" $\vec{B}= \nabla \times \vec{A} $? An inverse curl?
(I was thinking of taking the ... | You could try using the Helmholtz decomposition.
If $F$ is a twice-differentiable vector field on a bounded volume $V$ with boundary $S$, then it can be decomposed into divergence-free and curl free components.
$$F=-\nabla\Phi+\nabla\times \mathbf{A}$$
where
$$\Phi(\mathbf{r})=\frac{1}{4\pi}\int_V\frac{\nabla'\cdot F(\... | {
"language": "en",
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Absorption spectrum dependence on concentration/pressure I am having difficulties understanding the relation between absorption spectrum and gas concentration. The online resources I found, including many questions here, do not clarify my doubts.
Take for example this picture from wikipedia. It lacks any information ab... | The Beer-Lambert Law says that the transmittance of a sample is given by $T = e^{-n \sigma \ell}$, where $\ell$ is the path length, $\sigma$ is the absorption (or scattering) cross-section of the scattering species, and $n$ is the concentration of the species (molecules per volume.) If you halve the concentration ($n... | {
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Is there any physical difference between the absence of a force and a force with a magnitude of 0 Is there some sort of experiment one could perform that would differentiate between the absence of a force and a force with a magnitude of 0? Or are they just different ways of describing the same thing?
| Kinematatticaly they are the same but dynamically, there will be stresses built up in the object experiencing a net force of zero. Consider a spring for example, when you pull on its ends, even though the force is zero, there are still stresses in it.
| {
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Impact of distance from galactic centre on the value of energy in the cosmic ray spectrum where knee is observed? This question is based on the recommendation and great explanation by @Kyle_Kanos. Is it known what causes the "knee" in the observed Cosmic Ray spectrum?
Accepting the reason for the occurrence of knee aro... | For a highly relativistic proton $v\approx c$, moving with momentum $p\approx\gamma mc$, the Larmor radius is given by -
\begin{equation}
r_L = \frac{p}{eB} \approx \frac{\gamma m c}{eB} \approx \frac{E}{eBc}
\end{equation}
So, higher the energy, lesser will be the deflection due to linearly increasing Larmor radiu... | {
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What would a standing wave of light look like? I want to know what a standing wave of light would like and what properties it might have that are interesting.
| If you could stand at a node in a perfectly round monochromatic light two optic resonant cavity, you would see a small circle of light. If you could stand at the anti-node you would see a large circle of light.
No monochromatic light source is prefectly round so inside a real resonant cavity the light will have a cen... | {
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What happens to circularly polarized light when it hits a linear polarizer? I have seen a lot of examples of what happens when circularly polarized light passes through a circular polarizer composed of a quarter-wave plate and a linear polarizer, but what would happen to the circularly polarized light if it passed thro... | Circularly polarized light is composed of 50% linearly horizontally polarized light and 50% linearly vertically polarized light. The two linearly polarized components are 90 degrees out of phase. If perfectly circularly polarized light passes through a perfect linear polarizer that transmits horizontal (vertical) polar... | {
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Star convection gradient dependencies In star convection you can work with radiative and adiabatic temperature gradients, that for example the radiative one can be defined as,
$$\nabla_{rad}=\frac{3\kappa L P}{16 \pi a c G m T^4}$$
This can be seen for example in this source. Here they put emphasis in the dependency of... | The opacity, pressure and temperature all vary as a function of position in a star. For a spherically symmetric star you can assume they vary only as a function of the radial coordinate $r$.
