Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Can an atom be split and put back together? I had recent came across this question when unintentionally tearing a piece of my journal paper. These atoms' bonds are pulled apart when the paper is torn, but is there a way to put them back together?
Now i know that, depending on the object, the method can vary. According... | I just wanted to point out that an atom cannot be split (or cut loose in such a way that it remains like that freely), they would have to recombine in order to achieve their stable electron configuration.
| {
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Why don't the electric field vectors cancel each other out in a non-conducting infinite plane sheet? Why do these vectors not cancel each other out in spite of their being in the opposite directions?
| This is a inside look at the atomic scale:
The field effect is radial and the intersecting field effects sort of cancles out. The direction lines are not forces on the plate but the field effect direction from the plate. You only do that sort of vector cancellation if the force vectors are rather on the plate. If anot... | {
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Why is air pressure higher in winter than in summer? At the top of a mountain, say Mt Everest, atmospheric pressure is low.
So shouldn't the same thing be true for winter season.
I.e air pressure in winters should be lesser than that in summers.
But it's the opposite.
Can someone please explain why ?
| Air pressure is lower at the top of Mt. Everest because there is less atmosphere above it to compress the air, making the pressure less.
I can't be sure what you mean by "air pressure in winters should be lesser than that in summers", I have never heard of this being a straightforward observation before. But (to my kno... | {
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Why does the location of the north magnetic pole vary faster than that of the south magnetic pole? Noticing what Wikipedia asserts about the variation of the locations of the magnetic poles over time, e.g., 1998 $\sim$ 2000 to 2015, one would notice that the location of the north magnetic pole varies much faster than t... | Have a look on how the earth's magnetic field is modeled presently:
he Earth's magnetic field is attributed to a dynamo effect of circulating electric current, but it is not constant in direction.
So the question becomes why the circulating currents have a higher effect on the northern hemisphere than the southern o... | {
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Is every open circuit a capacitor? I think that even open-ended wires can let AC current flow through them, just with a low capacitance. I also think an antenna could be a capacitor and open ended. Am I thinking correctly?
| If one were somehow able to try to draw current from any point while feeding current to any other point without involving anything else in the universe, the points would behave as though there was some capacitance between them. A network of three points, however, may behave as though there is capacitance between the f... | {
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Quantum expressions for the Virasoro constraints I am trying to derive the quantum form of the Virasoro constraints.
$$ L_{m} = \frac{1}{2} \sum_{n} :\alpha_{m-n}.\alpha_{n}: $$
:...: meaans normal ordering.
Using the common commutator between modes of string when $ m=0 $
$$ [\alpha^{\mu}_{n}, \alpha^{\nu}_{-n}]= n \e... | There are several typos in MacMahon's formula on the bottom of page 79. It should read
$$ \color{red}{-}~\frac{d}{da}\sum_{n=0}^{\infty} e^{-na} ~=~\sum_{n=0}^{\infty}ne^{-na}~=~ \color{red}{-}~\frac{d}{da} \frac{1}{1-e^{-a}}
~=~ \frac{e^{-a}}{(1-e^{-a})^{2}} ~=~ \frac{1}{a^2}-\frac{1}{12}\color{red}{+{\cal O}(a^2)}.$$... | {
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How to calculate air resistance? What is the best way to calculate or take into account air resistance?
I have an assignment which goes as:
Drop an object by itself and with a parachute, calculate air resistance for the parachute. It is assumed the object itself has no air resistance
Im kinda confused how to proceed ... | Your teacher or professor that assigned the practical experiment to you wants to help you put air resistance into perspective, so you'll have to make a clear distinction between just the fall and the fall with parachute. If you can access a height of about 40 feet, this will be enough to provide the clearance to record... | {
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Why does the flame of a gas stove not spread backwards? On lighting a gas stove the flame is active only above the burner. However, the gas input from beneath the burner and all the way to the pipeline contains gas fuel. Why doesn't it all ignite up ? I am guessing it may be due to the pressurised flow of the fuel in o... | The methane that goes to the stove contains little or no oxygen, so it will not burn until oxygen gets mixed into it. This occurs at the burner to the extent that a blue flame is formed in order to obtain complete combustion. At the point where air is mixed into the methane, the velocity of the flowing methane and ai... | {
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Why does a car's steering wheel get lighter with increasing speed I've noticed it is difficult to turn the wheels of a car when the car is stationary, especially cars without power steering, which is why the power steering was invented. However, I've noticed it becomes feather light when traveling at speed (some model... | Imagine the car stationary. The tire sits on the ground with the contact patch touching.
As you start turning the wheel, the linkage to the wheels starts to rotate the contact patch on the ground. (There are also more complex motions because of the non-zero caster angle of the front wheel).
This rotation is oppose... | {
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Magnitude of the cross product of two bra-kets? From the mathematical perspective, one can take the magnitude of a cross product:
$$
|a\times b|=|a| |b| \sin{\theta}\cdot n,
$$
where $\theta$ is the angle between a and b in the plane containing them, and n is the unit vector perpendicular to them.
Does this apply to th... | Actually, the entire equation is
$$ \langle \nabla n |\times | \nabla n\rangle \rightarrow \sum_{m \neq n} \langle \nabla n | m\rangle \times \langle m | \nabla n\rangle$$
EDIT: It's Stoke's Theorem using a differential 2-form.
Stokes Theorem can be generalized to higher dimensions using differential forms.
The $ m\ne... | {
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Work when there is more than 1 force I know that for an object with an applied force, the work done is
$$W = Fd \cos \theta.$$
I was wondering what would happen when there is another force (e.g. friction)? Is it better to say that the work done for a general case is
$$W = F_{net} d \cos\theta.$$
| $\let\th=\theta \def\vF{\vec F}$
Let's begin by specifying the exact meaning of your formula
$$W = F\,d\,\cos\th.\tag1$$
Here it's understood:
1) that a force $\vF$ constant in magnitude and direction is given
2) that the point of application of $\vF$ undergoes a displacement of length $d$.
Note that it's not required... | {
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Why are degenerate states more likely to be filled at a given temperature? Consider if we have a simple two-level toy model, where the ground state has energy $E_0 = 0$ and the excited state has energy $E_1 = \epsilon$ and degeneracy $g$. The partition function for this system is
$$Z = 1 + g e^{-\beta \epsilon}$$
where... | $P(\epsilon) = \frac{ge^{-b \epsilon}}{z} $
where, $z = \sum_\epsilon ge^{-b \epsilon}$
So, for two states with some difference in energy, if $g_1e^{-b \epsilon_1}>g_2e^{-b \epsilon_2}$, then state with energy $\epsilon_1$ is more likely to be filled even though $\epsilon_1$ might be less than $\epsilon_2$
Now, if we ... | {
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How to interpret explicit moments in beams?
Consider the beam in the picture above. There are several forces that cause moments around all points in the beams. But there is also one "explicit" moment: 20kNm.
