Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why does it seem as if big vehicles "attract" mine when I drive close to them? When I drive a car at high speed and when I am near to another big car (like a van, or transport vehicle) I feel an attraction to or something push me toward the other big car. What's the physics in this case?
| When a vehicle moves through a gas or a liquid, it displaces the medium through which it moves, and gas or liquid must rush in to fill the void of displacement. It's exactly like the bow wave of a ship which must fill the area immediately behind the ship. This creates suction past the mid point and toward the stern o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/174274",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Limits of Integration Trig, Mag Field Infinite Length Wire I don't understand how the limits of integration should be defined when doing basic integrals of trig functions. It seems like it's an arbitrary decision, I don't understand it.
Here's the set up: For the field near a long straight wire carrying a current $I$, ... | With your definition of θ, The Biot-Savart formula reduces to (km)I/R times the integral of sin(θ)(dθ) which integrates to the -cos(θ) and evaluates to (1+1) at the limits 0 to 180 degrees.
| {
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Will the electrostatic force between two charges change if we place a metal plate between them? If a thin metal plate is placed between two charges $+q$ and $+q$, will this cause a change in the electrostatic force acting on one charge due to another? What is the concept behind this? What will happen if the metal plate... | The metal plate, being a good conductor, will have its electrons rearrange in such a way as to neutralise the electric field inside the plate.
The electrons would tend to bunch up in the plate at the point(s) closest to each of the two charges, alterring the electric field that they're exposed to and changing the elec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/174514",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Drying clothes with the sun's heat, without any air Will my wet clothes dry if I hang them under the sun, and if there is no air around the clothes? In other words, do I need both air and heat to dry wet clothes, or is heat alone (in the imagined absence of any air) enough to dry wet clothes? Related question : will w... | I think:
Without air arround, you have some kind of a black body. Depending on the distance to the sun your body will reach a constant temperature. If this temperature is above the boiling point, you wet clothes will become dry. Because the gravitational attraction of your clothes is much smaller than the pressure of t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/174658",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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Relation between 1D and 3D partition function In a solid state physics text author said $$Z_{3D} = [ Z_{1D} ]^{3} $$ $$<E_{3D}>=3<E_{1D}>$$
Where $Z$ is partition function. Can anyone convince me why it is so?
| You probably (you should really give more details when posting questions, so that those without your book can still help you) came across this in the Einstein model of the harmonic oscillators for the heat capacity estimation, in which case the energy eigenvalues in 1D (say for x-component) are given by:
$$
E_{nx} =\hb... | {
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Problem in one step of deriving Einstein's Field Equation from Caroll's book I have the proposed solution stated as:
$R_{\mu \nu} -\frac{1}{2} g_{\mu\nu}R=\kappa T_{\mu\nu}$ (4.43)
Caroll says:"note that contracting both sides of (4.43) yields (in four dimensions)"
$R = - \kappa T$, which I should get to.
But I get it ... | Note that Carroll says "in four dimensions". Recall that raising an index on the metric tensor gives the Kronecker delta: $g^{\rho\mu}g_{\mu\sigma}=\delta^\rho{}_\sigma$. The delta has $n$ entries of one on the diagonal in $n$ dimensions. So in spacetime we have a tensor with 4 ones along the diagonal. Thus, the trace,... | {
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How can static friction do work?
By definition, the work done by a force is $W = F\cdot d$, so how can static friction do work?
Can this force move the body a distance of $75~\text{m}$?
| Without friction between the crate and the truck bed, the crate would remain at rest in the frame of reference of the road, as the truck accelerates away down the road.
The crate moves in the frame of reference of the road, because of the force of friction acting on it.
So the work done on the crate, in the frame of re... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/175227",
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On the Bogoliubov transformation in the BCS I have a question regarding the diagonalization of the BCS-Hamiltonian using the Bogoliubov-DeGennes-transformation. I hope someone can help me, so I start with the following Hamiltonian, it is related to the kinetic term in the equation and follows Tinkham's book.
$$
\sum_{\... | Consider $c^+_{\boldsymbol{k}\uparrow}=(c_{\boldsymbol{k}\uparrow})^+=(u^*_\boldsymbol{k}γ_\boldsymbol{k0}+v_\boldsymbol{k}γ^+_\boldsymbol{k1})^+=u_{\boldsymbol{k}}γ^{+}_\boldsymbol{k0}+v^{*}_\boldsymbol{k}γ_\boldsymbol{k1}$, it yields the right result.
| {
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Is there any such thing as a change in acceleration (ex: 3 m/s/s/s)? If there exists something like that, then in $distance/time/time/time$, how is it expressed?
| http://wordpress.mrreid.org/2013/12/11/jerk-jounce-snap-crackle-and-pop/
Speaking derivatives to time:
*
*First position $x$,
*then velocity $v=x'=\frac{dx}{dt}$,
*then acceleration $a=x''=\frac{d^2x}{dt^2}$,
*then jerk $x'''=\frac{d^3x}{dt^3}$,
*then jounce/snap $x''''=\frac{d^4x}{dt^4}$,
*then crackle $x'''... | {
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Why do the $u$ and $d$ quark not have an associated quantum number? All the other quarks ($c$,$s$,$b$ and $t$) have quantum numbers of charmness, strangeness, bottomness and topness that are conserved in strong interactions.
This allows, among other things, flavour changing neutral currents in $K^0$, $B^0$ and $D^0$ m... | All quarks have baryon number 1/3, so that the nucleons can be built up. Baryon number is a conserved quantity in the standard model . In models where the proton can decay, it is not conserved, but no proton decays have been detected up to now.
One has to realize that the quantum numbers S,C,B,T are attributes for all... | {
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Generalized Bekenstein-Hawking temperature for Kerr-Newmann-dS black holes What is the formula for the Bekenstein-Hawking temperature in a Kerr-Newmann-de Sitter spacetime, i.e., the temperature for a black hole with Mass (M), angular momentum (J), electric charge (Q) and cosmological constant ($\Lambda$)?
| Just a small correction, the solution is called Kerr-Newman-dS (without Schwarzschild, because it is just non-rotating Kerr). And a quick search gives a couple of papers:
*
*paper 1
*paper 2
Hope this helps and answers your question.
| {
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Why do we use capacitors when batteries can very well store charges? Can batteries be used instead of capacitors? I am trying to figure out a basic, superficial and any obvious difference between the two.
| While a capacitor can be used to store charge, usually we are interested in other properties. Most notably, it has a voltage proportional to the amount of charge stored ($Q=CV$) which means it acts as an integrator of current. There are many circuit applications where you use this property - which incidentally also mea... | {
"language": "en",
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Are circles stronger than triangles? I've often heard in engineering that, "there is no shape stronger than a triangle." I also recall that arches are also very strong shapes, which can be crudely described as a perpendicularly-symmetrical half-an-ellipse; Which can be simplified to half a circle.
