Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Gradient of the potential originated from two similar magnetic vector potentials is not the same The magnetic vector potential $\textbf{A}$ can be defined up to a gradient of a field. Adding or subtracting such gradient should not change the physics of the problem. The same reasoning is applied for the time derivative ... | Hint: OP's gauge transformation of the magnetic vector potential $$\vec{A}^{\prime}~=~\vec{A} +\nabla \Lambda$$ can e.g. be described by a time-dependent gauge parameter $$\Lambda~=~ -(y+z)t. $$
But this means that the electric scalar potential $$\phi^{\prime}~=~\phi -\partial_t \Lambda$$ transforms as well.
| {
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"timestamp": "2023-03-29T00:00:00",
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Math / Physics Help - Barrel Pressure and Velocity Back in 1993 I derived the following equations to calculate projectile velocity and barrel pressure. Recently, I have noticed that I need to double the calculated results in order to obtain real word results.
I need some help to find out why I have to double the derive... | The values you used for barrel pressure (55 kpsi for .50BMG, 60 kpsi for 7.62mm) are all PEAK chamber pressures not $\bar P$.
$v_p=\sqrt\frac{2\bar P A L}{m}$
this is the last equation you wrote that was correct.
I looked at your excel sheet and found that you did $\sqrt\frac{2\bar P A L}{m}\over 12$ to obtain a $v_p$... | {
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How accurate is Newtonian Gravity? I know that really fast moving things need Relativity rather than Newtonian physics.
I also know the quirk of the Mercury´s orbit.
But just how much more accurate is General Relativity than Newton´s Law of Gravitation for predicting say the orbit of Earth or Neptune?
Can the "slingsho... | The anomalous perihelion shift of Earth is 3.84 arc-seconds per century, or about one tenth the size of Mercury's shift. The anomalous perihelion shift of Jupiter is 0.0622 arc-seconds per century, or about one thousandth the size of Mercury's shift.
I can't find calculations for the effect of GR on slingshots, but I b... | {
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Why does Newton's third law exist even in non-inertial reference frames? While reviewing Newton's laws of motion I came across the statement which says Newton's laws exist only in inertial reference frames except the third one. Why is it like that?
| This is a tricky question.
I will show a counter example:
Assuming only one thing exist in the world, a ball, and a frame.
The frame accelerates with constant $a$ as we wish since it is just something imaginary, and you see the ball has an acceleration as well, and conclude there must be a force acting on the ball:$$F=... | {
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"source": "stackexchange",
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Diffeomorphism Invariance of General Relativity I'm sorry I know this has been asked before, but I'm still a bit confused. I understand that an active diffeomorphism $\varphi:M\to M$ can be equivalently viewed as a coordinate transformation so that since the equations of general relativity are tensorial $\varphi^*g$ wi... | The diffeomorphism invariance of GR means we're operating in the category of natural fiber bundles, where for any bundle $Y\to X$ of geometric objects that appear in the theory, we have a monomorphism
$$
\mathrm{Diff} X \hookrightarrow \mathrm{Aut} Y
$$
Any diffeomorphism of space-time $X$ needs to lift to a genera... | {
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Oscillation of a Bose Einstein condensate in a harmonical trap We were asked to try to make a theoretical description of the following phenomenon:
Imagine a 2D Bose Einstein condensate in equilibrium in an harmonical trap with frequency $\omega$. Suddenly the trap is shifted over a distance a along the x-axis. The cond... | As long as you consider the BEC without inter-particle interactions (because they are negligible for instance) you can simply use the Schrodinger equation.
However, if you want to take interactions into account you may want to consider to take the Thomas-Fermi approximation.
When interactions are dominant in the dynami... | {
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Infinite Wells and Delta Functions In considering a delta potential barrier in an infinite well, I can just enforce continuity at the potential barrier-it doesn't have to go to zero. Why then does it need to go to zero at the walls of the infinite well? These two cases seem to be very similar to be, I even feel like th... |
Why then does it need to go to zero at the walls of the infinite well?
Because the proper way to find $\psi$ is to solve Schr. equation for finite potential well first and find how $\psi$ depends on the parameters of the potential. Then try to make the limit to the infinite potential well and look what happens to th... | {
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How can a block which is not receiving the direct force have a greater acceleration?