How do I interpret these kinds of moments? Here the arrow goes around the point 2m from A. So does this mean th... | I am very much aware that this thread has been a while but I am sure people keep coming here. If we look into the Euler-Bernoulli equation, this explicit moment is actually an imposed boundary condition (BC): the third derivative of the deflection wrt its horizontal axis (the x-axis).
In an Euler-Bernoulli, the input i... | {
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Is there a contradiction between isotropy and the Big Bang? Disclaimer: I'm not asking whether the Big Bang happened at a point. I'm asking whether the fact that the universe is isotropic and that the Big Bang happened contradict each other.
To be honest I am just starting to learn General Relativity and cosmology but ... | Einstein assumed space was isotropic and homogeneous because he believed the universe was closed.
And it simplified the model.
Also, an isotropic and homogeneous space is needed for constant curvature.
Cosmology principals assume the universe is isotropic and homogeneous - basically has a "stream line flow".
In fac... | {
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Can this be considered the Newton's rings?
It can be made by pointing a laser pointer directly to a mirror at low angle and observing the reflection behind the laser pointer. No convex or concave lens needed unlike the Newton's ring experiment we know.
So far, Newton's ring experiments and theories I read only involv... | It seems similar with Newton's experiment described in Second Book of Opticks, Part IV. He used concave mirrors of 1/4 and 5/62 inch thicknesses and light beam through a hole of the board which corresponds to the hole at the center of the rings on the screen in your drawing. I suppose that there is no special name for ... | {
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Maxwell Tensor Identity In Schawrtz, Page 116, formula 8.23, he seems to suggest that the square of the Maxwell tensor can be expanded out as follows:
$$-\frac{1}{4}F_{\mu \nu}^{2}=\frac{1}{2}A_{\mu}\square A_{\mu}-\frac{1}{2}A_{\mu}\partial_{\mu}\partial_{\nu}A_{\nu}$$
where:
$$F_{\mu\nu}=\partial_{\mu} A_{\nu} - \par... | Your expression is part of a Lagrangian. As the physics remains the same as long as the action remains the same, one can always do partial integration in the action integral over the Lagrangian to derive alternative Lagrangians describing the same physics.
| {
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Applying the Euler-Lagrange equations to Maxwell's Theory In Prof. David Tong's notes, specifically on page 10, he gives the Lagrangian of Maxwell's theory to be
$$
\mathcal{L} = -\frac{1}{2}(\partial_\mu A_\nu)(\partial^\mu A^\nu) + \frac{1}{2}(\partial_\mu A^\mu)^2
$$
and then he computes the following
$$
\frac{\part... | We have $\frac12 (\partial_{\mu}A^{\mu})^2 = \frac12 (\partial_{\alpha} A^{\alpha})(\partial_{\beta}A^{\beta})= \frac12 (\partial_{\alpha} A_{\sigma}) \eta^{\sigma\alpha}(\partial_{\beta}A_{\rho}) \eta^{\rho\beta}$ so the derivative w.r.t. $\partial_{\mu} A_{\nu}$ is
$$\frac12\delta_{\alpha}^{\mu} \delta_{\sigma}^{\nu... | {
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Poisson's ratio in analytical beam deflection equations After looking at some of the analytical expressions for analyzing beams, I noticed that none of the equations depend on the material's Poisson ratio. Some analytical expressions can be found in https://www.linsgroup.com/MECHANICAL_DESIGN/Beam/beam_formula.htm
I be... | Poisson’s ratio, ν, is defined as
ν = -lateral strain/longitudinal strain.
It is applied when analyzing the lateral strain on members subjected to axial forces (compression and tension). None of the beams in the diagrams of your link involve axial loading (loads applied to the ends of the beams along the axis of the b... | {
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Does the band gap increase or decrease in this case? Suppose I deposit a thin layer of a material A (with band gap Ea, say) on a material B (having band gap Eb) to form the film AB. What will the band gap of AB be? Will it be equal to Ea or Eb? Or will it be lesser or greater than them?
| If you have distinct layers of material, they will each maintain their respective band gaps. Then you have a heterostructure, not a single “effective” band gap. There are caveats to this, for instance if the thin layer is strained due to a lattice mismatch with the other material, then the band gap within the thin laye... | {
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Effect of gravity at center of Earth Imagine I was a hypothetical ant man the size of an atom, and I position myself at the exact, down to the atom, center of mass of the earth. A move in any direction will move me out of the center. Would I experience gravity pulling outward on my body in all directions?
| There's actually a very useful way to solve this using the Gauss law for gravity, which is given by:
$$\oint\vec{g}\cdot d\vec{A}=-4\pi GM_{enc}$$
where $\vec{g}$ is the gravitational field, $\vec{A}$ the area enclosed in the surface of interest, and $M_{enc}$ the enclose mass of the object by the gaussian surface.
As... | {
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The Cosmic Microwave Background Paradox I was reading an article on Olbers' Paradox (why the universe isn't as bright as the sun) and the more I read on it, the more the same question came to mind...
We know the observable universe is approximately 93G LY across and we know the age of the universe is 13.8 B years. We ... | If we can see a particular object at some moment, then we will always be able to see that object in the future, no matter how quickly the universe expands. It's analogous to how we can never see anything completely fall into a black hole. In both cases, the image you get just gets more and more redshifted over time. Th... | {
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The law of radioactive decay: explanation of a formula The law of radioactive decay can be expressed in terms of $\,\tau=1/\lambda$ (average life) as:
$$
N(t)=N_0e^{-t/\tau}, \quad \tag{1}
$$
Why deriving the (1) I have:
\begin{equation}
N'(t)=N_0(1-e^{-\lambda t})\, ?
\end{equation}
| It comes from solving the differential equation
$$\frac{dN}{dt} = -\lambda N(t). $$
This equation comes from observations of the number of decay events $N(t)$. It's found through experiment that the rate of decay over a given time interval is proportional to the number of events recorded during that time. You can arri... | {
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Principle of friction force When two equal and opposite forces act on a body at rest or in motion we say it is rest or in its state of motion. But when a body kept on a table starts moving uniformly due to a force applied, it overcomes force of friction.Does it really overcome the force of friction or is just equal to ... | You have two types of friction, static and kinetic (a.k.a sliding) friction. When you begin to apply a force on an object of mass $m$ on a table it is the static friction force that resists your effort to move it. As you keep increasing your force, the static friction force opposing you continues to increase, but only ... | {
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Propagation of light Suppose we are able to make any place free from the magnetic and electric field; then we turn on a light source at any place in that region (where there is no electric and magnetic field). Does light propagate in that region?
| Currently the accepted theory is the standard model, all the data from experiments supports that.
According to that model (and QFT), light consists of a herd of photons, and the photons are excitation of the EM (photon) field.
