Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Help with the analytical solution for the dispersion relation of an elastic wave with wave vector k I was studying Phonons and Lattice vibrations and came across the equation. I want the mathematical solution for this.
$$M\frac{d^2u_n}{dt^2}=C[u_{n+1}+u_{n-1}-2u_n]$$
from here it is argued that since the atoms vibrate ... | *
*The lack of the $e^{-i \omega t}$ term is just because we're using complex wave notation. If you've ever taken an electrical engineering course, it's the same sort of thing that is used there: We're using $A e^{i \omega t}$ to stand for $A \cos (\omega t - \delta)$, with the implicit assumption that we're only in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/190154",
"timestamp": "2023-03-29T00:00:00",
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Radius of curvature I have come across a question that asked me to find the radius of curvature of a projectile.
As far as I know, the path of a projectile is a parabola and I have found mention of the radius of curvature referring to lenses and mirrors. But in optics, the lens and mirrors were assumed to be part of a ... | A parabola does not have a radius of curvature. Each point of the parabola does. So, if you are asked to find the radius of curvature on a parabola, you must also be give the point on the parabola.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/190262",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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Can you dope insulators The question came in my mind because of the definition of doping. For p-type we create holes just above the valence band. This creates holes in the valence band which can contribute to conduction.
For N-type, you create electrons just beneath the conduction band, this pushes extra electrons into... | Yes, it's possible. I think the actual problem will be to find dopants, which have energy levels close to the band edges.
A good real world example is ITO (indium doped tin oxide). It's a transparent conductor, meaning it has a large bandgap and can conduct current.
| {
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Why does simmering sauce make bubbles and how Is it different from boiling water Why does simmering sauce makes bubbles at different places. Is this like boiling water? Why or why not?
| Water transitions from liquid to vapor when it hits the boiling point. With a pot of water approaching boiling, you'll see (and hear) boiling begin as small bubbles across the bottom of the pan, where the water is locally at the boiling point. The bubbles collapse, depositing their heat energy, when they reach cooler (... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/190615",
"timestamp": "2023-03-29T00:00:00",
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Phase transition without the Peierls' counter argument
Is there any proof of the existence of phase transition in models of statistical mechanics of the Ising type models without using the Peierls' argument and its variations?
By models of the Ising type I want to mean Ising models of first and seconds neighbors ove... | The $d=2$ (square lattice) Ising model has a special "duality" property (the high-temperature and low-temperature partition functions can be mapped on to one another) discovered by Kramers & Wannier in 1941. This doesn't rigorously prove that a phase transition exists, but it remarkably predicts the critical point wher... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/191081",
"timestamp": "2023-03-29T00:00:00",
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Dark Civilizations? I just read that maybe the dark matter could have dark forces.
Hence, I wonder: dark atoms, dark galaxies, dark intelligent beings. Basically a parallel, interpenetrating universe. Is this plausible?
| Assuming you take the usual position that dark matter interacts only via the weak and gravitational forces, then it doesn't just interact weakly with baryonic matter but it also interacts weakly with other dark matter. That makes it extremely unlikely that dark matter will form the sort of complex structures that make ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/191323",
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Cylindrical capacitor in an electric circuit I've come across a tricky question and would appreciate some hints or explanations as to why the given solution is the way it is. The question reads as follows:
A coaxial cable consists of a wire with radius $a$ (the core of the cable), which is wrapped with insulating mate... | Your "possible equivalent circuit" is correct and you have to just understand that the capacitor, in this case, happens to be particularly long, so that it happens to incorporate into its body both the wire up-top and the wire beneath.
As for "how can current flow?" the answer is "for long time scales a capacitor looks... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/191424",
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What would a closed timelike curve look like? What exactly are closed timelike curves. In a metric in which they would exist, what would they look like. What would it be like travelling through them? It obviously wouldn't look like a door. Would it be a region of space that if you wonder into, it can happen that see yo... | Consciousness, by definition, cannot traverse through the whole loop. So there is no way to define "what it would look like".
You cannot just assume "what if consciousness could exist in a closed timelike loop". It is a self contradictory assumption. Consciousness must work by gaining knowledge of the universe along it... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/191538",
"timestamp": "2023-03-29T00:00:00",
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Time-harmonic Maxwell's equations My question is about the time-harmonic or frequency domain (differential) form of Maxwell's equations. If one solves these and obtain the complex vector field $E$, are the real and imaginary parts independent or correlated? In other words, knowing the real part of the solution, does th... | No, because the coefficients of any Fourier expansion are usually independent of one other (unless some further conditions hold). The decomposition into real and imaginary part (or equivalently sine and cosine) is a special case of a more general Fourier decomposition
$$
\psi(\textbf{x},t)=\int d^3k\,d\omega\,\tilde{c}... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/192023",
"timestamp": "2023-03-29T00:00:00",
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Does the entropy of the universe change as expansion exceeds the speed of light? The potential encoded information in a photon that is at the edge of the observable universe would seem to be lost as the universe expands. Does that loss of information contribute to the overall entropy of the universe or is the informat... | For a vast over simplification - take the universe to be analogous to a very well insulated piston containing a gas. If you expand that volume normally it will be adiabatic / constant entropy - no heat loss by definition of it being well insulated.
Now add in the accelerating expansion of the universe such that regi... | {
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Are coefficients of friction invariant by switching the materials? I don't have the ability to make the experiment to answer these questions :
Let $A$ and $B$ be two materials. Is the static coefficient of friction of $A$ on $B$ equal to the static coefficient of friction of $B$ on $A$ ? I ask the same question for the... | They are the same.
If the force that A put on B were different than the force that B put on A, then the system would be in violation of Newton's third law.
The friction equation tells us that $F_F=\mu*F_N$.
$F_N$ is the normal force, or the force that each of the materials applies on each other.
Because the frictional ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/192339",
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Interpolation formula for BCS superconducting gap In BCS theory, the superconducting gap is given by solving at different temperatures the integral
$$\frac{1}{N(0)V}=\int_0^{\hbar\omega_c}\frac{\tanh\frac{1}{2}\beta(\xi^2+\Delta^2)^{1/2}}{(\xi^2+\Delta^2)^{1/2}}$$
In textbooks like Tinkham (2nd edition, page 63) and Ph... | It is just an interpolation formula. However, as Gross (3.11) mentioned in 1980, this formula can be rewritten as
$$
\Delta(T)=\Delta(0) \tanh \left( \frac{\pi}{\Delta(0)} \sqrt{a \frac{\delta C}{C} ( \frac{T_{c}}{T}-1} ) \right),
$$
where for s-wave superconductors, $Δ(0)$ = $1.76T_{c}$, a = 2/3; for the pure d-wave ... | {
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How do I calculate the change in water temperature as a function of depth? Let's say I have ground water at a depth of $3000m$ at $50^{o}C$.
If I now pump this water up to the surface, the water pressure decreases from the $\pm 300 atm$ at that depth to $1 atm$ at the surface.
