Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Proof that a Hermitian Matrix is not defective? I am taking an introductory course into Quantum Mechanics.
To me to seems pretty simple to prove most properties of Hermitian operators. However, I am stuck at an edge case, proving that if an eigenvalue has multiplicity $n>1$, it will have $n$ linearly independent eigenv... | Here is a highlight of the reasoning line:
*
*A theorem: The whole vector space is the direct sum of the generalized eigenspaces, where each generalized eigenspace is associated with an eigenvalue. The algebraic multiplicity $\mu$ is equal to the dimension of the generalized eigenspace associated. (See https://math.s... | {
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How does electrical energy gets converted to sound energy? I have seen that inside headphones there is a magnet with a coil of thin wire around it. There must be longitudinal waves coming out of it that is why we can listen to audio. There must be pressure waves created as sound is nothing but pressure wave. So, my que... | A permanent magnet has a fixed north/south polarity - in this example, lets say north is facing up and south is facing down. This magnet has a membrane of some kind attached to its north face.
An electromagnet beneath the permanent magnet can switch the direction of its north/south polarities by changing the direction... | {
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Why is amorphous classified solid? Because it does not have a crystal structure, it is hard to find physical similarities with a solid. Why isn't it then another state other than solid?
The physics of amorphous is also quite different from crystal solid.
| Glass is a typical amorphous solid.
Amorphous materials typically show no melting point but do have a Glass Transition Point ($T_g$). Below it, the material behaves like a solid, with a glass-like fracture surface when fractured.
Typical amorphous materials include several types of elastomer (rubber) like natural rubbe... | {
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Why is the Pythagorean Theorem used for error calculation? They say that if $A = X \times Y$, with $X$ statistically independent of $Y$, then
$$\frac{\Delta{A}}{A}=\sqrt{ \left(\frac{\Delta{X}}{X}\right)^2 + \left(\frac{\Delta{Y}}{Y}\right)^2 }$$
I can't understand why that is so geometrically.
If $X$ and $Y$ are inter... | It looks like Pythagoras, but it is only remotely related. The important concept, as presented in SteveB's answer, is that the variables are considered to be independent, i.e. one does not affect the other. In mathematics, independent parameters are said to be orthogonal , and can thus be assigned to separate axes in... | {
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How far do we need to be removed from the earth to show the curvature with a viewing angle between 42 and 48 degrees? I have seen already a couple of answers but none of them give an exact number of what should be the minimum height where we would be able to record the curvature of the earth
All I could find is minimum... | As a former sailor I can assure you that you can see the curvature of the earth from the crow's nest - all it takes is a calm sea.
Consider a light house that stands 50 meters above sea level. If you are in the crow's nest, say 25 meters above sea level), at what distance could you first spot the top of the light house... | {
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Sign of Wick rotation Suppose you have the integral
$$i \int^\infty_{-\infty} L_M(t) dt$$
and that $L_M$ contains two poles: when $t>0$ the pole lies above the t-axis and when $t<0$ the poles lies below the t-axis. Therefore you can rotate the contour from the real axis to the contour going from $i\infty$ to $-i\infty$... | Thanks for your help. I agree this was homework-like - should've posted it somewhere else.
This is an equality
$$\int^\infty_{-\infty}f(x)dx=\int^\infty_{-\infty}f(-x)dx$$
so I guess mathematically it doesn't matter the sign of your substitution.
| {
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What is the electric field exactly on the surface of a conducting sphere? Within a conducting sphere, the electric field is 0, but is the electric field still 0 exactly on the surface?
| The answer is "it depends what you mean by exactly on the surface".
The electric field depends on the amount of charge enclosed. From Poisson's equation:
$$\nabla\cdot E = \frac{\rho}{\epsilon_0}$$
If the charge on the surface is an infinitely thin sheet of charge, then the electric field will be zero on one side of th... | {
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Should 4 fundamental forces really be 3 because of electroweak unification? I read @ http://www.particleadventure.org/
Physicists concluded that, in fact, the weak
and electromagnetic forces have essentially
equal strengths. This is because the strength
of the interaction depends strongly on both
the mass of the force ... | A more practical answer is that in many cases it is more useful to consider them separately. You could compare with electromagnetism. If I want to design a motor, it is much easier to work with the magnetic field generated by the coils than to invoke the whole glory of Maxwell's equations. Similarly, if I want to ex... | {
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what is eigenvalue of $P^{1/n}$ operator if we know eigenvalue equation of $P$ ? If $P$ is an operator and $PΨ=pΨ$ ( $p$ as the eigenvalue ) then is it true to say $P^{1/n}Ψ=p^{1/n}Ψ$ ( n is an integer and positive number )
| In general, the operator $P^{1/n}$ is relatively hard to define: we have sort of the same problems we have with complex numbers (there are in general multiple $n$th roots of any nonzero $z\in\mathbb C$) except that we have them separately on every dimension, which sort of mostly kills the whole thing.
However, if $P$ ... | {
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How do I remove the negative sign from this derivation? A homework problem required me to show that the first equation below can be written in the form of the second equation. It was all fairly simple except for the negative sign. I'm not sure how this is supposed to cancel out. Might there be some conceptual way that ... | In the first equation you can replace the minus sign ($-$) by $i^2$, then factor that to be part of the $\alpha$.
| {
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Navier Stokes: what about angular momentum? I play with CFD for a while, and suddenly, a transcendantal question raises: :-)
Navier Stokes is basically Newton applied on a continuum in Eulerian.
For solids, we would consider linear, but also angular momentum.
Why don't we have to do that for fluids ?
Conversely, you ca... | The basic answer was given here: In a fluid, why are the shear stresses $\tau_{xy}$ and $\tau_{yx}$ equal?. Angular momentum conservation follows from linear momentum conservation (expressed by the Euler/Navier-Stokes equation) combined with the symmetry of the stress tensor.
Momentum conservation is the equation
$$
... | {
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Deriving Boyle's law from only the Gay-Lussac laws My physics professor during a lecture presumably mathematically derived Boyle's law from the two Gay-Lussac laws for ideal gasses. What he said is also printed in his own textbook.