According to the model, these fields exist throughout space everywhere. This is the only way... | {
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If you were to push a block in space in an ideal vacuum scenario with zero friction, what would be the final velocity of that object Say you push an object with 10 N force(just once and let it go) of mass 10kg object in space with zero friction and nothing in the way of its path. What would be the velocity of that obje... | If you don't have your space watch, but did bring a ruler, you could measure how far you pushed it (you pushed it $x$). Then the work you did is
$$ W = F\cdot x $$
where $F=10\,$N. That is equal to the object's kinetic energy:
$$ T = \frac 1 2 mv^2 = Fx $$
Of course, the average speed is $v/2$, so the time it takes to ... | {
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Parabolic motion of a projectile During a conference I have listened that an employee of an armed force, he has said that when a projectile fired from a gun upwards, it is very dangerous because when the projectile descends downwards it acquires a higher speed than the initial instant that is when the projectile was fi... | Can you please add some context on what are you trying to compare exactly? I might be oversimplifying the problem, but the way I see it, I would agree with the employee:
*
*If the maximum height of the projectile fired upwards is equal to the height the other projectile is dropped, then we would have around the doub... | {
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Self-interaction in spin-orbit coupling? In spin orbit coupling, in an atom motion of electrons about nucleus generates magnetic field and we consider this field to interact with magnetic moment of electron. It sound strange as in electrostatics a field is generate by a charge particle but this field does not interact ... | An electron has a magnetic moment. When the electron moves it is perceived as having an electric dipole moment as well. This interacts with the nuclear electrostatic field.
| {
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Difference between voltage, electrical potential and potential difference I am having hard time to visualize these two concepts in my mind seriously.
First of this confusion came from two parallel plates that was connected to a power supply, charged then disconnected from power supply and then separated from each othe... | You are mixing the properties of a point charge and that of a capacitor.
The formula you've written works perfectly for point charges and intuitively for two entities holding the same nature of charge and to be very precise, you should use $r$ instead of $d$ when dealing with point charges as the electric field from a ... | {
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Does an electric field penetrate through glass? I was just wondering something ridiculously simple; does an electric field penetrate through glass? Say I have a proton or charged cotton pulp ball inside a Pyrex glass container and apply an electric field on the outside, through the whole thing, do the particles 'feel' ... | Assume that a charge is completely surrounded by glass of any thickness. Gauss's law, in integral form, still applies to a surface surrounding the glass. The presence of the glass makes no difference for the outcome of the integral.
| {
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Finding the eigenstates of an operator I am currently taking a course in QM and can't see how the eigenstates have been found for examples like this one:
Question
Let $\phi _1$ and $\phi _2$ be two normalised wavefunctions orthogonal onto each other. Let the action of the operator $\hat{A}$ on these states be:
$$\hat{... | gabe has already given an answer in terms of matrices and using idempotency. I shall exhibit a rather dry approach.
Assuming that the $\phi$’s form a basis, then any vector can be expressed as $\alpha\phi_1+\beta\phi_2$.
Now let $\psi=\alpha\phi_1+\beta\phi_2$ be an eigenstate of $A$. Then we have,
$A\psi=A(\alpha\ph... | {
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Perpetual Rotation of Rigid Body Assuming no external torque or forces acting can a rigid body be set in perpetual rotation motion about an axis which is not its principal axis?
If no then does the earth continuously change its axis of rotation? as the principal axes of the earth changes changes continuously because o... |
Assuming no external torque or forces acting can a rigid body be set
in perpetual rotation motion about an axis which is not its principal
axis?
In a nutshell? No.
If a body rotates about a principal axis (an axis through its centre of mass) and no external torques act on it, then it will forever keep rotating.
N... | {
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What are equations of state in thermodynamics? So I am having real trouble understanding what equations of state are and how we form them. My issue stems from reading multiple sources. So I understand that an equation of state is used to build a relationship between variables to describe a state of a system.
For exampl... | Equations of state are literally just equations relating state variables. State variables are values that just depend on the current state of the system and not on how the system got to that state. Contrast this with things like work done on the system or heat leaving the system, which depend on the process a system un... | {
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How can a day be exactly 24 hours long? The longest solar day of year is approximately 24 hours 0 min 30 seconds (occurs at mid to late December) while the shortest solar day of year is approximately 23 hour 59min 38 seconds. If I average out both of these I come up with average solar day of 24 hour +4seconds. Why then... | The average value of a distribution is not the average of its minimum and maximum. For example, the average value of (0,0,0,4) is 1, not 2. Earth's orbit eccentricity is not 0, nor the Moon's one, so your distribution of day duration is probably slightly asymetric, hence the 4 seconds discrepancy. Sum all day duration ... | {
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How can I calculate the speed at which a gas flows from one volume to another? Suppose that there are two rigid Volumes A and B. Each of these contains a gas with know properties (pressure, temperature, number of moles, volume, composition). Suppose also that there is a pipe with a valve that connects the two Volumes.
... | Ah, in my link provided from my blog, I do have an equation which describes the flow in and out of a system which may prove useful:
$\dot{S}_2 - \dot{S}_1 = \dot{Q}(\frac{1}{T_2} - \frac{1}{T_1}) = \frac{\dot{Q}(T_1 - T_2)}{T_1T_2}$
It only applies to classical systems though. We can state the mass remains constant (m=... | {
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Can someone provide to me an intuitive explanation of the second integral of position with respect to time? I am aware of what the first integral of position, absement means (at least to a very superficial level).
However, I can find nothing regarding the physical intuitive meaning of absity, the second integral of pos... | Consider the gas pedal in your car. When you push the pedal down and hold it there, the car accelerates. Push it a bit further and the acceleration is larger. In other words, one's acceleration depends on the other one's position - which means that one's position (double integral) depends on the other one's absity (dou... | {
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Momentum conservation in Quantum Mechanics Most quantum mechanical potentials are not translationally invariant and therefore the expectation value of momentum varies.
The question is then where has this momentum been transferred to? Because as a whole the system must conserve momentum.
In electrodynamics of course... |
Most quantum mechanical potentials are not translationally invariant...
... because those potentials are externally imposed from some overarching system whose dynamics you're not explicitly considering. The momentum goes to that overarching system.
As an example, consider the hamiltonian of the electron in an $\rm H_... | {
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Why the time period of pendulum with infinite length is $84.6$ minutes? In a book I was reading about SHM it stated:
If the length of a simple pendulum is increased to such an extent that $\ell\to\infty$, then its time period is given by,
$$T=2\pi\sqrt\frac{R}{g}\approx84.6\text{ min}$$
Now I have many confusions like:... | I have also studied this relation. May be things get clearer in my explanation:
For a general pendulum, it is obvious that if the l is substituted to a large value the time period corresponding also increases. For a pendulum of very large length(comparable to radius of earth), we have to make a change in derivation. An... | {
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Can we know when rolling occurs without slipping? In school we solve a lot of physics problems involving rolling cylinders/hoops/wheels. Often it is specified in the question statement that "rolling can be assumed to occur without slipping". Then we know we can use the relationship between translational acceleration an... | This is how I have approached these problems
*
*Assume there is no slipping and calculate the required friction force to enforce this constraint.