I solved it like this:
$$F(\text{st max})=5\text{ N}$$
For the top block,
$$\begin{align}
6\text{ N} - 5\text{ N} &= 1a \\
a &= 1\ \mathrm{m/s^2}
\end{align}$$
For the lower block, the driving force will be the frictional force, so
$$... | Your calculations are wrong.
The basic assumption that friction = u x N
u = coefficient of friction
N = Normal force (in this case the weight of the block)
Above assumption is valid only if there is relative motion between the two blocks i.e a case of sliding motion, but before we consider that sliding occurs we shou... | {
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Block and inclined plane (INPhO Problem) The figure shows two blocks on an inclined plane of mass 1kg each.The coefficient of static as well as kinetic friction is $0.6$ and angle of inclination is $30^\circ$ . Find the acceleration of the system. (string and pulley are ideal). Take $g=10m/s^2$.
[This is not the real ... | The answer lies in the fact of how frictional forces work."Frictional forces always try to oppose relative motion between surfaces(and if possible they will completely eliminate the motion between the surfaces)."
We can write the equations of motions as(assuming $a$ as stated in the figure) as:
$m_1g-T=m_1a$
$T-m_2gsin... | {
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Have there been more distinctive names suggested for neutrino mass states $\nu_1, \nu_2, \nu_3$? The different mass states of neutrinos are generally named $\nu_1, \nu_2, \nu_3$.
By comparison, the names of quark mass states (up, down, strange, and so on) or the names of mass states of charged leptons (electron, muon, ... | No. The data is analyzed with $\nu_1, \nu_2,\nu_3 $, well defined by their mixing matrices in the PDG, but, before the resolution of the hierarchy, they cannot be identified firmly with the classroom poster placeholder names $\nu_L, \nu_M,\nu_H $, Lightest, Middle, Heaviest.
In the normal hierarchy, the two sets ident... | {
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Intuitive understanding of the entropy equation In thermodynamics, entropy is defined as $ d S = \dfrac{\delta q_{\rm }}{T}$. This definition guarantees that heat will transfer from hot to cold, which is the second law of thermodynamics. But, why do we denote entropy as$\dfrac{\delta q_{\rm }}{T}$ other than $\dfrac{\d... | The answer is plain and simple differential calculus $$ds = \frac{\partial s}{\partial e} \large{|}_vde +\normalsize{\frac{\partial s}{\partial v}} \large{|}_e dv$$ What does the differential change $$ds=\frac{\delta q}{T}$$ have to do with the first? For starters, an important question on everyones mind should be wh... | {
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Correct way to do a Thomas-Fermi approximation for cold gases I have calculated the total Gross-Pitaevskii energy for a 2D Bose-Einstein condensate in an harmonical trap, using a variational gaussian wave function with a variational parameter b. Now I want to compare the variational energy to the Thomas-Fermi result.
... | You simply take $|\psi|^2=1/g[\mu-V(x)]$.
This because now your time independent GPE is
$\mu\psi=(V+g|\psi|^2)\psi$
| {
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Purposes of QEC stabilizers I am going through the idea of stabilizer formalism.
Defined what is a Pauli group $P_n$ and its properties, we describe a stabilizer set $S$ as:
$$S\subset P_n$$
The stabilizer set establishes valid codewords for a state if the equation $$s\left|\psi\right\rangle=\left|\psi\right\rangle,\;\... | 1) If there is an error $E_j$, the new states $E_j|0\rangle_L$ and $E_j|1\rangle_L$ are eigenvectors, with eigenvalue $-1$, of all the stabilizers $s_j$ belonging to some set subset $S_j$ of $S$. (the elements of $S_j$ anticommute with $E_j$).This subset $S_j$ identifies uniquely the error $E_j$.
