Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why the work done by system not stored as potential energy? Now choose a spring mass system now work done by external agent in slowly moving from equilibrium position is stored as potential energy but where is work done by spring force gone.For genralization work done on system is stored as potential energy but where i... | To add to the previous answer. The energy stored is known as Elastic Potential Energy to the best of my knowledge. Thus, the energy is in fact stored as a form of potential energy - since the position of the mass in the mass-spring system determines the kinds of energy it possesses.
| {
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"timestamp": "2023-03-29T00:00:00",
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Do any quantum interpretations not include nonlocality? Are there any interpretations of quantum theory that have a mechanism such that there is no need to invoke nonlocality?
| I think so. In my work http://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-013-2371-4.pdf (Eur. Phys. Journ. C, (2013) 73:2371) I consider scalar electrodynamics (Klein-Gordon-Maxwell electrodynamics) and spinor electrodynamics (Dirac-Maxwell electrodynamics), show that the matter field can be algebraically e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/483108",
"timestamp": "2023-03-29T00:00:00",
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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... | You can certainly do this, and indeed it is regularly done. For example Alcubierre designed his FTL drive by starting with the metric he wanted and calculating the required stress-energy tensor. It is a straightforward calculation - it is somewhat tedious to do by hand but Mathematica would do the calculation in a few ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/483259",
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What is it that drives the electrons from one plate to another through a battery in a capacitor? The situation is as follows:
You have a parallel plate capacitor, disconnected from a battery on both ends.
We know the battery tries to maintain a constant potential difference between its two ends. The capacitor is unchar... | Note what you say:
"We know the battery tries to maintain a constant potential difference between its two end"
The wires connecting the battery ends to the capacitor plates, by being conductive extend the function of the two ends
So the question refers to what makes a battery maintain a constant potential at its ends... | {
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Does semi-classical gravity obey the equivalence principle? Question
I was recently wondering about semi-classical gravity :
$$ G_{\mu \nu} = \frac{8 \pi G}{c^4} \langle \hat T_{\mu \nu} \rangle_\psi$$
Does this obey the equivalence principle?
My intuition
Let's say I am in a lift and I want to measure the standard de... | So it seems like your question and intuition are asking two separate questions. Your intuition is asking about the way measurements are made in the classical world and in the quantum world. Semi-classical theories are known to be incomplete and so some parts of the physical process won't actually stand up, ie matching ... | {
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If entropy decreases for cold systems, isn't the heat death of the universe a state of low entropy? Entropy is a consequence of heat. The heat death of the universe results in an approach to absolute zero temperature. Does this mean the end of the universe is low entropy?
|
If entropy decreases for cold systems,
There is some misunderstanding in this statement, using the verb "decreases".
from the three laws of thermodynamics entropy either remains constant on increases.
If one compares a cold system, to the same system at higher temperatures, the entropy is higher in the hotter system ... | {
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How can electric fields be used to detect cracks in metals? My physics teacher brought this up in a lecture and I am not exactly sure what he is saying.
| Cracks and other flaws can be found in metal parts by scanning the surface of the part with a small electromagnetic coil, which induces a current flow in the metal part as if the coil and the part were two coils coupled together in a transformer. the presence of a flaw like a crack in the part perturbs the flow of indu... | {
"language": "en",
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Why cannot we determine our own velocity? I know it would violate the principle of relativity. But have there been serious experimental attempts to contradict that principle?
If I am in a moving train without windows and totally sound proof, is there absolutely no way for me to determine that I am moving?
Can this be ... | The principal of relativity essentially states the laws of physics are the same in all inertial frames.
As I understand it Galileo conducted (or it has been claimed he conducted) an experiment in which he dropped a rock from the top of the mast of a moving ship to show it would land at the base of the mast and not be... | {
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Intuition of 2D Velocity Vectors I understand 2D vectors in terms of displacement. For example, Bob moves 3m to the east and 4m to the north, the total change in position (displacement) equals 5m to the north east.
But I don't understand how 2D velocity vectors can be broken down into their horizontal and vertical comp... | Orthogonal axes make right angles, so you can use the Pythagorean theorem to get the hypotenuse. If you multiply the two shorter sides of a right angle by some unit transformation, or divide by a unit of time, the hypotenuse is identically scaled because of the Pythagorean theorem. It is Pythagoras's theorem that gives... | {
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Why don't we use Ampere's law to find the magnetic field due to a wire of finite length at its perpendicular bisector? I know that finite length doesn't have symmetry and thus it's hard to apply maths here but take the case of magnetic field of a wire of finite length at a distance $r$ from axis of the wire exactly at ... | How is the current in the finite length of wire to be generated?
*
*Using current carrying wires connected to the wire under consideration?
Then these current carrying
connecting wires will also produce a magnetic field which needs to be
included in the line integral $\int \vec B \cdot d \vec s$.
*Using charges s... | {
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General idea behind simplifying cube resistors I don't know if "cube resistors" is the right way of putting it, but I am wondering if somebody could walk me through the general procedure for solving problems in which you are asked to find the resistance from A to B through a cube with a resistor of some R on each line ... | If you are trying to find the resistance between two points, you suppose that a pd is placed between these points. You then look for symmetries that show certain points to be at the same potential. When you find such points, you imagine them to be linked by wires of negligible resistance, knowing that there will be no ... | {
"language": "en",
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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... | Blowing into a balloon is harder than just blowing into the air, because it takes higher air pressure to stretch the rubber. once the balloon is tied the stretched rubber continues to squeeze the air inside, so inner air pressure stays higher than outer air pressure. Untie the balloon and the stretched rubber will sque... | {
"language": "en",
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How do I use a sunstone? How does it work? I have acquired two pieces of Icelandic Spar (optical calcite) with surface and internal fractures that should be serviceable as sunstones.
I have observed the double refraction and cancelling double refraction, a rainbow effect, and varying intensity of stuff. I stood myself ... | Half an answer. I got it working but don't understand it yet:
I spent another half an hour outside trying this way and that to get something out of my sunstones. I got a double-banded rainbow effect when looking through either stone that moved with the stone (definitely not Haidinger's brush) and rotated with the stone... | {
"language": "en",
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Radiation of a charged particle Take a uncharged particle. It hits a resting charged particle. Will the charged particle radiate then?
| If one speaks about a neutron and a proton (or also an electron), in a collision an exchange of impulses occurs between them, minus a loss of energy.
In the sentence above there are some remarkable details:
*
*It doesn't matter whether the charge or the neutral particle moves in relation to the observer, only the re... | {
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Why are gold nanoparticles red? While watching the latest computerphile video (https://www.youtube.com/watch?v=FGiBHsUkVzU) I came across a solution of nanoparticles of gold
,
but to my surprise, they appeared as red, shouldn't gold be golden color?
| The phenomenon is called Localized Surface Plasmon Resonance (LSPR).