*Check that the friction force is less than the available traction. This is usually done in scalar form $\| \vec{F} \| \leq \mu \| \vec{N} \|$ where $\mu$ is whatever sta... | {
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Why doesn't Newton's third law mean a person bounces back to where they started when they hit the ground? When we drop a ball, it bounces back to the spot where we dropped it, due to the reaction forces exerted on it by the ground. However, if a person falls down (say, if we push them), why don't they come back to thei... | Newton's third law states that when a particle applies a force on another particle then the former experiences an equal but opposite force from the other.When a ball hits the ground it comes back due to the fact that it experiences an elastic collsion(that is does not undergo any deformation).Think about a fur ball,wil... | {
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If atmospheric pressure is 76 cm of $\text{Hg}$ , why won't 76 cm of mercury stay in an open tube when suspended in air? If we keep an hold a tube in air with the closed end up and open end downwards, containing mercury upto a length of 76 cm, why does the mercury not stay in place? Shouldn't atmospheric pressure exert... | In an open tube, air will press down on the top of the column of mercury, as well as up from the bottom via fluid pressure. The net force will be the weight of the mercury in the column.
In a closed evacuated tube, ther is no air pressure pushing down from the top; only the pressure from the bottom and the weight o... | {
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Minkowski space
*
*In Minkowski space, coordinates which satisfy
$x^2 = t^2 - X^2 > 0$
are in the region of spacetime that is time-like.
*If it's
$x^2 = t^2 - X^2 < 0$
the region is space-like.
*But if
$x^2 = t^2 - X^2 > 0$
then its "trajectory of light-like particles".
I have understood the first two points abou... |
My confusion is about why just light like particles? there are many other particles at quantum level.
You are correct. The terminology is historical in nature. Light was the first massless particle to be discovered. The terminology “lightlike” was established before any other massless particles were discovered. Once ... | {
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Geometrical Optics: Infinite Rays Normally in ray optics, we draw a parallel line from the top of the image to the lens and stop when this line intersects an angled line (drawn from the height of the real object) and intersects. However, why do we stop? We can draw infinite rays from this object and they should be able... | An image is formed when there is a one to one correspondence between a point on the object and a point in space where all light rays emitted from that point on the object meet up. In other words, if we find that different light rays from the same point of the object end up meeting up at different points in space after ... | {
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Rapidity in 4-vector Transformation In Lorentz transformation we have a concept of rapidity as related to boost. Rapidity is defined as a hyperbolic angle α such that $$\tanh(α)=v/c .$$ This further defines a matrix for Lorentz transformation in term of sinh(α) and cosh(α). This is also said to represent LT under a rot... | I will show you the idea with a simple example: a 1+1 space-time.
In ordinary Euclidean 2-d space $\mathbb{R}^2$, the rotation is all operation on points $(x^1,x^2)$ which holds the quantity
$$(x^1)^2+(x^2)^2=C$$
invariant. So with the fact that $\cos^2 \theta+\sin^2 \theta=1$ one can simply write down the form:
$$x^1... | {
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Why is normal force at the bottom dependent on normal force on top?
Why does the normal force on bottom of the track have anything to do with the normal force on top of the track? Why isn't the normal force at the bottom simply $mg$?
| This really is a centripetal acceleration equation, compounded by gravity. You know when you get to a1g acceleration, the normal force at the bottom is double it's resting Force and would be a normal force of zero at the top. To get to point six at the top you would have to add 75% more centripetal acceleration, and I ... | {
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Why does $\sqrt{\frac km}$ represent angular velocity and not frequency? When I break down $\omega = \sqrt{\frac km}$ (angular velocity for a simple harmonic oscillator) into its units, I get:
$$\omega = \sqrt{\frac{kg * \frac {m}{s^2}}{kg *m}}$$
which simplifies to:
$$\omega = \frac 1s$$
If I'm not mistaken, that is t... | Angular frequency (rad/s) and frequency (1/s=Hz) have the same physical dimensionality, as OP correctly figured out, but are related by a factor of $2\pi$.
The inverse of this quantity is time, in one case the time it takes to go one radian in angle and in the other to go the full revolution. (There are $2\pi$ radian ... | {
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Does the Central Limit Theorem hold for position measurements? A friend asked me recently if the Central Limit Theorem holds for quantum systems: i.e., if the distribution of measurements (e.g., of position) for any wavefunction would prove approximately normal, given enough samples.
My gut response was no, because I'v... | In the measurement of position the probability of finding a given value is given by one probability distribution. The position is a - in the sense of one - random variable.
The Central Limit Theorem refers to the sum of random variables each of which follows a given probability distribution (in the classical fomrulatio... | {
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Can we replicate the sound of thunder with just the lightning? Scientists are able to extract sound of a two black holes merging from the data they collected without actually hearing it, but we don't know how it actually sounds, that's just a representation of the data in a sound format. That made me think, given that ... |
That made me think, given that we can collect the data of a lightning
(and we know what it sounds like), can we replicate or even predict
with a high certainly the sound a thunder will make before we actually
hear it?
Yes, but not for that reason.
I want you to think about the sound of thunder. It starts high a... | {
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Why the source function is equal to Planck function when we have a local thermodynamic equilibrium? I understand that the source function $ S_λ $ for the special case of blackbody radiation is equal to the Planck function $B_λ $.
However, in the broader case of a local thermodynamic equilibrium (and not the special ca... | Remembering my lessons...
In LTE, the collisions dominate over the radiative transitions, then the probability of an emitted photon to be "destroyed" by a collision is much higher than to be scattered (abosrbed and re-emitted) by the atom. The $\epsilon$ parameter defines this concept ($\epsilon=\frac{C_{ul}}{C_{ul}+A_... | {
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Limitations of a vacuum pump Can a vacuum pump create a vacuum with a pressure lower than the product of it's pressure ratio and the ambient pressure? If you have a pump evacuating a tank to the ambient, it seems like we wouldn't be able to go below the pressure ratio times the ambient pressure.
Also, what influences t... | If the pressure ratio is a truly independent of the inlet pressure, then you should be able to get an arbitrarily low pressure as follows:
*
*Pump from some volume A and exhaust to the atmosphere until the pressure in A is as low as the vacuum pump allows
*Pump from some volume B and exhaust to A until the pressure... | {
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Arrow of time and CPT symmetry It's been a few years since my physics degree. But I've been wondering: if you look at pictures of collisions at CERN, isn't it obvious which way time flows - simply on a probability basis? The likelihood of a huge cascade reversing into a proton and antiproton is vanishingly small. CPT s... | This may not be the answer you’re looking for, but your sense of what is probable may have something to do with the way in which you categorize the states. Sure, it’s more likely to end up with a huge cascade, but there are many many different outcomes which you would call a “huge cascade”. The probability of one speci... | {
"language": "en",
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Why does quantum mechanics become unnecessary at sufficiently high temperatures? In my statistical mechanics intro class, we are taught that at sufficiently high temperatures, the quantum treatment of things becomes unnecessary. Why is this? Can this be shown using certain equations?
| Qualitatively, quantum effects can be ignored if the interchange properties of boson or fermions can be ignored, which is to say if the system is dilute. When will a system be dilute? A single particle occupies a volume of its thermal de Broglie wavelength cubed (in three dimensions). For massless particles, the the... | {
"language": "en",
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How to make an object stay under water? How to make an object submerged under water? Neutrally buoyant?
| Here is another way that I have used to ensure that the submarine dives- and also returns to the surface when the rubber power is spent.