He states that, given the variables $P$, $V$, $T$,
assuming only:
*
*$T \propto V$ w... | I think it can be done mathematically. Let T = T(P,V). Then, if T is proportional to P at constant V, then $$\frac{T}{P}=F(V)$$. Therefore, $T=PF(V)$. Now, if T is proportional to V at constant P, then $$\frac{T}{V}=P\frac{F(V)}{V}=kP$$In the above equation, $F(V)/V$ must be a constant in order for the right hand s... | {
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So Black Holes Actually Merge! In 1/5th of a Second - How? I've read a lot of conflicting answers in these forums. However, today saw the awesome announcement of gravitational waves. Two black holes merged: http://www.slate.com/blogs/bad_astronomy/2016/02/11/gravitational_waves_finally_detected_at_ligo.html
Not only th... | The rotation of an object around the black hole does not slow down (in terms of frequency). It is not affected by time dilation. The object gets sticked on the surface of black hole, even accelerates its rotation.
| {
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Why are Gravitational Waves so small? I'm sure you've all seen the diagrams and/or 3D visualizations of gravity; the ball sitting on a piece of fabric which makes it sink down. They've also started using it in the videos that explain gravitational waves. Two objects will be circling each other on the fabric and will em... | Actually the wavelengths often are the sizes of planets. If the period of something moving at $c = 3\times10^5\ \mathrm{km/s}$ is $1\ \mathrm{s}$ (similar to the recent LIGO discovery), its wavelength is $\lambda = 3\times10^5\ \mathrm{km}$. Other phenomena could well produce waves with wavelengths larger than the sola... | {
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Calculate the laser heating on a crystal Let's say I'm doing an optical experiment.
I focus a laser on a crystal with a certain amount of power.
The crystal's temperature is regulated to a certain temperature but it is localy heated by the laser.
How can I calculate the local temparature at the laser spot's location?... | Let us assume that you have continuous laser.
You need to solve stationary heat diffusion equation given in wiki, which is basically Poisson equation. For accuracy you will need to know penetration depth of your laser. It is better if you solve equation for exponential with depth source but Gaussian shape will give you... | {
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Why do detectors for gravitational waves have only two perpendicular arms, not three? I wonder why detectors for gravitational waves have only two perpendicular arms, not three. Having three arms appears to allow for better detection of direction, or may even increase sensitivity (I may be wrong). So far I came up with... | LIGO's arms are 4km long, which makes the problem even worse. Besides, you can just move a quarter of the way around the planet and build another 2-arm facility there, and it'll automatically be at right angles to your first facility (and as long as you do know their relative positions and orientations precisely, you d... | {
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Gravitational waves in other dimensions I know this question is purely speculative, as we don't know if more dimensions do exist and also we do not know if gravity is indeed stronger in other dimensions (if they were to exist). But, one of the possible explanations of why gravity is so weak compared to other forces is ... |
But, one of the possible explanations of why gravity is so weak compared to other forces is that it exerts its strength in other dimensions, which are too small for us to detect them.
why do you say that "gravity is so weak"? if you say that because the repulsive force due to EM between two protons greatly exceeds t... | {
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Do gravitational waves add mass to black hole? Due to the recent discovery of gravitational waves by LIGO I was wondering suppose a black hole stood between a gravitational wave then due to the fact that black hole can attract every thing then would the gravitational wave energy (that was lost from the objects producin... | If we accept that gravity will be successfully quantized, the question can be answered in a similar way as with photons, the gravitational wave emerging from the confluence of gravitons similar to electromagnetic waves emerging from a confluence of photons.
So, depending on the wave length ( the energy of the graviton)... | {
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What actually is the event that we think we have detected with gravitational waves? This answer shows the "event" that is creating excitement. It looks to the untrained eye like a single "blip" on a detector. It appears to last less than a second.
It is, later in the answer, referred to as a "black hole merger".
Are ... | Yes - the black holes actually merged in less than a second. If my memory serves me from the press announcement, at the time of final collision, the two black holes were moving relativitistically, at approximately 50% the speed of light. When you have compact massive bodies orbiting one another with very small orbits, ... | {
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Is the Landauer limit reversible As I understand it, the Landauer limit, $kTln(2)$, is the minimum amount of energy to erase a bit. Is it also the minimum amount to create a bit? I'm asking statistical, like Avogadro's number of bits, i.e., $RTln(2)$.
My thinking: $RTln(2)$ is the work required, probably both ways (... | One doesn't really create bits. One simply changes the state of a physical system to "store" a bit of information. At a microscopic level, all changes are governed by reversible laws, so that the state of the physical storage system before the storage must somehow wind up encoded in the physical state of the environmen... | {
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When I open a window to air out the room, how does the smell disperse? Let's say I'm in a room with some kind of noxious stink, possibly of flatulent nature. The quickest way to right the world that comes to mind is to open a window. When I open a window, how do the stank particles leave the room?
| That process is called diffusion, the stinky small in the room gradually leaves the room until the stinky smell is evenly distributed. when the air is evenly distributed the room assumes a new state of smell.
| {
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Relation between intensity of light and amplitude of electric field? A question in my textbook involve finding the electric field amplitude at a point in space given the intensity of light. It uses the following equation to solve it: -
$I=\frac{1}{2}\epsilon_{0}|E_{rms}|^2c$
But where did this equation come from? I am ... | As light is an electromagnetic wave, it is a combination of both electric field and magnetic field. So intensity of light is basically the power transmitted through electric and magnetic field divided by the cross section area of that light beam.
The energy density of the electric field is $\frac{1}{2}\epsilon_0 ... | {
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Accelerating potential Will an accelerating potential accelerate a neutral atom? For example, consider an atom of hydrogen subjected to an accelerating potential of $V$. As the kinetic energy of a particle accelerated by a voltage is given by $qV$, where $q$ is the charge on the particle, won't the kinetic energy of th... | A hydrogen atom consists of an electron and a proton. In a uniform field $E$ the force on the electron will be $+eE$ and the force on the proton will be $-eE$ to the two forces sum to zero. A hydrogen atom is not accelerated by a uniform field.
However if the field is non-uniform the atom can be accelerated. This is be... | {
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If pencil tip is heated why doesn't it write? Why doesn't a pencil write if its tip is heated in a candle flame?
| The lead (I'll call it lead for brevity even though it isn't made from lead) in a pencil is a mixture of graphite and clay pressed then sintered.
A candle flame is nowhere near hot enough to chemically change the lead. The clay requires many hundreds of degrees to sinter further and the graphite doesn't burn until gett... | {
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Scanning the universe - edit: expanding or shrinking I know that this may sound as a very basic question, but how come that we can
detect CMB radiation, light or gravitational waves from the big-bang era?
Shouldn't this radiation has overtaken us a long time ago?
EDIT: if i got it right , the answer to my question has... | The universe is expanding - and it is expanding, as far as we can tell, in all directions, at the same rate, everywhere all at once. So over a given period of time, a distance of 1000 units will become 1100 units, and in another passing of the same time, that distance will become 1210 units long, then 1321 units, and s... | {
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What is the dielectric constant of a pure conductor? Dielectric constant is the ratio of permittivity of a medium to the permittivity of free space. How to find dielectric constant of a conductor?
| Inside a metal, there is no formation of dipoles, hence there is no polarization as such. We have free electrons in metals not bound like that of a dielectric. Hence we can argue its electric susceptibility $\chi$ = 0. We know $\epsilon_r = 1 + \chi$, so it can be said that its relative permittivity($\epsilon_r$) is 1,... | {
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Betti number of Feynman graph Let $\mathcal{L}$ be a Lagrangian, which contains polynomials of bosonic fields $\phi$. After Wick's rotation we obtain a perturbation expansion od Green's function. In this expansion there are terms of the form
$$\frac{(-1)^n}{n!}\int\hat\phi(p_1)...\hat\phi(p_N)\prod\limits_{j\in A}\xi_j... | *
*In the momentum representation, we should integrate over all the internal momentum variables. The number of internal momentum variables is the number $E$ of internal edges in the Feynman diagram.