If there were no conv... | The short answer is, if you are making a bridge, triangles are, because the way they distribute weight when they are in a group makes them stronger. A single arch is stronger, but when you use lots of triangles when building a bridge it becomes stronger than using one arch. That is why we use triangles for most of our ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/176140",
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Arrow of time and entropy? The arrow of time is usually defined by the direction in which entropy increases. In a closed system, if there's a max entropy that the system can reach, does that mean time stops or at least become undefined at the max entropy state?
See also: For an isolated system, can the entropy decrease... | One may still describe the behavior of such a system at maximal entropy using a theory that does use the concept of time, or the time coordinate $t$. But it is true that operationally speaking, the passage of time ceases to exist because the equilibrium associated with the maximum entropy is incompatible with the exist... | {
"language": "en",
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Photon: speed and mass Is it correct to think that the speed of light does not depend on the speed of light source because photons have no mass, so they have no the kind of inertia that is associated with mass, so they can not "feel" (acquire) the speed of the light source?
|
Is it correct to think that the speed of light does not depend on the
speed of light source because photons have no mass
In a certain sense, yes.
The Lorentz transformations guarantee that the speed $c$ is invariant; an object with speed $c$ in one inertial reference frame (IRF) has speed $c$ in all IRFs.
But an ob... | {
"language": "en",
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Constants of motion in quantum mechanics What is the meaning of a constant of motion in quantum mechanics (an observable-operator that commutes with the Hamiltonian) in contrary with classical mechanics?
| Is the same idea of classical mechanics, but now this quantities can be undetermined if you apply some measurement of the complementary of this quantity.
e.g.
The total angular momentum is a constant of motion $\vec{L}$. You can measure some component $L_i$ of this angular momentum a lot of times and this yields to the... | {
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Why is charge of the electron negative? How did scientists figure out that the charge of the electron was indeed negative? I know how the cathode ray tube experiment works, but how did Thompson know that the plate that the cathode ray beam was attracted to was positive, meaning the cathode ray was negative? What is the... | That there are two distinct types of electric charge is a metaphysical fact.
But nature is indifferent to what we choose to label these charges; up / down, left / right, positive / negative, black / white, etc.
Electrons will still flow to the plate in a CRT regardless of how we choose to label the polarity of the ch... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/176589",
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In aircraft design why are light materials preferred to heavy ones? Especially given the relative cost between (say) steel and carbon composites. After all, I assume most fuel is consumed overcoming drag not accelerating mass. Once an aircraft reaches cruising speed it should not matter how heavy/dense the aircraft is ... | Check out this explanation.
Basically, when a wing is flying, it feels a force vector which is not vertical.
It points up and back.
We call the upward component lift, and the backward component drag.
Suppose a plane is loaded to twice its normal weight.
Then it needs twice its normal lift to support that weight.
It pay... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/176870",
"timestamp": "2023-03-29T00:00:00",
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Does the Higgs Boson exert gravity? The Higgs boson is considered to have mass. Would a field of Higgs bosons, W bosons, etc. give off a gravitational field for the duration of their existence?
| The quantum size of elementary particles is in conflict with the classical notion of "generating a gravitational field". The correct statement is that these bosons, as well as all other particles (even massless ones), do interact with the hypothesized massless spin two particle we call the graviton, through three or fo... | {
"language": "en",
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Time dependent Hamiltonian and Gauge invariance In general, in quantum mechanics we can prove probability current or the Schrodinger equation and other quantities are gauge invariant. However, the Hamiltonian isn't gauge invariant. Under a gauge transformation, the Hamiltonian operator changes(or have i understood wron... | The issue is that the electromagnetic field and its gauge transformations are treated classically here - they are not operators of the quantum theory, but "tacked on" because we want to describe how a quantum object interacts with the electromagnetic field without treating the EM field itself as a quantum object.
"Gaug... | {
"language": "en",
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Is the superconducting current made up of Cooper pairs? Inside the superconductor it should be $\mu_0\mathbf{j} = \mathbf{\nabla} \times \mathbf{B} = 0$, since B is 0 due to the Messner effect.
*
*This means that the current is carried by the surface.
*But if the surface is not composed of Cooper pairs some scatt... | You miss first of all that Cooper pairs do not exist as some physical quantities. If you prefer, they are not particles as electrons. They are just correlations.
The current is a collective response to a gradient of phase. You can generate such a gradient by a magnetic field, a voltage, a break of the condensate (like... | {
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What is meant by the term "single particle state" In a lot of quantum mechanics lecture notes I've read the author introduces the notion of a so-called single-particle state when discussing non-interacting (or weakly interacting) particles, but none that I have read so far give an explicit explanation as to what is exa... | Many particle wavefunctions are generally appallingly complicated objects. One way to get a handle on them is to break them down into simpler parts, understand those parts and then put them back together again. We do this by constructing the space of many particle wavefunctions as either a tensor product space or a Foc... | {
"language": "en",
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Is it possible to derive the angular frequency of a simple harmonic oscillator using total energy?
I want to show that
$$\omega=\sqrt{\frac{k}{m}}$$
using the fact that
$$E=K+U=\frac{1}{2}mv_x^2+\frac{1}{2}kx^2=\frac{1}{2}kA^2.$$
The issue is that I have derived a formula that isn't correct:
I first took the t... | Energy is conserved in a simple harmonic oscillator, so $dE/dt = 0$. From there you can get the angular frequency by your same logic.
Another way of seeing this: A is a constant of the motion, so its time derivative is 0.
| {
"language": "en",
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Does traveling through a wormhole cause you to go back in time? Here is a hypothetical scenario:
You have 2 planets A and B which are 10 light years apart. If I take a wormhole from A to B and I look at planet A through a telescope it would seem like it is 10 years in the past because light takes 10 years to travel fro... | For sending the light pulse, if you then go back through the wormhole to where you started (in the ‘present’), you will have to wait 10 years for the light pulse to end up at the planet, so it isn’t time travel.
But Albert Einstein’s theory of relativity states that space and time have been combined to make spacetime, ... | {
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"timestamp": "2023-03-29T00:00:00",
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Confusion regarding latent heat of fusion During vaporizing there is higher increase in internal energy (higher positive $\Delta U$) and more work is done by the liquid (higher $W$) as molecules become widely separated.
During melting, there is small increase in internal energy (smaller positive $\Delta U$) and less wo... | It should be (delta)U=q+-w, where +- means plus or minus, like the sign used in the quadratic formula.