As described by others here, you "ballast" the sub, but not for neutral buoyancy: you add slightly too much air so it barely floats. Then you add fins to the body of the sub, and ben... | {
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Role of AdS/CFT correspondence in the context of integrability I was wondering how the AdS/CFT correspondence fits in the context of integrability. As I understand, the AdS/CFT correspondence postulates a duality between gravity theories and CFT's. If one theory has a strong coupling, the other has weak coupling. AdS/C... | Having a weakly coupled gravity dual does not imply integrality. To the contrary black holes in classical gravity are the most chaotic objects there can be! See this article:
https://arxiv.org/abs/1503.01409
| {
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Light in classical electrodynamics I am starting to learn elementary electrodynamics with Griffiths.
In the book, he has shown the natural correspondence between light and electromagnetic plane waves.
The problem that has agitated me is that plane waves are "global solutions", i.e. they have non-trivial EM field almost... | @ErickShock's answer is perfectly correct, but let's look at some numbers. A HeNe laser spectrum shown:
with a peak at
$$\nu = c/\lambda = 473755.4646016\,{\rm GHz}$$
If we send out a $\tau = 1$ millisecond pulse, we can call that monochromatic pulse that 182 miles long--physically it is a very long pulse. It is not i... | {
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Does the center of a black hole have a physical body? From science class, I'm led to belive that all matter breaks down once it's sucked into a black hole. I get that part, but doesn't all that matter still exist in the center of the black hole? yes it's no longer what i used to be, but it's still there in a different ... | We don't know for certain what lies inside the event horizon of a black hole, since we can never observe what happens inside the event horizon. General relativity predicts a gravitational singularity at the centre of a black hole, but this may not be physically meaningful - how can the curvature of spacetime actually b... | {
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Why is the magnitude of friction acting on the rear wheels greater than the magnitude of friction acting on the front wheels? When a car is accelerating on a horizontal road , friction acts in the forward direction on the rear wheel and in the backward direction on the front wheel .
But I am not able to understand why... | I think you have misunderstood how friction slows cars down. The friction between the tires and road allow the car to move (think about it). The friction between the axles and wheel are what slow the car down.
| {
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If a satellite speeds up, does that make it move farther away or closer? If a satellite is in a stable circular orbit and goes about 41% faster (escape velocity) then it leaves its host forever. I get that. However, what if it speeds up by less than 41%?
Intuitively, it would seem to make the satellite move farther awa... | If the satellite will reach a velocity somewhat smaller than the escape velocity then the satellite (coming out of the circular motion), the satellite will get both closer and farther away.
It will follow an elliptic trajectory, the earth being one of the ellipse's two focus points. This means the satellite will pass b... | {
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Was it ever experimentally verified whether antimatter can form chemical bonds the same way matter does? It's "common knowledge" that antimatter only differs from matter in its charge, and if left alone, it would behave exactly as matter does. This would infer that atoms of antimatter would form similar chemical bonds ... | So far, although a lot of positrons and antiprotons have been produced, only a very small number of anti-hydrogen atoms have been created for study.
The positrons and antiprotons are produced with much, much more kinetic energy than the atomic binding energy. It requires some neat technology to slow and cool them, tra... | {
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Location of free charge in insulators I'm going through the introductory section to Electrostatics in Materials in Griffiths, and I have a question that I can't seem to find a satisfactory answer to.
If I have an insulator with free charge, is it necessarily confined to the surface?
In the case of a conductor, Gauss' l... | Dielectrics can be both conductors and insulators. For a capacitor plate, an insulator is the best thing to use. It is due to this insulation property that means no free charges, that creates an electric field to counter the one between the plates due to some surface charge density.
If you are talking about conductors... | {
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EMF generated by a rotating rod can be zero? I have taken a look at this question: Emf generated by a rotating rod
But my question is different:
A metallic rod is being rotated in a uniform magnetic field with a constant angular velocity $\omega$. The axis of rotation of the rod is vertical, and passes through its mid... | The pd set up by the redistribution of electrons would indeed cancel the magnetic force on the free electrons in the rod, preventing further motion (apart from random thermal). The same applies inside an open-circuit battery when charges have built up on its terminals.
Your question (and it's one I've not seen present... | {
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Resistors parallel to short circuit I have a trouble solving this problem.
(Actually, each resistor is not parallel with the bottom wire since the voltage across each of them is different with that of wire.)
In the manual, the bottom wire(which is red circled) is simply ignored and thus can be easily solved.
I don't un... | The following three circuits are equivalent:
Resistances given: $(R_1, R_2, R_3, R_4, R_5)=(5,4,7,1,20)\ \Omega$;
batteries $(E_1, E_2)=(480, 168) \ Volt$.
The resistance in the middle $R_{345}=R_5+\frac{R_3 R_4}{R_3+R_4}$.
I think you want the voltage drop across $R_5$ which is $U_5=I_5 R_5$. Use Kirchhoff's laws t... | {
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Origin of 2π normalization factor in chemical $J$-coupling compared to the Heisenberg model In chemistry, particularly the field of NMR spectroscopy, the interaction between two (nucleic) spins (or so I guess?) is governed by the Hamiltonian:
\begin{align}
\mathcal{H}=2\pi\cdot J_{ij}{\vec {S_{i}}}\cdot {\vec {S_{j}}}
... | Yes, chemists like J couplings in Hz. The NMR J or scalar coupling and the Heisenberg model occur in very different contexts. In NMR, the scalar coupling is typically more than 1000 times smaller than the Zeeman term in the Hamiltonian. Moreover, the temperature is more than 1000 times larger than the Zeeman term. The ... | {
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Why do we observe the nuclear force only in scatterings and decays? Why, at first glance, are the only forces we perceive to be gravity without quantizing, electromagnetism and nuclear forces only in disintegrations?
|
Why, at first glance, are the only forces we perceive to be gravity without quantizing, electromagnetism and nuclear forces only in disintegrations?