2) $|0\rangle_L$ and... | {
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Does a heavy body move with the slightest force on a frictionless surface? If I apply horizontal force on a body resting on the ground, my force will be opposed by the frictional force and the body will accelerate at the point where my force exceeds the force of friction = $\mu\, \mathrm{N}$ ($\mathrm{N}$ being the nor... | (Classical Physics only)
Any massive body has a property known as inertia, thus even a body floating in outer space would require some kind of force to be accelerated. Using Newtons second law, you would find
$$\tag{NII} \sum \vec{F} = \frac{\mathrm{d}}{\mathrm{d}t}\vec{p},$$ which for constant mass and one-dimension... | {
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Simple QM question about Sy matrix Given a spin 1/2 particle in state $|\alpha\rangle=\begin{bmatrix}a \\b\end{bmatrix}$, what is the probability of it being measured in the $S_{y+}$ state. Is this equivalent to, if $S_y$ is measured on this particle, what is the probability the result being $\hbar/2$? I think it's su... | Figured out what I was doing wrong. I had to write it out explicitly considering, a,b complex.
The answer is $\frac{1}{2}(|a|^2 + |b|^2 + i(a^*b - b^*a))$ Does anyone know a more succinct way of writing that last term? It's definitely real so no worries about that.
| {
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Does light have an unending journey? When we shine a torch in a room its light travels to the back of the room.
What happens to the light of a star ? I dont suppose we can say it continues to travel to the back of the universe as the universe has no back. Does the light continues its journey forever ? Or does it someho... | Light beams are electromagnetic radiations, they stops when they meet some material that can stop them, in space generally they continue propagate until they have energy.
| {
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Practical example of stabilizer codes Given the Steane code
$$
\left|0\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|0000000\right\rangle + \left|1010101\right\rangle + \left|0110011\right\rangle + \left|1100110\right\rangle + \left|0001111\right\rangle + \left|1011010\right\rangle + \left|0111100\right\rangle + \left... | It is correct. We may summarize all the operations :
1) Encoding one logical qubit as $n$ physical qbits (codeword) , $\alpha|0\rangle + \beta |1\rangle \to \alpha|0\rangle_L + \beta |1\rangle_L$, here $n$ = 7 for the Steane code.
2) Preparing $m$ ancilla qbits, here $m = 3$, in your schema allowing to detect phase-fl... | {
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momentum conservation and gluons The process is the following:
$$e^-e^+ \rightarrow photon \rightarrow quark + antiquark$$
Regarding the momentum conservation law, how come we have a photon of spin 1 and at the end some meson with spin 0?
Are gluons "behind this"? If this is correct, at which point are they radiated? ... | Ignore the gluon for the moment
Regarding the momentum conservation law, how come we have a photon of spin 1 and at the end some meson with spin 0?
First of all spins are angular momentum not momentum. Secondly the two quarks have a spin 1/2 which will add to either 0 or 1, and 1 conserves the angular momentum at ... | {
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Drag Force per point in the body Let us consider the common equation for drag force for any body.
$F_D = \frac{1}{2}\rho v^2C_dA$
Here the A is the representative area which is the so called area of cross section of the body for most shapes under conditions of stable velocity (that is the angle of attack/velocity/visc... | Each point on the surface will have a pressure (force normal to surface) and drag (force tangential to surface). By integrating over the entire surface you get the overall effect which is sometimes expressed in force/moments as
$$ F_D = \frac{1}{2} \rho v_{body}^2 A_{body} C_D
\\ M_D = \frac{1}{2} \rho v_{body}^2 \ell... | {
"language": "en",
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Why are we living in the $q$ part of the phase space? In Hamilton mechanics and quantum mechanics, $p$ and $q$ are almost symmetric. But in the real world, the $p$ space isn't as intuitive as the $q$ space. For example, We can uniquely identify a person by its position, but not its momentum. Two fermions can easily hav... | We are not living in the $q$ part of phase space : we indeed live in the full phase space since we're definitely not fixed-momentum objects.
However we give more importance to our position than to our velocity/momentum; then the question gets out of physics into psychology.
In my opinion, part of it may be because of t... | {
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Book Recommendation: Classical Relativistic Fields My bare bookshelves are crying out for the addition of a new family member, more specifically a book:
*
*Discussing the classical Klein-Gordon field, spinor fields, gauge fields and all other matter fields in a generally co-variant fashion.
