Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Plotting hydrogen wave functions This may sound a bit dumb but how do I plot the hydrogen wave functions? For example, what is exactly being represented in this image? Is it just the norm-squared of the wave function and is the z-axis sticking out of the page?
I'm not sure how to use any other application but I'm usin... | For Mac there still is Atom in a Box. It can display hydrogen wave functions in different ways. I found the view mode with "phase as color" very helpful for my understanding. The wave functions are displayed in 3D and animated in time. One can also display superpositions of different eigenfunctions (for example the hyb... | {
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Two Rolling logs Suppose we have two logs rolling down a hill, one of gold and the other of wood; the acceleration for both will be equal, something which is unclear to me; I get that this may be due to their form, which is the same, but how come the mass of the objects doesn't matter?
| All objects are accelerated by the same value in a gravitational potential in accordance with newton's laws of gravitation and motion
$F = mGM/r^2 = mg$ where G is newtons constant and M is mass of the earth.
Applying the equivalence of gravitational and inertial mass we have
$F = mg = ma => g = a$ (independent of ma... | {
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Why do we not use the SI system for distance in space? One of the closest stars to Sol is Alpha Centauri at 4.367 Ly according to wikipedia. Why do we not say that it is 41.343 Peta-meters rather? (4.367 Ly = 41.343 Pm)
Why does Light-years or Parsecs seem to be the standard rather than SI?
| Light years and parsecs have been used since long before SI existed, so a lot of it is tradition.
But using light years also makes it very obvious how long the light has traveled to get here, and thus which era of the universe we are seeing the object in. Something that is 11 billion light years away dates from the era... | {
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Is there a prohibited region in $P-V$ plane? Polytropic process generalize the particular thermodynamic processes with
$$P V^{n}= \mathrm{constant}$$
Where, if $n$ changes, the curve on $P-V$ plane changes, as shown in the diagram.
The orange region is not touched by any curve, so there is no value of $n$ for which t... | Assuming there is only one molecular in this box and assuming it is a closed system with initial P-V state is defined. The question becomes: can the system move to anywhere on the PV diagram?
Well we can adjust volume to any number. Then the question becomes: can pressure reaches to any values on PV diagram?
Pressure r... | {
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Why don't high pressure gases stored in containers lose energy? Containers holding gas at a high pressure don't slowly lose the internal energy of the gas. It seems like the high speed particles would collide with the metal walls and slowly transfer their energy to the slower particles outside the container.
Even if th... |
It seems like the high speed particles would collide with the metal walls and slowly transfer their energy to the slower particles outside the container.
The mechanism you describe is correct, but you have to keep in mind that average kinetic energy, $\langle K \rangle$, is only proportional to temperature:
$$\langle... | {
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Why Do Glueballs Have Mass, When Individual Gluons Are Massless? From Wikipedia Glueballs
Glueballs are predicted by quantum chromodynamics to be massive, notwithstanding the fact that gluons themselves have zero rest mass in the Standard Model. Glueballs with all four possible combinations of quantum numbers P (parit... | Because in relativity the mass of a collection of particles is not necessarily the sum of the masses.
Even two photons (treated as a unit) can have mass. Consider the total four-vector of a system with component four-vectors $(E,\hat{z}E/c)$ and $(E,-\hat{z}E/c)$. It has mass $(mc^2)^2 = (2E)^2$.
| {
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How to show mathematically that the electric field inside a conductor is zero? The electric field is characterized by the equations
$$\nabla\cdot \mathbf{E} = \dfrac{\rho}{\epsilon_0}$$
$$\nabla \times \mathbf{E} = 0$$
Or equivalently, $\nabla^2 V = -\rho/\epsilon_0$ and then $\mathbf{E} = -\nabla V$. The boundary cond... | You need to use Ohms law: $J = \sigma E$ which has to be added to Maxwell's equations as a bulk observation, as explained by this answer.
You can then conclude that the electric field is zero in a conductor for:
*
*perfect conductor where $\rho = 1/\sigma = 0$ and $J$ is finite
*static case where $J = 0$ and $\s... | {
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If change in position over time is average velocity, why doesn't change in position over time squared equal average acceleration? For example, let's say a car is experiencing an acceleration of $1$m/s$^2$, for $6$ seconds so it goes $18$m. Now the average velocity is found through dividing $18$m by $6$s which is in lin... | Why your computed average acceleration is wrong?
the average acceleration is defined as:
$\overline a=(v_2-v_1)/(t_2-t_1)$
where the $v$'s are instantaneous speeds. If you start with zero initial speed you can simplify it to
$\overline a= v /t $
$v$ is still the instantaneous speed at $t$. For a constant accelerati... | {
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Adjoint of the gauge covariant derivative Suppose $A=A_1dx_1+A_2dx_2$ is a 1-form connection in $\mathbb{R}^2$ and $D_A \phi=d\phi-iA\phi$ is the gauge covariant derivative with $\phi=\phi_1+i\phi_2$ is a complex scalar field. May I ask what the adjoint $D^*_A$ of the gauge covariant derivative? Thank you so much.
| For $D=d+A$,with respect to the usual inner product on $\mathbb{R}^2$ and the ones induced by it on differential forms, one has $D^{*}_{A}=-*D_{A} *$ where $*$ stands for the hodge star operator. For example, $$D^{*}_A (f_1dx_1+f_2dx_2)=-*D_{A} *(f_1dx_1+f_2dx_2)=-*D_{A} (f_1dx_2-f_2dx_1)=-*(\frac{\partial f_1}{\partia... | {
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How exactly does string theory make general relativity and quantum mechanics compatible? Correct me if I'm wrong, but the reason that quantum mechanics and general relativity are incompatible is because the quantum foam at Planck scales renders space-time discontinuous and doesn't allow Lorentz transformations to occur... | String theory does not say that GR or quantum field theory hold at those scales. It posits strings, and gets to the Planck scale and predicts what it might look like, foam or stringy things arising and changing and so on. At lower energies it is consistent with quantum field theory and GR. So, GR is a low energy descri... | {
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Does the speed of light in vacuum define the universal speed limit?
*
*Is light the thing causing the universal speed limit to be $299\,792\,458\,\mathrm{m/s}$? So the universal speed limit would be different if light travelled faster or slower?
*Or, is $299\,792\,458\,\mathrm{m/s}$ the universal speed limit anyway ... | The numerical value of $c$ does not have any fundamental significance. Rather it is the number we get based on the experimental fact (according to the number & unit system employed) . If some alien civilization ended with some different value of $c$ compared to us. Even that is not a problem. They will reach the conclu... | {
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Conceptual doubt in Tension force I recently studied that Tension in a string is a kind of force originated from electrostatic attraction between the atoms of the string in which the force is originating. My doubt was that:
Assume that I am pulling a rope with a force $F$, and the rope will develop a tension $T$ in its... | To simplify this answer assume that the string is made up of a line of molecules so each molecule bar the end ones have only two nearest neighbours.