*Each vertex obeys momentum conservation. (Note that the external momentum variables in a connected component are assu... | {
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Measuring Static Electricity Is it possible to measure the static electricity in a room using a VOM or some other digital meter? I have a lot of static electricity building up in a carpeted room, and would rather not spend the money buying a meter to measure this.
| In general, no. The input impedance of most cheap meters is too low. So, you either need a specialist meter for numbers, or a cheap and easy way to detect the static field and give you an approximate idea. This circuit, for example
| {
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Force on current carrying square loop I'm asked to find force on square loop (side a) carrying current $I$, flowing counter clockwise, when we look down x-axis, lying in yz plane. the loop is centered at the origin. The magnetic field is given as:
$\vec{B} = kz\hat{x}$
Its solution states that force on left an right ca... | first you take the direction of current vector and start turning /rotating screw from I towards the B vector ;if the rotation of the screw is clockwise screw movement will be perpendicular to the plane containing Current and Field vector and it will give you direction of the force .
if the screw rotates anticlo... | {
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Is the local Lorentz transformation a general coordinate transformation? There is a saying in Nakahara's Geometry, Topology and Physics P371 about principal bundles and associated vector bundles:
In general relativity, the right action corresponds to the local Lorentz transformation while the left action corresponds t... | By a "frame" in GR we tend to mean a tetrad or vielbein $e^\mu_i$, $\mu,i\in\{0,1,2,3\}$. See here for the precise definition. Now, we can think of this object $e$ as a matrix. It is common to refer to the index $\mu$ as a "coordinate" index and $i$ as a "Lorentz" index. Now, as Nakahara talks about in Chap. 7, a tenso... | {
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How precise must the energies match for absorption of photons? According to Quantum Mechanics, in order for an atom to absorb a photon the energy of the photon must be precisely that of a "jump" between energy states of the atom.
How precise must it be?
If I create a photon with an energy within an error of 0.0001% of... | The linewidth broadening everyone is talking about is actually a very classical effect that comes straight from antenna theory and depends only on the size of the antenna as compared to the wavelength of light. It is well known in classical antenna theory that the bandwidth of a lossless short antenna goes as the cube ... | {
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How is the universe flat? I have real trouble visualising what is meant by the descriptor 'flat' when referred to the shape of the observable universe. Which one of the below is more accurate?
a) It is flat in a 2D way, like a big disk mostly spread out on one plane, similar to a solar system or disk-shaped galaxy
b) I... | You probably learned Pythagoras' theorem at school, and this states that if you move a distance $x$ along the $x$ axis then $y$ along the $y$ axis the distance between your starting and ending points is given by:
$$ s^2 = x^2 + y^2 \tag{1} $$
If we extend this to three directions by including motion along the $z$ axis ... | {
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How does the drift velocity of electrons in a conductor depend on the temperature? How does the drift velocity of electrons in a conductor depend on the temperature?
I have two contradicting views for this.
*
*First, we can say that increasing the temperature of the conductor will increase the kinetic energy of the... | Both the cases lead to the same result: decrease in drift velocity!
In the first case the drift velocity is also going to decrease. Increase in KE will increase the speed of the electrons and not their drift velocity. An increase in speed will cause the electron to cover the same distance in a smaller interval of tim... | {
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Ammeter range and shunt resistance Its said that for an ammeter to give good reading, the full current in the circuit must pass through it. But if I am right, the ammeter is basically a galvanometer connected parallel to a very low resistance called a shunt. I am aware that connecting a low resistance in parallel wil... | In a practical ammeter there will be a number of fixed shunt resistances, selected by a switch. The galvanometer is acting as a high-resistance voltmeter, measuring the voltage across the shunt, and has little effect on the current through the circuit was a whole.
If we know the value of the shunt resistor, then the v... | {
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"timestamp": "2023-03-29T00:00:00",
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What carries electric field through space? A stationary charge "creates" a constant (but not uniform) electric field around it, and a moving charge "creates" a variable electric field around it. What "carries" the information about the existence of a stationary or a moving charge through space?
In particular, are photo... | Macroscopically we speak of electric and magnetic fields which follow the classical theory of Maxwell's equations.
A stationary charge "creates" a constant (but not uniform) electric field around it, and a moving charge "creates" a variable electric field around it. What "carries" the information about the existence o... | {
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In solids, is it phonons, or is it the oscillations of electrons in bands, that emit most of the blackbody radiation? In solids (most any object we see), which tends to emit most of the blackbody radiation: phonons (atomic, or molecular dipole, lattice vibrations) or oscillating electrons in their energy bands?
| A couple snippets from the web:
I can't find the actual document name, but it's here
Phonons are quantized lattice vibrations. They possess small energies
(up to approximately 100meV) and a momentum of the order of that of an
electron in a semiconductor.
Which suggests that phonon energy is far too small to emi... | {
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How is a human voice unique? Well, I am quite new to concepts of vocal sounds. From the physics point of view I believe a sound has two basic parameters i.e, frequency and amplitude.
Considering the end sound wave produced by human voice it must have frequency and amplitude as parameters. Well, when a human can speak i... | As stated by the others, a sound is made up by sinus-waves of different frequencies. The tuning you hear, is determined by the lowest frequency (fundamental). The other frequencies are multiples of that ground frequency and are called overtones.
Summarising what is shown below: the amount in which the different overton... | {
"language": "en",
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"source": "stackexchange",
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Lorentz Force and Apparent Conservation of Momentum Violation Useful for Unidirectional Force? My understanding is that the apparent violation of Newton's Third Law by the Lorentz Force necessitates a description of the system that describes the "missing" momentum as being absorbed/carried by the magnetic field itself.... | No, in this case Lorentz force is reciprocal: current in rod creates it's own magnetic force and acts on electron current loops in magnetic materials...
The same stands for current attracting iron rod and etc...
So no violation of Newton's Laws...
| {
"language": "en",
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"source": "stackexchange",
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Front velocity and Superluminal group velocity In some cases, according to Wikipedia, the envelope of a gaussian beam can go faster than speed of light hence leading to superluminal group velocity.
However, the signal/energy still propagates at subluminal speed which is seen from the speed of the rising front of the p... | Superluminal group velocity can occur in near absorption peak, known as regions of anomalous dispersion. So-called "superluminal tunneling" experiments have bee conducted in thes regions, but when carefully analyzed there is no information transferred faster than light.