In a nutshell: a plasmon is a charge (quasi) particle oscillation. In the case of light reflecting at an interface between a dielectric (e.g., like your liquid) & a metal,the SPR is excited in the metal and confined to the surface.
Gold nanoparticles ... | {
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First-order correction to energy in perturbed harmonic oscillator I know, from the perturbation theory, that, if I have the hamiltonian
$$ \hat H = \hat H_0 + \lambda \hat W$$
where $\hat H_0$ is the unperturbed hamiltonian of which I know its eigenvectors and eigenvalues, and $W$ is the perturbation. Then the energy ... | You can solve this Hamiltonian exactly. We can write
$$
\hat H = \left(\frac{1}{2m}+\beta\right)p^2+\frac{m\omega^2}{2}\left(x+\frac{\alpha}{m\omega^2}\right)^2-\frac{\alpha^2}{2 m \omega^2}
$$
Define $\bar{m}$ to satisfy $\frac{1}{2\bar m}=\frac{1}{2m}+\beta$, define $\bar\omega$ to satisfy $m\omega^2=\bar m\bar \omeg... | {
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Conceptual question regarding transistor biasing I know that in a transistor, the base-emitter (B-E) junction has to be forward biased while collector-base (C-B) junction needs to be in reverse bias.
Question: What would happen if we alter this biasing?
Case 1: Both B-E and C-B junctions are reverse biased.
Guess: Noth... | Case 1: Correct, nothing will happen. Only leakage currents will go through.
Case 2: Main disadvantage is that there is much less current amplification and lower breakdown voltage in this mode of operation.
In some cases amplification could be <1, which would make it rarely useful configuration. Heat dissipation is a... | {
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Setting spinors and $SU(2)$ representations on the same patch I am sorry for the naivety of this question, I am a mathematician and I am trying to put together different ideas.
I am trying to understand the vocabulary of physics, in particular, I want to know:
We know that the isometry group of Minknowski metric is the... | Reference: Srednicki, Quantum Field Theory ch. 33
The Lie algebra of the Lorentz group $SO(3,1)$ can be described in terms of 3 spacial rotations ($J_i$) and 3 velocity boosts ($K_i$):
$$ [J_i,J_j] = i \epsilon_{ijk} J_k $$
$$ [J_i,K_j] = i \epsilon_{ijk} K_k $$
$$ [K_i,K_j] = -i \epsilon_{ijk} J_k $$
To make the $SU(2... | {
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If the mass of the Earth is decreasing by sending debris in space, does its angular momentum also decrease? We are sending huge amount of debris into space from earth, and also very heavy satellites and rockets, then the mass of earth must be decreasing over time.
If the mass will decrease, then gravitational attractio... | The mass of material sent into orbit may seem huge to a naïve observer, but it is nothing at all compared to the mass of the Earth and wouldn't result in any detectable change in its orbit or rotation. Meanwhile, the mass of the Earth is actually increasing as it picks up dust, meteorites and micro-meteorites on its p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/486197",
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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... | If the sun emits $N=10^{45} $ photons per second, an observer at distance $R$ will receive $N/4\pi R^2$ photons per second per unit area. If human eye has radius about $r=10^{-3} m$, it will receive 1 photon per second if
$$\frac{N\pi r^2}{4\pi R^2} =1, $$
$$R \sim \sqrt{N} r \sim 10^{20} m\sim 1 kpc. $$
This is less t... | {
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Gravitational field (metric tensor) and speed of light between two massive plates Suppose I have two massive plates of size $l\times h\times w$ mounted parallel to each other with a distance of $d$ and with a mass density of $\rho$. I send a light beam in the middle between them along the length $l$ and in parallel to ... | The speed of light is always the same in vacuum (which I assume is the case for in between the plates here). Even if the plates were enormously massive, as long as the light ray travels in the middle of the gap there would be no bending and in ANY case no change to the speed of light, that is one of the main ingredient... | {
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Temperature of vacuum chamber on Earth Does the temperature of a vacuum chamber drop if left for 24 hours or more, since some in space in quite cold somewhere and quite hot how does vacuum become cold near to absolute zero.
| As pointed out by the comments, vacuum itself does not have temperature, since temperature is defined in terms of the kinetic energy of the particles. However, if you put an object (let's say an idealized blackbody) inside the vacuum, its temperature is not simply zero. The temperature will be actually related to the r... | {
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How a discrete $Z_2$ symmetry removes flavour changing neutral current from Two Higgs Doublet Model? By applying a discrete $Z_2$ symmetry to the theory of Two Higgs Doublet Model it is ensured that fermions of one type couples to only one doublet. But how FCNC is removed by doing so? Because if all the leptons for ex... | It is not true that any $\mathbb{Z}_2$ symmetry eliminates the flavor-changing neutral currents (FCNCs). A more accurate statement is that some $\mathbb{Z}_2$ symmetries eliminate the tree-level FCNCs. By assigning the quarks and leptons appropriate $\mathbb{Z}_2$ charges, one can avoid that two Higgs doublets couple b... | {
"language": "en",
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Explanation of covalent bond from physics point of view? We can explain ionic bond as the force between charged particles due to Coulomb electrostatic law. This got me wondering how is then covalent bond explained purely in terms of physics?
| Eventually, every kind of bond in condensed matter is reducible to electrostatics. Covalent bond, ionic bond, van der Waals forces, metallic interactions and even more sophisticated interactions like the phonon-mediated electron-electron attraction in a superconductor, are all reducible to purely electrostatic interact... | {
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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... | In short, the squared speed $v^2$ appears in the equation because when moving faster, you increase both
*
*how much momentum ($p=mv$) that is transferred to the air molecules (they must be moved away faster) and
*how much air that must be moved away (because you sweep through more air per second).
Increasing the... | {
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Recombination of hydrogen Suppose a slow-moving electron and a slow-moving proton are injected into a chamber, such that the two approach each other and are likely to combine to form an atom of hydrogen. How would one calculate the probable sequence of events, including likely emission of photon(s) over time? Will the ... | There are two basic types of recombination (of electrons with protons) into hydrogen atoms:
*
*ternary (three particles), this involves another electron, there is a transfer of energy of the order of the mean kinetic energy from one electron to the other
*radiative, emission of a photon, to conserve momentum (when ... | {
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Peskin and Schroeder Section 7.1 Mass Shift I'm slowly reading my way through Peskin and Schroeder. Near the end of section 7.1 they compare the mass shift of the electron from QFT to the classical value, both of which are divergent but in different ways.
The calculation from QFT gives:
$$\delta m = \frac{3\alpha}{4\p... | From a dimensional analysis point of view: Assume you need linearity in $m_0$ (aka. $\delta m \propto m_0$) by the argument given by MadMax above. This means you have $ \delta m \sim m_0 f(\Lambda,m_0)$ for some function $f$. Since the LHS and RHS both must have dimensions of mass, this means $f$ needs to be dimensionl... | {
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In Feynman lecture Vol1. chapter12 about friction, $F = μN$ will fail because of the excessive heat generated. Why is that? $F = μN$ will fail because of the excessive heat generated if the normal force or the speed of motion gets too big. Why is that?