When there is no tension force in a string then on average the molecules which make up the string are at their equilibrium spacing and have no net force acting on them.
I... | {
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What would occur between the parallel plates of the capacitor? In capacitors dielectric materials are sometimes inserted between the parallel plates. What would happen if a diamagnetic, or a paramagnetic material is inserted between the parallel plates of a capacitor?
| As long as neither diamagnetic or paramagnetic material acts as a conductor (no flow of charge between plates below breakdown voltage), it will still behave as a capacitor.
The dielectric polarisability of the material will however have an influence on the total storage of charge and charging profile of the capacitor, ... | {
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Multiplicity Identity in Kittel's Thermal Physics On page 25 of Kittel's Thermal Physics, the author derives the multiplicity of $N$ harmonic oscillators with total quanta of energy $n$, $g(N,n)$.
He writes
\begin{align}
g(N,n) &= \lim_{t\rightarrow 0} \frac{1}{n!}\left( \frac{d}{dt}\right)^n \sum_{s=0}^{\infty}g(N,s)t... | I figured it out. If you pull out the summation out front, everything except the $s=n$ term vanishes. The terms with a higher power than $n$ vanish when taking the limit while the terms with a lower power than $n$ vanish when taking the $n$th derivative.
However, it would be great if someone can come up with a better,... | {
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Notation about basis of gamma matrices in $4d$ In Quantum Field theories, we encounter gamma matrices a lot.
Reading from various textbook, i encountered some textbook use different basis for their gamma matrices.
Gamma matrices are defined such that $\gamma^{a}\gamma^{b}+\gamma^{b}\gamma^{a}=2\eta^{ab}$. Multiplying ... | I'd argue that the root of this is that different Gamma matrix bases give you different "good" features, and while the choice is equivalent (and amounts to a choice of basis for your Dirac spinor), which choice is "right" depends on what features you want to be obvious/trivial -- particle/antiparticle, left/right hande... | {
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How do I calculate a upward-pulling force on a swinging pendulum? I'm trying to implement a simple pendulum using a 2d physics system that can model rigid bodies with gravity. The problem is that I don't know how to calculate the upward-pulling force of the rope, as in this image:
I've only found equations for calcula... | A properly drawn free-body diagram will have a tension force vector acting along the line of the rope, toward the pivot point and a gravity vector acting straight down. If you establish a coordinate system which is instantaneously parallel and perpendicular to the rope, you then will decompose the gravity vector into t... | {
"language": "en",
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Temperature distribution in a column of air Say there is a sealed cylinder of air that has a height $\mathrm{h}$ and area $\mathrm{A}$ on the ends. The initial temperature throughout the column is $T_0$ and has a uniform initial density $\rho_0$. If the bottom of the cylinder is at sea level, what is the temperature at... | CAVEAT - I am giving a possible calculation, but I believe the answer may be off by a factor 2x (compared to the lapse rate observed in the atmosphere). I am leaving it here for you to ponder. Perhaps it can inspire you to find the correct solution yourself. Or perhaps the difference is due to the fact that this calcul... | {
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Transforming Qubits Into Bits From what I understand, a qubit exists in a superposition of states and once it has been measured, it must fall into one of the two possible states. Now, I have been told that once a qubit is measured, it is no longer proper to call it a qubit but a bit since it no longer exists in a super... |
One final thing, since measuring a qubit is inherent to a functional quantum computer, does this mean that quantum computers actually use bits as well as qubits?
The entire advantage of a quantum computer lies in the use of qubits. I've implemented a quantum computing algorithm(Grover's Search) on a classical compute... | {
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Distance between adjacent planes in a crystal This question has been asked before, but there doesn't seem to be a decent answer.
Many sources state that " For cubic crystals with lattice constant a, the spacing d between adjacent (ℓmn) lattice planes is:
$$ {\displaystyle d_{\ell mn}={\frac {a}{\sqrt {\ell ^{2}+m^{2}+... |
I could only find this poor-quality picture. It should give you an idea, anyway. For example, consider the first picture in the first row: $(l,m,n)=(1,0,0)$ in that case, and it is easy to verify that the distance between the grey planes is
$$d=a$$
In the second case, $(l,m,n)=(1,1,0)$, and you can see that
$$d=\frac ... | {
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Does the universe expand in every direction evenly? I've heard that the universe is expanding constantly and that galaxies are moving further and further away from each other because of this. However, does the universe expand in every direction evenly or does it expand in one direction more than another direction?
| Short answer: Yes
Explanation: The answer to this question is something well documented in astrophysics. The "Size" of a universe is modeled by metaphorical expanding fluids known as the Freidman Equations. These equations say that from a singular point, the universe will expand at rates according to the travel of its ... | {
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How we chose the height while calculating potential energy? I'm really confused how to chose height when calculating potential energy. If an object is right above a desk, suppose the will we take height from desk?
If we take it from a height $x$ from the desk and the level of desk is $y$ from the ground and we change ... | Potential energy stored in a body is relative. We have to first choose the potential at a finite point or infinity. In the case given above, we take potential energy to be 0 at the centre of the Earth. So according to the relation, $PE = mgh$ where $h$ is the height from the centre of the Earth. Generally, we take heig... | {
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Are black holes perfect spheroids? What I know about black holes (correct me if I'm wrong) is that they are the most compact objects in the universe that have been discovered. Due to all that gravity, wouldn't black holes be a perfect spheroid, sort of like planets are spheroids (due to centrifugal forces)? Can you mea... | The shape of a black hole's event horizon depends on who is asking. Observers who are moving quickly towards a hole, for example, will see a different shape compared to those who are not.
Per @benrg the event horizon of a static black hole is not observer dependent, similarly to how the shape of an expanding flash of... | {
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Can we exit the event horizon of merging black holes? I have an intuitive scenario. Consider we have a spaceship just below the event horizon of a BH, which is merging with another black hole.
Finally, the singularities merge and we have a single black hole again.
But, in the transient stage, it is unclear to me if a t... | Classically speaking, since total BH evaporation takes finite time, yet being at the event horizon stops all time (in your IRF), the black hole will evaporate before you can get to the event horizon.
| {
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What frequency is the scratching of finger nails on a blackboard? This is the frequency/intensity that sets my teeth on edge.
Does anybody know what frequency (roughly) it is? I am guessing it is near the top of normal human hearing, 20kHZ, but I'm not sure if that's why it affects me.
I am sure the same frequency is ... | In addition to the other answer by Cort Ammon, I have heard of other psychophysical/evolutionary explanation:
The frequency distribution of that sound closely corresponds to the frequency of a crying baby, which has been shown to drive people crazy when exposed to it for a short amount of time (we are genetically pred... | {
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How does the LHC explore extra dimensions? The Large Hadron Collider (LHC) has been smashing particles for a long time and sometimes people say that it has found new dimensions. How is it even possible for a particle accelerator to find new dimensions?
| It is important to understand how experiments work. With very few very very basic exceptions, all experiments and their measurements involve a theoretical framework.
