Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How is quantum teleportation possible when there's a continuum of possible states to send over? I'm trying to understand quantum teleportation and I was wondering if anyone could provide an intuition about it. I have seen the derivation but it still bugs me.
You start with an entangled pair of qbits in a Bell state: $$... | I do not know if this can be regarded as an answer. Anyway this is my picture to understand it.
If we check the computation procedure of the teleportation. Starting from ABC are initially in a product state:
(1) AB are entangled to $|00+11\rangle$ by a gate $U_{entangle}$.
(2) C is transformed to an unknown state $|a0+... | {
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Could the big bang singularity have been set into motion by a drop in the higgs field? Could the big bang have been set into motion by a drop in the energy level of the Higgs field?
| For the Big Bang to be set in motion by the breaking of the electroweak symmetry this requires that there was some stable state of the universe that existed at energies of around the electroweak symmetry breaking energy. While I suppose this is possible no-one I know considers it likely. It seems far more likely that a... | {
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If the wire of the secondary circut is thicker than that of the primary in a transformer, what type of transformer is this and why? There is this question in my physics book, and two teachers (a private teacher of a friend of mine and the school teacher) say that it's a step down transformer, while two other teachers s... | In UPS the wires from transformer connected to the 12V battery are thicker(E72332 AWM 1015 12AWG 600V.) Normally it is a step down transformer to charge 12V battery. In case of power failure it acts as a step up transformer to power the system. The wires are thinner (LL34978 18AWG 600V). Any comment. Thanks for your... | {
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What is the relationship between gravity and inertia? What is the relationship between Gravity and Inertia? Einstein told us that gravity and inertia are identical. And from the fact that two different masses fall at the same rate, I believe we can say that gravity and inertia are equal (That is, the inertia of a dro... | Gravity and inertia are not the same. Inertia is the “change” of the center of gravity. If gravity and inertia are the same, then there is no difference between a fast ball and a curve ball!
| {
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Why do cold chocolate bars crack randomly outside the crevasses when twisted? Why is it that an ordinary chocolate bar (e.g. 4 x 12 pieces) breaks easily where it is supposed to when the chocolate bar is at room temperature or higher but breaks "randomly" when the chocolate is cold? By breaking randomly I mean that it ... | Good question. Yes you would expect stress to concentrate, the material to yield at the minimum sections in the material. Our everyday experience with other materials tells us that. But chocolate seems to be different.
Although I don't know the answer, I'll take a stab at a hypothesis:
When you cool the bar below some ... | {
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When wood absorbs water, expands, and breaks stones, how is conservation of energy working? There is a traditional stone cutting method consisting of making a series of small holes in the stone, then inserting wood into the holes, and then adding water to the wood. When the wood expands, it will break the stone.
How i... | Dry wood consists of air-filled pores surrounded by cellulose fibers and lignin. As such it has extremely high internal surface area, all of which possesses a certain amount of surface energy, which has the ability to perform work. An easy way to get it to perform that work is by bringing the wood into contact with wat... | {
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Bogoliubov transformation for fermion (exercise in Piers Coleman) I am trying to solve the exercise 3.2 in Piers Coleman's Introduction to many body physics. It's about fermionic Bogoliubov transformation with only 2 fermion operators $a_{1}^{\dagger}$, $a_{2}^{\dagger}$, $a_{1}$, $a_{2}$.
The canonical transformation ... | Take $\psi=x \psi_{00}+w \psi_{01}+z\psi_{10}+y\psi_{11}$ then apply $c_1, c_2$ set equal zero. Then you get $w=z=0$ and one of $x,y$, and remember you need normalization condition to determine the last one.
| {
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Why does the kinetic energy of a photo-electron vary? Provided it is above the threshold frequency of the metal, when electromagnetic radiation is shone onto a metals surface photo-electrons are emitted. This occurs because 1 photon is absorbed by 1 electron giving it enough energy to be ejected.
We know that the ener... | There are a couple of reasons for this. First and foremost, the electrons are ejected from the surface of the metal in random directions. When you measure things like the "stopping potential" you're only sensitive to motion in directions that would carry the photo-electron to the anode. Because you're only sensitive to... | {
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What can be the simplest way to find the thickness of a soap bubble? Is it possible to measure the thickness of a soap bubble without using any sophisticated instruments such that anyone can do it?
| I actually did this as an experiment. So you need a scale, a ruler, a paper towel, and a bubble wand. Blow a large bubble to catch it on the bubble wand. Measure it using the ruler. Now set the bubble aside and measure the paper towel rolled up in a ball. Now try to fling the bubble so that it floats downward on the p... | {
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Kinetic energy when observer is moving and object is stationary I know kinetic energy is due to motion of an object. But what if, I, the observer of an object is moving and that object appears to be moving for me, then which one has kinetic energy. is it me or that object?I mean the object doesn't actually move but it ... | Kinetic energy depends on the reference frame of an observer. Therefore, kinetic energy is not a property of an object only: If you are moving along with an object and you define yourself as reference, then the kinetic energy of the object is zero (in this special reference frame).
The English Wikipedia article on Kine... | {
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How to determine the wavefront In case of symmetry around a point we can consider a sphere on whose surface points the waves are equidistant. But how to determine the wavefront around a linear source or a cylinder or triangle or of these or of an complex figure. Should I get the symmetry around every every point and in... | For an alternate process: According to Huygens Principle the wavefront at time $t$ would be the envelope (or tangent surface) of all the Huygens wavelets originating from each point on the surface of the 'complex figure'. The radius of the wavelets would be $ct$.
For an approximate graphical solution, you can draw a ... | {
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Is the Rindler vacuum invariant under Poincare symmetries? More generally, when we quantize fields in the Rindler space and obtain the Fock space of Rindler particles - does that carry a unitary representation of the Poincare symmetries? It should not, because Rindler spacetime is not invariant under global translation... | It depends on the requirements you impose on such a representation. So we assume that there is a strongly continuous unitary representation ${\cal P} \ni p \mapsto U_p$ of the orthochronous proper Poincaré group working on the Fock space constructed upon the Rindler vacuum $\Omega_R$ exploiting the standard static ... | {
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Fictitious forces and internal forces Say I have two blocks on top of each other and the bottom one is accelerated (relative to the ground) with a horizontal acceleration $a$. I would like to understand what the maximum acceleration $a_{max}$ can be such that the top body does not move relative to the bottom one.
If ... | In the ground frame:
The upper block experiences Friction in the direction of motion of the lower block. This is the only force which acts on the upper block.
so $m a_{max} = m g \mu$ where a is the acceleration of the upper block equal to acceleration of lower block.