"$F = μN$, where μ is called the coefficient of friction (Fig. 12-... | The friction coefficient, $\mu$, varies with temperature, so if excessive heat is generated, the coefficient would change. This doesn't explain why the relationship $F = \mu N$ would fail, however, as the relationship should still hold under these circumstances.
As a general rule of thumb, empirical relationships tend ... | {
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Flipping a coin with same initial conditions Today, in my physics class my teacher was talking about how we can never predict the outcome of a coin flip. So I thought:
Will the outcome of a coin flip be the same if we do not change the initial conditions (such as launch angle, force position where force is applied,etc.... | There are certain ways to find the exact probability of tossing a coin:
First before jumping to this i want to make some things clear over here
This is actually possible because the initial conditions is reproduced to the
entire system but g force can't be done because of distance which is inversely proportional.
*
*... | {
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In zero gravity! If spacecraft moving in a stable speed or acceleration suddenly stopped would an astronaut continue moving forward (such as a man in a train) ?
| “Zero gravity” is something that doesn't exist. Maybe you mean the situation of freely orbiting spacecraft, in which cosmonauts don't feel any attraction as they are orbiting together with the spacecraft.
Yes, the astronaut will continue to move forward, with all tragic consequences for him.
Note:
In the case of stabl... | {
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Can measurement of the momentum of a particle can be done without observing its position? Uncertainty principle says that one cannot measure exactly the position and momentum of a particle at same time. As per common understanding when we are measuring momentum of an object it is implicit that we aware of its positio... | I know a "kind of" answer.
A "velocity selector" AKA "Wein filter" will pass particles with a narrow fixed range of velocities. If we know the species (and therefore the mass) we have measured the momentum of all particles passing the filter without measuring position in the direction of travel (but we have measured po... | {
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How does a heated lid in a thermal cycler prevent evaporation? A thermal cycler is a chemistry lab device that increases or decreases the temperature of the material inside it. The lid of the device is heated to prevent condensation and evaporation of the mixture inside.
I understand the condensation bit, as a hot lid ... | We were discussing about this with a colleague, and we couldn't agree. I propose that it's due to the vapor going near the lid being heated more, therefore developing relatively more pressure than the column immediately under it, and therefore migrating to the lower pressure zone. This brings more vapor/air in its plac... | {
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Does electric field vary with cross sectional area in a non-uniform current carrying conductor? Suppose I have a non uniform conductor which is kept in a uniform electric field maintaining a constant potential difference across its ends.Both electric field and current density are a properties of points in space.Since c... |
Now according to Ohm's law $\mathbf J=\sigma\mathbf E$, as current density changes electric field should also change with cross sectional area. How is this possible if electric field is a property of point in space and we maintain a uniform field across the conductor.
We can't maintain uniform electric field across s... | {
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Acceleration and motion can be in different direction? I'm not getting what acceleration concept is and how it relates to motion and how motion and acceleration can be in different direction? And what's behind the concept of negative and positive acceleration?
| Try to remember the following things in short which will help you to develop this idea of your own.
(A) Acceleration is in the direction of motion, when you are increasing the speed of the car moving along a straight line.
(B) Acceleration is against the direction of motion, when brakes are applied to the car in motion... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/488980",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is the velocity of a string that is being rotated around a central point the same at any point on the string? Say that you have a weight attached to a 2 metre long string, and you are rotating the weight at 5 m/s. Is every point on the string going to be rotating at that same velocity of 5 m/s, or is the velocity of th... | Depending on the 'type' of velocity.
• Angular velocity will be constant for every particle / unit length of the string i.e. 5/2 revolutions s-1
• Linear velocity will change according to the distance from the point of rotation
V= r. w, where V is the linear velocity, r is the length of the string from the point of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/489118",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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How is it possible to have different answer using two different equation for same condition?
There are two blocks ${(m_1 ,m_2)}$ of different masses placed on a surface, connected with a spring of spring constant $k$. The coefficient of friction between the blocks and surface is $\mu$. Now we have to find the minimum ... | Sorry, a bit overread on my part. For the mass in question which just begins to slide, use balance of forces. For the other mass which is being pulled use energy gained by spring be equal to work doned by pulling force F and frictional force on mass being pulled.
So the answer arrived at in case 1 in original post wil... | {
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What are change of frame and change of coordinates? What's the difference between a change of frame and a change of coordinates?
I feel like both are transformations on the coordinates but change of frame changes also the vectors.
| There's a difference because your coordinates do not always specify your frame. It's true that coordinates always give you one particular choice of a frame, but you can choose to use a different set of basis vectors to represent the vector space at any particular point.
The first example of this you'll probably run in... | {
"language": "en",
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Rotating coordinate frame connection of coordinates and mass Hello I am still confused about rotating coordinate frames and want to ask a question about it.
Is it correct that strictly speaking the mass must be connected with the axis of rotation in the rotating coordinate frame? For example by a rod, or a rotary disk... | A rotating coordinate system is a non-inertial coordinate system. For general motion there is translational plus rotational motion. The motion of any object can be evaluated using either an inertial or a non-inertial system. There is no requirement for any fixed relationship between the object and any axes of any co... | {
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Thermodynamics: how does the deformation of partially elastic materials produce heat? When a perfectly elastic material is deformed, the energy associated with the strain remains stored in the body as elastic potential energy, called strain energy. Upon the removal of the deforming forces, the body completely regains i... | A partially elastic material (i.e., viscoelastic material) exhibits a combination of elastic and viscous behavior, and it is the viscous part that is responsible for the increase in internal energy (adiabatic case) or the emission of heat (isothermal case).
Imagine a spring and a damper (dashpot) in series. When the... | {
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Different concepts of phase transitions in spin models I am currently revising the lecture notes in which different spin systems
are analyzed, focussing on the occurrence (or absence) of phase transitions.
Different techniques are applied to analyze the different models and - seemingly -
also different notions of phase... | As for your 1.,2.,3., magnetization is a derivative of free energy with respect to magnetic field, so smoothness of free energy and smoothness of magnetization are closely related.
| {
"language": "en",
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How can I understand if an object stay (zero velocity) or moving with constant velocity (zero acceleration) I thought a scenario like; lets say I am looking an object and there is nothing except this object. Is there a way to understand that if this object is stay on its position or if object moving with a constant spe... | Constant velocity and speed have no meaning unless you specify the frame of reference with respect to which it is measured or observed. (The only exception is the speed of light).