Fact is, we almost never measure things explicitly. For crude examples consider:
*
*Temperature: a mercury thermometer measures length (that of the co... | {
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Is a light wave's amplitude stretched, along with the "red shift" stretch - making it brighter? When light waves are stretched and "red-shifted", is the amplitude of the light wave stretched as well, affecting the intensity/brightness of the light wave?
| Light waves are not necessarily stretched. The formula
(frequency measured by the observer) = (speed of the light relative to the observer)/(wavelength)
suggests that the frequency shift (blueshift or redshift) can be due to the variation of the speed of the light relative to the observer, not to wavelength change. Whe... | {
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Largest Mass Diffraction I have read "Matter-wave interference with particles selected from a molecular library with masses exceeding 10000 amu" which claims to observe diffraction patterns in objects of around 10'000 amu. What is the largest mass objects shown to have diffraction patterns and show wave-particle dualit... | Yes, up to now, that is the paper showing the largest-mass particle interference experiment. The possibility of using larger particles, like small viruses and other kinds of biomaterials are discussed in this paper:
http://iopscience.iop.org/article/10.1088/0031-8949/91/6/063007/meta
This is the most up to date referen... | {
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Satellite revolving problem gives two different answer Assume there's a satellite revolving about the Earth. If I would like to decrease its radius, should I increase or decrease its velocity?
I know the answer apparently should be decreasing its speed, but the following two formulas give different answers. Can someon... | Your question is puzzling but I think i have understood the answer.
When the satellite undergoes slow down (due to friction or something) it comes closer to the earth and gain additional velocity. This velocity is same as in your equation and as in @sammy gerbil 's answer.
$v^2=GM/r$
Friction reduces the energy of the... | {
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Using fermion-based analog computers to solve NP-hard problems in polynomial time If the fermion sign problem is an NP-hard problem as it seems to be proved by this work, is it possible to take an NP-hard problem, convert it into an equivalent fermionic state evolution problem, prepare the system physically, let it evo... | Scott Aarson gives examples of problems that might look like enabling such a reduction procedure, but fail in the paper 'NP-complete Problems and Physical Reality'.
Can NP-complete problems be solved efficiently in the physical universe? I survey proposals
including soap bubbles, protein folding, quantum computing, ... | {
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Is this constraint holonomic or non-holonomic? $$f(q,q^\prime, t) = 0, ~\mathrm df = \frac{\partial f}{\partial q}~\mathrm dq + \frac{\partial f}{\partial q^\prime}~\mathrm dq^\prime+ \frac{\partial f}{\partial t}~\mathrm dt = 0$$
I really want to know whether this constraint is holonomic or non-holonomic.
(As far as I... | *
*Firstly, recall that virtual displacements don't change time $\delta t=0$. Time is fixed, say $t=t_0$.
*Secondly, let $M$ be the position space, often call the configuration space, with generalized position coordinates $q^i$.
*OP is right that the constraint $\delta f(q,v,t) \approx 0$ doesn't depend on virtual... | {
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Why can any general motion of a rigid body be represented as translation + rotation about center of mass?
*
*Why can any general motion of a rigid body be represented as translation + rotation about center of mass?
*I am beginning to read rotational dynamics and my textbook states this fact without proof. I am wond... | If you want to describe the position of a rigid object in space, it is clearly not sufficient to give just the position of the center of mass - you also need to specify the orientation.
That orientation can be reached with a rotation about the center of mass - but you need to figure out what the direction of the rotati... | {
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Ground state of local parent Hamiltonians and invariance under local unitaries Assume that a finite-dimensional pure state $|\psi\rangle\in \mathcal{H}\simeq \mathbb{C}^m$, $m<\infty$, is the (unique) frustration-free ground state of a local parent Hamiltonian and suppose that the locality notion is given in terms of a... | Consider the toric code Hamiltonian situated on a spherical geometry. This has a unique ground state. Expand the sphere to an infinite radius. Consider a string excitation of the ground state, and loop the string around the sphere (an infinite number of local operations) such that it meets itself, returning our system ... | {
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What is the Continuity Equation in QM? I have an exercise for my homework that mentions the "continuity equation". Don't tell me how to solve it please, just tell me what the continuity equation is. I tried googling it but I couldn't find anything exact. Just stuff mentioning the probability current. The question is:
... | So the continuity equation is usually written as
$$\frac{\partial\rho}{\partial t} + \nabla\cdot \mathbf{j} = 0$$
where $\rho \equiv \rho(\mathbf{r},t) = |\psi|^2$ is the standard probability density and $\mathbf{j} = \frac{\hbar}{2mi}\left(\bar{\psi}\nabla\psi - \psi\nabla\bar{\psi}\right)$ is called the probability c... | {
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To effectively suppress normal audible sound, how wide and how absolute would a vacuum space have to be? I don't know if this question is too specific or simple, but: to effectively suppress (say 99%) of normal audible sound (say 20-20kHz @ 100dB), how wide (mm?) and how absolute (torr?) would a vacuum space have to be... | This is really a nice question. After reading your question I have searched the web with the idea that sound is a pressure wave and in order to hear them it must transfer energy to your ears. I have found this article which is really nice. It says that (and so was my intuition) the energy density of the sound wave is d... | {
"language": "en",
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Why aren't trigonometric functions dimensionless regardless of the argument? Consider this equation :-
$$y = a\sin kt$$
where $a$ is amplitude, $y$ is displacement, $t$ is time and $k$ is some dimensionless constant.
My instructor said this equation is dimensionally incorrect because the dimension of $[kt] = [\tex... | The quantity $kt$ is dimensionless.
If $t$ has the dimensions of time then the dimensions of $k$ must be $\text{time}^{-1}$ so your series expansion works.
You will meet this idea again and again in Physics and checking the dimensions often is a good way of checking a derivation.
The charging and discharging of a cap... | {
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Why is the surface of a liquid slanted when it is accelerated? Consider a uniformly horizontally accelerated tube of water. I know that the fluid experiences a pseudo force in addition to its own weight, so that it reaches equilibrium in the below diagram.
But why can't the water also exert a force like this, so it ca... | The reason that the second diagram you drew cannot represent what is happening is that it will not satisfy Newton's 2nd law for all parcels of fluid in the tank. Imagine that you had a tank like the one shown in the diagrams and, rather than accelerating it, you just tilt it at an angle so that base is no longer horiz... | {
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How is potential energy lost when a water droplet is dropping down slowly on a wall? When a water droplet is on a vertical wall, it usually drops slowly, which is different from free falling. As the dropping speed is slower than free drawing, so I guess some energy must be lost.
I guess it is lost as internal energy, ... | Energy lost because it create a layer of water as it slides down, and layer created due to the viscous force between the liquid - liquid layer and liquid - container layer.