PS- The forces on the lower block will be the ... | {
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What is a "decade" as a unit of measure (ex. a decade of the EM spectrum)? Reading through papers and online sources about radio galaxies, I kept stumbling across a term--a "decade" of the electromagnetic spectrum. Radio galaxy emission encompasses "11 decades of the EM spectrum". Or this quote from NASA:
Astronomers ... | From 10Hz to 100Hz is a decade (on a logarithmic axis this is $10^2$ to $10^3$).
| {
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Reparameterization and conformal transformation in SYK I have a simple question about SYK model.
For SYK in the IR limit, the Schwinger-Dyson equations have some so called rearamerization invariance
$$\psi_i(\tau)\rightarrow \psi_i(f(\tau))=f'(\tau)^{-\Delta}\psi_i(\tau)$$
I want to whether this transformation is relat... | The SYK model is a (0,1)-dim model. This means that because there is only a time dimension that there is no notion of spin. In one dimension there is also no notion of an angle so that every smooth transformation is conformal (Diff$(\mathbb{R})\cong$ Conf$(\mathbb{R})$). In the IR the solution to the Swinger-Dyson equa... | {
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How do charged particles interact with each other? As we know, charged particles have polarity and like charges repel each other and unlike charges attract each other, and we have Coulomb's law to find that force. But how does it work? Does it work like gravity, like when two like particles are apart do they still repe... | We have frameworks in physics where questions can be answered: the classical electrodynamics framework, the quantum framework, the special and general relativity framework etc. Frameworks differ in the variable's range of validity, but blend smoothly in the overlap region.
In current day physics particle is a name give... | {
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Newton's 3rd law of motion, related to Earth's gravity When a stone falls from a certain height above the Earth's surface, it accelerates towards the center of Earth under the influence of Earth's gravity. According to Newton's 3rd law, the stone also exerts an equal force on the Earth, but towards itself. So the Earth... | Consider the Earth and the falling stone as one system with no external forces acting on the system.
There are two internal forces which are the force on the Earth due to the gravitational attraction of the stone and the force on the stone due to the gravitational attraction of the Earth.
These two forces are a Newto... | {
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How can 2D flat holograms be considered holograms? When I think of a hologram I imagine this
where you shine a beam of laser light onto a holographic film to reproduce an object beam and see a virtual image of an object that can be viewed from many angles.
I don't understand how flat holograms, like that seen on mone... | The term "hologram" is used in a lot of ways. There are "3D" holograms, "2D" holograms, "E-BEAM" holograms, all of which use diffraction to produce an image and/or color. The term has been stretched in recent years to include anything that gives the impression of a 3D image.
So, don't worry about it. The diffracti... | {
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Derivative of proper time w.r.t. time? On page 86 of Theoretical Minimum (part 3 on special relativity) by Susskind, he writes:
$$\frac{d\tau}{dt}=\sqrt{1-v^2}$$
Where $v$ is the velocity of a moving reference frame relative to the restframe (which is the frame of coordinates $t,x$). He derives this from the equation (... | I'm not sure $\tau = \sqrt{t^2 + x^2}$ is the relation you're looking for, since you would be looking for $\Delta\tau$ rather than $\tau$. In any case, where his relation comes from is the Minkowski metric, which in one space dimension can be expressed $ds^2 = -c^2dt^2 + dx^2$ where $ds$ is the proper time, where $d\ta... | {
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Position when potential energy and kinetic energy of a spring are equal
I've been given that there is a spring holding a $.25kg$ mass where $k=10N/m$ and is held at $40cm$ and then let go. I've found that the max velocity is $2.53m/s$ and that when the spring is at $20cm$ the velocity is $2.19m/s$
What I'm having a h... | You know that energy is always conserved so at the point where $U$ and $K$ are equal a.k.a $$U = K$$, you also know that $$U + K = \text{Total Energy}$$. Now you have two variables two equations and I'll leave the rest for you to solve :D Good Luck! Does this help?
| {
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Why do turkey bacon slices form bubbles in the same places? Often, turkey bacon forms large bubbles when cooking. It's simply a fact of how it cooks. More interestingly however, I was making turkey bacon this morning when I noticed that all of the slices formed bubbles in nearly exactly the same place along the slice, ... | Maybe it's a trick of perspective, but it seems to me that it is an effect due to the fact that the bacon is bulging outwards in some parts (the pink-ish ones), and therefore the fat/water mixture that comes out because of the heat slides downwards, and then partly evaporates forming bubbles.
The bulging may be due to... | {
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Velocity of light in Galilean transformation What is the velocity of light in Galilean transformation? Is it infinity?
| Galilean transformations are a low speed approximation and therefore they are not a valid description of the physics when speeds approach the speed of light. Since light travels at the speed of light (obviously :-) that means it cannot be described by Galilean transformations. This is true as long as the speed of light... | {
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Proof for uniqueness of transformation between relativistic frames My understanding of the Lorentz transformation is that to ensure that laws of physics remain frame-independent, a transformation was devised, which we call today by the name Lorentz Transformation.
But how do we know that there does not exist any other ... | Assuming
*
*The Principle of Relativity (that the laws of physics are the same in all inertial frames),
*The isotropy and homogeneity of space,
*The transformations form a group, and
*Respect causality,
gives the Lorentz transformations with a free parameter C which specifies a maximum speed. If C is infini... | {
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Concept regarding Venturi Tube-Bernoulli application I was recently studying applications of Bernoulli Equation and came across the Venturi tube. This is diagram I have used to analyse the venturimeter. I understand how we obtain the first equation using bernoulli theorem which is
$$P_1 - P_2 =(1/2)ρ(v_2^2 - v_1^2) ... |
Lets say the atmospheric pressure at the top of each tube is . Now since the fluid in the two VERTICAL tubes are at rest and not moving, their velocities are 0. Hence, if I proceeded by applying Bernoulli equation.
1+ρ(21)/2=ρ(ℎ1)+ (3)
and
2+ρ(22)/2=ρ(ℎ2)+ (4)
3 and 4 are incorrect. Bernoulli theorem goes... | {
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Paradox in special relativity involving capacitor In the laboratory reference frame (LRF), a horizontally moving (with constant speed) flat capacitor would have a different size of plates therefore resulting in different capacity $C'$, namely
$$
C' = \frac{1}{\gamma}C,
$$
where C is a capacity in its own reference fram... |
So if capasitor is closed on a resistor in his reference frame then for me in LRF would be seen like there was more heat produced on a resistor since $Q=W'$ no matter what current was. So, wouldn't it be the way I distinguish one intertial reference frame from another?