If you see an object “moving”, then it is moving with respect to your frame of reference. If you see it as “still” it is still with respect... | {
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What does a coordinate representation of density matrix mean? A coordinate representation of density matrix $\rho$ is defined as
$$ \rho (x, x') \equiv \left<x\right| \rho \left|x'\right> .$$
When $x = x'$, this expresses a probability where a particle is in the state $\left|x\right>$.
Question: what does that mean wh... | The diagonal entries of the density matrix are called populations and provide information about the probability density of the particles (described by the density matrix), i.e. their probability of "being found" in real space.
This is easily seen from a density matrix $\rho = |\Psi\rangle \langle \Psi|$, and $$\rho(x,x... | {
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Is it possible to see individual photons impressioning film? As part of a course in physics teaching, I am developing a small curriculum that will teach (the basics of) quantum mechanics to high school students.
I need a simple way to show the quantization of light. My uni lecturer suggested that low-light photography ... | Silver halide film doesn't really respond to single photons; it takes four photons, absorbed within a short period of time, to expose a silver halide crystal in the film. An imaging photomultiplier or other photon-counting image sensor would be better, as @Pieter pointed out.
| {
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Does throwing a penny at a train stop the train? If I stand in front of a train and throw a penny at it, the penny will bounce back at me.
For the penny to reverse its direction, at some point its velocity must go to zero. This is the point it hits the train. Two objects in contact have the same velocity, so the train ... | It looks like there's a hole in your reasoning. If I understand correctly, you're saying this:
*
*At some point, the penny's velocity must be zero.
*At some point, the penny's velocity must be equal to the train's velocity.
*Therefore, at some point, the train's velocity must be zero.
Both 1 and 2 are true (assu... | {
"language": "en",
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Electromagnetic waves according to Maxwell If a variable Electric field creates a variable magnetic field and VICE VERSA (according to Maxwell's equations), then why don't we enter a loop where E vector and B vector keep creating one another until they reach infinite magnitudes?
| Ah, this was actually the great insight of Maxwell. What you are referring to is electromagnetic waves (i.e. light). These waves are just the electric and magnetic field continuously generating each other. Unlike what you may intuit though, looking at the actual mathematical solutions that yield such behavior shows tha... | {
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Zero mass Kerr metric When mass in Kerr metric is put to zero we have $$ds^{2}=-dt^{2}+\frac{r^{2}+a^{2}\cos^{2}\theta}{r^{2}+a^{2}}dr^{2}+\left(r^{2}+a^{2}\cos^{2}\theta\right)d\theta^{2}+\left(r^{2}+a^{2}\right)\sin^{2}\theta d\phi^{2},$$
where $a$ is a constant. This is a flat metric. What exactly is the coordinate ... | The transformation is given in page 15 of this paper: The Kerr spacetime: A brief introduction
BTW there is a 2017 paper that claims that the mass zero Kerr metric is not actually equivalent to Minkowski metric but is a wormhole instead: Zero mass limit of Kerr spacetime is a wormhole
| {
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Finding the quadrature variance of a superposition of squeezed coherent states How do you find the quadrature variance of a state $$\lvert x\rangle =\lvert a,b\rangle +\lvert a,-b\rangle$$ where $\lvert a,b\rangle = D(a) S(b) \lvert 0\rangle$?
$\lvert x\rangle$ is a superposition of squeezed coherent states.
| Starting with the expression for $S(z)$ we have:
$\hat{S(b)} = e^{b\hat{a}^\dagger \hat{a}^\dagger - b^* \hat{a}\hat{a}}$
Through the following BCH formula:
$e^BAe^{-B} = A + [B,A] + \frac{1}{2!} [B,[B,A]] ...$
We can see that, since $ [\hat{a}, \hat{a}^\dagger]=1:$
$\hat{S(b)} \hat{a} \hat{S(b)}^\dagger = \hat{a}cosh(... | {
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Motion of a charged particle in a constant and uniform magnetic field Assuming the following relationship has been demonstrated
$$r=\frac{m u_{0}\sin \theta_0}{qB\sqrt{1-\left(\dfrac{u_{0}^2}{c^2}\right)}}=\frac{p_0\sin \theta_0}{qB}$$
where $p_0=mu_0/\sqrt{1-\beta^2}$ represents the relativistic momentum of the parti... | When $\theta_0$ is zero, the trajectory is no longer a spiral around the $z$-axis; it is a straight line along the $z$-axis, for which $r=0$ in cylindrical coordinates.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "5",
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Varying of momentum for constant kinetic energy How is that If the momentum of the particle is constant with time, its kinetic energy ($E_k$) should also be constant with time a true statement but the converse is false...
When momentum is constant,
\begin{eqnarray}
p&=&mv \\
E_k=(mv^2)/2& =& (mv)^2/2m\\
E_k&=&p^2/2m... | Momentum is a Vector quantity, it is measured with both value and direction. Kinetic Energy is a Scalar quantity, measured only in value, but dependent on momentum.
If momentum is constant this means that we are traveling at a constant speed in a constant direction, our Kinetic Energy is then guaranteed by the equatio... | {
"language": "en",
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Do objects besides strings, ropes, and rods have tension? Why do we define tension only in strings and ropes and rods and such? Shouldn't every object experience tension force? Like when you pull a paper from opposite sides, it gets taut, and experiences what seems like a state of tension. If every object does experien... | If you are thinking something really fundamental, there's only four acknowledged fundamental force, and the "tension"(of something like a string) was usual treated as a result of electromagnetic interaction(electromagnetic force) from the atoms or particles.
However, tension in sub particle level can also resulted from... | {
"language": "en",
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If I stood next to a piece of metal heated to a million degrees, but in a perfect vacuum, would I feel hot? A friend of mine told me that if you were to stand beside plate of metal that is millions of degrees hot, inside a 100% vacuum, you would not feel its heat. Is this true? I understand the reasoning that there is ... | Actually, your friend is probably right but for the wrong reason. That much energy is going to fry you in very short order--and will probably kill the nerves before they can say "hot!"
Remember, energy goes at the 4th power of temperature. 100x the temperature of the sun equals 100 million times the energy. There is... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "75",
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Is Lorentz transformation the only way to preserve speed of light? Doesn't this transformation also preserve speed of light?:
$B$ is moving with speed $v$ relative to $A$ in the $+x$ direction. $B$ passes $A$ at $t=0$, and $A$ shines a torch at that moment.
Let $(x', t')$, the coordinates of the light beam in $B$'s fra... | Consider observer $C$, who is traveling at a speed relative $-v$ in the $x$-direction relative to $B$. By your logic, the coordinates $x''$ and $t''$ measured by $C$ should be
$$
x'' = x' - (-v) t' = (x - vt) + v (t - v/c) = x - v^2/c \\
t'' = t'( 1 - (-v)/c) = t ( 1 - v/c)(1 + v/c) = t \left( 1 - \frac{v^2}{c^2} \rig... | {
"language": "en",
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What is a mass moment? I am currently reading through a document Finding Moments of Inertia from MIT, page 4, and I am a little confused as to one of the concepts that they use.