Silly enough I thought of using the ideal ... | As you calculated, but seem to dismiss, the temperature change in water pumped up from deep, high-pressure zones to the surface depends very little on the change in pressure. Other factors would have far more effect:
*
*Pumping energy loss into the water
*Conduction from the pipe and its surroundings as the water r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/192714",
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Will a bullet travel the same after going through 2 substances (in different orders)? This may seem like a trivial question, however I am a little curious as to whether 'order matters' in the case of this system, or whether you would be able to treat any object as a 'black box' with given input and output.
My scenario ... | In general, the answer is no.
Let us assume that the drag in the "black box" is viscous - then the force goes as $\rho v^2$ (plus some other terms).
If the velocity is highest while traversing the medium with the higher density, the total stopping power will be greater. It's that $v^2$ term that gets you...
| {
"language": "en",
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A misconception in an application of Newton's laws When a body is kept in ground, and is at rest, the downward gravitational pull is balanced exactly by the Normal Reaction if we assume the earth to be an inertial frame. But this would mean that any external force provided to that body would lead to its motion. if this... | I think the apparent paradox is driven by a misunderstanding of the very nature of reaction forces. A reaction force is a force $F_N$ perpendicular to a surface which counterbalance the gravitational pull, or any other force perpendicular to the surface.
This is because reaction force are basically what prevent two bod... | {
"language": "en",
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Must we test whether e.g. $A=B$ and $A=C$ implies $B=C$ by experiment? Chaper 10, conservation of momentum in "The Feynman Lectures on Physics" in the chapter entitled, the authors write that
Suppose we know from the foregoing experiment that two pieces of
matter, $A$ and $B$ (of copper and aluminum), have equal mas... | I think the content of his statement is that "the assignment of mass to an object as defined using the conservation of momentum experiment is a transitive property". Not all relations are transitive properties (for instance, "Wolves eat Deer, Deer eat grass, but wolves don't eat grass"). For instance, if we had defined... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193266",
"timestamp": "2023-03-29T00:00:00",
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Universe without a fixed universal speed limit What would a universe without a fixed universal speed limit (like $c$ in the actual universe) look like? Would it be paradoxical? Would time travel into the past become possible?
| A universe without a speed limit would look just like our universe, except it would be far simpler.
Having a finite speed of light/speed limit leads to things like the theory of relativity. Without a universal speed limit, then the universe behaves according to newtonian mechanics. There aren't any paradoxes, because... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193345",
"timestamp": "2023-03-29T00:00:00",
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How are quadruple gluon vertices related to $SU(2)$ and $SU(3)$? I once read that the non-commutativity of the Lie Groups $SU(2)$ and $SU(3)$ is the reason that the weak and strong interactions have Feynman diagrams with quadruple vertices, where four gauge bosons interact.
Is that correct? Can somebody explain the rea... | General comment to the question (v3):
Non-abelian YM [such as, e.g., YM with gauge group $SU(2)$ or $SU(3)$] has besides quartic gauge boson interactions also cubic gauge boson interactions, while abelian YM (aka. QED) has neither.
This is because the Feynman-rules for the cubic (quartic) gauge boson vertices are lin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193523",
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A circuit that is net charged What differences would you measure if a circuit were significantly charged negatively? Would the resistance change? To be clear, I mean that excess electrons are added to the system. The circuit can be of any kind you can imagine.
| There are broadly three classes of materials: conductor, semiconductor, insulator.
The conductor contains a LOT of electrons per unit volume. If you were to charge it, you would add a few more electrons. How many?
Let's take copper. It has roughly $8.5\cdot 10^{28}$ electrons per $m^3$. If you have a wire of radius $r$... | {
"language": "en",
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Why are angles dimensionless and quantities such as length not? So my friend asked me why angles are dimensionless, to which I replied that it's because they can be expressed as the ratio of two quantities -- lengths.
Ok so far, so good.
Then came the question: "In that sense even length is a ratio. Of length of given... | It's true that length can be expressed as a ratio with respect to 1 metre (or any other unit). But that unit itself, i.e. the idea of "1 metre" itself is not dimensionless. What I mean to say is that the unit "1 metre" itself can't be expressed as a ratio of similar quantities of same dimensions; whereas, "1 radian" ca... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/193684",
"timestamp": "2023-03-29T00:00:00",
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Irreversibility Aristoteles law of motion I am watching the second lecture from the theoretical minimum and do not understand the argumentation of Susskind.
For those who do not want to watch the video. It is about the law of motion from Aristoteles defined as $$\vec{F} = m \cdot \vec{v}$$ whereas $\vec{F}$ determines ... | First, the equation is irreversible in the sense that changing $t\rightarrow -t $ leads to different behavior (unlike Newtonian mechanics). On the other hand, mathematically the past is not unpredictable, as formally you never reach the origin in any finite duration of time. So a math pedant would say Susskind is not r... | {
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Ozone elimination I have a potential problem with airflow through a high voltage capacitively coupled RF discharge (in a tube) producing ozone. How can I remove ozone from the airflow? The use of liquids is not possible. Flow rate is quite low, in the mL per minute.
| This may be cheating - but ozone is generated by the interaction of the high voltage discharges and the oxygen in the air.
Why not flush the system with nitrogen - if there is no oxygen, no ozone will be produced. And a few mL per minute is not a lot of nitrogen. A 70 L bottle of nitrogen at 200 bar should expand into ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194171",
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Effects of relativity on New Horizons spacecraft How much would an atomic clock on board the new horizons spacecraft drift in comparison to an atomic clock on the surface of the earth near the equator after the spacecraft's 10 year journey to Pluto?
| Let's say its moving roughly 32,500 mph or about 16.316 km/s relative to the Earth. If we consider special relativity then we have ten years of seconds divided by the square root of one minus 16 kilometers per second squared over the speed of light squared. The answer turns out to be roughly half a second!
| {
"language": "en",
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Where does particle borrow energy from to tunnel? Where does particle borrow energy from to tunnel? It is implied that particle can borrow energy and leaped over to the other side wherever that is, the shorter the gap the more energy it borrows my question is where does a particle borrow its energy from and what criter... | You mean quantum tunneling?