If we accept as given the standard model of particle physics,SM with the addition of an effective quantization gravity, it can be shown that it mathematically describe... | {
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Is thermodynamics only applicable to systems in equilibrium? So I was going through callen's thermodynamics book and their he says that thermodynamics is only applicable to systems which are in equilibrium and that naturally raised a few questions in my mind
Is thermodynamics really never applicable to systems which ar... | A "non-equilibrium" system held steady was coined "thermostaedics" by Prof. Ralph J. Tykodi (now deceased)who was my advisor on my M.S. Thesis under the title of a book that he published called, "Thermodynamics of the Steady State" at Illinois Institute of Technology. Thermostaedics seems to me best because it covers ... | {
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The Electromagetic Tensor and Minkowski Metric Sign Convention I am trying to figure out how to switch between Minkowski metric tensor sign conventions of (+, -, -, -) to (-, +, +, +) for the electromagnetic tensor $F^{\alpha \beta}$.
For the convention of (+, -, -, -) I know the contravariant and covarient forms of t... | Misner, Thorne, and Wheeler have a nice two-page summary of sign conventions in general relativity, in the front endpapers of the book, so that would be the first place I would turn for this kind of thing.
The electromagnetic tensor is defined by the Lorentz force equation, which gives the four-force acting on a charge... | {
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Direction of $d\mathbf{l}$ A solid sphere has charge $q$ and radius $R$. Find the potential at a point a distance $r$ from the center of the sphere where $r>R$, using infinity as the reference point.
My attempt:
From Gauss' theorem we may deduce that $\displaystyle\mathbf{E}=\frac{1}{4\pi\epsilon_0}\frac{q}{r'^2}\hat{\... | Potential is defined as the negative of the work done in moving unit charge at zero acceleration from reference to that point in field where the potential is being calculated. So dl represents a differential movement from reference (here infinity) towards r' (assumed straight line path, else tangential to path towards ... | {
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"timestamp": "2023-03-29T00:00:00",
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Expectation Value of displacement to the $n$th power quantum harmonic oscillator? Is there a closed-form expression for $\langle x^n\rangle$ for the ground state quantum harmonic oscillator, where $n =$ even integer $>0$? I am attempting to pursue this with rising and lowering operators but the foiling is getting out o... | You can get the answer without raising and lowering operators, by directly calculating the the overlap integral using the identity
$$\int_{-\infty}^{\infty}dx \ x^{2n} \ e^{-\alpha x^2} = \frac{(2n-1)!!}{(2\alpha)^n} \sqrt{\frac{\pi}{\alpha}}\ ,$$
which you can prove by induction or just look up in a table of integrals... | {
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Partition function in renormalization When studying statistical mechanics, renormalization is understood from attempts to calculate partition function by simplifying. (For example, David Tong's lecture note)
While I understand that partition function allows one to calculate important thermodynamic quantities, what I do... | The whole point of renormalization is that you are changing all of these parameters in the precise way that keeps the partition function intact. In a sense, you're trying to find all the solutions to the equation $Z(K_0)=Z'(K')$, where $Z(K_0)$ is whatever bare couplings you start with. Sometimes, when doing this, auth... | {
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Question on two-neutrino double electron capture There was a fascinating paper in Nature recently, on the observation of two-neutrino double electron capture in xenon, with a half-life time of $1.8\times 10^{22}$ years.
The process described in the article is
$$^{124}\mathrm{Xe} + 2e^- \to {}^{124}\mathrm{Te} + 2 \nu_... | This is explained by Scott Manley in Why a Dark Matter Search Also Observed The Rarest Radioactive Decays at around the 7:20 mark.
The short answer is that the process is electronically forbidden, because the iodine-124 nucleus has a higher binding energy than the xenon-124 nucleus. Using the data from Wikipedia, the m... | {
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What is an integrator lens? I was looking into how photolithographic mask aligners works and came across this diagram, I am curious as to what an 'integrator' is. It seems like these lenses are used to focus the light beam, am I correct? Is the diagram correct in showing these lenses as being flat or is their curvature... | To minimize the influence of the arc spread and its actual position there is a diffusing element placed in the secondary focus of the mask aligner (Integrator 1). The Integrator 1 is followed by the so-called Integrator 2. The Integrator 1 has the function to create a radiation field as uniform as possible at the plane... | {
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Examples of non-sine waves? What would be a non-sine wave? AFAIK, all sound is a sine wave, equally to waves on the sea. What would be a common example of something in nature that's a wave but not a sine wave? Or, would we have to look at man made regularities like bus timetables or stock prices to find non-sine waves?... | It is not true that all sound is sine waves. What is true is that one can find sinusoidal solutions to the wave equation. This allows an arbitrary wave to be expresses as a linear superposition of sines. It looks like the Soliton has been mentioned above. While this is one counter example it relies on the non-linea... | {
"language": "en",
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Adiabatic Approximation, Solving the Schrödinger equation In the adiabatic approximation one looks at the Hamiltonian
$$ H_0 = \sum_{i = 1}^{N_e} \frac{\vec{p}_i^2}{2m_e} + \sum_{i < j} \frac{e^2}{|\vec{r}_i - \vec{r}_j|} + \sum_{k < l} \frac{Z_k Z_l e^2}{|\vec{R}_k - \vec{R}_l|} + \sum_{i, k} \frac{- Z_k e^2}{|\vec... | So, the Hamiltonian of the question describe a set of atoms and electrons where the atoms are supposed to be fixed in space.
There are two answer to this question.
The mathematical answer is:
The existence of a complete set of solutions follows from the properties of the Hermitian operators, as stated in the other an... | {
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Why hydrogen lines are less visible in the Sun spectrum than in supernovae clouds? Supernovae clouds are very colorful, and if I trust documentaries I watched, the colors are due to excitation of elements, as in fireworks. Since the Sun is mostly made of hydrogen, I suppose those lines should be very apparent but they ... | The sun's spectrum is a blackbody spectrum with absorption lines superimposed. The blackbody spectrum comes from the photosphere, which is the highest elevation at which the sun is opaque. It becomes opaque because it's ionized to form a plasma. A plasma is opaque because it has free charges that interact strongly with... | {
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Unpolarised light falls directly on a half-wave plate Will an unpolarised light get polarised if it falls directly on a half-wave plate? If so, then what will be the state of polarisation?
| If you shine unpolarized light onto a half-wave plate, then the result will be similarly unpolarized.
It seems you really don't want to believe this answer, so let's address your two objections thus far:
*
*
But.... By the definition of half wave plate.... It says that an unpolarised light will be divided into two p... | {
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How do car rear-view mirrors work? I wonder, how does a car rear-view mirror work?
When there is a car behind me with high-beam, all I do is flip a tong at the bottom of the mirror to relax the lights!