In this document, there is mention of a mass moment. Could someone possibly define this for me please? I can't find anything too clear on the ... | To TNTCookie and anyone else who may be looking at this post in need of help
I have found the answer. It lies within the definition of a centre of mass:
$$x_{cm} = \frac{\Sigma_{i=1}^{i=N}m_i x_i}{M},$$
where $M$ is the sum of all masses in a system, and the sum in the numerator is the first moment of mass (mass moment... | {
"language": "en",
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"source": "stackexchange",
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Intuition of Maxwell's Equations Is there an intuitive explanation for Maxwell's equations?
I know they are axioms but is there a logical understanding of why instead of mathematical. Both forms don't explicate the scientific reasoning behind them to me.
I would appreciate a non- or minimally mathematical approach to t... | The two equations involving the divergence aren't dynamical (they have no time derivatives), and if they're satisfied initially, they're automatically satisfied at all later times. They tell us about the sources and sinks of the fields.
The two equations involving the curl have time-derivative terms and a current term.... | {
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References and papers to distinguish between the Heisenberg and Ising Model Does anybody have any good papers or references to explain the differences between the Heisenberg model and Ising model?
To the best of my knowledge, I am aware that the Hamiltonians are similar, however the Heisenberg model represents the spin... |
Does anybody have any good papers or references to explain the differences between the Heisenberg model and Ising model?
As the comments already suggest, this is more introductory textbook material. Parkinson and Farnell's "An Introduction to Quantum Spin Systems" (Springer Lecture Notes in Physics 816, 2010) might b... | {
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Queuing by the event horizon I understand that an observer outside the event horizon (EH) of a black hole (BH) will not see anything disappearing from outside the EH - only the effects of the time dilution near the EH.
Assume that a large number of objects are on its way towards the EH and the last objects can observe... | General relativity is based on the equivalence principle, and one way of stating the equivalence principle is that in small enough regions of spacetime, the effects of gravity become undetectable for free-falling observers. So if your cloud of observers is small, or if we restrict our attention to a small part of it, t... | {
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Anticommutation relation of Grassmann numbers Let $c,c^*$ be the fermion annihilation/creation operators and $\xi,\xi^*$ denote Grasssmann numbers where $$|\xi\rangle = \exp(-\xi a^*)|0\rangle$$ is the coherent state. Then why is it true that
$$
\langle \phi|\xi\rangle \langle\xi |\psi\rangle = \langle-\xi|\psi\rangle ... | When I read this part recently I got the same question, and I believe it is wrong too. Take a simple example that $\phi$ is a state of definite occupation with $p$ particles and $\psi$ is a state of definite occupation with $q$ particles, then switching the two amplitudes will cause an extra sign of $(-1)^{pq}$, wherea... | {
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Application of angular velocity to Euler angles According to a post here Angular Velocity expressed via Euler Angles you can express angular velocity from euler angles. If I choose Y-Z-Y as a rotation sequence the expression becomes.
$\theta_r, \theta_p, \theta_y$ = roll, pitch, yaw
$$
\vec{\omega} = \dot{\theta_r} \ha... | Suppose you have a Y-Z-Y scheme with a corresponding sequence of rotation angles $\theta_y$, $\theta_p$ and $\theta_r$.
After the first rotation (yaw), the 3×3 orientation matrix $\mathrm{E}_y$ and angular velocity vector $\vec{\omega}_y$ is
$$\begin{aligned}
\mathrm{E}_y & = \mathrm{rot}(\hat{j}, \theta_y) & \vec{\... | {
"language": "en",
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How is it possible to have four types of generating functions? Since the Hamilton's equations of motion remain unchanged in form under a canonical transformation $(q,p)\to (Q,P)$, the Lagrangians must differ by a total time derivative of a function of $q,t$. In other words, $$L-L'=\frac{dF(q,t)}{dt}$$
$$\Rightarrow (p\... | OP's first formula applies to the Lagrangian formalism in configuration space. In the context of canonical transformations (CT), it must be replaced with the corresponding formula in Hamiltonian phase space, i.e. the generating function $F(q,p,t)$ is also allowed to depend on momenta $p$. Since the new phase space vari... | {
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Is there 100% pure white? Is it possible to have an object 100% pure white without sky blue or sun color tinting the pure whiteness of the photons reflecting/deflecting off an object? Are there any lights that can produce pure white photons (RGB)? And can we see that the color is white or is our eyes going to trick us ... | You observe white if your RGB cones produce the same, strong signal. If the signal is not strong it will be seen as grey or black.
A white photon should have a sufficiently wide intrinsic bandwidth. Perhaps a pulsed optical laser with a very short pulse length fits the bill. If the pulse length is of the order of a sin... | {
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Newtonian Gravitational Waves I was thinking about the classical equations for gravity. I got stuck on two equations:
$$\vec{\nabla}.\vec{g}= 0$$
and
$$\vec{\nabla} \times \vec{g}= 0$$
The first equation is Gauss law of gravitation in vacuum and the second equation comes from the fact that gravitational forces are con... | I would say no, since the solution that you found is stationary, it cannot be propagating. For example, in one dimension, a propagating wave needs to have the functional form $\Psi = \Psi (x-ct)$, where $c$ is the (finite) velocity of the wave. In general, a propagating wave in the vacuum constitutes the solution of th... | {
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Why is more than one ripple created when a rock is thrown onto the still surface of a pond? I have tried making an analogy with a simple pendulum: if you give it a push it will probably make several oscillations. But why isn't there just one ripple that would carry the energy of the several ripples?
| A way to look at it is this: Every wave consists of a large number of wave components of various pure wavelengths. A very long continuous train of identical sinusoidal waves almost entirely consists of a single wavelength component.
An impulse like that of a rock hitting the water produces an initial disturbance tha... | {
"language": "en",
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"source": "stackexchange",
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Flat yet finite Universe I would like to ask you this question:
Let's assume that the universe is perfectly flat and big bang happened as described by our theories some 14 billion years ago. Shouldn´t, therefore, the radius of the universe still be finite, even if the geometry of the universe is flat? Even if inflatio... | While I have never studied relativity deeply enough to properly answer this question, I still would like to say that these type of global questions always remind me of Arthur C. Clarke:
Two possibilities exist: either we are alone in the Universe or we are not. Both are equally terrifying.
I like to extrapolate this ... | {
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What is the difference between position, displacement, and distance traveled? Suppose the question is somewhat like this:
If $v=8-4t$ and the position at time $t= 0\ \rm s$ is $2\ \rm m$, find the distance traveled, displacement, and final position at $t=3\ \rm s$
Since $\text dx/\text dt=v=8-4t$, ... |
What is the difference between position, displacement, and distance
traveled?
Succinctly:
(1) the position of an object is a vector with tail at the origin of the coordinate system and head at the location of the object.