*Discussing of the Schro... | Some of the topics you mentioned seem to be discussed in this book:
Mark Burgess, Classical Covariant Fields, Cambridge University Press, 2005
http://www.cambridge.org/us/academic/subjects/physics/theoretical-physics-and-mathematical-physics/classical-covariant-fields#contentsTabAnchor
| {
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Why does this perpetuum mobile not work?(Gases and Densities) I recently came up with the following concept. It is very simple, and may have been thought of before.
A picture says more than a thousand words, so here is it explained in a picture:
Note that water was used to make the example easier to understand. Anoth... | In addition to Bernhard's answer, just because three gases (Gas A,B and air - which is itself a mixture of nitrogen, oxygen, and other gases) have different densities, it does not mean they will remain seperated when in a container. In fact, as entropy of the system increases over time, Gas A, B and air will make an ev... | {
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Explain reflection laws at the atomic level The "equal angles" law of refection on a flat mirror is a macroscopic phenomenon. To put it in anthropomorphic terms, how do individual photons know the orientation of the mirror so as to bounce off in the correct direction?
| There are a few ways of approaching this. Visible light is about 500nm, while typical atomic diameters are on the order of 0.5 nm to be generous (citation for carbon is 0.2 nm). So from this point of view the rough properties of the surface can't be resolved. However, each individual atom will absorb and re-radiate dep... | {
"language": "en",
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What is the relationship between Maxwell–Boltzmann statistics and the grand canonical ensemble? In the grand canonical ensemble one derives the expectation value $\langle \hat n_r\rangle^{\pm}$ for fermions and bosons of sort $r$:
$$ \langle \hat n_r\rangle^{\pm} \ \propto \ \frac{1}{\mathrm{exp}[(\varepsilon_r-\mu)/k_... | The introductory paragraph you quote with horror says temperature ''high enough'' to avoid quantum effects. (It did not say anything like ''arbitrarily large''.) If the temperature is too low, things like Bose--Einstein condensation can occur, which invalidate Maxwell--Boltzmann statistics. The temperature should be... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Does antimatter curve spacetime in the opposite direction as matter? According to the Dirac equation, antimatter is the negative energy solution to the following relation:
$$E^2 = p^2 c^2 + m^2 c^4.$$
And according to general relativity, the Einstein tensor (which roughly represents the curvature of spacetime) is linea... | The sign of the stress-energy tensor does not change for antimatter. There are various energy conditions (ANEC, WEC, etc.) that stipulate various bounds on the stress energy tensor, but the only things that violate them are small scale quantum effects such as the Casimir force, the scalar inflaton field, and dark energ... | {
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How does that Boltzmann distribution interact with entropy? In an ideal gas, the Boltzmann distribution predicts a distribution of particle energies $E_i$ proportional to $ge^{-E_i/k_bT}$.
But, doesn't entropy dictate that the system will always progress towards a state of maximum disorder? In other words the system e... | What you say is not true. Macrovariables of a system will evolve towards and fluctuate around equilibrium values which maximize/minimize the thermodynamic potential corresponding to the constraint imposed on your system.
For an isolated system, this corresponds to maximum entropy states while for a system in contact wi... | {
"language": "en",
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Does time expand with space? (or contract) Einstein's big revelation was that time and space are inseparable components of the same fabric. Physical observation tells us that distant galaxies are moving away from us at an accelerated rate, and because of the difficulty (impossibility?) of defining a coordinate system w... | The simple answer is that no, time is not expanding or contracting.
The complicated answer is that when we're describing the universe we start with the assumption that time isn't expanding or contracting. That is, we choose our coordinate system to make the time dimension non-changing.
You don't say whether you're at s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/83531",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does the moon affect the Earth's climate? So, this morning I was talking to a friend about astronomical observations, and he told me that lately there has only been good weather when there was a full moon in the sky, which was a shame.
I jokingly said: 'maybe there's a correlation!', but then I started thinking: wait,... | I think the moon and sun do affect the weather more than we are led to believe, the moon is getting farther away and the sun is getting larger, these both must have an impact on earth. The suns solar flares and mass corona ejections also play a part.