Are there two mirrors in it, one darker than the other?
| For manual anti-glare mirrors, the glass is actually a prism with the silvered rear surface not parallel to the front surface
In day-time position, drivers are seeing reflections from the rear surface with large amounts of reflected light reaching their eyes
In night-time anti-glare position, drivers are seeing refle... | {
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Momentum matrix elements in a crystal I am trying to follow along a derivation (E. I. Blount, Solid State Phys. 13, 305 (1962)) in which he derives the matrix elements of the true momentum $p_{n,n'}(k,k')$ (not the crystal momentum). He arrives at the following expression:
$p_{n,n'}(k,k') = \delta(k-k')(\hbar k\delta_{... | I agree with aljg up to the third line from the bottom of his derivation. I would argue that from there, the derivation should go as follows.
\begin{align}
\langle \psi_{n \mathbf{k}} | \frac{\mathbf{p}}{\hbar} | \psi_{n' \mathbf{k}'} \rangle
&= \frac{1}{V} \int d\mathbf{r} e^{i(\mathbf{k}'-\mathbf{k})\cdot \mathbf{r}}... | {
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Binding energy of a molecular ion?
The protons in the $\text{H}_2^{+}$ molecular ion are $0.106 \, \mathrm{nm}$ apart, and the binding energy of $\text{H}_2^{+}$ is $2.65\,\mathrm{eV} .$ What negative charge must be placed halfway between two protons this distance apart to give the same binding energy?
Question: In ... | Just the protons, basically - it's the energy required to take the system apart into a single proton and an isolated hydrogen atom.
Separating the proton and electron from that hydrogen atom would take a fair bit more energy - an additional 13.6 eV.
| {
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Why is it that magnetic fields(or any field)not move in space? When I imagine a magnetic field produced by a magnet, or the electric field produced by a charge, I've learned that the fields are stationary, however, their value(across space) changes.
If I placed the magnet at a point $P$($0,0,0$), and then moved the m... | If the magnet is moved, the magnetic field changes to match the new position of the magnet. As the magnetic field changes, it also induces an electric field.
The details of this interaction depend heavily on how exactly the magnet is being moved, and may or may not involve the production of propagating electromagnetic ... | {
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Momentum average on phase space for free particle I'm studying from Greiner statistical mechanics, and he uses an approximation which I don't really understand.
On averaging over many phase-space points we have
$$\langle\vec{p}^2\rangle=3\langle p_x^2\rangle=3\langle p_y^2\rangle=3\langle p_z^2\rangle$$
since no di... | The claim on Greiner is
$$ \langle\vec{p}^2\rangle = 3\langle p_x^2\rangle = 3\langle p_y^2\rangle = 3\langle p_z^2\rangle $$
This claim follows from the fact that
$$ \text{E}[p^2] = \text{E}[p_x^2] + \text{E}[p_y^2] + \text{E}[p_z^2] $$
and that $(x,y,z)$ are indistinguishable:
$$ \text{E}[p^2] = 3 \text{E}[p_x^2] = 3... | {
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Regularising the Green's function in 2D The Green's function for the 2D Helmholtz equation satisfies the following equation:
$$(\nabla^2+k_0^2+\mathrm{i}\eta)\,{\mathsf{G}}_{2\mathrm{D}}(\mathbf{r}-\mathbf{r}',k_o)=\delta^{(2)}(\mathbf{r}-\mathbf{r}').$$
By Fourier transforming the Green's function and using the plane ... | The poles are still in the same place so what is stopping you using residue theorem?
| {
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Grassmann-even action I am currently studying supersymmetric quantum mechanics with the help of the book Mirror Symmetry by Kentaro Hori (and others). On page 155 where they introduce Grassmann variables they say that the action is Grassmann-even without an explanation. But i do not quite understand why this is the cas... | The Grassmann-odd path integrals are special cases of Grassmann-even path integrals. This follows since
$$
\int [d\psi]e^{-S}=-\int [d\psi]S=-\int[d\psi]d\chi (\chi S) = \int [d\psi]d\chi e^{-\chi S}
$$
for $S$ being Grassmann-odd and $\chi$ a fermion.
Let us work with an instructive example. If you have a Grassmann-o... | {
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Why aren't satellites disintegrated even though they orbit earth within earth's Roche Limits? I was wondering about the Roche limit and its effects on satellites.
Why aren't artificial satellites ripped apart by gravitational tidal forces of the earth?
I think it's due to the satellites being stronger than rocks?
Is th... | To add to other answers, also consider that artificial satellites are much smaller than natural satellites. This means that the difference between the gravitational force at the point the closest to the planet and at the point the furthest from the planet is much smaller in artificial satellites.
| {
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Convergence Property of Path-Integral Let the action be $$S= \int \bigg\{ \frac{1}{2} \big(\frac{dX}{dt}\big)^2 - V(X) \bigg\} d\tau$$
and the corresponding Path-Integral
$$Z= \int DX(t) e^{iS}.$$
Since the convergence is not clear we Euclideanize the time coordinate $t$ by the Wick rotation
$$ t \rightarrow -i \tau$$
... | You just have to look at the exponential. So assuming your Lagrangian is bounded from below when written in its euclidean version, you can see that the Wick rotation is taking an imaginary exponential which is oscillatory and turning it into a decaying exponential which can be approximated more easily, for example summ... | {
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Physical intuition behind torque converter A torque converter (also here) is a device used in some cars. It uses several "fans" coupled through a liquid (transmission fluid) in order to perform the function of a clutch, but more importantly it acts as a liquid gear in the sense that it multiplies the torque going from ... | A torque converter contains a propeller that is spun by the engine and another close by which is connected to the rest of the transmission. these two propellers face each other in a chamber filled with oil, so that when the engine-driven prop spins, it pumps oil through the second prop and causes it to spin as well.
B... | {
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Does the ideal gas law apply to a moving vehicle? If for example you have a car travelling along a road. There is obviously a high pressure region in front of the car, where the air is forced around the vehicle. Likewise, I understand that cars will leave a region of low pressure air directly behind them.
Air is descri... | "Incompressible" means different things in different contexts.
*
*In thermodynamics, an "incompressible substance" is one whose properties are completely insensitive to pressure. This is a good model for solids and liquids but not for gases.
*In fluid dynamics, "incompressible flow" means that the velocities prese... | {
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Why does the potential difference across a type of parallel circuit not act like a potential divider?
Image credit (Q3)
In this attached circuit, when $R_1=0\Omega$, I am failing to understand how the two cells affect the potential difference across the central resistor R3. I understand that potential difference is co... | If you are trying to view the system as a linear superposition of the two voltage sources, you must "kill" each source separately. To kill a defined voltage source (like the batteries), you should replace them with a short circuit.
Killing the 12 V source leaves $R_3$ and $R_2$ in parallel with the $10~V$ battery: $10~... | {
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Why is there no current between two capacitors connected in series? I want to ask a question about the figure below.
Why the current does not flow from $-Q$ term to $+Q$ term or from a to b since there is a voltage?
| I assume that the question is about the DC case. There is no current between a and b, as there is no voltage difference. The voltage difference between the plates opposite to a and b, say a' and b', is canceled out by the charges on a and b. The plates a and b are connected so form, a single conductor. The charges on a... | {
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Is velocity of a fluid the gradient of something physically significant? For incompressible flow,
$$\nabla\cdot \mathbf v=0.$$
That means $\mathbf v$ got to be the gradient of some scalar field.