In the frame where the capacitor with resistor a... | {
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The photon propagator term in Peskin & Schroeder Eq. 6.38 In Peskin and Shcroeder, when calculating the one-loop vertex correction, the line above Eq. (6.38) reads
$$ \rightarrow \int \frac{d^4 k}{(2\pi)^4} \frac{-ig_{\nu\rho}}{(k-p)^2 + iϵ} \bar{u}(p') (-ie\gamma^\nu) \frac{i(\displaystyle{\not} k' + m)}{k'^2 - m^2 +... | I found the answer. The original expression for all vertex corrections is $-ie\Gamma^\mu$. The expression on the left should hence be proportional to $-ie\delta\Gamma^\mu$ and the $-ie$ term on the left is removed with the same term from the photon propagator on the right.
| {
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Space and spin symmetry in light baryons In Particle Physics by Martin and Shaw in Ch.6 they show how the baryon supermultiplets are built from the assumption that the space and spin wave functions are symmetrical, so eg. $uud$ has spins up,up,down so that under exchange of the $u$ quarks the wavefunction doesn't chang... | Chapter 6 of Martin & Shaw does seem to say that the $aa$ quark pair in an $aab$ baryon must be in a spin-1 state, e.g. that the spin-up proton wave function is $u{\uparrow}\;u{\uparrow}\;d{\downarrow}$. You are right to be confused by this, since the actual proton flavour-spin wave function is
$$
\frac{1}{\sqrt{18}}(... | {
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Can all waves interfere with each other? What conditions must two waves have such that they interfere? Do they need to have the same frequency or amplitude? Should they pass through a given space at the same time? Should they have the same sources?
| For two waves to interfere (by which I mean that they produce a stable interference pattern on a screen) they must be coherent i.e., they must maintain a constant phase difference and have same frequency.
However, the explanation above is naive because the real situation is a bit more complicated due to the fact that ... | {
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How does holding a glass prevent it from falling? When I hold a glass of water,
$\hspace{1.5cm}$,
I am applying a force horizontally, but its weight acts downwards. Should it not fall?
How do you describe the equilibrium?
| In addition to the answer of @The Photon, consider that for many glasses, the sides of the glass taper inward towards the bottom of the glass.
For such a glass, friction is not needed. Simply holding your fingers a fixed distance apart will exert a force on the wall of the glass with an upward component, stopping the ... | {
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Projectile motion Need hint
stone is dropped from a cliff of height h at the same moment as another stone is thrown vertically upward from the bottom of the cliff with an initial velocity u. The stones are at the same horizontal level after a time t. Show the condition necessary for the stones to have equal speeds at ... | You could try thinking in terms of kinetic and potential energy. If they have the same speed at a given level that means that their potential energies are equal and their kinetic energies are equal too. Think of initial conditions that would satisfy this at some point.
| {
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Why is magnetic field zero for open circuit and electric field zero for short circuit? I read this statement in a book for a simple circuit (1 resistor connected to a voltage source). If we short out the resistor, the E field is said to be zero and if the circuit is broken (open circuit), the magnetic field is said to ... | The comment below is restricted to stationary or very low frequency circuits where any electric field is localized within a resistive wire via Ohm's law or between capacitor plates, while the magnetic field can be found only in a coil.
The short circuit case is easier to visualize. Assuming an ideal short such that it... | {
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In pair production does gamma rays actually strike a nucleus? I think the quetion is vagueless.I simply want to ask it is often printed that there must be a heavy nucleus present for pair production.It is answered that its needed to make electron and positron existable after prodution.Major question in that gamma rays... | No, the gamma ray doesn't strike the nucleus. You need something around to make it possible to conserve momentum and energy and to obey the relationship between them for every particle. In sum, there is no way to make two massive objects, like the electron and positron, move that will make the pair of them act like the... | {
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Lorentz transformation of polarisation vector I know that the polarisation vector is not lorentz invariant. But how exactly can I derive the lorentz boosted polarisation vector for a spin-1 particle (say photon)?
What about spin-2 particle's polarisation?
| The polarization properties of masselss particles with any spin (and hence in particular for spin 2) are discussed in detail in Weinberg's papers
S. Weinberg,
Feynman rules for any spin II. Massless particles,
Phys. Rev. 134 (1964), B882--B896.
S. Weinberg,
Feynman rules for any spin III,
Phys. Rev. 181 (1969), 1893--1... | {
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Question on Eigenstate thermalization hypothesis My understanding of a system that satisfies the eigenstate thermalization hypothesis (ETH) is the following. If we consider a local operator, $O_i$ we can relate its expectation value with respect to some eigenstate, $|\epsilon\rangle$ of the Hamiltonian, $H$ to a therma... | @DominicElse answer in the comment was great. Just a bit of add up:
Consider $DoS(\epsilon)$ as the density of state for your system.
If you chose an eigenstate in part of the spectrum where $dDoS(\epsilon)/d\epsilon > 0$, the temperature associated with that eigenstate is positive. Otherwise, in the region with a nega... | {
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Does a gap closing mean an occurrence of a quantum phase transition? If we have observed a closing of the excitation gap in the energy spectrum of a certain model, can we safely conclude that a quantum phase transition occurs?
| No. For instance, you could have just touched a phase boundary and returned into the same phase. Or you could have a short-range correlated system (such as a Toric Code wavefunction) which can occur both as a ground state of a gapped and a gapless Hamiltonian (see e.g. https://arxiv.org/abs/1111.5817), and interpolate... | {
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Is it possible to make a laser by sending sunlight through an optical apparatus? 1) Is it possible to create a laser from focused sun light by separating and using only one wavelength of light as a laser and using the proper mechanism to polarize it and make it coherent? ... | If you're asking about the possibility of making coherent light by filtering incoherent, broad-spectrum sunlight, the answer is "no". You could filter the light down to a very narrow wavelength band by throwing away all the other wavelengths, and end up with nearly monochromatic light. That leaves about 1/10000 of the... | {
"language": "en",
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Gauge invariance lost using Maxwell's equations I read a paper on superconductivity, and the calculations use Newton's second law and the Maxwell-Faraday law to write the "free electron current" as
$$
\textbf{J}_e=-\frac{ne^2}{m_e}\textbf{A}
$$
where $\textbf{A}$ is the vector potential ($\textbf{B}=\textbf{rot A}$). A... | You have lost gauge invariance because a specific gauge has been chosen, the Coulomb gauge $\nabla \cdot {\bf A} = 0$.
Gauge invariance of a theory implies some redundancy in how certain fields in the theory are defined, in that the physics is unchanged by different definitions of these fields. In classical electrom... | {
"language": "en",
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Are materials which are bad at conducting heat always bad at conducting electricity also? When defining a material's conductivity, we usually consider its conductivity of heat and conductivity of electricity separately. However, I realize that materials like metal conduct both heat and electricity well. In contrast, ma... | Diamond is a good thermal conductor but a poor electrical conductor.