What happens is the fluid experience, s a Shear force as it slides (tangential) , and this Shear force is cause of energy. Loss, as Water flows do... | {
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Superpotential is Supergauge Invariant? I was studying by the X. Tata & Bauer and I'm stuck with something:
In Chapter 6 - Supersymmetric Gauge Theories, it states that the superpotential is already invariant by a supergauge transformation, and explains that is because "it's polynomial in the chiral superfields".
I'm t... | A chiral superfield with variable change $x_\mu\rightarrow x_\mu+ \frac{1}{2}\bar\theta \gamma_5\gamma_{\mu}\theta$ will have similar gauge transformation as it's components and if the action does not contain derivative or complex conjugate of the chiral superfield and contains a polynomial part then under a local gau... | {
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What is optical density? I'm a zoology minor and we are doing protein estimation by colorimetric method. I have stumbled upon a term 'Optical density'. I don't understand the term well. Is it a measure of the extent of light that can pass through a particular object?
I've checked a related question of this community an... | For all intents and purposes, OD is the negative of the order of magnitude the factor by which the intensity of the light is reduced by the attenuating element with said OD.
In other words: OD = 6, means that the intensity will be reduced by a factor of 10 to the power of -6, a.k.a by a factor of a million.
| {
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Spring force on both sides of spring I am a little confused about springs. I just wanted to know that if I pull an ideal spring of spring constant $k$ such that the spring has been symmetrically pulled and its elongation (total) comes out to be $x$ then would the force on one side by $$F=kx$$ or $$F=kx/2$$ I am a litt... | When you state $F = k x$ the variable $x$ represents the extension of the spring and not the position of one of the ends.
In a symmetric pull each end moves by $ \frac{\delta}{2} $ then the total displacement is $\delta$. The spring force is then $F = k \delta$ on each end of the spring.
| {
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Why magnetic component of light is not shown in polarization diagram? Does polarization eliminate magnetic field? So far I knew about light-polarization is like this ...
in an event of a plane-polarization, the polarizer-crystal does NOT separate the electric-component and magnetic component of the light. The magneti... | You are (mostly) right, your geology friend is wrong.
As stated in the comments, an electromagnetic wave can not consist of only an electric nor of only a magnetic field. They go hand in hand.
| {
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Does empty space have energy? My physics friend suggested that "the answer to why matter exists in the universe" is because all massive particles are just the fabric of space excited into little packets. To illustrate, imagine a blanket on the ground. Then, pinch a small bit of the blanket and twist it. This is a parti... | Yes empty space does have energy.When you apply quantum mechanics and special relativity, empty space inevitably has energy. The problem is, way too much energy. It has 120 orders of magnitude more energy than is contained in everything we see!
| {
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Finding an equivalent system of an infinitely long cylinder with polarization vector $\vec P = P\hat y$ I am given an infinitely long cylinder, with the axis of symmetry on the $z$ axis, $y$ is right to left, and $x$ towards us.
It is polarized with $\vec P = P\hat y$.
My solution manual states that an equivalent syste... | The polarization will cause a displacement of all the positive charge relative to the negative charge in the y-direction, so that a top view of the cylinders will look like this:
Since the polarization vector points in the positive y direction, the electric dipole moment vector will point the same way, which tells you... | {
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What is the difference between these two ways to calculate average velocity? Average velocity:
$$v_{\rm avg,1}=\frac{v_{\rm final}+v_{\rm initial}}{2}$$
and average velocity:
$$v_{\rm avg,2} =\frac{\rm total\;displacement}{\rm time \;taken}=\frac{\Delta x}{\Delta t} $$
What is the difference between them and when do ... | The correct equation for the average velocity is the second equation of the both equations you gave. The first one is correct only under given condition that the acceleration of the body is constant. Second equation even holds for variable acceleration.
| {
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Can gravitational wave create anti-gravity, i.e. repulsive gravity? A very layman question as in title. Like every wave having a negative side, can a gravitational wave have anti-gravity.
To put it in different words, a gravitational wave passing through a complete vacuum, if in positive cycle, can create a denser spac... | Gravitational waves, though transverse, can be thought of as similar to sound waves:
A sound wave, as it moves through a medium the sound wave creates alternating volumes of greater and lesser particle density.
Gravitational waves do something similar, except the medium is spacetime itself. The result is that as a gr... | {
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Different net external forces If I apply an external force to an object, it gets transmitted internally and cancels out according to Newton's 3rd law. This leaves a net external force, causing the object to accelerate.
But when I attach two objects of different masses by an inextensible string and pull one object with... | Realistically, the redistribution of the force between the two masses is the same idea as the force being transmitted internally.
Within a single object, each individual "particle" will receive an appropriate force to cause it to undergo an acceleration that is equal to the rest of the particles within the object. Part... | {
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Why doesn't Helium freeze at 0K? I have read that Helium does not freeze at absolute zero under normal pressures.
How could this be possible given that the absolute zero is the lowest attainable temperature and at that temperature, all random movements of the atom stop?
Shouldn't the atoms just stop vibrating and soli... | At $0K$ there is still zero point energy. As He is very light and inert the associated zero point motion this is enough to prevent solidification.
| {
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Does a higher water volume increase pressure? I am constructing a gravity flow water system. I have 100ft point where I can put my tank. My question is does the size of my tank matter? I am using a 1" pipe. Will I get more pressure if I use a bigger tank? For example what is the difference in pressure if I use a 10 gal... | Gravity flow pressure can be figured, or measured, simply by two methods:
1) divide the drop in elevation (in feet) by 2.31 OR........2.31 feet of drop = 1# of pressure
2) if you have a system already established, screw an inexpensive water pressure gauge on a hydrant, or hose bibb and read the pressure
NOTE: the volum... | {
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Use of angular diameter to determine distance in special relativity Summary: at relativistic speeds, if you compute a planet's relative distance using angular diameter (roughly proportional to 1/angular diameter), will that computed distance increase or decrease linearly, assuming you are traveling directly towards or ... | Acceleration changes your speed which does change the angular diameter. You'll find this in the relativity textbooks under 'stellar aberration'.
Consider a photon from the rim of the planet. It has a transverse momentum $p_T=p \sin\theta$ and a longitudinal momentum $p_L=p \cos \theta$.
When you increase your speed, in... | {
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What is a phase arrow? Feynman say's that a photon takes every path while reflecting off a mirror when going form A to B, but we only see the middle one(where incident angle = reflected angle) because all the others are cancelled out as they have longer routes and while following them their phase arrows cancel out each... | Feynman's understanding of this effect probably came from optics where it is known as Fermat's principle. The mechanism behind this principle is based on the notion of stationary phase, which is the phenomenon that light will go in that direction where the phase coming from different paths varies slowly.