How can I find the scalar field? Is it physically important?
| Suppose that the flow is potential, then we have $\vec {u}=\nabla \phi$ and $\nabla .\vec {u}=\nabla ^2\phi=0$. Then the equations of motion are reduced to the Bernoulli integral.The Laplace equation $\nabla ^2\phi=0$ with boundary conditions is widely used in aerodynamics to calculate the distribution of velocity and ... | {
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What affects the propagation of secondary cosmic rays? Primary cosmic rays produce, upon entering the Earth's atmosphere, a whole load of secondary particles. These primary particles are necessarily stable particles such as protons, electrons, and neutrinos.
Wikipedia says: "When cosmic rays enter the Earth's atmospher... |
My question, however is, what happens with neutrons in particular?
Found this paper which estimates the effects of cosmic air showers on electronics.
Cosmic rays at sea level consist mostly of neutrons, protons, pions, muons, electrons, and photons. The particles which cause significant soft fails in ... | {
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Why do my books introduce the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$ without showing partial derivatives of $\mathbf{E}$ exist? In electromagnetism (electrostatics), we often come across the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$.
In order for this equation to be meaningful, $\ma... | The partial derivatives of the electric field do not always exist. They won't exist, for example, at a point charge, line charge, or charged plane -- situations where there is a singularity in the charge density. In these situations, Gauss's law still holds in integral form, if the Gaussian surface doesn't intersect an... | {
"language": "en",
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Apart from the sine wave, are there any other waveshapes that could be thought of as commonly appearing "in nature"? I'm familiar with the sine wave being something that can be used to model many types of oscillation in nature (and the way that multiple sine waves can be seen as sum to produce complex repeating wavesha... |
However, I'm struggling to think of any other waveforms that can be associated with phenomena in nature.
The motion of an ordinary pendulum of length $L$ is cyclic, but non-sinusoidal (it is only approximately sinusoidal for small angles). The exact non-sinusoidal motion is governed by the non-linear equation:
$$
\f... | {
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Why haven't we yet tried accelerating a space station with people inside to a near light speed? Is that something we could do if we use ion or nuclear thrusters?
Wouldn't people in the station reach 0.99993 speed of light in just 5 years accelerating at 1g and effectively travel into the future by 83.7 years?
That wou... | It is not feasible because it would cost an enormous amount of energy
to accelerate the spacecraft.
To prove this let's calculate with some concrete numbers.
Very optimistically estimated, your spacecraft may have a mass of $m=1000\text{ kg}$ (enough for a few people and a small space capsule around them, but neglectin... | {
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2 windows - will I see the reflections?
I have a question regarding photons nature. Let's say I have a single source of light - regular bulb and the observer - in the same room.
The observer looks through a glass window (normal glass window-nothing special about it) and sees his reflection, but some of the light is p... | Classical electromagnetism predicts that the observer will see four first order reflections, one from each glass-air interface. The reflectivity at each interface is 4%. Multiple reflections will also occur, for which light is reflected back and forth. They are at least third order in intensity, that is, are 4% of 4% o... | {
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Does pair production happen even when the photon is around a neutron? In order for a photon to decay into a pair of $e^+ e^-$, it must have at least $E_{\gamma}=1.022$ MeV and must be near a nucleus in order to satisfy the conservation of energy-momentum.
But would this happen even if the photon is near a neutron and n... | Yes, pair production can occur even near a lone neutron. The presence of a mass for the photon to interact with is required for conservation of momentum (further explanation can be found here). To my knowledge, the charge of the nucleus is not significant to the process of pair production, though the probability of pai... | {
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How strong are Wi-Fi signals? My family members dislike the idea of having many devices communicating wirelessly in our house, arguing that the signals have negative effects on our physical health.
I would like to tell them the EM signals are in fact weaker than the light from our lights but I could not really confirm ... | You only get out what you put in
This aims to be a layperson's answer, rather than specific complex formulae which are mind boggling to comprehend to a layperson, but the easiest way to prove the lightbulbs are more harmful than the wifi, is to consider the input power (as output can never exceed input; due to ineffici... | {
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Quantum field theory with only 3-point vertexes Given an arbitrary quantum field theory, can I always write it in terms of another (different) quantum field theory containing only operators with 3 fields? (i.e. vertexes with 3 legs)
I guess that should be possible introducing arbitrary additional fields that once integ... | Yes you can! I'm sure you can do this all sorts of ways, but here is a nice systematic one. Suppose you have a term in the lagrangian $\prod_{i=1}^{k} \phi_i\subseteq L$. We can start by introducing two new fields, $\lambda_1$ and $\sigma_1$. Add the term $i\lambda_1(\sigma_1-\phi_1*\phi_2)$. If we first integrate out ... | {
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Why doesn't the Earth's acceleration towards the Moon accumulate to create noticeable motion of the earth, towards the moon I get that Earth's mass is very large, so its acceleration is very tiny. But wouldn't the acceleration accumulate over a period of time and become noticeable?
| The moon is actually moving away from the Earth; 4 billion years ago it was much closer.
The moon raises tides which have the effect of slowing down the rotation of the Earth, so that the daylength is now much longer than it used to be, but some of the energy which has been lost by the Earth was captured by the moon, ... | {
"language": "en",
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Can a wire having a $610$-$670$ THz (frequency of blue light) AC frequency supply, generate blue light? We know that when we give alternating current across a wire then it will generate an electromagnetic wave which propagates outward.
But if we have a supply which can generate 610 to 670 terahertz of alternating curre... | An alternating voltage at that frequency is light. There's no 'generate' about it - the power supply is just a light source.
And if you have a wire, that is, a conductor made of metal, then the light won't propagate inside it at depths longer than the skin depth for that material at that particular frequency, which is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/482541",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "33",
"answer_count": 6,
"answer_id": 2
} |
Does rotation happen throughout the whole x axis of an object simultaneously? For example, if I draw a line on the side of a pencil top to bottom, then snap one end of it as in launching it due to the pressure of my fingers. Anyways, if I record the pencil launch in slow motion (perhaps it’s my phone that has to do wit... | No, the rotation would not occur instantaneously. When you flick one end of the pencil, the molecules (at the end) you imparted an impulse to will have gained momentum and would pull the molecules just beside them due to internal electrostatic forces holding the molecules together, (much like the propogation of a mecha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/482788",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 0
} |
How much energy is needed to make fire? I'm so curious about fire. So I searched a lot in the internet. And now, I knew that fire is some kind of chain reaction and combustion energy make the other molecule hot and the other molecule makes other chemical reaction and so on...
Then does the first given energy make this ... | The first given energy is called the activation energy. The chemical reactions of burning liberate energy in the form of heat and light (and probably some sound), and a small part of that energy activates further combustion. The amount of activation energy required to start the fire depends on what you're burning.
In ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/482887",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
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