Diamond at Wikipedia
| {
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In Atwood machine, does the tension of the rope do work? It seems in all Atwood machine exercises I can find, no one ever takes into account the tension of the rope when solving with conservation of energy. Why is this? Shouldn't the tension be a non-conservative force contributing to the net work?
| Depends on what particular subsystem you're looking at. The tension does work on each of the blocks, but since it's an internal force, it does no work on the Atwood machine as a whole.
| {
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Is Yellow a monochromatic light? I have got a serious doubt.
I have read,
"yellow light from a low pressure sodium vapour is monochromatic"
How can it be monochromatic when yellow light is a combination of red and green primary colours?
| The key here is that there are a basically infinite number of different mixings of photons of different wavelengths that will be perceived as yellow by our eyes or a camera. This is because our eyes are not spectrometers, and use a relatively crude three-color system (red, green, and blue-sensitive cone cells) to ident... | {
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Human body water storage effects on weather patterns There are 7.614 billion humans and counting. On average a human being consists of 60% water. With that water being locked away from natural circulation for an average of 80 years. Are there any adverse effects this could have on global weather patterns?
| Humans are not locking up water. You can use mass conservation and Kirchoff's first law (where you replace charge with water) to see why: if water was accumulating in human bodies, they would tend to get bigger. Over the span of a year a human consumes somewhere around half a ton of food and water, yet our weight usual... | {
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What is the quotient of two quantum operators? It's probably useful to explain the context, which led me to this question. We were asked the following question:
By writing ${L}^2 = \sum_{ijklm}\epsilon_{ijk}{x}_j{p}_k\epsilon_{ilm}{x}_l{p}_m$ show that: $$p^2 = \frac{L^2}{r^2}+\frac{1}{r^2}\left\{(\textbf{r}\cdot \text... | Yeah, it's a subtle issue. You can't just divide two non-commuting operators - you need to specify whether you're left-multiplying or right-multiplying the numerator by the reciprocal of the denominator. I would avoid ever using "division" notation and only multiply operators and their reciprocals, for clarity. You can... | {
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Could we construct an experiment to measure the speed of light greater than c? As I understood we were not able but then i read John Rennie's question and answer here:
Does light really travel more slowly near a massive body?
And got me a little bit curious.
He says:
We can extend our analysis to find the speed of lig... | You don't need to do a new experiment in order to see the coordinate velocity of light be different from $c$. A coordinate velocity can be any number you like, simply by your choice of coordinates. Pick any experiment that measures $c$, change coordinates, and express the speed of light in those new coordinates. For al... | {
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Effective action: Cancellation of odd powers (Altland & Simons) Consider a system of interacting electrons. Using the path integral formalism, we introduce the Hubbard Stratonovich transformation to decouple the interaction in the density channel. Then, we integrate out the fermionic degrees of freedom and extremize th... | I think the reason is rooted in the interpretation of the fluctuation around mean-field.
Back to the Hubbard-Stratonovich transformation, if we substitute $\phi_q$ with $-\phi_q$, the physics should not change. From another perspective of view, we can say the positive flucuation around the mean-field $\hat \phi=0$ is e... | {
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What exactly is deterministic in Schrödinger's equation? I have read the following on Wikipedia but I can't understand it:
In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic. However, the relationship between a system's wave funct... | Mathematically speaking, the Schrodinger equation is a type of linear PDE known as the wave equation. The wave equation, which you may be familiar with from other studies of PDEs, is deterministic, because it evolves in the sense that if you know the initial conditions at an initial time, you know exactly what the wav... | {
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Are there any electric fields associated to the scalar fields in quantum field theory? We know that electric field due to stationary charges is given by gradient of phi.
In quantum field theory the scalar fields associated with bosons doesn't have any electric fields but while dealing with em fields we get vector E as ... | I don't quite understand your question, perhaps you can clarify. Also, the boson mediating the electromagnetic interaction is a spin-1 particle, not a scalar which would be spin-0.
First of all, a electric field and a field in quantum field theory are not the same thing. The former is a measurable quantity for instan... | {
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What is the cosmological redshift drift effect? What is the redshift drift effect in cosmology?
What are the necessary cosmological conditions for there to be a measurable redshift drift effect?
| Redshift drift is the name given to the effect whereby as the universe expands, the redshift of an object will change with time. i.e. It will drift.
A galaxy at a fixed co-moving distance will have a redshift that changes with time and the first and second time derivatives of the redshift may prove to be valuable probe... | {
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How the current of a wire pass so quickly if it has that less drift velocity of electrons.? The rate of flow of electrons is known as current. When we switch on a light bulb, then it lights immediately. If drift velocity of electrons is so small--at least on the supply on 220V (supply of my home)--then why does the lig... | The conduction electrons that are already in the wire are moved by the electro-magnetic wave that can propagate once the circuit is closed.
With a 220V ac supply, actually the electrons are moving back and forwards, their net drift velocity is zero.
There are many other analogies to this. Sound moves in the air at 300m... | {
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Can there be general relativity without special relativity? Can General Relativity be correct if Special Relativity is incorrect?
| From a theoretical point of view, one may argue that it depends on how one defines the words GR & SR, and how abstract one wants to be. For starters one may generalize to other than 4 spacetime dimensions. Moreover, the local spacetime model could in principle be different from Minkowski spacetime. Instead of Einstein ... | {
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Comparing work in thermodynamics with work done in mechanics Let us the consider a gas as our system enclosed in a cylinder with piston.
1st case(Expansion of gas):
Here force on the piston is exerted by the gas in upward direction and during expansion piston moves up. So, the work done here is positive(force and displ... | Normally both results are the same for work but it is defined in another way as you wrote: $dw = -pdV$ so the work you can get by integration.
| {
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Rotational mechanics theory This is a statement given in my text book:
"The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass. These axis need not be stationary." ... | If it does not interact with other objects, a rigid body can be reduced to its center of mass. Then you can describe the motion of this point as the motion around an axis (in case of straight travel it's an infinitely far away axis). If for some reason you need to know more about what the constituent masses of the rigi... | {
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How to understand $L_4$ and $L_5$ Lagrange points gravity balance? It's relative easy to understand gravity balance of Lagrange points $L_1$, $L_2$ and $L_3$. But I am having a hard time to understand how a body would be "kind of" balanced out on Lagrange points $L_4$ and $L_5$.
| a small body occupying L4 or L5 point around a planet completes the full circle both around the planet and the star while the planet itself completes the full circle around the star in the same time span. By the way, L4 and L5 are the only stable Lagrange points, if there is a small perturbation on a body in L4 or L5 p... | {
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Group representations and active/passive transformations Suppose we are in Euclidean 3-space with coordinates $x$ and a scalar function $\phi(x)$ defined on it, and consider the group of rotations $SO(3)$ for simplicity. Take a rotation matrix $R \in SO(3)$; then the usual explanation for the difference between active ... | I think an "active" transformation is a left action, and a "passive" transformation is a right action.