The sign for w should be determine by the type of work done, ie. compression (+w) or expansion work (-w).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/177918",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does mechanical energy conservation work? I am a little confused about how mechanical energy conservation operates when it comes to things like predicting velocity. I know that if conservative forces are the only forces acting on a body, then we can say that mechanical energy is conserved. This is simple to see whe... | mechanical energy conservation is sum of all conservatives energy such that there is no external forces like frictional or an explosion.
basically we mainly deal with
Blockquote
GRAVITATIONAL energy and KINETIC energy
Blockquote
.
mgh + 1/2m sq.(v) = constant
when no other external forces like i perviously menti... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Physical meaning of quantum interpretations Do interpretations of quantum mechanics have physical meaning? An argument for no would be the fact that no matter the interpretation, one gets the same measurements. They also do not follow logical positivism.
| If interpretations actually had different physical consequences, we might go about calling them different 'theories' instead.
For example, one might say that the classical Newtonian model of gravity comes from many non-interfering (straight line) threads of variable length, maybe with complex infinitesimal modern art o... | {
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Electric field due to a finite line charge I was wondering what would happen if we were to calculate electric field due to a finite line charge. Most books have this for an infinite line charge. In the given figure if I remove the portion of the line beyond the ends of the cylinder. I believe the answer would remain th... | I have taken that line charge is placed vertically and one test charge is placed.
Now the electric field experienced by test charge dude to finite line positive charge.
$$E_x = \int dx \cos \alpha$$
$E_y$ will be cancel out as they will be opposite to each other.
$$E_x = \int k \frac{dq}{x^2+y^2}\cos\alpha$$
$$E_x = ... | {
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Resulting force when bending plywood My sister and I are working on a thesis in interior design on a plywood chair similar to the picture, where the red part bends. We are trying to work out how much the plywood would push back when a force F (human sitting on it) is applied on a distance d from the fixture. We have fo... | As long as the chair does not break, the force exerted on the person is equal to the force the person exerts on the chair.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/178489",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Lorentz-invariance of step function I was reading about the Lorentz invariant integration measure $\int \frac{d^3k}{2E_K}$, and ways to prove that this was Lorentz invariant. Many of the proofs I have read use the step function (or Heaviside function) $\theta(k^0)$, and claim that this is obviously Lorentz-invariant (e... | Thanks WetSavannaAnimal aka Rod Vance for the rigorous proof. Here I would like to add a short answer in a different perspective.
An orthochronous proper Lorentz transformation can always be split into a boost and a rotation. The rotation part doesn’t change the $k^0$ component. A boost on $k^{0}$ has the form
$$
k^{0... | {
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Can electricity flow through vacuum? People say yes, and give a wonderful example of vacuum tubes, CRTs. But can we really say that vacuum (..as in space) is a good conductor of electricity in a very basic sense?
|
But can we really say that vacuum (..as in space) is a good conductor of electricity in a very basic sense?
No, because vacuum is not a material object. The word conductor was meant for material bodies. It is not usually used to describe vacuum, because vacuum is not merely a different body from metal or dielectric, ... | {
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How to determine if a potential admits bound states? According to Griffith's Quantum Mechanics, "$E$ must exceed the minimum value of $V(x)$, for every normalizable solution to the time independent Schroedinger equation"
As an example, there is no acceptable solution to the time-independent Schroedinger equation for th... | The key here is that E must exceed the minimum of $V(x)$.
If one has a delta function well then the minimum is $V_0 = -\infty$ while for a delta function barrier the minimum is $V_0 = 0$
Hence for the delta function well, one can have bound states with $E<0$ or one can have scattering states with $E>0$.
For the delta... | {
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What does magnetic field vector mean? I am trying to understand what a magnetic field vector tells us about the magnetic field.
I understood that a vector is just a representation of a point and how much it is moved in x,y and z direction from its origin.
But how can this explanation apply to the magnetic field?
source... | A vector is a quantity having a direction and a magnitude.
Magnets have a magnetic influence, which can be visualized as a physical vector field.
A magnetic field vector allows you to predict the influence of a magnet on a magnetic material.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/179055",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can't I harness normal force? Lets say I have my palm flat with a book resting on top of it, and I have my feet on the ground. I extend my arm so that now it's kind of difficult to keep the book up. Why doesn't my hand just produce normal force on the book, cancelling out the force of gravity, and costing me no eff... | The force it needs to hold the book in its position is the same in both cases.
This forces is caused by gravity.
The book doesn't move (accelerate) which means there must be some other force, working against gravity. The sum of all forces is 0.
I extend my arm
And this is what makes the difference here. You are not j... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/179143",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
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What could explain the presence of Technetium in the spectral lines of stars? So, I understand that TC doesn't exist in nature [though, I don't know why every reference I see regarding TC says that and then goes on to state that it is found in some stars...] but, if that's the case, then why is it found in some stars? ... | This is really the same as my answer to your later question (I saw the later question first).
Technetium is thought to occur mainly by slow neutron capture. Repeated neutron capture in a complex chain of reactions eventually produces Technetium. There are details of the reactions in this PDF.
There is a paper here sugg... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/179200",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Decay of matter I was watching Stephen Hawking's documentary and in there he explained how he realized why black holes eventually disintegrate:
There are ripples in space, an antiparticle and a particle get created for a brief time then annihilate each other. When this happens very close to a black hole sometimes an a... |
... is this what is responsible for Radioactive Decay?
Sort of ... radioactive decay occurs when the final state (result of the decay) has lower energy than the initial nucleus and the barrier is occasionally surmounted. This barrier penetration and the virtual pair at the black hole horizon are both quantum process... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is the uncertainty principle? I looked on Wikpedia for information on the uncertainty principle, but after reading it I still had no idea. I know it has something to do with how many things you can hold at some spot for some amount of time (maybe?). This is inspired by this question.
| Let $X$ and $Y$ be random variables with density functions $f$ and $\hat{f}$, where $\hat{f}$ is the Fourier transform of $f$. Then the uncertainty principle is a lower bound on $\sigma_X\cdot \sigma_Y$ (where $\sigma$ is the standard deviation). In particular, $\sigma_X\sigma_Y\ge 1/4\pi$.
For example, take a partic... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can dimension analysis be used in developing more advanced physics equations? It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known.
My question is whether this is an accepted method to derive formulas o... | Dimensional analysis can help to "guesstimate" the form of many important results but it can, for instance, not produce general solutions to equations of motion. It's an invaluable tool to understand the structure of physical theory, including quantum mechanics and relativity, and to check results for consistency, but ... | {
"language": "en",
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"source": "stackexchange",
"question_score": "13",
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Electric potential at midpoint?
I understand that if you assume the field is uniform between R and S then you can use E=V/d to get E=(30-20)/(0.5)=20Vm^(-1), so the answer is C (which is correct according to the mark scheme).
But how do we know the field is unform between R and S in the first place? Or is there anothe... | Observe the potential lines for a moment. You will find that for equal change in distance, there is equal change in potential. Means, if I move 0.5 m to the left, the potential increase is 10 V.