I believe small changes in the moons orbit and distance and the suns... | {
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"timestamp": "2023-03-29T00:00:00",
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A simple conjecture on the Chern number of a 2-level Hamiltonian $H(\mathbf{k})$? For example, let's consider a quadratic fermionic Hamiltonian on a 2D lattice with translation symmetry, and assume that the Fourier transformed Hamiltonian is described by a $2\times2$ Hermitian matrix $H(\mathbf{k})=a(\mathbf{k})\sigma_... | I agree with your argument, but I thought I would just rephrase the same logic in a slightly different way, similar to how one would prove it in an algebraic topology course. (I would have done this as a comment, but it's a bit too big for that.)
Basically the Chern number measures the topology of the map $\newcommand... | {
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"timestamp": "2023-03-29T00:00:00",
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Why does $[xp_{y},x]$ commute? I'm looking at a solution in my book that says $[xp_{y},x]$ commutes.
Does bracket notation imply:
$[A,B]=AB-BA$
so that
$[xp_{y},x]=xp_{y}x-xxp_{y}$
Taking the comment from Max Graves and solving a slightly different commutation relation:
\begin{align}
-[yp_{x},x]f &= yi\hbar\frac{\pa... | You may just not bother to use a test function, here. This problem is so easy you can work it all just using the properties of the commutator.
$$[xp_y,x]=x[p_y,x]+[x,x]p_y$$
Now $[p_y,x]$
vanishes because of the fundamental commutation relation between $p_i$ and $x_i$ which is $$[p_i, x_j]= -i\hbar \delta_{ij}$$
On the... | {
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Why is Planck mass much larger than the smallest mass that we actually know about? The three fundamental constants $h$, $c$ and $G$ are manipulated and rearranged in different ways to get the Planck time, Planck mass etc. The Planck time is said to be the smallest time possible and Planck length the smallest length(If ... | These things don't have to be 'smallest' or 'largest'. They are simply (what especially high-energy physicists would agree to be) the most natural units in which to carry out calculations when doing fundamental research. The crux is realizing that things like a 'second' and a 'meter' or a 'kilogram' are purely invented... | {
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Understanding the Eötvös experiment The aim of the Eötvös experiment was to "prove" that for every (massive) particle, the quotient $\frac{m_g}{m_i}$ is constant, where $m_g$ is the gravitational mass and $m_i$ is the inertial mass.
The experiment:
Consider two objects with coordinates $x(t)$, $y(t)$ and with masses $... | The torque about $\bf{e}_3$ is zero when the masses weights are balanced on the rod. For example the distance from $M$ to the support must be equal to $c = \frac{m_g}{M_g+m_g} r$
There is torque about $\bf{e}_2$ if the centrifugal forces are not propotional to the weights.
$$ \tau_2 = M_i c \ddot{x}_3 - m_i (r-c) \ddo... | {
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What is the meaning of $U''(x)=0$? Most potentials with a minimum can be described approximately as a harmonic oscillator.
So the procedure is to Taylor expand $U(x)$:
$$U(x)=U(0)+U'(0)x+\frac{1}{2}U''(0)x^2 +...$$
If we suppose that the potential is cero at the origin an it has a minimum there, we get:
$$U(x)=\frac{... |
Does it just mean that to a small approximation a body will not
oscillate?
It means that you must always remember the context in which a formula is valid and not "blindly" apply it.
Where does the formula come from? Consider the homogeneous differential equation for the harmonic oscillator:
$$\ddot x + \dfrac{k}{m... | {
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Expanding Universe Balloon Analogy - Anything Similar for Time? It is difficult to imagine the infiniteness of space and how it itself is expanding rather than the universe expanding into something else. A helpful analogy is that of drawing little dots (representing galaxies or some other sub-universal structure) onto... | time will disappear in the same way it appears I don't know how to explain it but in easy way the the end is just the beginning and it will look like a cycle as it began it will end
| {
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Do all planets have an electric charge? Do all planets have an electric charge?
If yes, is positive or negative?
And how much each magnitude?
I have read some articles which really confused me. Some of these articles said that all planets have a negative charge and the sun has a positive charge. Some other articles ... | In general, I would think that planets would not have a net electric charge at all.