The reason that luminosity and mass are written as $L(r)$ and $m(r)$ is to remind us that these do vary with radial coordinate an... | {
"language": "en",
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Does the 1-loop correction for $g\bar\psi\psi$ term leads to the counterterms for additional terms in the Lagrangian? I have the Lagrangian in 4 dimensions:
$$
L = \frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2+\sum_{i =1,2}\bar\psi_i(i\not\partial-m)\psi_i-g\phi\bar\psi_i\psi_i.
$$
Assuming there are... | Yes, one must for consistency as a minimum include all possible renormalizable terms that are not excluded by symmetry, cf. my related Phys.SE answer here. The $\phi^n$ vertex with $n=1,2,3,4,$ is e.g. generated from a 1-loop diagram of Yukawa $\phi\bar{\psi}\psi$ vertices with the fermion running in a loop.
| {
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Why $F = m(v_f - v_0)/2$? Force is directly proportional to mass and velocity and inversely proportional to time so why don't we write $F=1/t+m+v-v_0$ where $m$ is mass, $v$ is final velocity, and $v_0$ is initial velocity?
| One way to convince yourself of this is that force is measured in $\rm{kg\cdot m/s^2}$ which is a Newton. This can be formed by multiplying mass kg times velocity m/s divided by time s. You cannot get there by adding the units.
More generally, you cannot add any units (or the corresponding dimensioned quantities) unle... | {
"language": "en",
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NIF Ignition Achievement Although the National Ignition Facility achieving positive energy output is hailed as an achievement in fusion energy, I am curious whether their configuration could ever be adapted to produce continuous power. The fuel is at the center of a symmetric array of lasers, and it is hard to see how ... | Yes, there is the Laser Inertial Fusion Energy (LIFE) concept. It includes a light-gas gun that would inject 15 targets per second into the target chamber, and a tritium breeding ratio of 1.05. Pursuit of this concept was canceled after ignition was not achieved as promised by the end of 2012. However, the repeated dem... | {
"language": "en",
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Multiplication of probability in quantum mechanics Consider a ket-space spanned by the eigenkets of an observable $A$ and let $B$ be an additional observable on the same ket-space. We can build a filter that only lets an eigenvalue $a$ of $A$ through and afterwards subject the outgoing beam to a second filter that sele... | The issue is whether the probabilities are independent. I believe that this is an assumption of the notion of "projective measurements" which are approximations to what actually happens in an experiment. You really need a Hilbert space ${\mathcal H}_A\otimes {\mathcal H}_B \otimes {\mathcal H}_{\rm system}$ where $A... | {
"language": "en",
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Kinematics 1D-Problem In the below question, what does the phrase "the time taken by the particle to hit the ground" mean? Does it mean time taken by the ball to cover distance from the point of projection to the ground or does it mean the time taken by the ball to cover the distance from the point of projection when i... | The time taken to reach highest point is,
$$t_1=\sqrt{\frac{2H}{g}}=\frac{u}{g} $$
And when the particle reach the bottom again, displacement in y is 0. So,
$$0=ut_2-\frac{gt_2^2}{2}⟹t_2=\frac{2u}{g}$$
So, $2t_1=t_2⟹n=2$. Now you can see according to your options.
| {
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Do water wheels slow down the water downstream in a river? Since the speed of the water may vary across the river, let us focus on the speed at the river mouth.
When a water wheel is placed in a river, part of the kinetic energy of the water is stored. Therefore, the water should flow slower than without the water whee... | The water wheel cannot change the flow rate of the water. If it reduced the flow rate then water upstream of the wheel would flow towards the wheel faster than the water below the wheel was flowing away. That means the depth of the water upstream would increase steadily with time and eventually overflow the river banks... | {
"language": "en",
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Does the formula for time period of a simple pendulum hold up for larger angles? When calculating the time period of a simple pendulum as an experiment in junior classes we used the formula
$$T = 2\pi\sqrt{\frac{l}{g}}$$
But recently seeing the derivation of the formula using Simple Harmonic Motion, I can't understand ... | The exact solution is given by this equation:
$$T=4\,\sqrt{\frac lg}\int_0^{\pi/2}\frac{d\vartheta}{\sqrt{1-k^2\,\sin^2(\vartheta)}}\tag 1$$
where $~k=\sin(\theta_0/2)~$ and $~\theta_0~$ is the pendulum start amplitude.