Some references are given here: https://www.rp-ph... | {
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Adiabatic compression and expansion and isothermal expansion? Please help me in understanding the concepts
*
*Why in adiabatic compression and expansion small volumetric change occurs while in isothermic compression or expansion very small pressure is applied and why the volume changes very significantly? Here, I a... | Let us look to your first question.
In an adiabatic process, pressure change is due to two factors: change in volume (due to work done) and internal energy change (due to the temperature change), but in an isothermal change, the pressure change is due to change of volume only (since temperature is a constant). Thus, ... | {
"language": "en",
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"source": "stackexchange",
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Uniqueness of the magnetic vector potential? I am trying to find the magnetic vector potential a distance of $s$ (cylindrical radial variable) from an infinite wire carrying current $I$. The magnetic field at a distance $s$ from a wire is $$B=\dfrac{\mu_{\circ}I}{2\pi s}\hat{\phi}.$$
Using the fact that $\nabla\times ... | One can indeed "simply let go of the unicity of the magnetic potential", but there is an alternative: to build the theory of electromagnetism from the Fermi Lagrangian, as I have done in my paper at https://arxiv.org/abs/physics/0106078. In this theory the vector potential is uniquely determined by the requirement that... | {
"language": "en",
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When is an attractor meaningful? I’m originally a computer scientist; so I hope my question is not trivial. I’m working with time series and want to reconstruct the phase space from the time series based on time-lagged versions of time series. For this purpose I need to calculate $m$ and $\tau$ which are the embedding ... | I don't believe the time lag is critical. Selecting a bad one might mean that you need to analyze more data to fill in the phase space, but it should still generate it given sufficient time. As for the meaningful aspect, that does depend critically on the embedding dimension. Usually one uses the human capacity for p... | {
"language": "en",
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Why we have a leak in the pipe if the fluid pressure is lower than the atmosphere? I've read in many books that if our flow pressure is lower than the atmospheric pressure then we'll have a leak in our pipe, but I already know that the flow is always from the high pressure point to the lower one. So the flow must be fr... | it depends in fact.
if your fluid is in touch with air in two places(upside of fluid and hole place)
so although pressure of fluid is lower than air we have a flow.because the equation of pressure in that place would be
P(air)+p(fluid)>p(air)
the left side is the pressure which we have in the fluid in that place outwar... | {
"language": "en",
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Simplest Live Demonstration of Adiabatic Transport I have to give a presentation on Berry phase. I would like to give the simplest live demonstration of adiabatic transport. If I move an object in a loop and return that object back into its original position then the phase changes. I was thinking about a moving a simpl... | I think that for a reliable demonstration of the spinning wheel system, a design using bearings would be essential, in order to achieve frictionless reactions.
A demonstration can be achieved by means of the linear planimeter , which measures areas enclosed by plane curves, by measuring a rotation angle of its wheel.... | {
"language": "en",
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Can two photons form a gravitational bound state? I've always wondered if it's possible to bind two photons, in particular by gravitational interaction. Photons don't have a rest mass, but do nevertheless have a gravitational mass, by which they can attract each other. However, I can't imagine a bound state. My intuiti... | I agree with Lewis Miller that they cannot form a bound states if the binding is thought to be of gravity essence. By definition, a quantum state is understood only in small scales which is way too smaller than the bounding distance between two photons; it will be bigger than the size of Visible Universe. However, I wo... | {
"language": "en",
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Photon emission between an electron and positron If I placed and electron and a positron at a certain distance apart in a vaccumm, they would attract each other and annihilate producing 2 or more gamma rays. But, what I would like to know is, does the electron and positron emit photons as they are attracted towards eac... | My 2 cents:
If only two gamma rays are produced with each of their energy equaling the rest energy of either e- or e+ (which is 511keV) then, it could possibly mean that there is no net linear momentum, which possibly means that this e+ and e- pair are very very close to each other and after collision, the gamma rays a... | {
"language": "en",
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"source": "stackexchange",
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Normalization of a wave function in quantum mechanics A more simple question, so I am watching a quantum mechanics lecture on potentials of free particles and am doing the general solution of schrodinger's stationary equation for a free particle when I was told to normalize the solution (which I can do all well and goo... | One peculiar fact about a real life wave function $\psi$ is that it can be normalized. In order to analyze and compare the various outcomes of the solution of a Schrodinger equation, one need to assign a quality that is unique to all the wave functions, that which is to transform them such that their area is always 1... | {
"language": "en",
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Impulse Equations A solid sphere of mass $m$ rolls without slipping on a horizontal surface and collides with a vertical wall, elastically. The coefficient of friction between the sphere and wall is $\mu$. After the collision, the sphere follows a parabolic trajectory, with range $R$. What is the value of $\mu$ to maxi... | If the collision is elastic, then energy is conserved; however, this cannot mean that the horizontal velocity is the same on the way to the wall, and on the way back: the ball will also have a vertical velocity, and rotational kinetic energy.
This means that the impulse cannot be $2mv$ as you stated; you have to solve ... | {
"language": "en",
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Propagator in Quantum Mechanics What does the propagator in Quantum Mechanics mean? I mean, except from the mathematics behind it, what does it tell us? Is it something that has to do with translations in time?
| Propagator in quantum mechanics is just a different name for Green's function for time-dependent Schroedinger equation. It is a unique function that enables us to write, for any time $t_0$,
$$
\psi(x,t) = \int G(x,t;x',t_0)\psi(x',t_0)\,dx'
$$
for all $x$ and all $t$. This means the $\psi$ function of $x$ (at any time ... | {
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Examples of Bernoulli Numbers, Euler-Mascheroni Integration, and the $\zeta(n)$ in physics In Arfken's Mathematical Methods for Physicists, there is a subsection of the "Infinite Series" chapter which covers the Bernoulli numbers, Euler-Mascheroni integration (or summation), and the connection these have with the Riema... | In quantum field theory, especially in the treatment of divergent series and divergent integrals (like Feynman integrals which arise from calculation of self energies for example) and during the process called "regularization", lots of "Euler Mascheroni" constants arise.
For example, I remember during the calculation o... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to derive the components $\Lambda^i_j$ of a Lorentz-transformation given a boost $\vec{v}$? I am stuck in deriving a specific formula concerning Lorentz-boosts.
In my Classical Mechanics skript there is a chapter dealing with special relativity. In this chapter the Lorentz transformations are defined as being those... | There is an error in your expression for the $\Lambda^i_{\;j}$ components. They actually read
$$
\Lambda^i_{\;j} = \delta^i_j + (\gamma -1)\frac{v^i}{v}\frac{v_j}{v} = \delta^i_j + \frac{\gamma -1}{\beta^2}\frac{v^i}{c}\frac{v_j}{c}
$$
with $\beta = v/c$, $v^2 = v^iv_i$.
Keeping this in mind, separate once again time... | {
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Crookes' Maltese Cross Tube and the anode I understand that Sir William Crookes' Maltese cross tube shows that cathode rays travel in a straight path but I am unsure of why the cathode rays aren't affected by the anode as there is an electric field and therefore bend.