I'll try to ex... | {
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How does an off balance Load affect Direct Drive Dc Motors on a robotic "vehicle" I write the autonomous program for my local robotics team. The robot has 4 wheels directly fixed to an Andy Mark motor. there is no leveling or balancing system. due to placement of different modules with in the robot each side is under a... | The 'power proportional to weight' algorithm is unlikely to be completely correct. If your wheels deform under load, that deformation may be changing the effective
radius of a driven wheel, not only the retarding force. That would
call for load compensation of velocity, not power.
In forward acceleration, we can see... | {
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Deceptively simple mass-spring problem? This question is inspired by two other, similar, so far unanswered questions (posed by different OPs).
Mass $m_2$ sits on a incline with angle $\theta$ that provides just enough friction for it not to start sliding down. It is connected by a massless string $S$ and perfect sprin... | You have derived an equation which predicts the minimum force $F_{\text{min}}$ required to get the block $m_2$ moving up the slope.
$$F_{\text{min}} = \mu m_2g\cos \theta+m_2g\sin \theta$$
Until the tension in the string is equal to that value of force the block $m_2$ will not move so the spring mass $m_1$ system can b... | {
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What's the difference between Quark Colors and Quark Flavours?
Each of the six "flavors" of quarks can have three different "colors". The quark forces are attractive only in "colorless" combinations of three quarks (baryons), quark-antiquark pairs (mesons) and possibly larger combinations such as the pentaquark that c... | One is talking quantum mechanics and attributed quantum numbers to elementary particles.
A simple quantum number is charge and it it assigned to quarks ( and antiquarks) as +/-1/3 or +/-2/3 as in the table
Charge is connected with the electromagnetic force.
Flavor is assigned as a quantum number to each quark, and it... | {
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What exactly are "primordial fluctuations"? Are "primordial fluctuations" essentially the same as "virtual particles" and "quantum fluctuations" that created the universe from nothing like what is featured in the Lawrence Krauss book, A Universe from Nothing?
| I haven't read Krauss' book, but it seems the "quantum fluctuations" referred to is something invoked to explain the origin of the Universe itself; i.e. why is there something rather than nothing.
This is not what the term "primordial fluctuations" refers to. Although this is also quantum fluctuations, in the sense tha... | {
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Finding out how long a light bulb will light A cylindrical wire used to form a light bulb filament has radius 3.7 micrometers and length 1.7 cm. The resistivity of the wire is 5.25 * 10^-5 ohm meters. The light bulb is connected to a 12V battery.
With the given information; resistance equals 20.75 ohm meters. Current w... | You've done all the hard work and now there's one little part left.
You're being asked, given a certain battery capacity in amp hours and a certain current in amps flowing out of the battery, for how many hours (or seconds) will the current flow? The assumption is that as long as the current is flowing the light will b... | {
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Can someone please explain what happens on microscopic scale when an image becomes unfocused on a screen from a projector lens? My questions is basically asking when you move a projector back farther from a screen the image tends to blur unless you focus it. Logically I would think that every point(ray of light) of th... | When a sharp image is formed, every point on the object is reproduced in the image, and all the points around that point on the object are reproduced in the same relative positions of the image.
So, a diverging cone of rays from a point on the object hits the lens and the lens then refracts those rays so that they all ... | {
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Does gravitational time dilation happen due to height or difference in the strength of the field? The reason why you have to tune differently the atomic clocks in GPS is because the GPS is higher or because there is less gravity there, or both? In other words in a constant gravitational field which doesn't differ with ... | Gravitational time dilation is caused purely by "resisting" the gravitational field, in other words by accelerating in order to maintain a fixed position within the potential well. There is no gravitational time dilation in free fall.
| {
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What is the physical meaning of the Schwarzschild radius for objects that aren't black holes? Earth has a Schwarzschild radius of a little less than a centimeter. What does this mean for the matter of Earth's core that is within this radius?
A related question comes up for what happens when an almost black hole accret... |
What does this mean for the matter of Earth's core that is within this radius?
Nothing, since the mass outside the radius does not contribute to the force (see Newton's shell theorem).
A related question comes up for what happens when an almost black hole accretes matter and slowly becomes a black hole.
In the syst... | {
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How is heat represented on a quantum level? Heat is just a form of kinetic energy for molecules, because as temperature rises, the heated molecules are "shake" and "vibrate" more and more. But how does that show up on a quantum scale? What element actually carries the kinetic energy: the heated molecule as a whole, its... | The equipartition theorem says that all modes of excitation carry heat. There may be some modes which are too energetic to be excited at a given temperature, but the remaining modes are all excited. In overly simple terms, everything that can shake will shake.
| {
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At what distance we see actual size of object? At different distances object is seen of different sizes but there is some distance at which actual size of object is seen through eyes. Is it 25cm?
| The "size" of an object that you see is related to the angle subtended by the object at your eye.
The angle is called the visual angle.
This will determine the size of the image of the object on your retina.
The closer the object is to your eye the bigger the image on your retina and so the bigger the object appears... | {
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Why is a $5-60 mph$ time slower than a $0-60 mph$ time for some automobiles? This doesn't make a lot of sense to me, from a physics 101 point of view. I've read a few blog entries on why this is, but none of them explain it well or are convincing. "something-something launch control. something-something computers."... | In the rolling start there is no tire slip or revving on the engine and so the run starts at low rpm where the engine is making less power.
A rolling start might have the engine at 2000rpm making for example 200 lb-ft (or 76hp) resulting in 0.45g of acceleration at 5mph (this example yields the acceleration to be 0.002... | {
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How does curved spacetime affect gravitational waves? How differently will a LIGO detector detect a gravitational wave which came directly to it with a detector which happened to have a black hole between it and the source?
| A weak gravitational wave with $\square \hat h_{++}~=~0$ and $\square \hat h_{\times\times}~=~0$ is similar to an electromagnetic wave. We could think of the weak graviton as a sort of "diphoton," so the gravitational wave is similar to an electromagnetic wave with two polarization directions. It is also much more weak... | {
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Solving first order perturbation exactly in this situation I have this homework problem in QM Perturbation Theory
The Hamiltonian of a system is given by $$H_0 = A L^2 + B L_z$$ where
$A$ and $B$ are constants. If a perturbation $V = C L_y$ is added to
the system (where $C \ll A, B$ , find the lowest order correct... | As Valter Moretti answered in the comments, adding this here for archive purposes.
Define $N=B^2+C^2$. Using a unitary transformation $U$ corresponding to a certain rotation, you have $U(AL^2+BL_z+CL_y)U^∗=AL^2+NL_z$. Unitary transformations do not change the eigenvalues. Therefore the exact eigevalues are $Al(l+1)+Nm$... | {
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D3-brane in AdS/CFT correspondance I was reading a paper by Veronika Hubeny The AdS/CFT correspondence 1. Maldacena chose a D3-brane system to derive his conjecture. So I was wondering, why "D3-brane"? In other words, I need to know the importance of D3-brane system, so that is used in the AdS/CFT correspondence. It wo... | $3$-branes are special in the following sense: only for $p=3$, the black p-brane solution admits a constant dilaton, while it is running for $p\not=3$. In particular, the dilaton $\phi$ diverges at the horizon of extremal $p$-brane solutions for $p\not=3$, which means that the string coupling $g_s=e^\phi$ cannot be kep... | {
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Weight factor in Path Integral Formalism In Quantum Mechanics, transition amplitude between two states in given by (path integral approach):
$$
\left\langle q';t'|q;t\right\rangle= \int[\mathrm dq] \exp \left(i \int L(q,\dot{q})~\mathrm d\tau\right)
$$
This tells that contribution of the paths to the amplitude is given... | The intuitive explanation is really not there. I have a very fuzzy argument in the favor calling this "the weight factor". Let's see if that helps you at all.