(2) the displacement of an object is the vector difference of the current position vector of th... | {
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Circuit - solve Kirchhoff's laws with determinant? Here is an exercise from my textbook.
]1
At first I solve it by using Kirchhoff's laws directly and using complex impendance:
$$U_{in}=\frac{1}{Cs}(i_1-i_2)+i_1R_1$$
$$0=R_2i_2+\frac{1}{Cs}i_2+\frac{1}{Cs}(i_2-i_1)$$
By solving above equations, both $I_1$ and $I_2$ bec... | I have added some theory before the recipe.
$s= \ j \omega$ where $\omega$ ids the angular frequency and $G$ is the conductance of a resistor of resistance $R$ with $G= \dfrac 1R$
There are three Kirchhoff's current law equations which can be set up for each of the nodes 1, 2 and 3.
For node 1 $(V_1-V_2)sC +(V_3-... | {
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Could you extract energy from a rotational white hole? I understand it is possible to do it in a black hole, and its also possible to reach the event horizon of a black hole and increase its size.
But in a white hole, no wave (electromagnetic or gravitational) can reach the white hole's event horizon. So, if you apply ... | A white hole is the time-reverse of a black hole. So, a "white hole penrose process" necessarily is the time-reverse of the ordinary penrose process, which would be a particle absorbing a wave or particle coming from the event horizon, leaving the white hole "spun up".
If this sounds weird, it's because it is weird,... | {
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Does stacking two magnets together increase the magnetic strength? Just wondering if adding two (or more) identical magnets together increases their magnetic strength (in Tesla) as I am doing a physics write-up on the Lorentz force (Fleming's left-hand rule) as I tried stacking magnets together but found that the force... | Yes, stacking magnets does increase the field, but not always by a lot---it depends on the physical arrangement.
For your first test, make a small spacer and put two magnets one on top of the other on either side of this spacer. The field between the two magnets will be strong, approximately twice that of either magnet... | {
"language": "en",
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If inflation is an exponential expansion, is the exponent known? Inflation is often called exponential expansion.
I can't seem to find what that exponent is. Is it 2, or 20, or completely unknown?
| In cosmic inflation, the Friedmann scale factor $a(t)$ of the universe doesn’t grow as some power of the time, such as $a\sim t^2$ or $a\sim t^{20}$. These are not exponential expansions at all. Exponential expansion means that time appears in the exponent: $a\sim e^{t/\tau}$ or $a\sim 2^{t/\tau}$ or $a\sim 10^{t/\tau}... | {
"language": "en",
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Is the acceleration of car greater when hitting the accelerator, or the brakes? Is acceleration of car greater than when pedal the pushed to the floor or when break pedal is pushed hard? I do understand that the signs would change in either but I am more considered about the magnitude....
| The breaking time and distance of a car are affected by many variables, such as road conditions, the condition of the brakes and the type and condition of the tires. Also, of course, the reaction time of the driver and the vehicle speed. The accelerations of cars varies widely.
In order to compare gas pedal accelerat... | {
"language": "en",
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Minus sign in perturbative expansion via Green's function (Schwartz QFT)? In Schwartz's QFT textbook Section 3.5, the Lagrangian for the graviton $$\mathcal{L}=-\frac{1}{2}h\Box h+\frac{1}{3}\lambda h^3+Jh$$ with EOM $\Box h-\lambda h^2-J=0$ is perturbatively expanded in $h$ to yield:
$$h(x)=\int d^4y\delta^4(x-y)h(y)=... | Figured this out as I was typing the question...
The d'Alembertian $\Box_y=\partial_y\partial_y$, so to 'swap' it with an adjacent element, it requires two uses of integration by parts.
That is, $\int_U A\Box B=\int_U A\partial_\mu\partial_\mu B=\int_{\partial U} A\partial_\mu B-\int_U\partial_\mu A\partial_\mu B=-\int... | {
"language": "en",
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Momentum replacement in the axial anomaly calculation in dimensional regularisation (‘t Hooft prescription) I have been studying the axial anomaly and everywhere I see the calculation of the triangle loop using dimensional regularisation (see for example pages 661-664 of section 19.2 of Peskin). In the ‘t Hooft prescri... | As the integral has rotational invariance in $d$ dimension, each $\ell$-component should yield the same value. There are $d-4$ non-zero components in $\ell_\perp$ and $d$ non-zero components in $\ell$, we should thus have
\begin{equation}
\frac{1}{d-4}\int \frac{d^4 \ell}{(2\pi)^4} \frac{{\ell}_\perp^2}{(\ell^2-\Delta)... | {
"language": "en",
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Infinite parallel plates have the same electric field between no matter the distance? I saw this in a lecture about gausses law in application to infinite charged planes:
How is it possible that the electric field above the top plane and below the bottom plane is always zero, given that the effect of each plane near i... | The electric field from a uniformly charged infinite plane is constant, it doesn't fall off with distance. Coulombs Law is a statement about the force between two charged particles, which is why it works out differently when you talk about planes. You can actually apply Coulombs Law to reach that conclusion:
$$ V(r) = ... | {
"language": "en",
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Can the flow be irrotational if the viscous forces act on fluid? I tried to answer the question only using the definitions and the Navier-Stokes equation:
$$\rho \frac{Dv}{Dt} = -\nabla P +\rho g -\mu[\nabla \times(\nabla \times v)] $$
In my opinion if the vorticity is zero, then the fluid is irrotational, regardless ... | I'm not sure your momentum equation is correct. For the x-momentum, we should have:
$$\rho\frac{Du}{Dt}=-\frac{\partial \rho}{\partial x}+\rho g_x+\frac{\partial \tau_{xx}}{\partial x}+\frac{\partial \tau_{yx}}{\partial y}+\frac{\partial \tau_{zx}}{\partial z}$$
For Newtonian fluids,
$$\tau_{xx}=-\frac{2}{3}\mu\nabla \... | {
"language": "en",
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Coulomb's law and the continuous charge model in an infinite charged plane The $E$-field of an infinite plane with a uniform charge density $\sigma$ has a constant magnitude equaling $2\pi\sigma$.
Now, this magnitude assumes a continuous charge model throughout the plane.
In reality, the plane is made up of discrete c... | No. The continuous model is an approximation which breaks down when you get too close to the discrete charges.
| {
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Huygens-principle Huygens principle states that every point on the wave front acts as a source. If it is true, then why can't a single source (let's say a bulb) illuminate a whole big room? Why is it dark after some distance from the bulb? According to him it should continue to infinite.
Where am I wrong?
| Every point on a spherical wave front acts as a source of a new spherical wavelet. The tangent surface to all of the wavelets becomes the new wavefront. And this process is repeated using the new wavefront to advance (propagate) the wave.