Sorry if this is a silly question but I am relat... | The left hand image is a schematic of the Crookes' tube arrangement.
The tube had gas at low pressure inside it and electrons which original from the cold cathode were accelerated towards the anode.
A lot of the electrons were travelling so fast that they were unable to turn the corner towards the anode and there we... | {
"language": "en",
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Derivation of Displacement current term in Ampere's Law I have a quick question:
In deriving the displacement current term for Ampere's Law, my book has the line:
$$\Phi_E= \int_S \mathbb{E} \cdot \hat{n} da= \int_S \frac{\sigma}{\epsilon_0} da = \frac{Q}{A \epsilon_0} \int_S da= \frac{Q}{\epsilon_0}$$
My question is:... | I have never understood why this sort of derivation in textbooks is not made conceptually easier by choosing an appropriate bulging amperian surface as the one shown below.
Because the surface is flat and has a plane perpendicular to the electric field in the region of the electric field the flux is easy to calculate.... | {
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Why fuse needs to be slightly more able to bear current than the appliance? if I have a bulb with rated current of $4 A$ then why I need to connect an $5A$ fuse?( which has slightly more ability to bear current.)
| The role of a fuse is not to protect the equipment from damage. It's to ensure that in the event of a fault, the wiring doesn't overheat and cause a fire.
The fuse needs to be rated slightly higher than the maximum operating current of the protected device, so that the fuse won't blow when the equipment is used. It sh... | {
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What is the meaning of $\mathrm{d}^4k$ in this integral? From Gerardus 't Hooft's Nobel Lecture, December 8, 1999, he states the following equation (2.1):
$$
\int \mathrm{d}^4k \frac{\operatorname{Pol}(k_{\mu})}{(k^2+m^2)\bigl((k+q)^2+m^2\bigr)} = \infty
$$
in relation to weak interactions theory, where $\operatornam... | The equation is a term in the calculation of a scattering probability. Obviously a scattering probability must be between zero and one, like any other type of probability. So when the calculation of a scattering probability returns a value of $\infty$ that isn't physically possible, and it shows that the method we are ... | {
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Why is it said that standing waves do not transfer energy? The author of my physics textbook writes that standing waves, unlike travelling waves, do not transfer energy. He says that this is because a standing wave is composed of two travelling waves carrying energy in opposite directions. Is this explanation sufficien... | In case of electromagnetic waves the energy transfer is described, in most general terms, by the Poynting theorem:
$$
-\frac{\partial u}{\partial t} = \nabla\cdot \mathbf{S} + \mathbf{J}\cdot\mathbf{E},
$$
where the Poynting vector (i.e., the energy flux) given by
$$
\mathbf{S}=\mathbf{E}\times\mathbf{H}.$$
Note that i... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Putting a capacitor into a strong magnetic field, will this change the capacity? I'm wondering, does a magnetic field change the number of electrons, placed and displaced on the two plates of a capacitor. To prove or disprove this, I think the capacitor could be connected to an other capacitor outside the magnetic fie... | It is worth recalling that a charge that is at rest with respect to a static magnetic field incurs no force from that field. From that it follows that the steady-state capacitance should be identical to that of the same capacitor outside the field.
Or at least it would follow for a capacitor with vacuum between the pla... | {
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Killing equation manipulation Why does the killing equation $$K_{\mu;\nu}+ K_{\nu;\mu} = 0$$ equal $$K_{\mu,\nu}+ K_{\nu,\mu} -2\Gamma^{\rho}_{\mu\nu}K_{\rho} = 0 $$
when in general a covariant derivative
$V_{\beta;\alpha} = (\partial_\alpha V^\lambda + \Gamma_{\alpha \nu}^{\lambda}V^{\nu})g_{\lambda \beta}$?
Where doe... | Your expression for the covariant derivative is wrong: it should be with a minus sign (plus sign for vectors=upper index, and minus sign for covectors=lower index):
$$
\begin{aligned}
\nabla v^\alpha\sim \partial v^\alpha\color{red}+\Gamma^\alpha v\\
\nabla v_\alpha\sim \partial v_\alpha\color{red}-\Gamma_\alpha v
\en... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Nearly Free Electron Model and the Reduced Zone Scheme When for example studying the vibrational modes of a one dimensional diatomic chain we find that the dispersion relation $\omega(k)$ is periodic in the one dimensional reciprocal lattice vector $\frac{2\pi}{a}$, and so the dispersion relation can all be displayed i... | Mechanical vibrations of the periodic atomic chain and electron motion in periodic fields are pretty different problems, although they have similar features related to the periodic boundary conditions. The frequency of the diatomic chain has upper bound that depends on the interatomic coupling. The energy of electrons ... | {
"language": "en",
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"source": "stackexchange",
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Differences between eigenstates, bound states and stationary states I am not very clear about the differences between eigenstates, bound states and stationary states.
| *
*Eigen state : Particular to an operator, which when operates on it, gives a scalar number (or the eigenvalue) times itself.
*Stationary state : The state of a particle that does not vary with time.
*Bound state : The state of a particle bounded by within a potential, meaning - the energy of the particle in that s... | {
"language": "en",
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Are residuals supposed to have error bars? Hopefully I'm asking this in the correct section. So I've got a graph with a linear trend of data and a best fit line plotted. The data points on the main graph obviously each have their own error bars. I've also made a subplot of residuals.
My question is: do the residual sub... | Yes, residuals should have error bars.
If your residuals are the difference between your data and your model, and your data are well-described by your model except for independent, normally-distributed errors which you have modeled correctly with your uncertainties, then your residuals should be (a) randomly distribute... | {
"language": "en",
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Help! An 8 year old asked me how to build a nuclear power plant I would really like to give an explanation similar to this one.
Here's my current recipe:
(i) Mine uranium, for example take a rock from here (picture of uranium mine in Kazakhstan).
(ii) Put the rock in water. Then the water gets hot.
(iii) [Efficient way... | Well, if you have a really adventurous kid you can follow the recipe of the Radioactive Boy Scout
...and became fascinated with the idea of creating a breeder reactor
in his home. Hahn diligently amassed this radioactive material by
collecting small amounts from household products, such as americium
from smoke d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/244158",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
"answer_count": 5,
"answer_id": 3
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Change in energy during orbital decay Suppose we have a planet orbiting a star and the planet radiates away some amount of energy $\Delta E$. I want to find by how much the orbit decays (i.e the change in orbital radius).
One way to do this is to find the total energy as a function of radius $E(r)$ (it's equal to half ... | By talking about orbital radius you're assuming the orbit is circular, but that may not be the case. In general you need both energy and angular momentum to specify your orbit, and to solve completely you'd need to know the specific mechanism of energy loss to find out what happens to the angular momentum.