The reason is that planets are constantly being struck by various charged particles (protons & electrons with some metal1 ions). If a planet had a net negative charge, it would repel the electrons and attract the protons & ions; if it ... | {
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What is the correct Hamiltonian for a system of coupled quantum oscillators? The Hamiltonian (see Eqn. 1 in Appendix 2 of this paper) for a system of coupled quantum oscillators is given as
$$H=\frac{1}{2}∑_{i}p^{2}_{i}+\frac{1}{2}∑_{j,k}A_{jk}q_{i}q_{k}$$
Yet, in my QM course, the Hamiltonian for such a system was giv... | They almost are. Clearly you replace $q_j$ by $x_j$ since the canonical commutation relationships are the same between these two and the $p_j$. Your QM course equation is then a special case of the one in the paper: if you then expand the last term in your QM course equation, you have equivalence if $A_{11} = A_{NN} = ... | {
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Is the symmetry group of two spin 1/2 particles $SU(2) \times SU(2)$ or $SU(4)$? This is a simple question. Please forgive me, as I am a lowly experimentalist.
Suppose we have two free spin 1/2 particles, i.e. a 4-fold degenerate system. What is the set of symmetry operations on this system? Is it $SU(2) \times SU(2... | My answer is in two parts.
First part. $SU(2)$ has representations of any dimension $2j+1$ with integer or half-integer j. Direct product of two $j=1/2$ representations is reducible to a direct sum $j=0$ (singlet) and $j=1$ (triplet). All remain representations of $SU(2)$ which defines the spin in the first place.
Now... | {
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Hydrostatic pressure? What what I understand, hydrostatic pressure is the "weight" of the water pushing against objects. But if this is true, why is hydrostatic pressure perpendicular to the surface it acts on instead of always going down?
For example, if you placed a book on a desk, the book's weight would push agains... | Hydrostatic pressure concers pressure that happens on perfect fluids in equilibrium. A perfect fluid is slippery, devoid of viscosity: when it is in equilibrium, it cannot exert nor resist shear (tangential force). Therefore, on the walls of a vessel sustaining a perfect fluid at rest, the normal component is solely re... | {
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What is the use of this formula 1 Tesla = 1 Newton/Ampere/Meter? What does Newtons/Ampere/Meter stand for?
From this formula: 1 Tesla = 1 Newtons/Ampere/meter
what can it be used for? To do what?
Ampere/meter Is the same unit as a field's intensity H? Or what is it?
Edit by public: How can this equation be used with re... | From Wikipedia:
A particle carrying a charge of 1 coulomb and passing through a magnetic field of 1 tesla at a speed of 1 meter per second perpendicular to said field experiences a force with magnitude 1 newton, according to the Lorentz force law.
So 1 Tesla = 1N / (1C . 1m/s), and one Coulomb per second is one Amper... | {
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Why don't metals bond when touched together? It is my understanding that metals are a crystal lattice of ions, held together by delocalized electrons, which move freely through the lattice (and conduct electricity, heat, etc.).
If two pieces of the same metal are touched together, why don't they bond?
It seems to me ... | While simple contact between metals isn't enough for most metals to bond, relative motion will achieve the fusion between the metals (at small contacts). A common occurrence is seizing up of mechanical devices due to insufficient lubrication.
I don't think screws stick due to metal-metal bonding- its mostly simple dis... | {
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how long do large hadron collider experiments take? This travel stackexchange answer has kinda got me wondering... how long do experiments involving the large hadron collider usually take? I'd expect you run it for a few seconds and bam - higgs boson detected or whatever. Maybe it'd take a few months to set the experi... | This document (NB it's a pdf) contains details of the beam operation. Here's a key graph nabbed from the presentation:
At the end of an experimental run the beam is dumped, and it takes about an hour and a half to get the beam back up to full energy and intensity. Once the beam is at full strength the LHC generates da... | {
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Lorentz covariance of the Noether charge The invariance under translation leads to the conserved energy-momentum tensor $\Theta_{\mu\nu}$ satisfying $\partial^\mu\Theta_{\mu\nu}=0$, from which we get the conserved quantity$$P^\nu=\int d^3\mathbf x\Theta^{0\nu}(x)$$But I cannot see explicitly how this quantity is a four... | You may use the following notation for hypersurfaces in four dimensions :
$d\sigma_\mu = \epsilon_{\mu\alpha\beta\gamma}dx^\alpha dx^\beta dx^\gamma$
For instance $d\sigma_0= d^3x$
The expression of the momentum-energy is then :
$P_\nu = \int d\sigma^\mu \Theta_{\mu\nu}$
The same kind of expression could be used with ... | {
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Absorption of radiation due to temperature I was wondering if the temperature of an object affects the amount of radiation it absorbs.