The particle doesn't really "borrow" energy, actually a particle will have a higher probability of tunneling through a barrier if it has a high kinetic energy. A naive analogy would be that the more energetic the bullet is, the higher the probability it has of piercing through a wall, that ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194309",
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Difference between Rayleigh scattering and fluorescence spectroscopy How can we differentiate Rayleigh scattering from fluorescence spectrum?
| Essentially, fluorescence "scattering" is inelastic - transferring some energy to the fluorphore and decreasing the energy / frequency of the emitted light relative to the excitation - and Rayleigh scattering is elastic - conserving energy and thus wavelength. Rayleigh scattering is also very fast: elastic scattering o... | {
"language": "en",
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If two objects have all the same conditions except different masses. Will their terminal velocity be different? I can't seem to find a straight forward answer to this. I really just want to know if changing mass of an object affects the terminal velocity. If two objects of the same dimensions except one had twice the m... | Suppose your object is a sphere with a radius $r$ and mass $m$. The aerodynamic drag on a sphere is given by:
$$ F_{drag} = \tfrac{1}{2}C_d \rho \,\pi r^2 \,v^2 \tag{1} $$
where $\rho$ is the density of the air and $C_d$ is the drag coefficient. The drag coefficient varies with speed (the NASA article I linked shows ho... | {
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Is double-slit experiment dependent on rate at which electrons are fired at slit? I am a mathematician and I am studying string theory. For this purpose I studied quantum theory. After reading Feynman's book in which he described the double-slit experiment (Young's experiment) I was wondering if I send one electron per... | Yes, the interference pattern will occur, although you'll have to wait a while to be able to see it. As long as the average arrival time between photons is markedly greater than the travel time from slit to detector, the actual rates don't matter - each photon interacts with the slits by itself.
This URL shows such an ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194570",
"timestamp": "2023-03-29T00:00:00",
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How is the superconducting coherence length measured experimentally? In a superconductor, the coherence length is the mean distance between two electrons in a Cooper pair. How is the coherence length experimentally measured?
| I would disagree here. The coherence length is the length scale where the electrons stay in their coherent, superconducting state. This gets important on boundaries of a superconductor (i.e. the proximity effect) or at vortices of a type II superconductor in the mixed phase. In both examples, you can measure the cohere... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/194696",
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If both neutron stars and white dwarf stars can have the same mass, what determines what a star of that mass will become when it "dies"? My understanding is that roughly 1.4 solar masses is the upper limit for white dwarf stars, and that the lower bound for neutron stars is around 1.1 solar masses. Is there any way to ... | Yes, there are theoretical models of stellar evolution that tell us what to expect.
Broadly, we expect that stars with an initial mass less than 8 solar masses ($8M_{\odot}$) will end their lives as white dwarfs. So I think there is a misconception in your question - the progenitors of white dwarfs and neutron stars ar... | {
"language": "en",
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Conservation of energy in a moving frame I know a similar question has been asked but i'm still kind of stumped.
Imagine the earth on the left and a small mass to it's right separated by some distance h.
You are in the frame of reference where the earth and the small mass are moving to your right at some speed v.
So, b... |
So the earth won't gain any significant energy
There's your error. The Earth will gain a significant amount of energy, enough to compensate for the loss of energy of the ball. But because the Earth is so massive, its speed won't significantly change.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/195017",
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Relativistic probability amplitude of a particle to be in certain position In the book “The story of spin” by Tomonaga on page 110, it says
They insisted that a concept like "the probability of a particle to be at $x$ in space" is meaningless for relativistic particles—be they electrons, photons, or Klein-Gordon parti... | I think the text in question is quite vague, but there are some issues that come up with relativistic theories.
For instance if something, say $p(x),$ is a probability density, then $\int p(x,t)dx=1.$ But if you have a relativistic theory then you should also be able to compute $\int p(x',t')dx'=1,$ where $x'$ various ... | {
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How can space be cold? Its a vacuum? I was reading that space is very cold and also it is a vacuum, and so my question is quite simple, if temperature is the "jiggling" of atoms and molecules and heat is distributed through jiggling particles passing the energy by hitting other atoms thus cooling or getting hotter. Th... | You are correct that space is not filled with jiggly stuff with energy ½ KT per degree of freedom. However, space is filled with cosmic microwave background photons. Their distribution in energy is that of a black body distribution with temperature 2.7 degK. If you put some material out in space (away from other hea... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/195197",
"timestamp": "2023-03-29T00:00:00",
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The Makeup of the Pentaquark Why is it that when they have the artist's rendition of the Pentaquark it shows two downs, two ups, and one anti-strange quark? Is this or is this just for show? Follow up to this question: if this configuration is just for show, what is the Pentaquark truly made of?
| In Scientific American, they said it was this specific grouping as illustrated, though with arbitrary coloring. It briefly stated how it must involve which quarks based on decay channels. I lost my hardcopy of the magazine so I can't easily look upmthe quotation now.
I think it was not as you describe though...
Yea,... | {
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How to choose the proper loop correction? I review my QFT lecture notes and I am having hard times to figure out the significance of Ward identity in vacuum polarization.
In class, we calculated one loop correction stated as
$$
i\Pi^{\mu\nu}_2(q)=\frac{(-ie)}{(2\pi)^4}^2\int d^4k Tr\Bigg[\gamma^{\mu}\frac{i(\require... | Your statement that the integral "is actually" $\propto g^{\mu\nu}\Pi$ is incorrect because you can clearly see the $q^\mu q^\nu$ in the numerator of the integrand.
The correct expression that you have in your final equation is not a choice, it is the result of calculating the loop using dimensional regularization.
Fin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/195559",
"timestamp": "2023-03-29T00:00:00",
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Why is friction force negative in ice skater problem?
A 68.5 kg skater moving initially at 2.40m/s on rough horizontal ice comes to rest uniformly in 3.52s due to friction from the ice. What force does friction exert on the skater?
I am not really asking about the answer here, because I can calculate that, but more ... | The force/ acceleration of the skater comes out as negative because: the force or acceleration is in the opposite direction of motion.
You can also think of it like this, frictional force always tries to oppose relative motion. In this case the skater is moving forward w.r.t the ice and the ice is moving backwards w.r.... | {
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Proof for Resistance is directly proportional to length and inversely proportional to the area of cross-section? I have heard that Resistance is directly proportional to length and inversely proportional to area of cross-section. Can someone give me a practical explanation for this?
| The formula is $$R = \rho \frac{l}{A},$$ where $R$ is the resistance, $l$ the length of the medium current is flowing in and $A$ its cross-sectional area. $\rho$ is the resistivity, a property of the material.
An intuitive way of understanding the dependence on $l$ and $A$ is the following.
The longer the wire (increa... | {
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What happens to a radioactive element or isotope's electrons when it undergoes alpha decay? It seems to make sense that when an atom loses two protons, it would lose two electrons as well, but I don't actually know what happens.
| After alpha decay, the alpha particle can be thought of as a doubly positively ionized helium atom, and the parent atom is now a doubly negatively charged ion. Under normal circumstances, the two ions will eventually neutralize their charges. In a near vacuum, this may take some time.
In a crystalline solid, the nucl... | {
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Why do semiconductors remain neutral outside the depletion region? Why there is a sharp cut off of the charged region outside the depletion region, like on this image?