You can get ... | {
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Fourier transform of Hamiltonian for scalar field In the Srednicki notes (http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf) page 36 he goes from
$$H = \int d^{3}x a^{\dagger}(x)\left( \frac{- \nabla^{2}}{2m}\right) a(x) $$ to
$$H = \int d^{3}p\frac{1}{2m}P^{2}\tilde{a}^{\dagger}(p)\tilde{a}(p) $$
Where $$\tilde{a}(p... | Srednicki goes from
$$
H = \int d^{3}x\ a^{\dagger}(x)\left( \frac{- \nabla^{2}}{2m}\right) a(x)
$$
to
$$
H = \int d^{3}p\ \frac{1}{2m}p^{2}\ \tilde{a}^{\dagger}(p)\tilde{a}(p)
$$
where $p^2$ is just a number (an integration variable, not an operator). Therefore, it commutes with everything.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Could an asteroid land slowly on Earth's surface? The concept in my mind is that an asteroid is on a vector similar to Earth's, but slightly slower (e.g., 50kmh slower). As Earth passes it, it enters the atmosphere at a sharp angle, and since Earth was passing it, it just barely touches down due to Earth's gravity and ... | Well, technically, the answer is no as the other answers and comments also say.
The approach speed can not be less than escape velocity.
But in order for such a thing to happen, nature has to be really creative and totally in our favor. For example, the asteroid can have a very very lucky combination of these:
*
*Th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/244606",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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Units don't match in the torsional spring energy! According to Wikipedia's description of torsion springs and according to my understanding of physics the energy of a torsional spring can be written as
$$U=\frac{1}{2}k \varphi^2$$
where $k$ is a constant with units of $\rm N\,m/rad$.
I am freaking here because if the... | In the SI system of units, the radian is a special name for 1 (see SI brochure), that is,
$$\mathrm{rad}=1.$$
Therefore,
$$[k] = \mathrm{N\,m/rad} = \mathrm{N\,m}$$
and
$$\mathrm{J\,rad} = \mathrm{J}.$$
Since the last revision of the SI, the radian is no longer a supplementary unit: an angle is now defined as the rati... | {
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"url": "https://physics.stackexchange.com/questions/244650",
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"source": "stackexchange",
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Calculating force with two fulcrums and many forces I may not be wording the question the right way.
I have a lever. About 2/3 the way back there is a pivot point. We'll call this B
On the very front (end of the lever) there is a block that the lever rests on. Let's just assume the block is actually a point at the very... | I assume by fulcrum you mean resting points/pivot points and that the lever is not attached to the fulcra. If it is, then the mass of the fulcrum at the back counts in this equation.
The equation for torque is Torque = Force * distance from pivot. If I apply a force of 10 N 1 m away from the pivot point, then I have 10... | {
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Is acceleration relative in relativity? Suppose a box A is moving relative to a Box B, then by time dilation equation if I take 1 sec passed for an observer in A then for an observer in B will be little longer. Now if I suppose that the box B is moving while A is stationary under the same condition, then by the time di... | Acceleration is not "relative" even in classical mechanics, accelerating frames have fictitious forces in them (like overload, centrifugal, etc.), while inertial ones do not. It is not relative in special relativity either.
So if A is accelerating and B is inertial then A and B are not "equal", and if they are both ine... | {
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Why does the temperature of the gas in a container moving with constant velocity not change?
Systematic changes do not affect thermodynamic equilibrium.
What does this mean? And what kind of systematic changes are allowed?
The container with gas is stationary till some time then it's given a constant velocity and the... | Where are you measuring the temperature?
If you measure it using a thermometer that is inside chamber, travelling with the gas, then you will not observe any difference relative to when the chamber is at rest (obviously, we are assuming some classical, global reference frame here...).
However, if you measure from outsi... | {
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Explanation for concept of relative density I am in class $9^{th}$, I'm reading my physics book in which it is written that: $$\mathrm{Relative\ Density} = \frac{\mathrm{Weight\ of\ solid\ in\ air}}{\mathrm{Loss\ of\ weight\ of\ solid\ in\ water}}$$
As I mention my level that I'm in class $9^{th}$, Plaese help me to u... | The method can only be used to measure the relative density of something more dense than water, otherwise the object will float.
The loss of weight of the object in water is the upthrust $U$ on the body, from Archimedes' principle (the same as the weight of water displaced).
The weight can be measured by a spring bala... | {
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How to write BdG Hamiltonian in graphene? In Beenakker's paper:Specular Andreev Reflection in Graphene, the BdG Hamiltonian is written as:
$$
H_{BdG}=\begin{pmatrix}H-E_F&\Delta\\ \Delta^*& E_F-H\end{pmatrix}
$$
from equation (1).
Where $H$ is the Hamiltonian of pure graphene and it is:
$$
H=\begin{pmatrix}H_+&0\\ 0& H... | It is a very beautiful paper! But as all the old Physical Review Letters a bit cryptic, the supplementary material in the arXiv (http://arxiv.org/pdf/cond-mat/0604594v3.pdf) version is helping a bit.
In the full $8\times8$ Hamiltonian, electrons from valley K are coupled with holes from valley K' via the proximized su... | {
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Is it possible to determine the slit a photon went through in the double slit experiment by measuring its flight time? In the double-slit experiment, quantum mechanics states that if you try to determine which slit the photon goes through, you won't have a resulting wave pattern.
But, knowing the time it took for the p... |
But knowing the time it took for the photon to go from the source to the observing screen, you can deduct the distance of the photon path and so which slit it passes through
... and indeed such information will make it impossible for fringes to appear.
Interference experiments use wavepackets that have a long durati... | {
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Synthetic Photometry - Calculating a colour index I have a theoretical black body spectrum as described by plancks law. I also have the bandpass sensitivity function for various filters. I would like to calculate a colour index from this information, so I can compare it to an experimental result.
My proposed method is ... | It isn't a convolution, you are just integrating the product. I.e. if your (normalised) filter bandpass is $b(\lambda)$ and the spectral flux from the star is $f(\lambda)$, then the thing you are trying to calculate is a magnitude, which will be given by
$$ m_b = -2.5 \log_{10}\left[ \int b(\lambda) f(\lambda)\ d\lambd... | {
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Translation Transformation on the Invariant Interval (Spacetime) So we know that the invariant interval in a two-dimensional spacetime in special relativity is given by
$$ s = -c^2t^2 + x^2 = -c^{'2}t^{'2} + x^{'2}$$
So this scalar should hold true in all frames. I'm trying to show that it is true under a spatial tran... | If anyone else is interested, I figured it out.
Consider a 2D spacetime
$$\triangle s^2= -c^2(t_2 -t_1)^2 + (x_2 - x_1)^2 $$
A translation would mean $ x_1 \rightarrow x_1+x_0 $.
Now we go back to the unprimed frame and consider a 2-vector $\textbf{A}_i = (t_i,x_i) $. Let me also set c = 1.