Active transformation:
$$(R_1 \cdot (R_2 \cdot \phi)) (x) = (R_2 \cdot \phi) (R_1^{-1} x) = \phi(R_2^{-1} R_1^{-1} x) = ((R_1 R_2) \cdot \phi) (x)$$
Passive transformation:
$$(R_1 \cdot (R_2 \cdot \phi)) (x) = (R_2 \c... | {
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Imagine a steel bar floating in space. Assuming the bar wouldn't break or bend, if I shoot a bullet at one end, would it rotate, fly away, or both? Is there a formula to calculate both the translational and rotational velocity? Does the bar always bend, and if so is there a formula on how it bends (maybe related to the... |
Imagine a steel bar floating in space.
With you so far.
Assuming the bar wouldn't break or bend, if I shoot a bullet at one end
What do you mean "one end"? Be specific. Precisely describe the bar and where the bullet hits it.
would it rotate, fly away, or both?
That depends entirely on where the bullet hits it. I... | {
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How the velocity of the air is slowing down in different distances from a fan? Is it determined completely by the air pressure and the temperature? Do I need to take into account also the geometry of the "air cone" of the fan or is it determined by the speed of the air when it leaves the fan?
Practically I would like t... | A general approach of finding a required CFM based on a desired air speed at a given distance from a fan comes down to knowing the shape of the cone, which is a function of the fan construction. Presumably, you can get this information from a manufacturer or from some other sources.
If you know the shape of the cone, y... | {
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Active and passive pulling - is there a physical difference? Let's suppose we have two people Alice and Bob in a vacuum. The are connected by a rope.
At first, Alice pulls Bob with force $F$ and Bob only clings to the rope. Afterwards, the experiment is repeated with Bob pulling with force $F$ and Alice only clinging t... | If my understanding of this experiment is correct, a person A that pulls the rope remains stationary and a person B, that clings to the rope, moves.
We should assume that person A holds on to something or relies on the static friction - otherwise, he or she will move as well.
Person B will accelerate and gain some kin... | {
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EM Plane wave, the changing electric field is in all directions right? I just want to confirm this, because this type of diagram seems pretty popular.
The electric field and magnetic field actually surround in all directions orthogonal to x axis, right? It is not just 2d pointing only in the y direction and z direction... | The wave in your figure is linearly polarized with E along the $\hat{y}$ axis and B along the $\hat{z}$ axis. That's built into the wave when it was created, and it stays that way. You won't find any E along $\hat{z}$ or B along $\hat{y}$ for that wave.
Some other wave might be different. If could be linearly pola... | {
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How are real particles created? The textbooks about quantum field theory I have seen so far say
that all talk in popular science literature
about particles being created spontaneously out of
vacuum is wrong. Instead, according to QFT those virtual particles are
unobservable and are just
a mathematical picture of the pe... | The difference between real and virtual particles in QFT has to do with whether the particles are represented by an internal line or whether they have at least one free end.
For real particles, their momenta and energy need to be considered in the overall conservation of energy and momentum. This is represented, ad-ho... | {
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AP physics 1 rotation problem could someone help me with this problem?
the correct answers are a and d. one issue i have with it is that i just don't understand what the problem is asking. like what spool? what table? i tried making some sense of the question and the answers, but i can only see d moving the wheel clo... | The question is worded poorly and the diagram is not very helpful, the setup looks like this:
[Source]
Now imagine wrapping a rope around the axle like this:
[Source]
Now imagine those arrow represent pulling the free end of the rope. Hopefully your intuition can get you the rest of the way there.
Edit:
The second i... | {
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Electric flux through finite width/ infinitely long plane due to a point charge The question is as follows:
Consider a point charge Q placed at $(0,h,0)$ (Cartesian coordinates). Find the flux in an area formed by $y=0$, $z\leq0$, $x\geq l$ and $x\leq a$ $( l\leq x\leq a )$.
I tried this by considering the two extreme ... | If Q is a point charge in empty space then the flux through a surface $\:S\:$ is
\begin{equation}
\Phi=\dfrac{\Theta}{4\pi}\dfrac{Q}{\epsilon_{0}}
\tag{01}
\end{equation}
where $\:\Theta\:$ is the solid angle(*) by which the point Q "sees" the surface $\:S$.
Now, if $\:0=\ell \leq a \:$ and the strip has a finite heigh... | {
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Special Relativity Muon Decay When talking about how muons reach earth even though their half-life is very short the explanation of time dilation is given. From earth's frame of reference, the Muon's clock is "slowed down" so is has longer to live and keep racing at it's speed, I think I understand this.
However, will... | You have to be consistent in each reference frame you consider.
1. In the earth frame the muon proper time runs slower, but the distance it covers is not length-contracted. The length contraction refers to the muon itself, in principle the muon dimension in the direction of motion is contracted, but that is irrelevant ... | {
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A gravitational field is path independent. Why does a rocket not fly in serpentine lines? in theory a gravitational field is path independent, a gravitational field is a gradient field and so conservative. why doesn't a rocket fly in serpentine lines to exit the gravitational field of the moon, as said the gravitationa... | What you say would be true if rockets were held up by, say, a very long string. Since real rockets don’t have such a string available they have to do something much less efficient: fight the gravitational force by pushing fuel downward. A rocket needs to exert energy just to stay in the same place, let alone move in a ... | {
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Is this derivation for schwarzschild radius for a black hole of mass $M$ correct? Consider a body of mass $M$.
We know that light can’t escape a black hole.
Speed of light being the highest possible could be set as the escape velocity.(??)
Then
$$\text{Escape velocity}^2=(2GM/r)$$
Solving for $r$ we get
$$r=2GM/v^2$$
S... | If you assume that a sufficiently compact object does have an event horizon, then the relationship has to be of the form
$$r=\alpha GM/c^2,$$
where $\alpha$ is a unitless constant. This is because there is no other way to combine the mass with the universal constants $G$ and $c$ in order to get units of distance. The f... | {
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Where do the particle and antiparticle wavefunctions originate from in the Klein Gordon equation? In my textbook (Sakurai) it is given that
$$\left(D_\mu D^\mu+m^2\right)\Psi(\mathbf{x},t)=0$$
where $D_\mu=\partial_\mu+ieA_\mu$ is the covariant derivative.