For example why don't electrons on the conduction band in the n-type side rush towards the positively charged area making the whole piece positively cha... | The negative charges in the n type side are repelled by the negative ions in the p type region and positive charges in the p type side are repelled by the positive ions in the n type region in the equilibrium condition of diode. That's why charges are unable to travel across the pn junction. I hope you know about the n... | {
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Gravitational redshift in a general stationary metric Suppose you have a general metric $g_{\mu \nu}(t,r,\theta,\phi)$ which don't depend explicitly on $t$ coordinate, i.e a stationary metric. Light travels along a geodesic from A (at which the frequency is $\omega_0$) to B. Along the geodesic the metric and the Rieman... | Cinsider an observer who is stationary at point $A$. Because they are stationary $dr = d\theta = d\phi = 0$ and the metric becomes:
$$ ds = \sqrt{g_{00}(r_A, \theta_A, \phi_A)} dt $$
And likewise for an observer at point $B$:
$$ ds = \sqrt{g_{00}(r_B, \theta_B, \phi_B)} dt $$
The relative change in the frequency of the... | {
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How is relativity related to anti-particles? I have heard that a positron is like an electron moving backward through time. Can someone elucidate this statement for me. I would like to hear a deeper explanation of what we believe anti-matter to be, why it annihilates with matter and how this relates to relativity.
| The necessity of anti-particles was first noticed when trying to construct quantum mechanical descriptions of particles that obey the relativistic energy-momemntum-mass $m^2c^4 = E^2 - (\mathbf{p}c)^2$ relationship.
The Schrödinger equation is intuited from a combination of de Broglie's rules $E = hf$ and $p = h/\lambd... | {
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Why is it difficult to hear when speaking in the presence of strong wind? We say that sound waves require medium for their propagation, but during heavy storms or strong wind we cannot hear sound properly. Even if wind is flowing towards specific direction and we speak in that direction we cannot hear it well. Why is i... | The process of auditory masking can partially answer the question. A constant wind can present fairly high intensity middle and high frequency noise (pink noise) to the ear. This will mask these frequencies in the speaking voice. These frequencies (>1 kHz) are generally responsible for the "diction" of speech, so you m... | {
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Why do people say "finite temperature" instead of "nonzero/positive temperature"? This question is about terminology. The term "finite temperature" is often used to mean positive temperature, or equivalently finite inverse temperature $\beta = 1/T$. It seems to me that better choices would be "nonzero temperature" or... | Definition of finite is a bound and non-zero number.
| {
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Is it true that spring has more force acting on it at its positive maximum amplitude than than at the negative one? Am I missing something?
It seems obvious to me that at $+A$ and $-A$, the spring has restorative forces equal in magnitude but opposite in direction.
But since gravity is always pulling it down, the spr... | In accordance with Hooke's law the force is linear with distance. Incorporating gravity only means that the equillibirum position of the spring has changed, the "zero" around which it oscillates. The gravitational pull is already compensated by the spring. Thus the magnitude of the force is euqal at $-A$ and $+A$.
Edit... | {
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Many cells in parallel If two or more cells of unequal voltages are connected in parallel (with the same terminal on the same side), is there a formula that gives the net potential difference?
Also, by Kirchoff's loop law, if we go round in the loop (the internal one, not the external one), we gain $V_1$ going in the d... |
What does this mean?
It means that your model isn't valid.
Only in the context of ideal circuit theory does a voltage source produce a voltage across independent of the current through.
In this context, connecting two (ideal) voltage sources in parallel leads to a contraction, e.g.,
$$1 = 2$$
But physical voltage sou... | {
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Why spinning a pen makes it easier to remove it from the stand? I have a ballpoint pen stand on my desk. The pens are held inside their caps with the point down, like this one (but not as fancy):
If I try to simply pull up one pen, the friction between cap and pen is strong enough to lift the stand, instead of simply ... | This is not a complete answer, but by spinig the pen you give to your system the same energy as if you pull it out directly, in two diffrent forms.So the ''spinning'' energy overcomes the friction and the rest pulls out the pen.
| {
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Why is a sine wave considered the fundamental building block of any signal? Why not some other function? It is mathematically possible to express a given signal as a sum of functions other than sines and cosines. With that in mind, why does signal processing always revolve around breaking down the signal into component... | You are not required to. Functions can be decomposed into a wide array of orthogonal basis functions, including the Bessel functions (in the Hankel transform) and the Legendre functions. The sine function just happens to be the overall simplest to deal with in the general case.
| {
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How is angular momentum conserved? A uniform vertical turntable (mass M and radius R center O) is at rest on the xy plane and is mounted on a frictionless axle, which lies along the vertical z axis. I throw a lump of putty mass m with speed v towards the edge of the turntable, so it approaches along a line that passes ... | Notice that you have implicitly chosen to measure angular momentum about the axle of the platform.
That means that all the forces exerted by the axle on the platform are applied through the axis for rotation, meaning the torque they exert is $$\text{force} \times \text{lever arm} = F \times 0 = 0\,.$$
And there are no... | {
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Reynolds Average Navier Stokes equations and turbulence scale To obtain the time average of an unsteady term like $\frac{\partial u_{i}}{\partial t}$ by definition we perform the following:
\begin{align}
\overline{\frac{\partial u_{i}}{\partial t}} &= \frac{1}{T}\int_{t}^{t+T} \frac{\partial }{\partial t}(U_i + {u}'_i... | It's simply a definition of the properties of a fluctuating component. We require that, on large enough time scales, the fluctuating component averages out to zero:
$$
\frac{1}{T}\int_t^{t+T}u'(t)\,dt=0
$$
so that you are left with just the bulk flow term, $U$, that contributes to the mean velocity, $\bar{u}$.
I think ... | {
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Planetary alignment of the gas giants? There is this nice and new applet of the orbits of the planets around the sun:
Solar System Orrery
You can click and drag any planet and watch their relative orbits evolve in time. I was curious about planetary alignments$^\color{red}{1}$ and have these questions:
*
*I have ob... | This isn't an answer, but too long for a comment.
I emailed the site owner, Jeroen Gommers, and it turns out the planets do not move the same number of degrees per unit time (most noticeable for Eris). Here is his reply to my question re formulas for the orbits:
The interactive doesn't actually use any formulas to con... | {
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How can we calculate pion decay constant in Chiral Perturbation Theory?
The above diagram is a one-loop contribution to the pion decay constant $f_\pi$. For example in this paper (Eq.7) they have written down the pion decay constant to one loop, but the calculation is not given. Usually the pion decay constant is defi... | In the end, you cannot calculate the pion decay constant in chiral perturbation theory. All you can do is adjust the parameters in your n-loop calculation so that the physical value is reproduced. The standard reference for the one-loop renormalization of ChPTh is Gasser and Leutwyler, Chiral Perturbation Theory to One... | {
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Solving the two body problem numerically I'm trying to solve the two body problem numerically, setting up $G$, $m1$ and $m2$ to be equal to 1.
then I located each mass on positions -5 and 5 respectively along the $x$ axis and gave them both 0 on the $y$ axis.
I'm having trouble finding the initial conditions fitting fo... | Your question is about finding the initial conditions to a circular orbit, which has already been answered very well. This answer instead tackles determining the initial conditions for more general orbits. This will allow you to simulate different orbit shapes.
Below are a few shapes of different orbits:
There are two... | {
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Difference between $|d{\bf r}|$ and $d|{\bf r}|$ What is the difference between $|d{\bf r}|$ and $d|{\bf r}|$ and why are both of them not always equal to each other?