To get the difference, $$\t... | {
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How to interpret the units of the dot or cross product of two vectors? Suppose I have two vectors $a=\left(1,2,3\right)$ and $b=\left(4,5,6\right)$, both in meters.
If I take their dot product with the algebraic definition, I get this:
$$a \cdot b = 1\mathrm m \cdot 4\mathrm m + 2\mathrm m \cdot 5\mathrm m + 3\mathrm m... | On dot product you get magnitude, in units of product of operands.
On cross product you get vectors with direction , in units of product of operands.
| {
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Wave intensity and superposition Let us say we have 2 point sources of sound. My question is how do we consider the intensity to vary according to position?
Let's say both have same amplitude, frequency and speed, just different phase.
Does intensity add up individually or do we calculate the net displacement in pressu... | At a point in space you have two waves arriving with amplitudes $A_1$ and $A_2$ and with wave 2 in advance of wave 1 by a phase angle of $\delta$.
I have chosen amplitudes just to be able to differentiate between the two waves.
It is not unreasonable that you add displacements if you think of one wave trying to disp... | {
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Physical meaning of $Tr(\rho ^2)$ If $\rho$ is the density matrix of a system then $Tr(\rho ^2) \leq 1$. If the equality holds the system is in a pure state and it is in a mixed state otherwise. But, what is the physical meaning of $Tr(\rho^2)$ ?
$Tr(\rho) = 1$ for all valid density matrices. This stems from the norm... | If the system is in a pure state, the density operator is just the projector onto that state, and so $\rho^2 = \rho$. Since, $\mathrm{tr}\,\rho=1$, in a pure state clearly $\mathrm{tr}\,\rho^2=1$.
Since probabilities must be non-negative, $\rho$ has only non-negative eigenvalues ($\rho$ is positive semidefinite). With... | {
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Airplane on a treadmill - Variant Thought Experiment This thought experiment is in a way related to the (in)famous airplane on a treadmill problem.
If you take a ball and place it on a treadmill, will the ball:
*
*Move backwards relative to the ground at the same speed as the treadmill (as if placing any other non-c... | I've thought about the steady state scenario, for a ball rolling without slipping on a horizontal treadmill surface.
The rotational velocity of the ball will be given by $\omega = v/r$, where $v$ is the velocity of the treadmill. However, the motion of the ball's centre of mass due to its rotation will be $u = \omega r... | {
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Does rest exist? I initially thought that the concept of rest depended on an inertial frame of reference. So for example, if the Earth and everything on it were the only things in the universe, and the Earth was floating with constant velocity, we would assume anything with the same velocity from an outsider's point of... | Whether you observer a magnetic force or an electric force depends on you frame of reference. This doesn't turn out to be a way to establish an absolute rest frame. See Michael Fowler's Modern Physics page from the University of Virginia
| {
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Doubt about Motional Emf In the derivation of a motional emf, we assume that as the conducting rod moves, the free electrons also move in the same direction as the conducting rod. However, the Tolman-Stewart Experiment showed that the motion of a conductor in one direction would lead to the movement of electrons in an ... | The electrons lag behind. They aren't left behind at rest nor do they move backwards. They still move in the same direction as the conductor, just more slowly.
In the reference frame of the conductor, the electrons move the opposite direction, but that's not what causes a motional EMF. What we care about is the moti... | {
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Quantum versus classical computation of the density of states If I consider for instance N non interacting particles in a box, I can compute the energy spectrum quantum mechanically, and thus the number of (quantum) microstates corresponding to a total energy between $E_0$ and $E_0 + \delta E$. In the limit of large qu... | Well there is a reason in this case of non-interacting particles- it is the so called "Thermodynamic limit". But I can answer this question without invoking the thermodynamic limit.
One very simple way to see this is using $h$. We know $h \ll 1$ so $P = h^{-N}$ for $N \gg 1$ will give you $P \gg 1$. And in some large l... | {
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What Color Are Black Holes Really? (Yes, a serious question) So I got into a mini-debate in science class today because I proposed that black holes aren't really black, they only look black because light can't reflect off them. But if you were to take the material that makes up that black hole and decrease it's density... | The material part of a black hole is (classically) compressed into a zero volume area, and almost all of the information of the matter that eventually became the black hole was dissipated away, so the original notion of your question is unanswerable.
There IS another sense in which we can think of your question, though... | {
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Are there star systems orbited by stars? I never really heard about such occurencies and now asked my self if this could be possible.
So could there be systems with a star (or black hole) that is so heavy that other less heavy stars are orbiting it?
I could imagine 2 things that would both be a no.
First, this isn't po... | There are binary stars (orbiting around their centre of mass) and there are stars orbiting around neutron stars or black holes (or rather, again, around the centre of mass of the system).
I don't think many stars would orbit a black hole, except... There is the black hole at the centre of most galaxies, including our o... | {
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How can 2 EM waves null each other at a point but continue to propagate? how can 2 EM waves (travelling in opposite directions) null each other at a point in space but continue to propagate beyond the point in space where they interact to null each other?
| You describe an impossible scenario.
If two electromagnetic waves travel in opposite directions and their electric fields point in opposite directions, then their magnetic fields point in the same direction.
If two electromagnetic waves travel in opposite directions and their magnetic fields point in opposite direction... | {
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A question about different intensity of a sound source in a room A few days ago, I entered a temple room with dimensions (which are only approximate) shown below in the diagram. There was a low humming sound of the exhaust fan which was at a height of approximately 6 feet from the ground in one corner of the room. Inte... | This is related to so called room modes. These are caused by standing waves forming between two walls or between the floor and ceiling. With a room that you described the frequencies where these waves form should be somewhere around 50-100Hz.
What this means in practice is that when standing in a position where such a ... | {
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What is the importance of vector potential not being unique? For a magnetic field we can have different solutions of its vector potential.
What is the physical aspect of this fact?
I mean, why the nature allows us not to have an unique vector potential of a field?
| There is no "physical aspect of this fact". The physical variables are the electric and the magnetic field, not the potentials. Introducing the potential is aesthetically and technically pleasing, but it is not necessary. A gauge symmetry is not a physical symmetry.
The reason you can have a non-unique potential is tha... | {
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Role of Cavity Resonators in continuous wavelength-electron paramagnetic resonance(CW-EPR) Why is it necessary to place the sample in a cavity resonator for obtaining EPR spectrum in CW-EPR? What role does a cavity resonator play in a CW-EPR spectrometer?
| The use of a resonator in X-band EPR is required to overcome the intrinsically low signal over noise ratio, that is of the order of 1ppm. Using a resonator, the oscillating magnetic field is amplified and the electric component is cancelled, avoiding dielectric losses.
To take advantage of a resonator, it must be prope... | {
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Ohm's law deviation In terms of superconductivities and diodes (I do not know anything else except these), Ohm's law deviate from a linear relation. I search many titles or tags for this but I did not understand properly how it becomes. I wonder somethings related with this.