Thus if $~\theta_0=0~$ you obtain that period $~T_L=2\pi\sqrt{\frac lg}$
This graph gives you period... | {
"language": "en",
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Understanding this Lagrangian calculation I was trying to understand this section of a Wikipedia article:
$$0 = \delta \int \sqrt{2T} d\tau =
\int \frac{\delta T}{\sqrt{2T}} d\tau =
\frac{1}{c} \delta \int T d\tau$$
For the life of me, I can't figure out how does one get from $\displaystyle \delta \int \sqrt{2T} ... | $T(\tau)$ is a function. $dT(\tau)$ is also a function that is "small" i.e. less than some $\epsilon$ for all $\tau$. $T(\tau) + \delta T(\tau)$ means you perturb the function by adding a small perturbation at all $\tau$. If you do this then $\sqrt{2(T + \delta T)} \approx \frac{\delta T}{\sqrt{2T}}$. Here you kind of ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Second Law of Thermodynamics Restatement with usable energy instead of entropy Is it technically accurate to state the Second Law of Thermodynamics as:
"The total amount of usable energy only decreases in a closed system"
I ask because it doesn't evoke the term "entropy", which usually only confuses the average perso... | What you suggest is the so-called Exergy, a term introduced in the fifties for a concept (the available energy) that dates back to Gibbs. The decrease in exergy is the counterpart of the usual increase in entropy.
However, I notice that after more than sixty years, the concept of exergy has not substituted entropy. Ent... | {
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Why does the motor "flinches" when its motor starts spinning? I'm wondering why motor "flinches" when it starts spinning.
Is there any physics law causing this?
If so, if a satellite in space has a rotating parts in it then would the satellite also moves due to the same reason?
| Every action has an equal and opposite reaction. The torque that accelerates the rotor is associated with an opposite torque on the motor body. If the motor is on flexible mounts, that torque will rotate the body until the mounts can provide enough torque to balance it. Of course, the mounts then torque whatever they'r... | {
"language": "en",
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About vertical circular motion I have two cases here.
In the first case, we have a body moving at the speed shown. As we know the normal force on it due to the surface under it is just 9.8 * 10 = 98 Newtons.
Now, in the second case, the body is moving in a vertical circle. But at that instant at the top, the velocity v... | Force and acceleration are vectors. I assume the magnitude of the velocity is constant for both of your cases in the question.
For the first case (purely horizontal motion) the velocity vector is in the horizontal direction and does not change direction or magnitude, so the horizontal acceleration is zero. That means ... | {
"language": "en",
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liquid-vapor interface goldstone modes The free energy of a liquid-vapor interface (far from critical point) can be approximates as
$$
\mathcal{F}=γ A+\frac{γ}{2}\int dxdy|\nabla h(x,y)|^2
$$
where $h(x,y)$ is the height of the interface at a given point (x, y), $\gamma$ is the surface tension, and A is the area of a c... | No symmetries are broken at the liquid-gas phase transition. Therefore no Goldstone modes are expected either.
| {
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Why does water feel hotter at larger volume? Why does a 104°F pool/tub feel boiling hot, whereas a pot/cup of water at the same temperature does not feel hot at all.
(Normally a pot/cup of water won't be hot enough to cause one to immediately remove ones finger from the water till it's around 165-175°F).
Probably same ... | It depends on the surface area of your body that is exposed to the hot water. If you get into a hot tub, most of your body is exposed to the heat, whereas dipping your fingers into the water only exposes a small surface area.