The action is given by $S = \int L(q,\dot{q}) dt$. Now classically the path of the particle is determined by minimizing the action. i.e. the particle will follow... | {
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Number of degrees of freedom of the coupled pendulum problem In Chapter 4 from the book Theoretical Mechanics of Particles and Continua by A. L. Fetter and J. D. Walecka, it is solved the problem of a coupled pendulum system while considering small oscillations.
There, they say the number of degrees of freedom needed t... | There are naively three degrees of freedom: the length $d$ of the spring, and the angles $\theta_1$ and $\theta_2$. We also have the constraint
$$d - d_0 = l(\theta_1 - \theta_2).$$
You can use this constraint to eliminate any one of these variables, leaving two independent degrees of freedom.
| {
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Why does increasing resistance decrease the heat produced in an electric circuit? If $H=\frac{V^2}{R}{t}$ ,then increasing resistance means decreasing the heat produced.
But, isnt it that the heat in a circuit is produced due to the presence of resistors? Moreover metals with high resistances are used as heating elem... | Agreed it is confusing, but consider two ohmic resistors, where resistor 1 is half of the value of resistor 2. And let us say that the same voltage is applied across both resistors. Now since the current through each resistor is inversely proportional to the resistance, then current in resistor 1 is twice the current... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Quantification of entropy mathematically when $T$ and $V$ both change
$$ln\frac{W_f}{W_i}=N ln\frac{V_f}{V_i}=n N_a ln\frac{V_f}{V_i}$$
$$\Delta S=nRln\frac{V_f}{V_i}$$
$$ln\frac{V_f}{V_i}=\frac{1}{n N_a}ln\frac{W_f}{W_i}$$
$$\Delta S=\frac{R}{N_a}ln\frac{W_f}{W_i}=kln\frac{W_f}{W_i}=klnW_f-klnW_i$$
hence $$S=klnW$$... | It seems to me the first derivation is simply assuming that S = k ln W, because it looks like it was inserted along the way and then pulled out at the end as if it was a conclusion of the logic. What's more, by considering only position and not momentum, it seems to me that derivation is assuming the particles are not... | {
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Entropy and reversible paths I'm a little bit confused about calculating entropy changes along irreversible paths by integrating over a reversible path. When using the central equation I can understand the argument, entropy and all the quantities we use to calculate the entropy change are state functions that have well... | There is an implicit but crucial assumption in thermodynamics (your calculations are based on it): Any irreversible process can be closed by a reversible process to become a cycle. If it is false, thermodynamics would collapse:
http://philsci-archive.pitt.edu/archive/00000313/
Jos Uffink, Bluff your Way in the Second... | {
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Partial derivative of probability density (squared modulus of the wave function) wrt to position (1D)? Here's a snippet from Introduction to Quantum Mechanics by David Griffiths (Sec 1.5):
I understand how we used the Schrodinger equation to go from a partial in time to a double partial in position. But why is there a... | You should try solving this on a piece of paper. I don't think that you understand correctly how the author passes from $\partial/\partial t$ to $\partial^2/\partial^2 x$. You can not use Schrodinger's equation for $|\Psi|^2$, it is only valid for $\Psi(x, t)$:
$$ i \hbar \frac{\partial}{\partial t} \Psi(x, t) = -\frac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/278941",
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Does Gravity Depend on Spatial Dimension? Consider a line containing two point masses, $m$ and $M$. The line is a $1D$ space.
What's the gravitational force between the two masses?
Newton's formula for the gravitational force $F$ between two masses $m$ and $M$ in 3D space is
$$F=\frac{G M m}{r^2}$$
where $G$ is a cons... | There is nothing in Newton's laws that restricts the force of gravity to behave as $\propto r^{1-D}$.
Yes, if you imagine the gravitational vector field to be like the velocity field of flowing water, then it should have zero divergence, and that indeed implies $\propto r^{1-D}$ behavior, including the constant $D=1$ b... | {
"language": "en",
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Boltzmann statistics and density matrix for a simple spin 1/2 system. (NMR) I have a system with spin 1/2 particles (protons) in a magnetic field. The Zeeman effect leads to two energy levels (Spin up, spin down). Thus I have a state
$$
\left|\Psi\right> = a\left|\uparrow\right> + b\left|\downarrow\right>
$$
At room te... | There is no relation. $|\Psi\rangle$ is a pure state, while the thermal state $\rho$ is a statistical mixture. Since they describe different states, there is no relation.
| {
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Collapse of wave function Suppose a quantum system is initially at a state $\psi_0$ and that a measurement of an observable $f$ is performed. Immediately after the measurement, the system will be in a state that is an eigenvector of the operator $\hat f$ associated to $f$, the eigenvalue being the result of the measure... | Hermitian operators corresponding to physical observables act on the Hilbert space of physically valid states. It's clear from the definition of an eigenvector that for any vector space $\mathcal{H}$ and linear map $f: \mathcal{H} \to \mathcal{H}$, the eigenvectors must lie in $\mathcal{H}$. Therefore, the eigenvecto... | {
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Super-renormalizable theory and $\beta$-function There is the statement that $\beta$-function vanishes for super-renormalizable theories. In $D=2$, scalar field has mass dimension zero. So any polynomial interaction is super-renormalizable. Then shouldn't all of them have vanishing $\beta$-functions? But there are many... | In a qft, it may be possible to redefine other parameters than coupling to absorb the infinities coming from higher order corrections. In this way, coupling constant does not get renormalized and hence the beta function vanishes. It is a possibility in super-renormalizable theory as fewer diagrams are divergent and the... | {
"language": "en",
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How do electrons move at an atomic level? This was meant to be a sub question in the comments of my last question but I think it is big enough to have its own post.
I know that electrons move because of the potential difference across the wire.