It states that since it is a second order differntial equation... | The two equations you wrote at the bottom of are just definitions of $\phi$ and $\chi$. They have no physical interpretation at this point in Sakurai's argument. The physical interpretation comes later when he rewrites the Klein-Gordon 'probability' density in terms of them (see 8.1.20)
There is a standard way to turn ... | {
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Where does the work come from if tidal forces are stretching elastic objects? An elastic object e.g. a rubber band will be stretched
*
*in accelerated expanding FRW-spacetime
*during radial free fall in Schwarzschild spacetime
by tidal forces due to Ricci- and Weyl-curvature resp., until equilibrium with its intern... | In the case of a rubberband falling into a Schwarzschild blackhole, the work comes from the increasing differential in binding energy between the two ends of the string. This is completely analaguous to the Newtonian case. Binding energy is well defined due to the existence of a time translation symmetry (i.e. timelike... | {
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Can an electromagnetically induced dipole be explained with photon interactions? An incident electromagnetic wave will cause a dipole moment in the medium it passes through, displacing positive and negative charges in accordance with the EM field. How much of this interaction (if any) can be explained via the particle ... | One of the main reasons we declare that light (and matter) carry both wave and particle properties is because in some situations, we observed that light behaved as a wave, and in others, we observed that it behaved as a particle. The resolution of this was to declare that it must be something that is both, and hence th... | {
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What is cosmic ray albedo neutron decay (CRAND)? I need a small description of what is cosmic ray albedo neutron decay (CRAND), where it comes from and what effects they have?
| I've never heard the specific acronym CRAND.
However, cosmic rays which reach Earth's ground level lose energy by, among other processes, spallation on the heavy nuclei in the soil and rock. Some of these spallation neutrons will leak back out of the surface of the ground, having partially thermalized$^1$.
These neutr... | {
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Reference Request: Basis-independent formulation of tensor networks I could not find any references for a basis-independent formulation of tensor networks: All papers I have found use pretty much (explicitly or implicitly) the canonical computational basis by defining tensors as lists of complex numbers.
While this is ... | https://arxiv.org/abs/1210.7710 develops a framework of MPS modulo their gauge degree of freedom (which includes basis choice) as a fibre bundle.
| {
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How can electrons spin if they have no volume? My understanding of electrons is that they have no volume, eg they are point particles. If this is true, how can a point spin?
| If you ignore the location/velocity of an electron, each electron carries one bit (or, more precisely, q-bit) of information: whether it is spin up or spin down with respect to a chosen axis. This information is encoded in a vector with two components and complex components. That is, the "spin state" of the electron ca... | {
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Is there anything like a "polarizer rejection spectrum"? In general, if you shine some EM radiation through an arbitrary polarizer which works for visible light, it's not guaranteed to polarize your EM radiation. E.g. you can take polarizing sunglasses and shine unpolarized X rays or radio waves through it, and this ra... | The quantity I was interested in is called polarization extinction ratio. See the usage of this term e.g. in the description of this wire grid polarizer, like in the following graph taken from that page's Graphs section:
| {
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From "Matrix" form to "Component" (tensor) form Given
$\omega=-\eta\omega^T\eta^{-1}=-\eta\omega^T\eta$,
where $\eta$ is the usual Minkowski metric.
Is the following logic correct?:
$$
{\omega^{~\mu}}_{\nu}= -{\eta_{\varepsilon\nu}}{\left(\omega^T\right)_{\sigma}}^{~\varepsilon}~\eta^{~\mu\sigma}= -{\left(\omega^T\r... | No, as you can see your indices don't match up. You must have an equation of the form $A^\mu{}_\nu = B^\mu{}_\nu$.
The correct way to do it is
$$
\omega^\mu{}_\nu = - \eta^{\mu\rho} ( \omega^T)_\rho{}^\sigma \eta_{\sigma\nu}
$$
Note the way the indices are always adjacent since this is matrix multiplication. Next, we... | {
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Bose-Einstein Condensation in lower dimensions Bose-Einstein condensation occurs at 3 dimensions. However, it is not possible to happen at 1 or 2 dimensions; in fact I am able to prove this myself. What is the explanation for this?
| For simplicity, I will consider non-interacting gases. The idea here is that there is a bound on the density of excited states in 3 and higher dimensions, whereas no such bound exists in 1 and 2 dimensions. This bound enforces a condensation of the gas particles into the ground state for 3 and higher dimensions but not... | {
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Why is the relativistic adiabatic index 4/3? I was told that in the relativistic limit the adiabatic index approaches 4/3 for a monoatomic gas instead of 5/3 in the non-relativistic case. I was told this occurs due to a reduction in degree of freedom but this may be incomplete and does not quite explain the new express... | I don't know what a reduction in degrees of freedom is in this case. But statistical physics has well known methods to compute properties of ideal gases. Ultra-relativistic particles dispersion relation has the form
$$
\varepsilon(\vec{p}) = c|\vec{p}|
$$
Correspondent partition function of a monatomic classical gas is... | {
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Reason for body attached to a string being in free fall? This is a question I found in a book:
A string is wrapped around a uniform cylinder as shown in diagram. When cylinder is released string unwraps without any slipping and the cylinder comes down.
I assumed that an equation $T - mg = ma$ could be formulated an... | Your equation $T-mg=ma$ seems right to me. The reason the tension does not do any work is not because $T=0$, but rather because the point where $T$ acts does not move.
This is simply because of the "no slipping" condition : the point of contact of the cylinder has speed 0. Hence, the work produced by $T$ is simply $W =... | {
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If the 3-Body force problem hasn't been solved, how do rocket scientists plan orbits of spacecraft? What methods would they use to predict what would happen in a situation when a probe is being acted upon by the gravity of two stars, say?
| The three body problem isn’t “solved” in the sense that there is no known closed form solution that works for any general initial conditions.