Note that the wavelets are spherical so their amplitude is reduced inversely to ... | {
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Can force be applied without accelerating? When I push against a wall, I am applying force on the wall and the wall applies an equal force against mine therefore the wall doesn't move and neither does my hand. But isn't acceleration required to apply force? My hand is not accelerating when I am applyin the force. Still... | Acceleration happens when the net force on an object is not zero.
You can apply as much force as you like to an object and it won't accelerate if something else is applying an equal and opposite force.
| {
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Calculating mean velocity: using time or velocity? Background
I have been running tests which involve timing an object moving a certain (fixed) distance, $s$.
Each test has been repeated 3 times, and the 3 times ($t{_{1}}, t{_{2}}, t{_{3}}$) for the object to travel $s$ m are recorded.
However, when calculating average... | The average velocity of 3 trials IS the average velocity, you should not be getting different answers if you are doing everything correctly. Are you carrying out your multiplications and divisions to enough decimal points? Leaving out slight remainders could change the answers slightly. Test each equation with whole nu... | {
"language": "en",
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Does disentangling A and B always imply entangling A and B with an environment? Does disentanglement of a bipartite entanglement between systems A and B entail actual breaking of this bipartite entanglement or is it rather the beginning of a tripartite entanglement between A, B, and Environment?
I've only found example... | Yes, one can break entanglement without getting entangled with something else.
Consider e.g. two spins interacting via the Heisenberg interaction $\vec S_1\cdot \vec S_2$, which are initially in a state $\lvert\uparrow,\downarrow\rangle$. As time evolves, the system first gets entangled, and subsequently gets disentan... | {
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Understanding Fermi gas number density According to Wikipedia, the number density of a 3D Fermi gas is given by:
$$\dfrac{N}{V}=\dfrac{1}{3\pi^2} \left( \dfrac{2 E_F m}{\hbar^2} \right)^{3/2}$$
This means that if the mass of the particles increases, the number density will also increase: why is it so?
| If the mass of the particles increases and the Fermi energy stays the same, then the number (density) of the particles must decrease. But the energy levels of the particles depend on their masses as well.
For example, suppose we have a set of $N$ electrons in a cubical box and $N$ protons in another cubical box of the... | {
"language": "en",
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How to prove that a $d$-dimensional Hilbert space can only have $d^2$ equiangular vectors (i.e. that a SIC is a maximal collection of that kind)? It is an open question if every $d$-dimensional Hilbert space contains a collection of $d^2$ states, such that for every two of them the squared absolute value of the scalar ... | I found one answer in this paper. Let $S$ be the $d \times N$ matrix whose columns are the SIC vectors, and let $G = S^\dagger S$ be their Gram matrix. The rank of $G$ is equal to $d$ unless the vectors live in a proper subspace of $\mathbb{C}^d$. Now, consider the matrix $G \cdot G^T$ where the dot means the entrywise... | {
"language": "en",
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Magnet position for maximum voltage in an ac generator (Lenz's Law)
Animated gif credit
The picture above shows, that the voltage of a phase is greatest, when the magnet alligns with the coil of the phase. Why is that?
To my knowledge of lenz's law the voltage and induced current should be 0 when the magnet aligns w... | The smaller is the gap between coil's core and the magnet, the greater is the flux change through the coil from the same magnet displacement. Thus the EMF is the highest at this phase (Faraday's law).
Now, if you add a load to the generator (in the most extreme case, short the winding of the coil), then the induced cur... | {
"language": "en",
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Why do all fields in a QFT transform like *irreducible* representations of some group? Emphasis is on the irreducible. I get what's special about them. But is there some principle that I'm missing, that says it can only be irreducible representations? Or is it just 'more beautiful' and usually the first thing people tr... | Gell-Mann's totalitarian principle provides one possible answer. If a physical system is invariant under a symmetry group $G$ then everything not forbidden by $G$-symmetry is compulsory! This means that interaction terms that treat irreducible parts of a reducible field representation differently are allowed and generi... | {
"language": "en",
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How to find the possible measurements of a quantum system? A wave function of an infinite square well is given as
$$ \psi(x) = \frac{1}{\sqrt{5a}}\sin\left(\frac{\pi x}{a}\right) +\frac{2}{\sqrt{5a}}\sin\left(\frac{3\pi x}{a}\right),\quad x\in[0,a] $$
How do I find the possible results of the measurement of the system... | In order to find the energies and corresponding probabilities, it's best to rewrite the expression in terms of eigenfunctions. The eigenfunctions of the infinite square well between $x=0$ and $x=a$ are
$$ \phi_n(x) = \sqrt{\frac{2}{a}} \sin\left(\frac{n\pi x}{a}\right). $$
Using these, your wave function is
$$ \psi(x... | {
"language": "en",
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If an earthquake can destroy buildings why it cant kill us according to physics? Most earthquakes with magnitude 5.5 and higher can damage or destroy buildings. However, according to my knowledge and experience, I have never seen someone dying from an earthquake itself. Rather, they die from an associated tsunami, dama... | In addition to the other answers provided, resonance cannot be ignored (Resonance is where the object is vibrating at its natural frequency and as a result the vibrations are amplified). To put simply, people and buildings have different resonance frequencies and the lack of being anchored to the ground (for people) mi... | {
"language": "en",
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Unable to understand why diffracting an unpolarised source of monochromatic light through a single slit causes the emrgent wave to coherent So in Young's Double slit experiment the source of light that passes through the double slit must be monochromatic and a coherent source (from my undertanding, this is to get a uni... | The single slit is in order to generate a point source in two dimensions.
A point source, by construction will allow only specific wavelengths to its size to go through and spread radially. This means that the wavefront can be described mathematically with sinusoidal functions with fixed phases. For details look at ... | {
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Two-photon interference inside Mach-Zehnder interferometer Imagine there's a strong laser beam, not just an attenuated stream of single photons, entering a balanced Mach-Zehnder interferometer.
One-photon picture: Each photon interferes with itself on the second beam splitter. As a result, all photons leave out of the ... | It depends on the quantum state that entered the interferometer. In general the sate is described by a coherent state. To see what happens quantum mechanically one can apply the unitary operator for a beam splitter on the coherent state (with a tensor product with a vacuum state, because we assume nothing enters in the... | {
"language": "en",
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On proving that charge is linearly proportional to potential for a conductor In Mr. Purcell's Electricity and Magnetism, page 103, it is stated,
An isolated conductor carrying a charge $Q$ has a certain potential $\phi _{0}$, with zero potential at infinity. $Q$ is proportional to $\phi _{0}$. The constant of proporti... | Here's a non-finished, non-rigorous attempt:
Let us say we have a conductor having a surface $S$ at a potential $\phi_{0}$ and having a charge $Q_{0}$.
Supposing all the charges are located on the surface, the potential can be defined at any point in space as:$$\phi (\textbf{x}) =\int _{S} \frac{ \sigma(\textbf{x}')... | {
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Does the equivalence principle imply that light must move slower when moving away from a massive object? Thought experiment: Elevator going up at an extreme acceleration, pulse of light bouncing up, and down between mirrors on the floor, and the ceiling. Won't it take light longer to travel from the floor to the ceilin... | Light is ALWAYS traveling in the same speed of $c$ in ALL reference frames. This was confirmed by various experiments such as Michelson & Morley experiment and the others.