But do the electrons jump from the valence shell of 1 atom to the valence s... | It does not make sense to talk about how an electron moves in an atom. The standard orbitals, shown below, are amplitudes for the occurrence of the electron. For very high Rydberg atoms with the electron put in extremely high orbitals the wave packet can then localize and orbit around the nucleus. One has to apply a we... | {
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Is speed of Hot air rising gravity dependent? Would say a heated air rise twice as fast in 2G than in the environment with standard Earth gravity?
| Initially, on an air parcel, buoyancy force would be twice as much when gravity doubles, which will impart higher initial acceleration, helping air parcel reach a higher speed before being counterbalanced by viscous forces. Of course there is much complication here, because an air parcel loses its momentum also by mixi... | {
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Why does this planet (J1407 b) and Saturn's ring center on its equator? Why is the material in J1407 b's or Saturn's rings stay in a disk not scattered? Is it the gravity and/or magnetic field that causes this? Does it differ with other large bodies that might not have a electromagnetic field?
| The reason it's a disk and not spread out is actually simpler than you might imagine.
Consider all of the mass in the system as a whole. It will have a certain centre of mass, angular momentum, etc, which much be conserved no matter how the distribution changes. That defines a preferred axis of rotation, and perpendicu... | {
"language": "en",
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Discontinuity of the geometric phase Does the geometric phase accumulated along a closed trajectory (in some parameter space) has to be continuous?
| The geometric phase can experience discontinuous dependence on the parameter space in the vicinity of diabolical points (i.e., points where the Hamiltonian eigenvalues are degenerate but the eigenvectors are distinct) and exceptional points where both eigenvalues and eigenvectors are degenerate. Exceptional points appe... | {
"language": "en",
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In what coordinates is the following Kerr metric writing in? In this book the kerr metric was given by
I am confused because of the appearance of the $2d\nu dr$ term because in the standard Kerr metric I know this term doesn't appear. Does anyone know what coordinates is this metric given by and the relationship betwe... | Sorry but have you read that book/section you referenced? The line element you gave is given in eq. (19.45) and in the text directly below it says
"The coordinates $(\nu,r,\theta,\bar \phi)$ are the Kerr coordinates."
The section 19.4.1 in your reference discusses in detail how to get from Boyer-Lindquist coordinate... | {
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Heisenberg uncertainty and Lorentz contraction Consider a particle in a frame moving with speed $v$ relative to the lab frame. By Lorentz contraction, the width of the wavefunction will be smaller in the lab frame, resulting in smaller $\Delta x$. If $v$ is high enough, then the uncertainty principle $\Delta x \Delta p... | You're trying to apply relativity (Lorentz contraction) to a result from nonrelativistic quantum mechanics (Heisenberg uncertainty), so of course you get a contradiction.
In nonrelativistic quantum mechanics, the effect of a boost is given by the Galilean transformation
$$\psi(x) \to \exp((im/\hbar) (vx + v^2t/2))\, \p... | {
"language": "en",
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Why was an 8 TeV collider needed to find a 125 GeV Higgs? This might be very naive, but why wouldn't a (say) 209 GeV LEP do the job?
| You not only need enough kinetic energy to create the new particle, but enough to create the new particle after losing kinetic energy to all the shrapnel particles. At the very least, collisions produce a lot of photons that carry away energy due to the electromagnetic interactions between the colliding particles. Also... | {
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Question about tensor form of Maxwell equation By variating the Maxwell Lagrangian we get the equation of motion. The remaining two Maxwell equations can be written as
$$\epsilon_{\mu\nu\rho\sigma}\partial^{\rho} F^{\mu\nu} = 0.$$
I have also seen it written as the Bianchi identity: $$\partial_{[\lambda}F_{\mu\nu]} = 0... | It's basically just a duality relation analogous to the cross product in three dimensions. But if you want to do some work to show the equivalence, then:
Going from the second equation to the first is easy, just hit it with $\epsilon_{\mu\nu\rho\sigma}$.
Going from the first to the second equation, is a little trickier... | {
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Lagrangian and finding equations of motion I am given the following lagrangian:
$L=-\frac{1}{2}\phi\Box\phi\color{red}{ +} \frac{1}{2}m^2\phi^2-\frac{\lambda}{4!}\phi^4$
and the questions asks:
*
*How many constants c can you find for which $\phi(x)=c$ is a solution to the equations of motion? Which solution has the... | Thanks to all you guys I have found that my mistake was at confusing the kinetic and interaction terms. so here is my answer to this question:
this problem is basically finding the values for $\phi$ that minimizes the effective potential and I have found them above named $c_1$,$c_2$ and $c_3$ considering those are corr... | {
"language": "en",
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Neutral points in a system of charges on the vertices of a square There are four positive charges of equal magnitude placed at the four vertices of a square. Is there any point where the electric field vanishes (neutral point) within the square and in its plane, other than its center?
| No.
Think of this Geometrically.
if each charge generates a field: $ \vec{E}_i = {kq \over {|\vec{r}-\vec{r}_i|}^2} \hat{({\vec{r}-\vec{r}_i})} $ one can see that the center of the square is the only point where $\Sigma \vec{E}_i =0$. This is because of the fact that any point, to the left or to the right, up or down,... | {
"language": "en",
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Space bends relative to what? We all are aware of gravitational waves, as it bends space and time, black hole squeeze space, but the squeezing, bending, expanding happens reference to what? Since the observable universe is the universe existing within itself, so it bends in reference to whose perspective?
| You do not need to have an "external reference" to see consequences of the bending of spacetime. For instance, light travels on a straight line if spacetime is flat. If spacetime is locally bended by a very massive object, a ray of light will follow a curved path when travelling close to this object.
| {
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Understanding tension based on assumptions of pulley system If we consider a simple pulley system with two masses hanging on each end of a MASSLESS and INEXTENSIBLE string around a MASSLESS and FRICTIONLESS pulley, how then can one reason that the tension at each end of the string must be the same?
My own reasoning:
MA... | In general case such system moves with acceleration...
If rope is extensible we cannot assume that the magnitudes of accelerations of the two masses are the same( they will NOT move "jointly"). If the pulley has a mass then tensions on left and right of the pulley must differ to ensure the pulley's rotational accelera... | {
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Can the carbon nanotubes in Vantablack absorb sound? Say you wanted to create a sensory deprivation room surrounded with the Vantablack material. As well as absorbing light, would the carbon nanotubes also be able to absorb sound, eliminating the shape of the walls and floors of an anechoic chamber?
| https://www.acoustics.asn.au/conference_proceedings/INTERNOISE2014/papers/p124.pdf This research paper here has done the experiments with the CNT that you were curious about. Along with the performance of the CNT they've also compared it to normal materials used nowadays. The shape will definitely play an important rol... | {
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Finding conserved quantities I have the 1-form $$\alpha = pdq-\frac{(p^2+q^2)}{2}dt$$
and the vector field
$$v=p\frac{\partial}{\partial q} - q\frac{\partial}{\partial p}.$$
How would I find conserved quantities using Noether's Theorem?
Additionally, is there a difference between finding conserved charges and conserved... | Well, the system is secretly on Hamiltonian form, meaning that there is lurking a symplectic structure $$\omega ~=~ dp\wedge dq$$ in the background, and there is a Hamiltonian $$H~=~\frac{p^2}{2}+\frac{q^2}{2}.$$ Here $$\alpha~=~\mathbb{L}_H~=~pdq-Hdt$$ is the Hamiltonian Lagrangian one-form. If $\gamma: [t_i,t_f]\to \... | {
"language": "en",
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Help needed with applying pseudo force I have read in my book that to apply a pseudo force,
We make sure that the object ( our reference frame ) is accelerating and then we add the negative of it's acceleration vector to the object that we are trying to apply the pseudo force at.