The sensitivity of different parts of your body will also play a part. Your fingers and hands ... | {
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Telegrapher's equation and complex wave equations I am not sure if this falls into engineering or physics, but since I am confused more about the underlining mathematics, I am posting it here. For the transmission of a TEM wave, telegraphers equations are derived for the propagation of current and voltage over an infin... | Your last displayed equation is correct. The solutions of the telegrapher's equation describe damped (decaying) waves whose phase velocity depends on frequency unless the Heaviside condition $LG=RC$ is satisfied. They do not satisfy the usual wave equation unless both $R$ and $G$ are zero.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can you add pressure and internal energy in relativistic enthalpy? In relativistic fluid dynamics the relativistic enthalpy in natural units is defined as:
\begin{equation}
h = \frac{e+p}{\rho},
\end{equation}
Where $e$ is the total energy density and $p$ is the thermodynamic pressure.
In contrast, the Newtonian en... | So, following @Ghoster's comments, $e$ and $p$ simply have the same dimensions in both systems of units:
\begin{equation}
e = \underbrace{(M\ L^2\ T^{-2})}_{energy} \cdot \underbrace{L^{-3}}_{per\ unit\ volume} = \left( \underbrace{(M \ L \ T^{-2})}_{force} \cdot \underbrace{L}_{times\ length} \right) \cdot \underbrace... | {
"language": "en",
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How to find the corresponding energy given the wave function? So I was struggling doing the following question:
Given the wave function $\psi(x) = A\, \mathrm{e}^{-ax^2} $ with potential $V = \frac12 kx^2$, find the corresponding total energy in terms of $k$ and $m$.
I did the calculation for $\left<x^2\right>$ and $\l... | Since $\hat H\psi(x)=E\psi(x)$ just act on $\psi(x)$ using $\hat H$ and presumably the result is a multiple of $\psi(x)$.
Alternatively, to build on your calculation, if $\psi(x)$ is suitably normalized (and your expression is not):
$$
\langle H\rangle=\frac{1}{2m}\langle p^2\rangle+ \frac{1}{2}k\langle x^2\rangle
$$
a... | {
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Atmospheric pressure in non-nertial frame? Any object kept in an accelerating container of water feels different pressure than unaccelerated. Because if we go into the frame of water the g effective changes. Since air is also a fluid, a container of liquid accelerating upwards should experience more atmospheric pressur... | Existing answer is correct but I will present it in less technical terms.
If the air is not moving relative to the ground, then the atmospheric pressure at the ground is whatever is enough to prevent the air from the next layer up from falling down towards the ground.
If the whole system (ground and air) is acceleratin... | {
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In the Lorentz force equations, can the magnetic field be assumed to be singular at one or more points? Consider the relativistic Lorentz force equation (in a simplified form) given by
\begin{equation}\
\left(\frac{u'}{\sqrt{1-|u'|^2}}\right)'= E(t,u)+u'\times B(t,u).
\end{equation}
Here, $E$ and $B$ denote respectiv... | Of course, in case the potentials are due to a moving point particle, both scalar and vector potential are functions of distance with a component proportional to $1/r$.
| {
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How distance affect wind speed from a fan? I noticed that when you feel the wind force from a fan close up, it feels like more force than from far away. Can someone give me an equation, where given a base wind speed $v$ in mph of the fan, and a distance $d$ in miles, one can get the wind speed from distance d away from... | Check Landau & Lifshits, vol.6 ("Fluid Mechanics"), ch.23 ("Exact solutions of the equations of motion for a viscous fluid"), item (3) "submerged jet". I believe this is the closest thing for an analytical expression for your problem.
| {
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Compressed water Normally, water is incompressible, but what happens if I have a fixed volume and keep pumping water into it?
Let's say I have a compartment full of water. The compartment is completely sealed off, with only one entrance where a pump is connected. What will happen if the pump keeps running, pumping wate... | for a positive displacement pump with a small motor on it, pumping into an enclosed volume will stall the pump. in the case of a large motor, it will burst the container, split the pipes, or break a connecting rod inside the pump mechanism.
For a non-positive displacement pump (like an impeller pump) the flow will stop... | {
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Distinction between "types of heat" in thermal efficiency The definition of thermal efficiency I see in several sources is "total work" divided by "heat input".