My question might seem stupid to some and will probably get downvoted but I have thought on the question but still can't comprehend any difference betwee... | Using polar coordinates it holds $ |d{\bf r}| = \sqrt{(d|{\bf r}|)^2 + |{\bf r}|^2(d{\bf \phi})^2}$. From this equation you can see, the two expressions you are asking about are actually only equal (in absolute value) for a straight line through the origin, thus otherwise different. For them to be exactly equal, the $d... | {
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Why do edge states in graphene exist between the valence and conduction band? I read in a review that there are two Dirac points in graphene, where the conduction band and valence band touch each other. Near these points electrons obey a linear dispersion relation. Breaking of time symmetry leads to a quantum hall stat... | There is a very nice review of this here.
The point is that graphene has (approximate) particle-hole symmetry, so any special has to happen right in the middle of the gap, since this symmetry exchanges the valence and conduction bands.
| {
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What does it mean for a physical quantity if its mixed second partial derivatives are not equal? This goes for every problem (either in electromagnetism or fluid dynamics) that has to do with vector fields. Say we have a fluid flowing in a closed circular pipe (or an electromagnetic field, the concept does not matter).... | A discontinuity in the flow of water could be a wall, or a clog that water is still getting around, but not flowing directly through. In finite electric current it could be a substance with a different conductivity, notably zero or ∞. In theory, the mixed partial second derivatives would not be generally equal, just on... | {
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What is the relationship between quantum physics and chaos theory? I am not a physicist, I am looking for a non-technical explanation.
Articles such as this one seem to hint at the fact that "macro reality" regulated by classical mechanics is somehow a pattern emerging out of quantum-level chaos. Is that correct? Can a... | That's an interesting question, and just off the top of my head you might want to look at "Fractals, Chaos, and Power Laws" which discusses chaos in a wide variety of contexts, including quantum mechanics. I agree with the above response in that the difficulty of uniting chaos with quantum mechanics is that the former ... | {
"language": "en",
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Is there any evidence to suggest that subatomic particles have 3D physiscal size? What I'm asking is do subatomic particles like a proton have a volume or any 3 dimensional size? Or are they just points?
| The elementary particles of the Standard model are pointlike. This has been determined by numerous experiments. All other particles except the ones in the table are composites of some of the ones in the table, and these have dimensions that have been measured using scattering experiments to find their form. Here is an ... | {
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Unpaired Majoranas in the Kitaev chain How can we see unpaired Majoranas for a Kitaev chain in topological non-trivial phase? By looking at the equation below (obtained by making $c_{j}=\frac{e^{-i\phi/2}}{2}\left(\gamma_{B,j}+i\gamma_{A,j}\right)$ in the original Kitaev chain):
$$H=-\frac{i\mu}{2}\sum_{j=1}^{N}\gamma_... | Perhaps a way to understand all this in a slightly different way: when $\mu=0$ and $\Delta=t$, a half-second look at your Hamiltonian shows that $\gamma_{j}^{A}\gamma_{j+1}^{B}$ is an eigenmode of the problem. Similar with $\gamma_{j+1}^{A}\gamma_{j}^{B}$ when $\mu=0$ and $\Delta=-t$. In both cases two Majorana are lef... | {
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Is a bomb's shockwave strong enough to kill? I'm watching a movie, The Hurt Locker, and the first scene shows an IED explosion which kills a soldier. Of course movies don't depict explosions with maximum realism, but I noticed the debris and smoke / flame didn't reach him, and it made me curious about whether invisible... | Blast can definitely kill you, although it is only lethal at much shorter ranges compared to shrapnel. A building can be destroyed by 5psi overpressure while a Human can withstand up to 45psi and live. Some data here:
A 5 psi blast overpressure will rupture eardrums in about 1% of
subjects, and a 45 psi overpressure... | {
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Material that changes transparency when lased from side? I am into photonics research, and have been searching about this topic in vain, but almost nothing from Google shows up. So i turned here for some light.
Do you guys know any material that changes its transparency when a laser (or light) illuminates from its side... | Can you define "side"? Are you looking for a material which changes its absorptivity in one axis only when illuminated from a different axis? I tend to doubt that even hyperboic, aka metamaterials, can demonstrate such a behavior.
As you may know, there a variety of organic dyes which are used as either saturable ... | {
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What does it mean to differentiate a spinor-valued field? Peskin and Schroeder, equation 3.28, states that the Klein-Gordon equation $$(\partial^2+m^2)\psi=0 \tag{3.28}$$ is a valid choice of equation for a Dirac spinor field. Their explanation makes sense (the spinor transformation matrices obviously commute with diff... | Formally, the meaning you assign is just the usual meaning of the derivative.
$$\partial_\mu \psi(x^\nu) = \lim_{h \to 0} \frac{\psi(x^\nu + h\delta^\nu_\mu) - \psi(x^\nu)}{h}$$
You can indeed compute it componentwise, because you can subtract two spinors, as in the equation above, just by subtracting their components.... | {
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What is it exactly that conflicts when trying to unify all 4 fundamental forces? Everyone knows that there are 4 fundamental forces:
*
*Gravity
*Electromagnetic
*Weak
*Strong
At school and university you're taught that no one has been able to unify these 4 fources. However, not a single person really explains w... | General Relativity predicts "infinities" at the singularity of a black hole. Quantum Mechanics, Realativistic Quantum Mechanics, and Quantum Field Theory ignore gravity.
The Firewall Paradox here give a good explanation of a problem encountered when trying to describe things governed by both Quantum Mechanics and Rela... | {
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Paradox of potential energy of gas molecule We know that when water is heated at its boiling point, it will become vapors. Then because there is no change in temperature, the heat supplied will be transferred to the potential energy of the molecules. So, if molecules are far from each other so the Internal Potential en... | Unfortunately people like to teach over simplified physics, which then leads to confusion outside of the setting where the simplification wasn't over done.
So, what is temperature? Is it average kinetic energy per particle? No, it isn't.
Temperature is that number $T$ such that
$$\frac{1}{k_BT}=\frac{dS}{dE}.$$
Where $... | {
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Can a classical 50/50 probability be distinguished from a quantum superposition with a single measurement? $\renewcommand{\ket}[1]{|#1\rangle}$
A "false" (equally superimposed qubit) is created by mechanically firing with 50/50 probability a resonance photon at a Hydrogen atom qubit in the ground state. This qubit is ... | Not with certainty. However, Alice can probabilistically tell them apart by performing a measurement that asks "is the state of the system $(|0\rangle + |1\rangle)/\sqrt{2}$?" For example, if the qubit were a spin $1/2$ particle and $|0\rangle$ and $|1\rangle$ were spin up and spin down, this would correspond to measur... | {
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Are there more photons than nuclei within the Sun? Are there more photons than nuclei within the Sun? Is there a good way to estimate what the ratio would be?
| The number of atoms in the sun is on the order of $10^{57}$, see here.