For example, if I have a box that is hotter, will it absorb more energy as compared to the same cooler box?
| The rules of Black Body radiation say: no. Assuming the composition of the box doesn't change, its absorptivity is the same regardless of temperature. What does change is the amount of energy it'll radiate, which is a direct function of temperature (black body again).
This often confuses folks, as the spectral absor... | {
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What is negative Energy/Exotic Energy? So I have been researching around a little as I am highly interested in Astrophysics and I came across an energy I have never heard of before; negative energy also commonly known as exotic energy. Now I started to research this however I found the concept rather hard to grasp due ... | In general relativity, the energy content of a region is given in terms of a stress-energy tensor. The elements of this tensor are not given by general relativity itself and can differ depending on what matter and fields are present. To try to draw general conclusions about what is allowed and forbidden in general rela... | {
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Why do we must know the Weyl tensor for 4-dimensional space-time? I heard that we must know the Weyl tensor for fully describing the curvature of the 4-dimensional space-time (in space-time with less dimensions it vanishes, so I don't interesting in cases of less dimensions). So I have the question: what is physical (o... | The Riemann tensor encapsulates all information about the 4-dimensional space-time. This information can generally divided into two sectors:
*
*Information about the curvature of space-time due to the existence of matter. This is given by the Ricci tensor according to the Einstein equation
$$
R_{\mu\nu} - \frac{1}{2... | {
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Is two cars colliding at 25 mph the same as one car colliding into a wall at 50 mph in reference to injuries? This question has been asked using 50 & 100 mph reference, see this Phys.SE post and links therein. However, I am interested in the potential injuries to occupants of the autos. As the one going into the wall h... | Severity of injury is going to be proportional to the rate of change of momentum. Two cars colliding head-on will have a lower value of rate of change of momentum than one car striking a typical wall. Reason: a typical wall will not cushion an impact as well as a typical car.
More cushioning means the actual collision ... | {
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Do low frequency sounds really carry longer distances? It is a common belief that low frequencies travel longer distances. Indeed, the bass is really what you hear when the neighbor plays his HiFi loud (Woom Woom). Try asking people around, a lot of them believe that low sounds carry longer distances.
But my experience... | Another thing that happens that can lead you to think that low frequency sounds attenuate quicker is that if you record yourself one time being close to the microphone and another time being farther away, you'll notice that the farther you are the more the lowest frequencies are picked up. This is due to the proximity ... | {
"language": "en",
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Will the heat flow of Joule heat be different, if the Joule heat is dissipated in a material that has a temperature gradient beforehand? Let us assume one dimensional heat transfer, for example a finite length wire starting at point $0$ and ending at point $\ell$. If the current passes the wire, the Joule heat $I^{2}R$... |
Had the wire had a constant temperature T, the half of the power $I^2R/2$ will be passing the left end, the other half will be passing the right end.
I think this is a wrong statement. This is a common assumption used in a thermo-electric circuit theory to derive the equations. I would argue that this is valid in the... | {
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Reference request for exactly solved models in statistical mechanics Can someone recommend a textbook or review article that covers exactly solved models in statistical mechanics, such as the six- or eight-vertex models? If there is literature at the undergraduate level, that would be ideal. I'm only familiar with Baxt... | I would like to add that it is very important to know what you can find out without knowing the exact solution. Kardar's book "Statistical physics of fields" teaches that in a very engaging way. To get quickly started, I suggest the topics of Scaling theory, and real space renormalization in 1-d ising model. Your motiv... | {
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Photons from stars--how do they fill in such large angular distances? It would seem that far-away stars are at such a distance that I should be able to take a step to the side and not have the star's photons hit my eye. How do stars release so many photons to fill in such great angular distances?