Now take a look at this picture whe... | Your statement about pseudo force is not entirely correct. For example, a rotating observer at the center of a merry go round is not accelerating, but still you need to add centrifugal forces.
Does your observer at $B$ self-rotate as well? If he is not self-rotating, then observed by him, $A$ will be rotating. If he is... | {
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Orbital maintenance of a Mars cycler How much orbital maintenance (i.e. corrections), if any, would a Mars cycler need.
As far as I understand it, a cycler needs no corrections to its orbit unless something extraordinary happens like gravitational interference from a passing comet or something of that sort.
I'm having ... |
As far as I understand it, a cycler needs no corrections to its orbit unless something extraordinary happens like gravitational interference from a passing comet or something of that sort.
Buzz Aldrin's Road map to Mars
The paper from which this table is taken is only 10 pages long, and most of it is spent discuss... | {
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Can a lens focus all types of em waves? A glass lens is usually used to focus visible light, but is this glass lens capable of focusing other types of electromagnetic waves? If not, are there lenses made of different materials that can be used for em waves of different wave lengths (radio waves, micro-waves, x-rays, .... | This question is really about how the refractive index of glass (and other materials) varies with frequency.
Here the term refractive index being used in its broadest sense it that it has a real part which is a measure of the speed of light through the material and an imaginary part which is called the attenuation coef... | {
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Average Velocity: $( v_1+v_2)/2$ While searching for the answer regarding, why acceleration is needed to be constant for using the formula $(v_1+v_2)/2$ , I found many simple and easy proofs regarding this, here in this Physics.SE website, one of which is ,
But can anyone come up with a daily life simple explanation... | A visually geometric answer is that the average velocity with respect to time over an interval is the area under a velocity-time curve (assuming rectillinear motion, of course), divided by the length of the time interval.
This area is only equal to the mean of the end velocities if the curve is a straight line, in whic... | {
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Schwarzschild metric in expanding Universe In Schwarzschild coordinates the line element of the Schwarzschild metric is given by:
$$ds^2=\Big(1-\frac{r_s}{r}\Big)\ c^2dt^2-\Big(1-\frac{r_s}{r}\Big)^{-1}dr^2-r^2(d\theta^2+\sin^2\theta\ d\phi^2).$$
In the asymptotic limit where $r>>r_s$ the Schwartzschild metric becomes:... | Matching the Schwarzschild metric onto the metric of an expanding universe is not trivial. Einstein and Straus tried it in the 1940s but their paper, as I recall, has a mistake. A solution was given in 1956 by C. Gilbert in the MNRAS:
http://adsabs.harvard.edu/full/1956MNRAS.116..678G
As I said, the solution is not t... | {
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Could the universe be shrinking? It is thought the universe is expanding because of the red shift of most galaxies but if all the matter in the universe was actually falling into a massive black hole wouldn't most galaxies still be red shifted because the black hole would accelerate every galaxy and every galaxy that w... | The universe as a black hole would have observable consequences. The Schwarzschild metric
$$
ds^2~=~c^2(1~-~2m/r)dt^2~-~(1~-~2m/r)^{-1}dr^2~-~r^2d\Omega^2
$$
defines the curvature of spacetime. Here we have $m~=~GM/c^2$. The Riemann curvature tensor components to $O(c^2)$ are
$$
R_{trtr}~=~-\frac{2mc^2}{r^3},~R_{t\thet... | {
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How would you include gravity in a momentum problem?
Say you have a big ball of mass $m_1$ and a little ball on top of that of mass $m_2$ (assume they are a small distance apart, like $1~\mathrm{mm}$). Now lets drop these from a height of $h$ so that the big ball will bounce off the ground and collide into the little ... | Use kinematics to find the velocity of both balls, so that tells you their momentum, except the lower one has its momentum reversed when it bounces. Then conserve that total momentum, and kinetic energy, during the collision at the ground. Then solve the kinematics of what follows. (By kinematics, I mean the fomulae... | {
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Equations of motion for a free particle on a sphere I derived the equations of motion for a particle constrained on the surface of a sphere Parametrizing the trajectory as a function of time through the usual $\theta$ and $\phi$ angles, these equations read:
$$ \ddot{\theta} = \dot{\phi}^2 \sin \theta \cos \theta $$
$$... | I checked, and these equations of motions correspond to motion in of an otherwise free Lagrangian. Something that will make your life easier in solving this is to recognize that angular momentum is conserved here. Because velocity is guaranteed to be perpendicular to the radius:
$$\begin{align} |\mathbf{L}| &= mvr \\
&... | {
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Motivation behind the theory of cosmological perturbations What is the main motivation behind the theory of cosmological perturbations? Is it the observational data, observational hints, or perhaps the theory of inflation?
| None of those. If you mean by motivation what it means in English, what was the reason for doing perturbations, it's more or less straightforward.
It was to try to find approximate solutions to how deviations from an ideal homogeneous and isotropic universe evolves. Since people figured that probably gravity had somet... | {
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Classically, why is the gyromagnetic ratio always $q/2m$? For uniform charge and mass distribution for a rigid body rotating with a uniform angular velocity about its centre of mass, I want to know if it is just a mathematical artifact of integration which cancels out the factors of moment of inertia (angular momentum)... | Although you question is not particularly precise, here is my honest guess to what might give you an answer:
The classcial gyromagnetic factor is obtained by the following straightforward calculation. Consider a single particle of mass $m_e$ and charge $e$ orbitting on circle of radius $r$ with velocity $v$. Then its m... | {
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Fusion boosted fission reactor With weapons, fusion boosted fission seems to already be a thing. But I'm not interested in weapons.
Are there any types of fission reactor (other than a nuclear explosive) that would make more efficient use of fissile material by mixing in fusionable material?
Obviously the average tempe... | Something very close to this is the fusion-fission hybrid idea where fusion does not have to be at the point of self-sustaining burning (so it is below the ignition threshold) but rather driven by an external power source. Still, such a driven fusion reactor can produce lots of neutrons that can be used for driving fis... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why is it that the change in internal energy always uses the formula with Cv in regards to pressure/volume/temperature changes on a gas? Normally I would associate the use of $C_v$ with finding the energy taken into or leaving a system when the volume is kept constant. However, the formula to find $\triangle E_i$ (chan... | First, for arbitrary process, this formula applies only to ideal gas. For the special case of constant-volume process, this applies to all gases, by definition of $C_v$.
Now internal energy $U$ is a state function. So if you know temperature in initial and final states for an ideal gas, change in $U$ is thereby complet... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/283054",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 3
} |
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