The number of photons emitted per second is on the order of $10^{44}$, see here.
The difference is on the order of $10^{13}$. So if photons emitted for $10^{13}$ seconds, 315,00 years, the number of photons would begin to overtake the number of atom... | {
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Multiplicity vs Partition function I'm a little confused between all the different notations for the multiplicity and partition function. They're not the same thing, are they?
I know that entropy can be expressed as
$ S = k \ln\Omega $
or
$ S = k\ln Q + kT \frac{\partial \ln(Q)}{\partial T} $
in terms of multiplicity a... | There is a little known fact that is relevant here. The energies of microstates are only specified up to an arbitrary additive constant (as with all energies, which are always referenced to a zero of the energy). For example, it is common in statistical mechanics to reference all microstate energies relative to the e... | {
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Physical intuition behind negative values for wave function? So a positive and a positive wave function create a bonding orbital where the probability of finding an electron is summed while a positive and a negative create an anti-bonding orbital with a lower electron probability in the region between them leading to a... | As John Rennie has pointed out, the wavefunction $\psi$ itself isn't observable, and any expectation value is calculated squaring the wavefunction $$\langle A \rangle = \int \textrm{d}x \psi^*(x) A \psi(x)$$ Therefore, you are allowed to change the overall phase of the wavefunction without changing the expectation valu... | {
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How does one integrate an equation with a tensor? I was looking at the equation for the differential force $dF$ caused from a stress tensor $\sigma$ acting on a differential surface $dS$. In mathematical terms,
$dF=\sigma \cdot dS$
Taking the integral of both sides yields.
$$F=\int \sigma \cdot dS$$
What is the nature ... | Seems as though my idea is the correct one. Here's an example.
Since, $dS$ is normal to the surface and has a magnitude equal to the area of a differential. $dS$ can be represented by a cross product of the differentials of the relevant surface.
Given,
$$\sigma= \begin{bmatrix} 1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1 \\ \e... | {
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Nonlocal dielectric function - what does it mean? I'm reading this* article and in the second sentence of introduction I encountered a term I haven't heard of before. Namely: nonlocal dielectric function. What does this nonlocality mean? And how does it differ from locality? What is its physical meaning?
*R.Ruppin Phys... | Just to add, nonlocal dielectric response also leads to the permittivity being dependent on the wavevector. Nonlocality is thus tightly bound to the notion of spatial dispersion.
This has profound implications on the light propagation is nonlocal media. The dispersion curves can be bent upwards or downwards with the w... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Nuclear decay of V-48 I have a question on the "decay" of Vanadium-48. The reason it's in inverted commas is because I'm not sure whether decay is the right word.
Basically what I'm trying to work out is whether it's likely/possible that I can, via a few steps, get from V-48 to Sc-46.
Is it possible that if I start wi... | According to wikipedia, Vanadium-48 decays via $\beta^+$ (positron emission) to Titanium-48, which is a stable isotope.
The emission of neutrons for Vanadium-48 isn't allowed becuase it doesn't conserve energy: Vanadium-48 has a mass of 47.9522537 u, and Vanadium-45 plus 3 neutrons have a total mass of 44.965776 u +3·... | {
"language": "en",
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Eccentricity of planetary orbits: What information is contained? I'm having a little trouble understanding what makes a planetary orbit explicitly elliptical. Is it simply that the initial velocity was different from the circular orbit case for a given starting position (radius from the sun) and this becomes an ellipti... | The orbit (in polar coordinates) of a body under a inverse-square force, $-K/r^2$, is given by
$$r(\phi)=\frac{L^2/mK}{1+\sqrt{1+\frac{2L^2E}{mK^2}}\cos\phi},$$
where $E$ and $L$ are the energy and the angular momentum of the particle. The equation above is just the polar representation of a conic section of conic para... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Eigenspaces of angular momentum operator and its square (Casimir operator) The casimir operator $\textbf{L}^2$ commutates with the elements $L_i$ of the angular momentum operator $\textbf{L}$:
$$
[\textbf{L}^2, L_i] = 0.
$$
However, the $L_i$ do not commute among themselves:
$$
[L_i, L_j] = i\hbar\epsilon_{ijk}L_k.
$$
... | The eigenspaces of the quadratic Casimir $L^2 = L_x^2+L_y^2+L_z^2$ of the Lie algebra of infinitesimal rotations $\mathfrak{so}(3)$ are precisely the irreducible representations of $\mathfrak{so}(3)$ - we usually label a representation by its highest weight $l$, which is in this case just a number telling you what the ... | {
"language": "en",
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Niagara Falls mist I am at Niagara Falls and noticed that the mist increased significantly at night and in the early morning. I guess it is acting like a cooling tower. Why is this happening?
| Warm air supports greater humidity (absorbs more moisture) than cool air. At night and in the early morning, when the air is cool, evaporation from river water at Niagara Falls hits cooler air which does not as readily absorb water, so is capable of less humidity, than warmer air during the day, so the river evaporati... | {
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How does the hot cup of tea cool down? I am not sure about my answer. I think that the cup of tea cools down by the following modes:
*
*Radiation between the surface of the tea and the air molecules.
*Conduction between the tea and the cup itself and between the cup and the table or whatever the surface is.
Do yo... | An open cup of hot water loses a lot of its heat through evaporation. You can easily test this: prepare two cups of hot water, and then float a thin layer of cooking oil on top of one. Come back in a half hour: you'll find that the cup without oil is a lot cooler, and the water level has also significantly gone down.
E... | {
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Why do electrons and positrons exhibit opposite helical motion in a magnetic field? When you throw an electron through a solenoid, it moves helically around the field lines, as per this schoolphysics illustration:
© Keith Gibbs 2013
Then if we were to throw a positron through the solenoid, it would also move helicall... | There are two factors at play here.
*
*The Lorentz force which causes the paths to bend with a radius proportional to the particles velocity and with a sense that dependent on both the particles charge and the direction of the particles velocity. In high energy (compared to $m_e$ events) such as the one pictured, t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Does work done require interaction between system and surrounding? There's no work done for a person climbing upstairs because the energy is converted to PE within system only. The person is the system.
How true is the above statement?
|
There's no work done for a person climbing upstairs because the energy is converted to PE within system only. The person is the system. How true is the above statement?
I think it's true enough. You do work on a brick when you lift it up. You add energy to it, and we call this energy gravitational potential energy. T... | {
"language": "en",
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What happens to the units when squaring a variable? What happens to the units of a squared variable?
For example, if I squared velocity, would the units, metres per second (${\rm m}/{\rm s}$), change as well?
| I think your all wrong. You can not square a velocity. It is nonsense. Draw me a illustration of a squared constant velocity. It's not possible. If it is a constant velocity and over any unit of time you can not produce a square..