Wikipedia, for example, says: "For a heat engine, thermal efficiency is the ratio of the net work output to the heat input".
I don't understand this definition... | The way to track this in complete generality, for a reversible process, is to track the system entropy. If the entropy went up, then heat came in. If the system entropy fell then heat went out.
If you want a method that does not involve any mention of the concept of entropy, then proceed as follows. For a given change ... | {
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Is it possible to statically generate lift with the difference in pressure like wings? If I understood it correctly, the shape of the wings and/or propellers generates lift/thrust with the difference in pressure in both sides of the wings/propellers; where the lower side has higher pressure airflow and the uper side ha... | The purpose of wings is to generate this lift in a dynamic situation.
If there is a low pressure area and a high pressure area in a system and they are connected, then air will flow from the high pressure area to the low pressure area. Air will go around the wing from the bottom to the top.
Something would have to be ... | {
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What fraction of heat is exchanged by thermal radiation (by ordinary objects)? I understand that heat can be transferred by conduction, convection and thermal radiation.
So, lets say when I bring a cold glass of milk in a room at room temperature, then what fraction of heat is transferred to the milk by radiation and w... | Heat transfer via radiation scales like the fourth power of the temperature in degrees absolute. It is very small for objects near room temperature like your glass of milk but climbs rapidly as you go above room temperature. at a couple hundred degrees above room temperature it is significant (think: hot stove) and a f... | {
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Does touching something cause quantum entanglement? Disclosure: I'm pretty uneducated when it comes to quantum entanglement.
I was aware that there are a few ways for particles to become entangled. Is physical interaction one of them?
I read this question and answer: Quantum entanglement question
Then I thought when I ... |
Say I touch a wall, is my hand partially quantumly entangled with the wall?
In principle yes, though in practice there is a process called decoherence that removes the entanglement of massive objects so fast that it could never be observed. So your hand is not entangled with the wall in any physically meaningful sens... | {
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"answer_id": 0
} |
Does $\exp(-i \theta \sigma_m \otimes \sigma_n)$ represent a rotation operator? It is well known that $\exp(-i \sigma_k \theta)$ where $\sigma_k$ $(k=x,y,z)$ is a Pauli matrix, represents the rotation operator about $k$-th axis. What physical interpretation does $\exp(-i \theta \sigma_m \otimes \sigma_n)$ have, where $... |
It is well known that $\exp(-i \sigma_k \theta)$ where $\sigma_k$ $(k=x,y,z)$ is a Pauli matrix, represents the rotation operator about $k$-th axis. What physical interpretation does $\exp(-i \theta \sigma_m \otimes \sigma_n)$ have, where $\otimes$ is the tensor product?
If we use the common physics terminology and s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/746975",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 0
} |
Does rate of acceleration change as object gets closer or further to center of a mass? I learnt that newton's law of universal gravitation F = G(m1m2)/R^2, and thought if the R is distance and determined gravitational strength, why do we use 9.81 as default acceleration of earth's gravity when it is not even constant a... | The local gravitational acceleration at a height $h$ above the surface (of water) is given by $$g = \frac{G\,M_{\rm earth}}{(R_{\rm earth}+h)^2}$$
with $g_0 = 9.80665\;{\rm m/s^2} \approx 9.81$ when $h=0$ on average.
Your question is why use a constant value when there is a dependency on $h$?
Well, check how much does... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/747083",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Why is the current the same after passing through a resistor even when the drift velocity goes down? A resistor converts some of the electrical energy into heat energy, implying that the energy goes down, implying that the force with which an electron moves, and consequently, the drift velocity goes down.
Now, I=naeV w... | Electrons are accelerated by the electric field, but slowed down by scattering with impurities, phonons, and other electrons. The velocity that enters the equation $I=nAeV$ is so-called drift velocity, i.e., the average velocity when both the acceleration of electrons by the field and their slowing down by collisions a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/747275",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 7,
"answer_id": 0
} |
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