In other words, we have equidistant equipotential lines which is a graphical way of denoting uniform field. Whenever you see ... | {
"language": "en",
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What is the state of water at exactly 0°C? Theoretically speaking, what is the state of water at bang on 0°C - not any lower or higher?
Any lower would make it a solid whereas any higher would make it a liquid. But what about bang on 0°C?
Thanks in advance
Edit: I understand that other factors are involved, such as pre... | I'm assuming 1 atm pressure. It will be a mix of solid and liquid. It takes a certain amount of thermal energy to change the state of water. Until that amount of energy is reached, it will be a mixture of solid and liquid, both at 0°C. With more energy, a higher portion will be water. Once all of it is liquid, any furt... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Kinetic energy and Potential of a photon How does the potential and kinetic energy of a photon relate? Do they mean the same thing?
Also how does De broglie wavelength and Potential relate?
| Imagine a beam of light, going towards a massive object. It has potential energy in the gravitational field. Of course, the potential energy has to become kinetic energy. This is done by shifting frequency. The energy of a photon is given by $E = hf$ so to increase kinetic energy we must increase frequency. If the beam... | {
"language": "en",
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Understanding view-/formfactor for radiation with a specific example There is radiation coming from a point source (black body).
How much of the total emitted energy (from the point source) hits a spherical surface given by $\phi = 0 - \pi $ and $\theta = 0 - \pi/2 $?
What are the correct names for the angles $\phi$ an... | The equation that you have is right, but actually a little more complicated than you need for this problem. A point source is infinitely small and you don't need to integrate over it . This problem can be handled without working through integrals formally.
Consider a full sphere around the point (rather than the partia... | {
"language": "en",
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Magnetic monopoles and special relativity I was thinking about magnetism as a product of special relativity and the result of this approach to the magnetic monopoles.
So if magnetism is a product of electricity(like electricity from another point of view),then why do we need monopoles to exist?I know that many theories... | Neither classical electromagnetism nor special relativity requires monopoles. These theories merely allow them and can calculate what would happen if you had one. Some high energy physics theories do predict that magnetic monopoles actually have to exist somewhere and these theories will need modification if someone pr... | {
"language": "en",
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Electric field in a conductor Is it always true that the electric field in a conductor is zero?
What would happen if I put a very big charge inside an ungrounded hollow conducting sphere like this image?
The charges inside the conductor are supposed to rearrange so as to cancel the field created by the big charge.
So ... | The point is: what do you call a "conductor"? If you are talking about a medium which follows Ohm's law $ \vec{j} = \sigma \vec{E} $, then $\vec{E}$ has no reason to equal zero (well, in steady state, $\vec{j}=\vec{0}$ so...).
But if you are dealing with a perfect conductor, in which $\sigma \rightarrow +\infty $, then... | {
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Do quarks violate quantization of charge? Does existence of various kinds of quarks like up, down, strange, charm, top, bottom violate the quantisation of charge or just redefine it as up quark have charge +2/3 and have -1/3. Or do things get even complex for unified theories like the proposed string theory?
| That is a good question but I think you might be a bit confused. The quark charges are quantised as they are fractional values of the electron charges, so when you refer to 2/3 and -1/3 these mean 2/3 of the electron charge and -1/3 of the electron charge respectively.
As such, a Hydrogen atom with a proton in the nucl... | {
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Can adding weight to something make it tilt slower? Let's say we have 2 sticks, both a meter long. We put both of them on the ground vertically. To the top of one of them we attach a weight. Then we tip both of them over and let them fall.
Assume that there is no air resistance and that (the lower ends of) the sticks ... | Yes you are right. There is a resist in gravity because of an applied weight. Therefore the acceleration of the beam falls slightly slower depending on the mass of the object. Unless nothing are holding them together, both beams would fall at the same rate except the applied weight on the top would fall slower. For an ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can I tell if the spectrum of an operator in QM is degenerate? I know that the collection of all the eigenvalues of an operator $\hat{Q}$ is called its point spectrum, and sometimes two or more linearly independent eigenfunctions share the same eigenvalue, and in this case the spectrum is said to be degenerate.
My ... | Assuming that your operator has a spectrum consisting of isolated points you can look for all the independent solutions of the eigenvalue equation
$$(Q-\lambda I)\xi = 0$$
Let these solutions generate a vector space $V_\lambda$ and then compute the dimension of $V_\lambda$. If it is greater than 1 then the eigenvalue $... | {
"language": "en",
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Is there a definite boundary between a powder and a fluid? Given a powder of solid substance what will happen if we make the granules smaller and smaller mechanically? Will this eventually make a liquid or gas from the powder?
Can there be gaseous substanse made not from single molecules but from microscopic granules o... | A powder is a state with microscopic grains, a fluid has sub-nanoscopic grains.
A powder is a granular material, it therefore presents a jamming transition, where the size of grains induces non-linear flowing of the material.
This jamming transition can be seen as an effect of the rather small number of particles in su... | {
"language": "en",
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Proof for Negele and Orland equation (2.34) The equation (2.34) of Negele and Orland has
$$\mathcal H_\text{A}(\hat{\mathbf p},\hat{\mathbf x}) =
\frac{1}{2m}\left(\hat {\mathbf p} - \frac e c \mathbf A(\hat{\mathbf x})\right)^2.\tag{2.34a}$$
And it says in normal form,
$$\mathcal H_\text{A}(\hat{\mathbf p},\hat{\mathb... | *
*Yes, the missing dot in the dot product of the second term
$$\tag{2} -2\frac{e}{c}\hat{\mathbf{p}} \cdot \mathbf{A}(\hat{\mathbf{x}}) $$
of eq. (2.34b) is a typo. The operators $\hat{\mathbf{p}}$ and $\mathbf{A}(\hat{\mathbf{x}})$ do not commute, due to the CCRs
$$\tag{CCR} [\hat{x}^i~,~ \hat{p}_j]_{-}~=~i\hbar\de... | {
"language": "en",
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Expansion of a ket-physical interpretation of coefficients Consider I have a state represented by the Ket:
$$|\psi\rangle=\sum_i a_i |\phi_i\rangle$$
What are the physical interpretations of the coefficients $a_i$? My guess is that $|a_k|^2$ represents the probability that the 'paritcle' is in the state $ |\phi_k\rang... | The coefficients $a_k$ quantity the projection of the state $|\psi\rangle$ onto the $k^\mathrm{th}$ basis state. So if you measure in that basis you would expect $|a_k|^2$ of the time to measure state $|\phi_k\rangle$. If you change the basis you will need to recalculate the projection coefficients.