Especially the speed of light. The speed of light is the product of a circle . Light... | {
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Compression of non-gaseous substances I learned about gas laws and their ability to compress. My science teacher told me that solids and liquids are incompressible. But when I learned about nuclear fission in bombs, it talks about compressing the uranium. How is this so?
| In a nuclear fission, the heavy,unstable and radioactive uranium nucleus is hit by a fast moving neutron having kinetic energy in excess of 5 MeV. The process continues with subsequent emission of highly-energised neutrons and other fragments. This suggests that a very high temperature and a high pressure is required f... | {
"language": "en",
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Is there a way to get the Bethe Roots, that belong to a given eigenvalue of the transfer matrix? (Quantum) integrable systems, that belong to solutions to the Yang-Baxter-equation, are often solved by the (algebraic) Bethe Ansatz. Solutions to the Bethe-equations lead to the eigenvalues of the transfermatrix and in tha... | Yes, there is a method known as McCoy’s method. You can find a detailed description in section 2.2 of the paper http://arxiv.org/abs/hep-th/0307095 . The idea is to use the fact that the eigenvalues of the transfer matrix are (Laurent) polynomials together with the Baxter TQ equation. Knowing a priory the eigenvalues a... | {
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Why don't photons split up into multiple lower energy versions of themselves? A photon could spontaneously split up into two or more versions of itself and all the conservation laws I'm aware of would not be violated by this process. (I think.) I've given this some thought, and a system consisting of multiple lower ene... | The are two factors going into the decay of any particle. There is the matrix element, which comes from fundamental physics, and the density of states, which comes from kinematics, mostly how heavy the mother particle is relative to the daughter particles. Either of these being very small slows down the decay (or being... | {
"language": "en",
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Shouldn't dark matter distort light and therefore be directly detectable? It is an established fact that gravity bends space time and therefore distorts light. We know that Dark matter acts gravitationally. So, just for giggles, lets say I had a sphere of dark matter ejected and floating in intergalactic space. Then, s... |
Then, shouldn't this sphere be detectable via the way it lenses light coming from galaxies that lie behind it (relative to earth). Similarly, a mass of dark matter within our own galaxy, should be detectable via the way it lenses light from stars that lie behind it ( again relative to earth). Has anything like this ev... | {
"language": "en",
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Why can we see through rain? I am gazing through my office window into a heavy rain. I am thinking that raindrops are like small lenses that bend the light. Thus I am surprised, that I can clearly see other buildings through the window.
So, why is it that we can see through the rain? Is the density of raindrops simply... | I would dispute that we can see through rain.
Any line-of-sight that ends on a rain drop is blocked from reaching the distant object. As we look deeper into the field of rain, more lines-of-sight end on raindrops and images of distant objects become less distinct. Eventually, when the probability of a LoS ending on a r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/203576",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Bragg Scattering of Thermal Neutrons I'm currently reviewing Bragg scattering. The particular problem below has me slightly confused on whether I'm thinking about it correctly.
Questions
Is the problem below referring to the kinetic energy of the neutrons when it mentions "energy"? Does the "other energies" of neutrons... | While your answer has elements of "check my work" in it, as discussed in the comments above, I think the basic questions you posed are legitimate.
Yes, the question refers to the kinetic energy of the neutrons, and the de Broglie wavelength associated with them; and yes, "other energies" will appear because higher orde... | {
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Photons have a property from the matter they interact with? When a photon leaves its source and hits our eye, our brain sees the source of the photon (Like a lightbulb or a star). When a photon is ejected from its source and bounces off of an object we see the object it bounced off. I hope
I've been right so far.
My q... | A photon is an elementary particle with zero mass, moves always with the velocity of light c, and has energy given by E=h*nu . It has spin +1 or -1 and its wavefunction also has a polarization which will build up the polarization of the emergent from many photons classical electromagnetic wave.
Its energy is a property... | {
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Reason for strange magnetic ball movement I was playing with a set of those neodymium magnet spheres and noticed a couple of strange behaviors (which I believe are related so I'm only positing a single question) and I was hoping to get an explanation for.
When I roll a single magnet in a straight line on a wooden table... | The spinning is just the same effect as for the ice skater spinning faster when he pulls his arms in. Here the distance of the mass around the center of motion is reduced, which leads to an increased angular momentum. Same goes for your balls. If you roll them such that they would miss another, but are within the range... | {
"language": "en",
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how can $\frac{kqq_o}{r}$ be $U$ for both a particle and a system of two particles? If there is a charge $q$, at a distance $r$ from it there is a voltage and the potential energy of a test charge $q_o$ would be $\frac{kqq_o}{r}$.
Now if I construct a system of two charges a distance $r$ apart, it has energy $\frac{kq... | Potential energy is the energy associated with the interaction between two objects. It's related to the force between two objects. That is: potential energy requires two objects.
You can talk about the potential energy of one object, but you would be being a little loose with language. We are in the habit of talking... | {
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Confusion I have regarding Einstein's 1905 derivation of LT In his 1905 paper, Einstein derives the Lorentz transformation using the two postulates of SR;constancy of $c$ for all inertial frames and the Invariance of the laws of physics for all inertial frames.
I'll summarize his mathematical derivation and then ask o... | So what you wrote here isn't exactly what Einstein writes in the paper, and the difference there is what's causing your confusion (also he changes what he means by $\phi(v)$ halfway through the paper, which is the real problem). On page 7 of the pdf you linked, these equations appear:
$$\xi = a \frac{c^2}{c^2 - v^2} x'... | {
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Entanglement and coherence I have come across a wonderful review of entanglement by Chris Drost in his answer to this post. One part that left me puzzled was: (This post is merely an attempt to understand a portion of Chris' answer, unfortunately I do not have enough reputation to ask this as a comment in his post, so ... | To me, to to make sense of the explanations above, it helped to have the following pictorial description:
Coherence is when I can imagine something being two things locally, at the same time, consistently; but this cannot happen to one of the pieces of an entanglement, since the other end would not be defined either. T... | {
"language": "en",
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What is thermophoresis? I read wikipedia article and I saw a bad youtube presentation on thermophoresis, however I don't have a clear insight about the subject. I assume the forces are basically Brownian molecular forces involved. I believe the principle of the thermophoresis phenomenon is simple, yet I am not sure. Ca... | Phoresis is a suffix that means migration.
Thermophoresis is simply the result of responses to temperature gradients by motile particles in a mixture. Particles larger than the mean free path of molecules of the gas in which they are suspended, are impacted by gas molecules and driven toward less energetic regions.
Th... | {
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Twins Paradox - Does ageing depend on motion? I am trying to understand the Twins Paradox (relativity) and its implications.
Can we infer from the Twins Paradox that the ageing process (cell decay or other biological processes) depends on motion? When I move fast, will my rate of ageing slow down?
I know the theory say... | When you are moving fast, your aging will slow down - see the Minkowski diagram: There are 3 worldlines of spaceships traveling in t=10 minutes (Earth time) 1, 2 and 3 lightminutes. The proper time τ is decreasing from 10 minutes to 9,54 minutes. The ratio τ/t decreases with increasing velocity. That means that when yo... | {
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Why doesn't the coupling spring provide restoring force in longitudinal oscillation of two masses? I was reading longitudinal oscillations of two masses from Crawford's Waves.