However, when you have two massive bodies and one that is considerably lighter, you can estimate the trajectory with almost any degree of accuracy. Furthermore, numerical techniq... | {
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Statistical mechanics and thermal averages in $\mu-$space and $\Gamma-$space What is the relation between the thermal averages in $\mu-$space and $\Gamma-$space of a system having $f$ degrees of freedom in statistical mechanics? For a system with $N$ particles (and having $n=3N$ degrees of freedom) the thermal average ... | The precise relation is given by
$f(q,p,t)=\int \rho(q^N,p^N,t)\delta(q-Q)\delta(p-P)dq^Ndp^N$,
where $Q$ is the center of mass of $q^N=(q_1,\ldots,q_N)$, and $P$ is the total momentum, the sum of $p^N=(p_1,\ldots,p_N)$. With this identification, both formulas give the same expectation value when applied to a 1-partic... | {
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Link between integrability and soliton solutions I have been doing some research on the properties and dynamics of solitons (in particular, solitons in superfluids) and several works and papers mention the link between solitonic solutions and integrability of the non-linear differential equation describing the physical... | There is plenty of integrable partial differential systems which are dispersionless a.k.a. hydrodynamic-type (i.e., can be written as first-order homogeneous quasilinear systems; apparently in the case of more than three independent variables the dispersionless systems form an overwhelming majority of all known integra... | {
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Why is $ \frac{\vec{r}}{r^3} = \frac{1}{r^2} $? I know it's surely a beginner's question but I don't see why you can write
\begin{align}
\frac{\vec{r}}{r^3} = \frac{1}{r^2}\cdot \frac{|\vec{r}|}{r}
\end{align}
Could someone explain it please? It would help understand quite a few things ...
| $$\frac{\vec{r}}{r^3} = \frac{1}{r^2}\frac{\vec{r}}{r}=\frac{1}{r^2} \vec{u_r}$$
where $\vec{u_r}$ is an unitary vector with the direction of $\vec{r}$
| {
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How do you expand $\langle x'-\Delta x'\rvert \alpha\rangle$? In my textbook (Sakurai) the following identity is often used:
$$
\left< x'-\Delta x' \, \middle| \, \alpha\right>~=~\left< x' \, \middle| \, \alpha \right> - \Delta x'\frac{\partial}{\partial x'} \left< x' \, \middle| \, \alpha \right>
\,.$$
How can this id... | you have to derive the taylors expansion. I wont give the full proof but I will give how you proceed.
$$f(x)-f(x_0)=\int^{x}_{x_{0}}f'dx$$
and
$$f'(x)-f'(x_0)=\int^{x}_{x_{0}} f''dx$$
then if you substitue latter to former you would have
$$f(x)-f(x_0)=\int^{x}_{x_{0}}f'(x_0)dx+\int^{x}_{x_{0}}\int f''(x)dx$$
and
$$f(x)... | {
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What atomic forces are acting to resist me pushing an air filled bottle underwater? Yes air is less dense than water but how does the bottle know to rise or indeed to move? It's not electromagnetism I think. Does this have a relation to gravitational forces? Is it to do with the number of protons in the molecules of th... | Archimedes figured this one out around 250 BC. If you push an empty bottle underwater you have to raise the surface of the water by the same volume. This is the counterforce that you feel.
| {
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Modifying the Bohr Model for Muonic Hydrogen I am trying to find the energy between the $n=2\leftrightarrow3$ transition for Muonic Hydrogen. My approach was to modify the Bohr model for standard hydrogen but taking the mass of the Muon $m_\mu\approx 207m_e$ instead of the mass of the electron $m_e$ and then substituti... | $E_n = \frac{Z \alpha^2 \mu} {2 n^2}$ for hydrogen like atoms in the nonrelativistic approximation. For the hydrogen ground state ($Z=1$, $n=1$, $\mu=\mu_e$) this gives 1 Ry. Your answer should therefore be about $\mu_{\mu} /\mu_e$ times $1/4-1/9$ Ry, that is about 26 Ry ~ 400 eV ~ 6.4 $10^{-17}$ J.
| {
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Why is a vacuum balloon impossible? According to Can Impossible Vacuum balloon be possible with this idea?, a vacuum balloon is impossible. Why is that?
| A simple vacuum balloon that consists just of a spherical shell of uniform thickness is not possible at all in air at 1 atm. I only know how to prove it can't be done with a material with uniform properties such as an amorphous solid but I believe it can be shown that it can't be done with any material. Suppose you hav... | {
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Why can a wave be expressed with a sine function? I see many expressions which express waves with the sine function like $y=\sin(kx-\omega t)$.
Waves really look similar to the shapes of a sine or cosine function, but does this guarantee that expressions that show wave-like movement are sine or cosine functions or is t... | Suppose $f(x)$ is a period-$2\pi$ function. Why would it be expressible in terms of only the $e^{ikx}=\cos kx+i\sin kx$ with $k\in\mathbb{Z}$? Well, define the Fourier transform $\tilde{f}(k):=\int_\mathbb{R}f(x)e^{ikx} dx$ so $$e^{2\pi ik}\tilde{f}(k)=\int_\mathbb{R}f(x)e^{ik(x+2\pi)} dx=\int_\mathbb{R}f(y-2\pi)e^{iky... | {
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What is the evidence for a supermassive black hole at the center of Milky Way? Black holes cannot be seen because they do not emit visible light or any electromagnetic radiation. Then how do astronomers infer their existence? I think it's now almost established in the scientific community that black holes do exist and ... | Sagittarius A* (the black hole at the center of our galaxy) has some of the best observational evidence for black hole I have ever seen. Here, check out the animations from UCLA made from our observations. This is from data taken over a span of 20 years. You can see the bright spots (stars) orbiting around a patch of ... | {
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Is zitterbewegung physical or not? It appears that zitterbewegung, a frequency associated with the total energy of a particle or system, is widely considered to be an unphysical quantity (e.g., Kobakhidze et.al.), @Lubos Motl, McMillan). However, a few physicists including Hestenes, Recami et.al.,consider it to be a f... | I think the answer to your question might be that no one yet knows whether zitterbewegung is physical or not because no one really knows what the physical underpinnings of quantum physics are yet.
For a discussion of what zitterbewegung might mean physically, I would study walking droplets / hydrodynamic quantum analog... | {
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What are the physical conditions for general ohms law? A problem presents Ohm's law as $$\vec{J}=\sigma \vec{E}$$ where $\sigma$ is the conductivity given by a scalar. The problem asks what physical conditions must be satisfied for the equation to hold.
I understand that the material must be isotropic for the conductiv... | A trivial condition is that the temperature should be constant with current. An important one is that the mean free path of the charge carriers should be much shorter than the distance between the contacts.
| {
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why does rolling without slipping imply no work done by the frictional force? Suppose we have a cylinder (mass $m$, radius $R$, and moment of inertia $I$) that rolls without slipping straight down an inclined plane which is at an angle $\alpha$ from the horizontal. The quickest way to solve for the motion is to use con... | Friction without slipping can do work. Consider two blocks stacked on top of one another. If you push the bottom one, it will do work on the top one, and the two blocks will move together. The key here is that both blocks are moving, as in your second example.
Note that "work done" is a quantity that depends on the ref... | {
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Help with D. Tong example on Noether in QFT In this lectures, example 1.3.2 on page 14 concludes that the Noether current is
But how can the current be a two index object when it is defined in eq. (1.38), which is
as a one index object? If I apply the formula I obtain something of the form $j^\mu$. Can someone mak... | It's OK to have multiple indices on the Noether current; you just need to know how to lose all but one of them to form the most general conserved current that results.