If you are in a no... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does lithium-6 "decay" when hit by a neutron? I am talking about the nuclear reaction
$$
^6\text{Li} + n \rightarrow\ ^4\text{He} +\ ^3\text{H} + 4.78\text{MeV}
$$
A neutron hits a lithium-6 nucleus and together they form an alpha and triton particle. Is it valid to say that the lithium nucleus "decays" when hit by a n... | A ground state $^7\mathrm{Li}$ nucleus is stable, so this reaction is either direct or involves a unstable, intermediate, excited state of the lithium-7 nucleus.
If you are studying that excited state1 then you consider this reaction as
$$ ^6\mathrm{Li} + n \longrightarrow
\, ^7\mathrm{Li}^* \longrightarrow
\, ^4\mat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/183391",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is true black possible? Black is the absence of light because it absorbs light, but when we create black paint or black objects, light is always reflected, either in all directions in matte or smoothly in shiny black objects, making it never a true black. Would it be possible to use polarization to create an object tha... | The only thing I can think of being true black would probably be a black hole. As light does not bounce off a black hole.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the rigorous definition for current in a closed circuit? I know that $I = \frac {dq} {dt}$, but I have trouble reconciling that derivative definition with my intuitive understanding of current. At an arbitrary point in wire, the current is obviously the amount of charge flowing in and out per unit time -- but s... | imagine a small section of the conductor, say 1mm thick...indeed on the left side, there is a given amount of charge exiting this section, but from the right side, there is an equal inflow of charge. For that reason, the total amount of charge in the section of conductor does not change
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How does one calculate or even approximate the force observed by a magnet as its dropped inside of a diamagnetic cylinder? How does one calculate or even approximate the force observed by a magnet as its dropped inside of a diamagnetic cylinder?
Wikipedia and Google does not provide much information on this topic. Wik... | In diamagnetic material a magnetic dipole moment will develop in presence of external field. Magnetic dipole moment per volume is:
$$\mathbf{M}=\chi\mathbf{H}= {\chi\mathbf{B} \over \mu}={1 \over \mu_0}{\chi \over \chi+1}\mathbf{B}$$
In a non-uniform magnetic field there would be a force on a magnetic dipole:
$$\mathbf... | {
"language": "en",
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Polarisation by Reflection - oscillation direction I'm currently studying polarisation by reflection, and have come across two pieces of information from the same source, which I can't seem to understand on how they differ.
*
*The oscillation direction of the field polarised in the plane of incidence is parallel to ... | Finally found out, what I was getting so confused about, here's the answer (credit to Dr Sebastian Steinlechner) with a relevant diagram.
The incoming light is assumed to be unpolarised. We can, however, describe it as a combination of two orthogonal polarisations: one is polarised in the plane of incidence (the arrows... | {
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Resistors in parallel: How do I make this rigorous? In my revision guide it says "when two resistors are in parallel, the current has two paths it can flow through so there is less opposition to the current. This is why the combined resistance is less than the separate resistances."
This is of course a true statement, ... | It perhaps is not as rigorous as you want, but it is simple and intuitive:
$$
R = \frac{\rho L}{A}
$$
Where $\rho$ is the resistivity, $L$ is the length, $A$ is the cross-section area. When you plug resistances in series, you "are" increasing $L$, and thus $R$ increases. If you put in parallel, you "are" increasing $A$... | {
"language": "en",
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Explain relationship between angular diameter distance and luminosity distance, Etherington Theorem I have a question relating to the Etherington Theorem.
The luminosity distance is defined by the equation for flux, i.e.
$F=\frac{L}{4\pi D_L^2}$
where flux is in units energy per unit time (luminosity) per unit area.
T... | This relation is quite important, non trivial, and mathematical, and was proved by Etherington along with the other closely related theorem in this paper
I. M. H. Etherington (Philosophical Magazine ser. 7, vol. 15, 761 (1933))
This theorem only depends on photon conservation and the fact that photons only travel in ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How electrons move so fast in a electric circuit? Whenever we switch on a bulb......it takes almost no time to glow up.....But we know that the atoms of a solid are tightly packed and there is a very little space between them.
So how the electrons travel through them irrespective of so much blockages in the conductor??... | The electrons themselves don't move all that fast. The wave energy is the part that moves quickly.
Picture it this way.
You have 500 meters of pipe, with a small hole at the other end. The pipe is full of water and you increase the pressure at your end. Water will flow out the other end immediately. This is the electr... | {
"language": "en",
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Lagrangian for free particle in special relativity From definition of Lagrangian: $L = T - U$. As I understand for free particle ($U = 0$) one should write $L = T$.
In special relativity we want Lorentz-invariant action thus we define free-particle Lagrangian as follows:
$$L = -\frac{ m c^2}{\gamma} - U$$
At the same p... | A very informal approach would be to understand how the mathematics develops:
since 'Action' in the Lagrangian sense is never a vector, it must be a scalar. It is in this case the energy. From special relativity we have the postulate that the laws of physics are the same for all observers in all inertial reference fram... | {
"language": "en",
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What physics paper would a high school student be able to read? I'm looking for a physics paper which a typical high school student who is new to physics would be able to read and grasp the general idea of the purpose, setup and results, if not the details. To be clear, I don't expect that high school students will un... | From the details I assume it needs to concern a specific experiment, rather than just some musings.
In recent news, in Nature Chemestry, "Coulomb explosion during the early stages of the reaction of alkali metals with water" (online version) has the Mythbusters appeal. When combined with the you-tube lead-up to the fo... | {
"language": "en",
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Do holes have physical existence? We know that holes are created due to electrons hopping from one covalent bond to another. But does a hole have a physical existence or it's just a fictitious positive charge, an illusion created by electron movement?
| Presumably you are referring to semiconductors. A hole physically exists in that it is the absence of an electron. Just like a hole in a piece of paper physically exists. However, if you are asking whether the hole is a particle, then no, it does not physically exist.
In a semiconductor, we deal with electron hole pair... | {
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Does General Relativity imply loops in space? Everyone who has been interested in modern science has heard explanations (certainly simplifications) of general relativity, mostly that space is curved. The analogy with a rubber sheet is popular. In such an analogy, orbiting planets are said to be naturally following "a s... | No.
A loop has to start and end at the same point. In GR that means it has to start and end at the same spacetime point i.e. the same point in time as well as the same point in space. Such loops are called closed timelike curves, and with the exception of some obviously non-physical geometries they do not exist.
| {
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Applying unsteady Bernoulli (to a balloon attached to a tube) Using Bernoulli’s equation for an unsteady irrotational motion of an inviscid incompressible fluid, solve the following:
Water of density $\rho$ is driven through a horizontal tube of length $L$ and internal radius $a$ from a water-filled balloon attached to o... | Generally you would have $p(t) = p_0 + \beta V(t)$. Yes, the velocities at both end are equal but you should conservation of mass to get a relation between volume of balloon and the velocity. As for your last question I would say not using the potential form of unsteady Bernoulli equation is more intuitive but the velo... | {
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Where does the majority of the mass of the usual matter come from? I apologize in advance to experts for the naivety of the question. It should be a duplicate but I didn't find any satifying question or answer about that.