The only thing that changes - is the light frequency,- if light looses energy somehow then it's frequency is red-shifted, but speed is the same $c$... | {
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Is electron capture partially responsible for matter decay? Sorry for the very likely ill-posed question. I have lately started reading a lot about quantum physics and the nature of electrons and I read about a phenomenon known as "electron capture" which can happen with a finite probability when an electron "finds" it... | The answer to the title question is "sometimes". Some atomic nuclei decay via electron capture, in which case it is at least partially responsible for decay.
The question asks about something else, whether all matter can decay via electron capture. This time the answer is no. Electron capture (like other forms of nucle... | {
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Does metal thickness change with rise in temperature? When a metal pipe or metal cylinder is heated uniformly in furness, inner and and outer diameter of cylinder increase and its length also increase but does thickness of the cylinder change with change in temperature?
| Yes. I find the best way to think about it is that, when a metal object is heated, all of its dimensions increase as it expands (assuming its not being constrained externally somehow, has isotropic material properties, etc.). So, hole diameters increase and wall thicknesses will increase.
| {
"language": "en",
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Factor of 3 in Photon Diffusion coefficient From definition of Diffusion coefficient:
$$D = c/3(\mu_a+\mu_s),$$
where $c$ is the speed of light front, $\mu_a$ is absorption coefficient and $\mu_s$ is scattering coefficient.
I wonder where does factor of $1/3$ comes from? I assume it is coming from dimensionality, but I... | The factor of three enters from the flux equation during the derivation. Not a full answer, but this was too large for a comment.
See here equation 5.
| {
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What's the problem with Euclidean geometry for astronomical phenomena? This passage from John Pierce, An Introduction to Information Theory:
"also note that while Euclidean geometry is a mathematical theory
which serves surveyors and navigators admirably in their practical
concerns, there is reason to believe that... | On the scale of most astronomical phenomena, general relativity (GR) is the relevant theory.
There are many aspects in which this theory is incompatible with Euclidean geometry. An illustrative and often used analogy is that Euclidean geometry is already inaccurate for a being confined to the surface of a sphere - if y... | {
"language": "en",
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Is electric potential always continuous? In electromagnetism, we say that any conservative electric field $\vec{E}(\vec{r})$ is associated to a scalar potential $V(\vec{r})$ such that $\vec{E}(\vec{r}) = -\nabla V(\vec{r})$. If the electric field is continuous, the respective electric potential must be differentiable b... | No. For example, the potential of a point charge is discontinuous at the location of the point charge, where the potential becomes infinite.
Since all charges in nature seem to be point charges (elementary particles such as electrons and quarks), electric potential always has discontinuities somewhere. When we work wit... | {
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(Why) Is there only one Lyapunov exponent? Lyapunov exponents describe how two (infinitesimally) close initial conditions behave (exponentially) in the long run. If a system is chaotic, the largest Lyapunov exponent is positive. However, as far as I understand it, if we have say, three ODEs depending on time, each stat... |
each state variable has one Lyapunov exponent. But how?
The equation you give is for the maximal Lyapunov exponent, while what you're referring to here is Lyapunov spectrum.
You can find how to calculate it in almost any text on chaos theory - Wikipedia as usual could be a good start for getting the overall picture. ... | {
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Energy-momentum Tensor for a Real Scalar Field Lagrangian I'm currently working through Schwartz's QFT book, and I'm trying to find the energy-momentum tensor for the following Lagrangian:
$$ L = -\frac{1}2\phi(\Box+m^2)\phi. $$
Am I correct in thinking that,
$$ \frac{\partial L}{\partial(\partial_{\mu}\phi)} = 0$$
owi... | Your operator $\Box$ can be expressed via $\partial^\mu \partial_\mu$, so that you
can write the Lagranian density $\mathcal{L}$ as
$$\mathcal{L} = \frac{1}{2} \partial_\mu \Phi \partial^\mu \Phi - \frac{1}{2} m^2 \Phi^2$$
Therefore, the answer to your question is
$$\frac{\partial \mathcal{L}}{\partial(\partial_\mu \Ph... | {
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Linear momentum of a system remains conserved, but with respect to which frame of reference? I have studied that linear momentum of a system remains conserved. But i can't figure out with which reference of frame it is conserved. Is it conserved with respect to system reference frame or in a reference frame attached to... | It is conserved in any inertial reference frame.
A frame attached to one of the bodies, or even the system reference frame, are not necessarily inertial - non-inertial frames are sometimes easier to work with than inertial frames.
| {
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Equivalence Principle holding in Special Relativity? (let alone QFT) Motivation
I am pretty confused of why people are hopeful to find a version of the equivalence principle ("the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system") within QFT. I personally a... | Yes, I think you can use the equivalence principle within the realm of special relativity if, at least, the observer(s) is (are) inertial. In short, a person located at the center of a rotating disc, for a small compartment located a distance $r$ away from the center which orbits the observer, measures an anti-gravity ... | {
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Derivation of Conservation of Energy from Newton's Second Law Given Newtons's Second Law: $$ \frac {d}{dt} (m \boldsymbol{\dot r}) = \mathbf F $$
How is it possible to derive the conservation of energy equation with a constant mass?
That is how can you derive $ \mathbf F = - \nabla V(\mathbf r) $ where $V(\mathbf r)$ i... | Here is another approach to the question.
We know that work done by the force, $dW = \vec{F}\cdot d\vec{r}$.
Now, if the force is conservative, by definition it means that work done is independent of the path taken and only depends on the end state. Hence $dW = \vec{F}\cdot d\vec{r}$ should be exact, i.e. writable as... | {
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Why do things cool down? What I've heard from books and other materials is that heat is nothing but the sum of the movement of molecules. So, as you all know, one common myth breaker was "Unlike in movies, you don't get frozen right away when you get thrown into space".
But the thing that bugs me is that things in the ... | You exchange heat with the objects around you.
If the objects around you are hotter than you, you'll heat up.
If the objects around you are cooler than you (neglecting the heat you're generating due to metabolic processes), you'll cool off.
In space, the objects around you (mostly interstellar medium) is cooler than yo... | {
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"answer_id": 1
} |
What happens to net acceleration in a non-inertial reference frame with cenripetal force? In a non-inertial reference frame, the centripetal force is balanced by a centrifugal force. Therefore, shouldn't the net acceleration be zero? Yet, you still feel an acceleration outwards? Why is that?
| What you feel is the centrifugal force, not an acceleration. Acceleration is rate of change of velocity. If you are not moving (or starting to move) in the rotating frame, your acceleration is zero in that frame.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/503508",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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