*
*What is the basic of this deviation? ... | Ohms law states that the voltage and current will maintain a linear relationship under the pretenses that the material is kept at the same physical condition. This often falters at higher voltages/current because of the material increases in temperature resulting in micro changes to the way electrons move.
| {
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How Are Quantum Computers Able to Store Any Data at all? So if qubits can have more than two states, and according to this video,
https://www.youtube.com/watch?v=T2DXrs0OpHU
you don't know what you get until you actually "open the box", if its all randomness and probability,then how can it store anything?
Like, if you... | When you measure a qubit, you force it to be (and find out if it's) either all-On or all-Off. If it was all-On, flip it over. Now the qubit is definitely all-Off.
Use that process to zero as many qubits as you need, then run your computation.
Note that the process I described isn't creating neg-entropy (which would vi... | {
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Diffraction grating (finding number of emission lines) I came across a question on isaacphysics.org where youre given information about a diffraction grating, the spacing of the gaps and the colour and location (in degrees) of 8 different maxima, of four colours.
The question asks how many emission lines are evident fr... | If they are calling the angles listed on the chart emission lines then I see eight all together. Starting with violet at an angle of 32.7 followed by 35.5, 33.1, 35.2, 42.4, 46.6 and 35.4.
After reviewing I'm wondering now if it has more to do with the way the eight points blend together. 46.6 and 46.7 combine to make... | {
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how the form factor (stress - torque) is derived? I am working on an experiment of rheology and I need to calculate shear stress in order to calculate the viscosity. After some research I found that for the type of viscometer I will be using (cone-plate), the stress is calculated by dividing the torque given by the app... | In a cone-plate rheometer the plate is a disc, and the geometry means the strain rate $\dot{\gamma}$ is constant everywhere. The stress is given by:
$$ \tau = \mu\dot{\gamma} $$
Since at equilibrium the viscosity is constant, that means both variables on the right of the equation are constant so the stress is constant ... | {
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Why can't I use conservation of energy to find ratio of final velocities on different planets? The question is
An object of mass $m$ is allowed to slide down a frictionless ramp of angle $\theta$, and its speed at the bottom is recorded as v. If this same process was followed on a planet with twice the gravitational a... | The velocity does not double if the acceleration is doubled. The relevant SUVAT equation is:
$$ v^2 = u^2 + 2as $$
where in this case $u=0$ so we get:
$$ v = \sqrt{2as} $$
A doubling of acceleration means that the velocity would double if the travel time was kept constant. However in this case it's the travel distance ... | {
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Explanation of crystal formation in a Fitzroy's storm glass with the change in weather conditions I was recently reading about Admiral Robert FitzRoy's storm glass and how it was used to predict the weather conditions based on the formation of camphor crystals in a sealed glass tube containing distilled water, ethanol,... | Recently, as part of the debate on climate change, it has been proposed that cosmic rays have an influence on the nucleation of water particles that initiate the formation of clouds. It is possible that a similar effect aids initiation of camphor crystals. As clouds mean rain then perhaps this explains the clouding o... | {
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Methods for handling close approaches in $N$-body simulations In direct gravitational $N$-body simulations, what are the preferred methods for handling close approaches between bodies in order to preserve the accuracy of the evolution of the system?
| I assume you're talking about the numerical instabilities that arise from having an infinite potential at $r=0$. Here are three common solutions:
*
*Use a soft-core potential that behaves like $1/r$ except very close to $r=0$ where it levels off to a finite value. For example, $1/\sqrt{\epsilon+r^2}$ instead of $1/r... | {
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Can lasers lift objects? I have been fascinated by a very intriguing question - Can lasers push objects up?
I have done the below math to find out
Lets say we have a $1000~\text{mW}$ laser and we would like to lift an object of weight $100~\text{g}$.
By definition: $1~\text{W} = 1 \frac{~\text{J}}{~\text{s}}$
That mean... | Laser is stimulated emission of highly energetic photons. Fundamental use of laser is heating, propulsion is very distant aim which lasers can achieve.
Few kW rating lasers can actually lift the mass (very small values though) because incident energy beam has momentum associated with it. Your assumption is not correct... | {
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What is the moment of inertia really? Is moment of inertia or second moment of inertia, simply the resistance of a body to rotate it over an axis? What is radius of gyration? What if the axis is via the center of mass or somewhere different? can you give me please an overview of these issues with SIMPLE words, and with... | Basically, it is how hard it is to spin an object. If you know what regular inertia is, moment of inertia is the rotation equivalent of it.
Regular inertia is how hard it is to push an object, and only depends on its mass. For instance, picture an ice rink with a hockey puck. If it is very light, then it is very eas... | {
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How to determine the direction of arrow on Feynman diagram for $W$ boson line? I am somewhat confused. Looking through these slides (especially the 11th), which show Feynman diagrams involving $W$-bosons, I can't figure out which way to draw the arrow near the $W$ boson? How do people determine if it is to the "right" ... | In general in Feynman diagrams an incoming particle can be read as an outgoing antiparticle and W+ is the antiparticle of W- and vice verso. Quantum number conservation holds at the vertices. (charge , lepton number..)
The reaction studied in 11 is a change of a proton to a neutron through the weak interaction. The ch... | {
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Which coordinate is to be considered for the energy of simple pendulum? For an simple harmonic oscillator energy can be represented as in picture. Consider in particular picture (b) with the energy as a function of the coordinate $x$.
Consider now a simple pendulum. The coordinate $x$ in (b) is the coordinate of an ho... | The potential energy of the pendulum is $U(θ)=mgl(1-\cos θ)$. For small angles, $U(θ)≈mglθ^2\!/2$ and you get a harmonic oscillator. So $θ$ (or equivalently $lθ$) may be taken as the oscillating variable. However, since we are considering small angles, we may as well use $x=l\sin θ≈lθ$.
Addendum: You may wonder which a... | {
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Why doesn't a swing make a full revolution on a swingset in a park? I'm familiar with the concept of swinging of a swing in a park, but I'm confused why it doesn't it swing at a complete circle around the center bar?
| why it doesn't it swing fully ?
I think the question does point to the fact that swings which are usually available in the park does not provide free swinging , low amplitude of the swing and needs constant pushing.
All the above is related to energy dissipation of the initial potential energy provided to the swing- a... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
Deviation of free falling objects (Coriolis effect) using conservation of angular momentum I read this pdf on non inertial frame, in particular I have a question on the deviation of free falling object due to Coriolis effect.
Consider a ball let go from a tower at height $h$. The displacement due to Coriolis effect, ... | Considering conservation of angular momentum for the dropped ball, $\omega(z)$, the angular velocity of the ball as a function of z, is not constant for the dropped ball. $\omega(z) = {(R + h)^2 \over (R + z)^2} \omega_e$, where $\omega_e$ is the angular velocity of the earth. As the ball falls, $z$ decreases and its ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/249423",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
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