The proton is composed by two up quarks and one down quark.
mass(proton) $\sim 940 \ MeV/c^2 ... | The equivalence principle tells us that energy and mass are really just two sides of the same coin, and are related by $E = m c^2$. Rearranging, we get that $m = E/c^2$, so instead of asking where all that mass comes from, let's ask where all that energy comes from. In the case of the proton, there are some quarks an... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Do rainbows have ultraviolet bands and infrared bands? We have seen that rainbows looks so colorful as we are only able to see only the visible light. But Do they also have ultraviolet bands and infra-red bands, that we are unable to see?
I know someone has already asked the same question but I am concern about the spe... | engineer already answered it completely, I only want to add that the question is completely valid even if you already know that separation of wavelength occurs.
The thing is, some materials are practically opaque or too much transparent (refractive index is equal to that of air and no separation occurs) in infrared and... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is the lowest level things have temperatures? Something can be cold. If you split it in half, it will still be cold, keep doing that and it will still be cold. My question is, what is the lowest level things can have temperature? Do atoms have temperatures? Do quarks?
| Temperature is a measure of mean kinetic energy. So as long as particles can move, they will have temperature.
And yes, quarks do have temperature. The highest man-made temperature was attained in a quark-gluon plasma at LHC in 2012.
| {
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Why the heat capacity doesn't diverge in the Kosterlitz-Thouless (KT) phase transition? The KT transition has a special properties that, during the phase transition the heat capacity stay finite (so the behaviour of the heat capacity cannot reflect any critical behaviours). However, the correlation length and the susce... | I am not too familiar with KT transitions yet, but I would like to learn about them myself.
I have read in the notes of Prof. Jensen
(available online http://www.mit.edu/~levitov/8.334/notes/XYnotes1.pdf)
in the end of chapter 4.2 that the divergence in the specific heat is so fast that it is experimentally not observa... | {
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$F=ma$, so if acceleration is zero the force must also be zero? I was just pushing a huge rock which I couldn't move at all. Given that the acceleration was zero as a result of my efforts, since $F=ma$, doesn't this mean that the force must also have been zero?
But, in reality, I was applying a force $F$, there is a hu... | This type of question keeps reccuring. I suppose either teachers don't teach this correctly, or students do not pay attention in class. $F=m a$ is really $$\sum F = m a_{cm}$$ These two distinctions (the sum, and the acceleration of the center of mass) make all the difference in the world (At least read on Newton's Law... | {
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What does it mean when we say that power of a bulb is 10 W? Since $V/I=$ resistance is a constant, how can power $=VI$ be a constant? My question is simple. In Ideal situation, at constant temperature, we know that normal appliances like a filament bulb has straight Voltage vs Current graph, meaning its resistance is c... |
Since I understand that power = V x Current, the power for a bulb can not be a constant if its resistant is assumed a constant. A normal mathematical thinking can confirm that.
If the voltage and current don't change, then the power is constant. The electricity supplied from the wall is at 115V (more or less). If the... | {
"language": "en",
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Is it possible to have a line rather than a point where the three states of a substance can exist? Most of us are familiar with state diagrams that define which of the three states a substance will take given the pressure and temperature. And that some substances, such as water for example, exhibit the behavior of a tr... | A pure substance can only have a point where three phases coexist.
With two components we can have a whole line of coexistence of three phases. Here is an example you can do in your kitchen: mix water and oil (or heptane or any other hydrocarbon) and bring to boil. You then have three phases: liquid water, liquid hydro... | {
"language": "en",
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How does a spacecraft enter Earth's atmosphere? If Earth whirls around the center of our galaxy at some 220 kilometers per second, how can a spacecraft, which is much slower, enter Earth's atmosphere when returning from Mars for example?
| It all comes down to the fact that we are moving too.
How can the bird drop down and catch the worm, if the earth and the worm are moving so quickly. It can because the tree, the bird, and the air are moving at the same speed, cancelling out.
If we launch a spacecraft from Mars to the earth, the spacecraft is zooming ... | {
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If the speed of light is constant in all reference frames, why does the mirror clock experiment show light travelling on an angle? I was recently looking for answers as to why time slows down the faster you travel and regularly came across the mirror clock experiment. This experiment has a beam of light bouncing betwee... | No - the light is moving with the mirrors. To an observer in the mirror / clock frame, because they're in the same frame the light will appear to only move from one mirror to the other (up/down).
However an observer not traveling with the clock, would still observe that inside the clock system (mirrors and the trapped ... | {
"language": "en",
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Why can velocity and acceleration be negative? Why is speed and acceleration negative when $V_1$ of an object is say 150m/s, $V_2$ is 0 m/s and $\Delta d=0.50\,\rm m$? I found the time it takes which is 0.0033s and the acceleration to be 90909.09 m/s$^2$.
My questions:
*
*What do negative velocity and negative acce... |
In this acceleration graph, velocity is going down. Remember that in this graph, the slope is acceleration, so the acceleration is negative. Negative acceleration is what some people call acceleration (slowing down). If the velocity starts negative, however, then negative acceleration is speeding up.
For negative vel... | {
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Is 'Boltzon' an accepted name for particles following Maxwell-Boltzmann (MB) statistics? In my curriculum during one of my statistical mechanics visiting lecture classes, our teacher was referring comparatively macro particles following MB statistics as "Boltzon". But I have searched Internet, checked few sites and my ... | I found theses definitions in "Statistical Thermodynamics" by M.C. Gupta :
*
*boltzons : particles are distinguishable and there is no restriction of the occupancy of the energy state
*corrected boltzons : particles are indistinguishable
in context of Boltzmann statistics
| {
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What about a surface determines its color? Light falls on a surface. Some wavelengths get absorbed. The other are reflected. The reflected ones are the colors that we perceive to be of the surface.
What is the property that determines, what wavelengths are reflected and what are absorbed? Is it electronic configuration... | Interesting question. I believe it has to do the energy levels of the atoms of the surface. I assume you understand the concept of atomic orbitals - When light encounters a surface, the wavelengths absorbed are those that contain the right amount of energy to move electrons up to the next orbital.
... Upon a google sea... | {
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Basic question about acceleration Very basic question.
Please show where I'm wrong in the following reasoning.
The movement of an object in function of time could be described as
$$
x(t) = v t + x_{i}
$$
if velocity is constant.
If velocity is not constant then
$$
x(t) = v(t)\cdot t + x_{i}
$$
where
$$
v(t) = a t + v_{... | The place you are wrong is in supposing $x(t) = v(t).t + x_i$ when acceleration is constant.