(source: rochester.edu)
The displacement of $m_1$ is given by $\psi_a$ & that of $m_2$ is given by $\psi_b$. The differential equations that Cr... | If $\psi_b-\psi_a \gt 0$, the center spring is stretched longer than its normal length. It will then pull to the right on mass $a$ and to the left on mass $b$. The difference in signs reflects this. If $\psi_a$ had been measured positive to the left, making the diagram symmetric, the sign would be minus.
| {
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Physical interpretation of Convolution Let us say that we are interested in finding the voltage (potential difference) $y$ across the resistor.
The circuit consists of a battery, a resistor and an inductor. The problem can be solved by following the Laplace transform "recipe".
$$
-U + L\left(s\left(\frac{Y}{R}\right)... | The way to understand the convolution operation intuitively is to look at the differential form. $dy(u) = f(u)g(t-u)du$ (we will add up $dy(u)$ from $0$ to $t$ to get $y(t)$). At any moment $u\ (0\le u\le t)$, an amount of some quantity $f(u)$ is produced, then it undergoes a change according to function $g$ from that ... | {
"language": "en",
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Light and momentum question? Each photon of light bulb carries momentum. Why does the light bulb not recoil from conservation of momentum?
| Even if it did, the energy-to-momentum ratio of light is $c$, a fantastically huge number.
For example, even if you house the light bulb in one big perfect mirror with a tiny collimated (all in one-direction) aperture that all of the light goes out of, and even if the light bulb is a perfectly efficient radiator which ... | {
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How does fusion work in the Sun if neutrons have more mass than protons? According to my textbook, the next result of the fusion reactions in the Sun is:
4H -> He + neutrinos + gamma photons
However, if hydrogen atoms are basically a proton and helium atoms are 2 protons and 2 neutrons, how can this reaction work? Neut... | The key is that the mass of a nucleus is not just the sum of the masses of its protons and neutrons. As a bound state, there is a binding energy associated with $^4\mathrm{He}$ that is not associated with the system of noninteracting $2n+2p$. There are different conventions on what sign to give this energy, but in the ... | {
"language": "en",
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Different actions equivalence in general relativity? I started reading up on the different actions that appear in GR. I have come across two:
*
*When looking at geodesics I found:
$$S=\int \sqrt{-g_{\mu \nu} \frac{dx^\mu}{d\lambda} \frac{dx^\nu}{d\lambda}}d\lambda$$
(I have also seen this with a coefficient of $-mc... | The first action is the action of a point particle. The second is the action of the gravitational field itself. You can easily use the two of them together to get both the geodesic equation and the Einstein Field equations with a point particle as its source (in this case, you will have $L_M = \sqrt{-g_{\mu\nu} \dot{x}... | {
"language": "en",
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Transition of H to hydrino H(1/4) by HOH as the catalyst Is this real, is there a more stable form of Hydrogen atom?
Source :
Mechanism of Soft X-ray Continuum Radiation from Low-Energy Pinch Discharges of Hydrogen and Ultra-low Field Ignition of Solid Fuels
– R. Mills, J. Lotoski, Y. Lu, submitted.
EUV radiation in t... | As of Oct. 28th, it appears that the answer is now true. At a conference for investors and industry partners, Mills has publicly presented a device that uses this process to produce extraordinary heat (over 2700K) using only H -> H[1/4] reactant. Incredibly, the device can produce a self-sustaining plasma for minutes w... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Deriving the Lienard-Wiechert Potentials Let $\mathbf{w}(t)$ be the trajectory of a moving charge. Let the observation event be $(\mathbf{r},t)$.
The scalar potential is:
$$\varphi = \frac{q}{4\pi\epsilon_0}\int \frac{\delta\left(\mathbf{r'} - \mathbf{w}\left(t - \frac{|\mathbf{r} - \mathbf{r'}|}{c}\right)\right)}{|\ma... | The general rule (see the "Composition with a function" section of the Wikipedia article on Dirac delta functions) is (for suitably well-defined functions):
\begin{equation*}
\int_{-\infty}^\infty {\mathrm dx \, f(x)\, \delta(g(x))} = \sum_i {\frac{f(x_i)}{|g'(x_i)|} }
\end{equation*}
where $x_i$ are the roots of $g(x... | {
"language": "en",
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Heisenbergs Uncertainty Principle in different intertial frames Say there is a single particle in a box. If we switch to a different inertial frame (without the box) travelling close to the speed of light we see the box get smaller. At a high enough speed the uncertainty principle will cause the particle to have a high... | If by 'we' you mean 'you and the box' then travelling at relativistic speeds will change nothing for you, you wouldn't notice anything. Only if you kept the box stationary and accelerated the particle to relativistic speeds would it maybe be able to break out of the box, depending on the potential barrier of the box.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does a gun exert enough gravity on the bullet it fired to stop it? My question is set in the following situation:
*
*You have a completely empty universe without boundaries.
*In this universe is a single gun which holds one bullet.
*The gun fires the bullet and the recoil sends both flying in opposite directions... | Making an assumption that the mass of the gun ($M$) is much greater than that of the bullet ($m$) , the net force on the bullet is: (From the gun's frame.)
$$m \frac{d^2r}{dt^2}=mv\frac{dv}{dr}=-\frac{GMm}{r^2}$$
The equality is obtained from the fact that acceleration is $\frac{dv}{dt}$, which equals $\frac{dv}{dr}\fr... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there an equivalent of probability current for the Wigner distribution? I know that for a wavefunction, I can derive a probability current $\mathbf{J}$ that satisfies the continuity equation: $$\nabla \cdot \mathbf{J}=-\frac{\partial}{\partial t} \big|\psi\big|^2$$
Can a similar quantity be derived for the Wigner di... | It's intuitively clear that this current must exist because the integral of the Wigner function is conserved by unitary evolution. This current is known as the Wigner flow, and it exists but it's not particularly pretty. For an example of the Wigner flow in use, see arXiv:1208.2970; in short, it is the current
$$
J=\be... | {
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Probability amplitude for motion from $x_i$ to $x_f$ in Heisenberg picture In M. Nakahara's book Geometry, Topology and Physics on page 19, the probability amplitude for a particle to move from $x_i$ at time $t_i$ to $x_f$ at time $t_f$ is given as
$$
\tag{1}
\langle x_f, t_f | x_i, t_i \rangle
$$
where the Heisenberg ... | I) OP's question (v1) seems to be spurred by a common confusion: The Heisenberg instantaneous position eigenstate $|x,t_0\rangle_H $ does not evolve in time $t$ but does depend on a time parameter $t_0$. In detail,
$$\tag{1} | x, t_f \rangle_{H}~=~ e^{i\hat{H}\Delta t/\hbar} | x, t_i \rangle_{H}, \qquad\Delta t~:=~t_f-... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/206857",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
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