The Killing vectors satisfy $\nabla_\mu\xi_\nu+\nabla_\nu\xi_\mu=0$. (Replace all $\nabla$s in what follows with $\partial$s if you only care about flat... | {
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How to draw Penrose diagram for a particle of mass $m$ in between two Schwarzchild black holes? I am reading Hobson's GR book. I am curious about Penrose diagrams so I asked.
| You can't draw a Penrose diagram for a spacetime that lacks the necessary symmetry and isn't conformally flat. Normally our first step is that we take a slice or projection to reduce the number of dimensions to 2. If the spacetime lacks symmetry, then this step leaves you with something that doesn't give you complete i... | {
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Does a black body have a higher temperature when moving away from us at high speed? When a black body moves away from us at high speed the average velocity of its constituents will be higher. This means the body's temperature has increased. The whole spectrum of the wavelengths though will have been increased when arri... | If "high speed" means at some fraction of the speed of light, then the blackbody will appear to be cooler.
First off, as lesnik notes, the idea of measuring the temperature of a BB is basically a comparison of the average KE compared to itself. What you get is a curve, and that curve's shape will be independent of the ... | {
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Redshift - How can $z$ be greater than 1? I'm having trouble understanding the equation for redshift:
$z = Δλ/λ ≈ Δf/f ≈ v/c$.
If $z = v/c$ and $c =$ speed of light,
how can $z>1$ (as nothing can exceed the speed of light)?
| If we denote z as a Doppler redshift (due to velocity of an object moving through space away from us) and z’ as cosmological redshift (due to the expansion of space), then conceptually, ONLY z’ should be applied to spatial expansion throughout the range of z’ and general relativity (GR) solved for distance as a functio... | {
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Is the equation of motion for a spring-damper system the same whether oriented upward or downward? So every spring-damper system I've found online has the equation of motion:
$$mx''+cx'+kx=0$$
I can understand how this is derived when downwards is positive, but what about when upwards is positive? Wouldn't it be
$$mx... | Let $\hat d$ and $\hat u$ be unit vectors in the down and up direction.
Looking at your right (correct) derivation you have made down $\hat d$ as positive and the displacement of the mass from the equilibrium position is $x \hat d$ leading to the velocity being $\dot x \hat d$ and the acceleration being $\ddot x \hat d... | {
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Potential due to line charge Is it possible to calculate the electric potential at a point due to an infinite line charge? Because potential is defined with respect to infinity.
| Since this an infinite line - not an infinite sphere - there are plenty of points in space infinitely removed from it, which you can use as your zero reference points.
So, once you know how the field of the infinite charged line looks like (you can check here), you can calculate the electric potential due to this field... | {
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How does emitting light while moving not break the law of conservation of energy? Say you have 2 identical LED monochromatic flashlights. The battery lasts exactly 1 hour. We are able to calculate the energy emitted as photons from the LED by Planck's Law: $E = h\nu$.
Now if we were to move one of our flashlights thoug... |
I feel that the energy required to accelerate the flashlight to $\frac 12 c$, does not need to be counted for here, as that energy is conserved until the flashlight needs to be slowed back down to stationary.
Actually, it does need to be counted. The energy(mass) of the flashlight is reduced after it emits the photo... | {
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Surface tension molecular theory How does the surface of water behave like a stretched membrane? What's the cause for that?
I know that the surface molecules experience a net force downward so there is dense layer of water molecules in the surface but how does this leads to minimizing the surface area? Please help me ... | Every one of the water molecules in the bulk liquid exerts a small amount of attractive force upon its nearest neighbors. The total energy of the ensemble of water molecules is minimized when the molecules are pulled close to one another by this force.
When a portion of liquid water is in contact with air, the molecule... | {
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Data - Monte Carlo Correction techninques in Particle physics It is said that the data does not always match with the Monte Carlo simulations in particle physics.(I guess even in the Higgs to gamma gamma channel, the peak in real data was at about 127GeV and thus it was corrected) .Thus,I wished to know what are the di... | You have to understand that a Monte Carlo simulation is a way of integrating the predictions of a model.
Theoretical models are often calculable, and can be inserted with "simple" generators. i.e. every event is generated with the probability given by the quantum mechanical calculation.
This is not enough to allow comp... | {
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In QM why can wavefunctions be written as $\psi (x,t)= Ae^{i(kx-\omega t+\phi)}$? In my textbook, a wave traveling in the positive $x$-direction can be described using $$\psi(x,t)=Ae^{i(kx-\omega t+\phi)}. $$
I understand that the equation for a classical wave can be extrapolated by solving the differential equation as... | As stated in the answer by @my2cts, $\psi(x,t)=Ae^{i(kx-\omega t+\phi)}$ is the solution of the free particle Schrödinger equation, but $\psi(x,t)=A\cos(kx-\omega t+\phi)$ is not, even if it is a solution to wave equation $\frac{\partial^{2}\psi(x,t)}{\partial x^{2}}-\frac{1}{v^{2}}\frac{\partial^{2}\psi(x,t)}{\partial... | {
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Meaning of crystal orientation If I have a crystal, say (001)-oriented ABO3, what does the 001 imply, from an experimental perspective? I understand that the 001 is referring to a plane as described by Miller indices, but what is it about this plane that is relevant? Is it that this plane is the same plane as the surfa... | When someone says (hkl)-oriented anything, they almost always mean the surface normal of the sample is parallel to (hkl). So Si-(111) would mean silicon oriented so the surface normal is along the (111) direction.
If you have a layered material, then having a (001) orientation means the c-axis is perpendicular to the s... | {
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Sound, Ultrasonic waves: Distance travelled and spreading angle I am working on a project related to measuring distance using sonic/ultrasonic waves(i.e. sending a pulse and calculating the time between the echo and then distance). I was reading a lot about the optimum frequency that I can choose for getting a sufficie... | 1)"How much distance can these waves travel so as to generate enough echo to be detected." It depends on your receiving transducer and electronics noise levels, among other things.
For attenuation in air see:
https://physics.stackexchange.com/a/52246/45664
2)"what are the factors affecting the distance traveled by thes... | {
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How strict are the boundaries that divide dimensions? Is a single-layer sheet of graphene 2D or 3D? I would like to know if there is any theory that describes a set of rules that define the boundaries of dimensions.
For example, does a single layer sheet made of graphene considered a two or a three dimensional object?
... | As anna already answered, rigorously, any object is either zero- or three-dimensional.
That said, it can be very useful to approximate a 3D object by a 2D or 1D one. Graphene in particular can often be well approximated as a 2D sheet.
Being an approximation, there's no strict rule about when it can be used: as long as ... | {
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"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
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