You will have to derive the relation using integration. The above relation only holds when velocity is constant, but when velocity varies(i.e acceleration is non zero), this relation is no longer true.
| {
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Spin angular momentum conservation and entanglement Suppose we have a system with $S=0$ . Suddenly, this system decays into two particles, A and B, so we know the sum of the spin of these two particles is zero. Suppose we measure the spin of A in the z direction and get
\begin{equation}
s_z,a=1/2
\end{equation}
Then w... | Note that the total angular momentum is conserved in this system. After the decay of the particle with total angular momentum of $0$ the total angular momentum of the system is described by
$$\mathbf J = \mathbf S_A + \mathbf{S}_B + \mathbf{L} $$
, where $\mathbf L$ is the relative angular momentum between $A$ and $B$.... | {
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Spectral function with negative value How does one understand a negative value in the spectral function
$$\chi=-\mathrm{Im(G)}$$
where $G$ is the Green function and $\chi$ is a spectral function?
| The Green's function and the spectral function can be defined as
$$ G(\mathbf r,\mathbf r',\omega) = \sum_n \frac{f_n(\mathbf r)f_n^*(\mathbf r')}{\omega - \epsilon_n + i\eta}, $$
where $\eta \rightarrow 0^+$, and
$$ A(\mathbf r,\mathbf r',\omega) = \sum_n f_n(\mathbf r)f_n^*(\mathbf r') \delta(\omega - \epsilon_n). $$... | {
"language": "en",
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Paradox in the two block problem UPDATE (regarding duplicate) :
This question is not a duplicate of another question. Sure, the situation in both the questions is same and, yes, both questions ultimately provide a methodology to solve the problem and finding the correct value of friction, but the moderator should reali... | In the second calculation, the $10N$ force is not acting on the m1 block. The only force on the block is the friction force from m2. The frictional force will be exactly the amount required to keep m1 and m2 moving together. The frictional force will be given by:
$$F = m_1 a = (5 kg)(1.25 m/s^2) = 6.25 N$$
Checking wit... | {
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Black Body Radiation ELI5 If a black object and a shiny object were left in vacuum and bombarded with thermal radiation would the shiny object eventually reach the same temperature as the black object?
The reason I ask is I am having a hard time wrapping my head around Kirchhoff's law and Boltzmann's law and thermal ra... | If the two bodies are put in equilibrium radiation, they will both adapt their temperature to common temperature. The black object will do so faster.
| {
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Mathematically modeling two frequencies So i'd like to model a recurring event (I don't think this is a statistics problem though) that is affected by another event with a different frequency. Say event A has a slower BASE frequency (about every 2.7 seconds), and event B has a higher frequency (about every 1.6 seconds)... | This situation can be solved exactly, and it will not have any significant statistical behaviour. The point is that once event $B$ triggers event $A$ for the first time, they become synchronized and they enter a completely periodic loop, whose period is the separation between synchronization events, and is completely d... | {
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Is simultaneity well-defined in general relativity? In special relativity for each event and reference frame we can find a plane of simultaneous events.
I wonder is it possible to do the same in general case in curved space? Is simultaneity even meaningful in GR?
| "Simultaneity" has a well-defined technical meaning in SR, as well as in GR.
What I am referring to is the "Einstein’s convention for the definition of simultaneity", namely the set of events that are considered by an observer $O$ as being simultaneous to a given reference event on its worldline. The answer of @FenderL... | {
"language": "en",
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Conservation of Baryon number for this proton decay The conservation law requires that Baryon number be conserved; that is, the sum of the Baryon number before and after a reaction/ decay must always equal the sum of the Baryon number after the reaction.
This sounds fairly simple and I thought I've understood it until... | Within the standard model, protons don't decay.
As you've pointed out, it doesn't conserve baryon number, and you can see it doesn't conserve lepton number either.
However, it does conserve their difference, and in some Grand Unification Theories (Theories which at high energies describe the electromagnetic interaction... | {
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Photons at Event Horizon The escape velocity at event horizon of a black hole is same as speed of light, So this questions is not about all photons travelling into a black hole, but for those which are tangential to the event horizon, So let us assume that a photon is travelling along a tangent to event horizon, we kno... | For a non rotating spherical black hole the event horizon is at a circle of circumference $4\pi MG/c^2$. And gravity gets weaker the farther away you get.
At that location even moving straight outwards at light speed won't let you travel to someplace where gravity is weaker.
But if you aren't moving straight away then ... | {
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Are all trajectories parabolic? I've heard this before, and it makes sense. Is it true?
This being: Due to the effects of gravity and inertia, an object in movement not being acted on by any other force will form a parabolic curve with its trajectory.
| The assumptions of a parabolic trajectory is:
*
*(gravity) force is a /constant/, /downwards/ force,
*/no other forces/ acting on the object,
*the object under observation does not affect the (gravity) field,
*classical mechanics
In practice, this approximation is almost true with gravity when:
*
*there is o... | {
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Relation of resistance between two metals and capacity My schoolbook goves the resistance between two metals in a material with conductivity $\sigma$ as $R=\frac{\epsilon_0}{\sigma C}$, but they don't show how they got this result. Can someone show me how to derive this formula?
| The conductivity of a material of length $l$, cross section $A$ and resistance $R$ is found by $\sigma = \frac{l}{R A}$. See Wikipedia.
The capacitance $C$ of two parallel plates is $C = \frac{\epsilon_0 A}{l}$. You can find it on this page.
Substitution leads you to $\sigma R = \frac{\epsilon_0}{C}$.
| {
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What was the largest object/particle tunneling observed? What is a current record? Reference to that would be nice. and what can be expected in near future? what are the theoretical limits?
| Stars are a great example.
Quantum tunneling is basically just getting over an energy barrier that is unpenetrable in classical mechanics. Stars survive off of this phenomena. Stars usually do not have enough energy to fuse hydrogen into helium. The hydrogen atoms (a small percent, but since there are so many atoms, i... | {
"language": "en",
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Newton's Law of Cooling on a calorimeter with two systems Having the previous calorimeter with adiabatic walls, we've proven, based on Newton's law of cooling, that the equations are...
(source: gyazo.com)
$m_{b} \times C _{pb} \frac{\mathrm{d T_{b}} }{\mathrm{d} t} = k_{t}(T_{c} - T_{b})$
$m_{c} \times C _{pc} \frac{... | Just apply the energy balance once again to the water. The rate of accumulation of energy in the water is equal to the rate of heat gain from c1 minus the rate of heat loss to c2:
$$m_wC_{pw} \frac{dT_w}{dt} = hA\left ( T_{c_1} - T_w \right ) - hA\left ( T_w - T_{c_2} \right )$$
Notice I have introduced the area $A$, s... | {
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Different signatures I was working out the christoffel symbols, once where the metric that I am using has (+---) signature and another time where it has (-+++) signature because two books had different signatures and I had to check for any inconsistencies. I had the christoffel symbols the same for both but the curvatu... | If you stick to one convention out of many other conventions, you should have same results regardless of signature of metric. Here I follow Carroll's conventions: http://amzn.com/0805387323 or http://arxiv.org/abs/gr-qc/9712019.
For Christoffel symbol, we have
\begin{equation}
\Gamma^\lambda_{\mu\nu}=\frac{1}{2}g^{\lam... | {
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Interacting fermions on a lattice My rough understanding about lattice simulations of bosonic quantum field theories is that the partition function can be approximated by explicitly summing over a large number of field configurations, chosen by some Monte Carlo algorithm for instance. But is there a similar way to simu... | The standard trick is partial bosonization, a.k.a. the "Hubbard-Stratonovich" trick. Consider ${\cal L}=g(\bar{\psi} \psi)^2$. Introduce a dummy field $\sigma$ with purely Gaussian lagrangian ${\cal L}_\sigma=-\frac{1}{g}\sigma^2$. You can always insert a factor 1 in the path integral
$$
1=\frac{1}{Z}\int D\sigma \exp(... | {
"language": "en",
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What happens to the air in a water bottle when it falls? (ignoring the air resistance that causes the bottle to take positions in mid air. Let's say it is dropped in a vacuum with earth's gravity accelerating it downwards) I just cannot catch what happens with the bubble with my bare eye, and I thought I should better ... | In the short term, the sloshing of the water as you not-completely-cleanly let go of the bottle will be the dominant effect. In the long term, since you're ignoring air resistance, and if we assume the bottle isn't spinning in any way, then surface tension will dominate.
Different material interfaces have different ene... | {
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How fast does heat travel via conduction? I have read this question which seems to ask an identical question, but I'm not sure - it had far too many words I don't understand, let alone the equations. Perhaps someone can answer with a heat-for-dummies answer.
I understand that given thermal conductivity, and thermal mas... | I think the average velocity can be estimated from the average time required to move distance L:
$$t = L^2/2\alpha$$
where $\alpha$ is the thermal conductivity (k) divided by heat capacity (C).
Since velocity (u) is distance/time:
$$ u = L/(L^2/2\alpha) = 2\alpha/L $$
| {
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Why the electric potential energy the charges carry in a electric circuit does not vary with its distance to the opposite terminal? I understand that with wires assumed to be ideal, there is no resistance and subsequently no force acting on electrons, hence no work done and p.d. across any segment of wire.
However, as ... | Technically you are correct and there is a voltage drop with distance but since the voltage drop is current * resistance and your resistance on a PCB track is usually measured in the milliohms it's ignorable unless your doing something really hairy with LOTS of current or ultra sensative.
| {
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Is net work and total work same? According to my text book
Total Work = Delta Kinetic Energy = KEf - KEi
But then work is defined to be
dot product of Force (vector) and Displacement (vector).
Also to my knowledge work is positional.
So, if we assume an object running in circle, and it completes one cycle,
Is it correc... | Work is defined as the line integral $\int \mathbf{F} \cdot \mathbf{d\ell}$. The force on an object can be a function of position or time, and could represent external forces placed on the system. Net and total work refer to the same concept, the sum of all work done on an object.
For your example, you cannot simply sa... | {
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Why does a Yo-Yo sleep, and then awaken? What are the mathematics / mechanics principles behind a sleeping Yo-Yo,
and in particular, what changes with a wrist-snap flick that
causes it to "awaken" and return to your hand?
(Image from www.wikihow.com/Make-a-Yoyo-Sleep.)
There must be some s... | If the yoyo is spinning without winding the string, then it must be that the friction between the inner barrel and the string is insufficient to lead to winding.
A flick of the wrist or some other movement can lead to an increase in the friction and the beginning of winding.
Once winding begins frictional forces betw... | {
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How may one calculate the escape velocity of a binary system at a given radius from the COM? Apologies if this is a bit general, even some pointers in the right direction would be great (reading material etc.)
Given an object of mass $m_3$ travelling outward at speed $v$ from the centre of mass of a binary star system ... | For the sake of simplicity assume the binaries' motion to be circular. Then you can use the formalism of the circular restricted 3-body problem (CR3BP) to model the motion of the test particle $m_3$. Your Lagrangian will be time-independent and the conserved quantity (Jacobi constant) can be evaluated at infinity to gi... | {
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Medical Radioisotopes Technetium -99 can travel though the blood stream. A detector outside the patient's body detects gamma rays, and uses this to form a picture of a flow of blood. Technetium has a half life of 6 hours. Why do radiologists use technetium -99 to image patient's blood flow, and not ruthenium-106 which ... | The Technetium-99 gamma ràys are long and more easily detectable. It's Gamma radiation waves exit the body quicker ie. 6hrs and does no cellular damage compared to the Beta radiation (which are particles) in ruthenium-106 with a half life of 371.5 days.
| {
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How to find tangential/radial/angular velocity for motion in any curve? Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction? If so why?
Please try to give a different explanation than saying that the radial velocity points in t... | Consider an arbitrary trajectory $\vec{r}(t) = r \hat{r}$ measured from the origin, in polar coordinates (https://en.wikipedia.org/wiki/Polar_coordinate_system).
The velocity is then: $\vec{v} = \frac{d}{dt}\vec{r} = \frac{dr}{dt}\hat{r} + r \frac{d\theta}{dt}\hat{\theta}$. Relative to the origin, the radial part of t... | {
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Why can't the angular momentum vector be parallel or anti-parallel to the applied magnetic field? This is the excerpt from my book, Arthur Beiser's Concepts of Modern Physics:
An atom with a certain value of $\displaystyle{m_l}$ will assume the corresponding orientation of its angular momentum $\mathbf{L}$ relative t... | I think the statement is nonsensical. In quantum mechanics the vector $\mathbf L$ is not a world-vector. Its components are not numbers, they are operators. However, the expectation value of $\mathbf L$ in a given state, $\langle \mathbf L \rangle$ is a world-vector and it can be aligned with any given axis. (The magne... | {
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Photon Emission/Absorbsion from the Photons Perspective First some assumptions.
1) Photons travel at the speed of light.
2) From the photon's reference spacetime is contracted to 0 length in the direction of photon travel.
3) From the photon's reference it is emitted and absorbed at the same time and in the same place.... | Your question has nothing to do with the (hypothetical) photon's reference frame.
Even if the spacetime interval of lightlike movements is reduced to zero, the order of events is persisting - In the same way as when you cover one sheet of paper by another, you cannot reach the hidden sheet even if their respective dist... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/190048",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 3
} |
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