| So starlight propagates spherically and each human eyeball creates localized photons just at the intersection of wavefront and retina. No matter where you are in relation to the star some part of this wavefront will reveal the photon stream. Some kind of sensor that could image the path of all the photons/wave function... | {
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What applications would room temperature super conductors have? I've heard that a room temperature super conducting material would be a major discovery. How likely is this within the next century and if discovered what would be possible?
| As said in the comments, this is a very broad question, so instead of writing a very long post, I point you to a good article titled "Superconductivity and the environment: a Roadmap": http://iopscience.iop.org/0953-2048/26/11/113001 . The article lists a lot of emerging technologies that make use of superconductors.
T... | {
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Why are rockets so big? I'm curious why rockets are so big in their size. Since both the gravitational potential one need to overcome in order to put thing into orbit, and the chemical energy burned from the fuel, are proportional to the mass, so if we shrink the rocket size, it would seem to be fine to launch satellit... | Consider the problem in the from of a ratio, what is the ratio of mass used to lift the rocket(fuel), to the mass finally put into orbit(cockpit). That proportion will be much the same regarding smaller objects that must be put into orbit. If you use the same ratio or proportion to calculate the needed fuel mass for a ... | {
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Is there a way for an astronaut to rotate? We know that if an imaginary astronaut is in the intergalactic (no external forces) and has an initial velocity zero, then he has is no way to change the position of his center of mass. The law of momentum conservation says:
$$ 0=\overrightarrow{F}_{ext}=\frac{d\overrightarrow... | For those that are cat-challenged, here's an alternative explanation and demonstration you can try at home! This demonstration was taught to me by my math lecturer. All you will need is:
A swivel chair
and a heavy object (e.g. a big textbook)
Stand on the seat of the chair (watch your balance now) holding the heavy o... | {
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Electromagnetism: Conductors Even though the thermal velocity of electron in a conductor is comparatively high, the thermal velocity is not responsible for current flow? Why is this the case?
| For something like a metallic crystal, if you apply an electric field then the (Bloch) electrons just keep accelerating until they reach the end of the Brillouin zone (the momentum space box that they occupy), and then "wrap around" to the opposite end so that their average momentum is zero (Bloch oscillations). So a ... | {
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Commutator evolution operator and position operator Let $H= \frac{p^2}{2m}$, then I am supposed to calculate $[x,e^{-iHt}]$.
My idea was to use $[x,p^n]=i \hbar n p^{n-1}$ and so I ended up by using the series for the exponential function with $-\frac{t \hbar}{m} e^{-iHt}$.
Could anybody tell me, whether this result is... | Yes. Also note that in the momentum representation, $x = i\hbar \frac{d}{dp}$, which is what your commutation relation proved as a special case. You could use this shortcut right off the bat.
| {
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Relationship between power and max. speed I'm talking about the maximum speed if let's say I have a car with the power $P = 1000 \text{W}$ and a force of friction of $5 \mbox{N}$ acting in the opposite direction. After some googling I found that the maximum speed is given by $P=Fv$, where $P$ is the power, $F$ is the f... | Consider your simple example: a car with a fixed power output of $1000 \text{ W}$ accelerating against a constant frictional force of $5\text{ Newtons }$ (Even better, assume that there is no friction, but the car is climbing a very gentle slope, such that gravity exerts $5\text{ Newtons}$ of force back along the slo... | {
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What is the physics of a spinning coin? When we spin a coin on a table, we observe 2 things:
*
*It slows down and stops after sometime.
*It does not stay at just one point on the table but its point of contact with table changes with time.
I was trying to explain quantitatively this but I am stuck at how to take fr... | There is no easy way to model a spinning coin and calculate these observations. It slows down mostly because of air resistance and friction(here you must take velocity dependent friction-angular velocity in your case-) and it moves due to the combination of torque of gravity(a.k.a. precession) and friction.
Velocity d... | {
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Are coherent states of light 'classical' or 'quantum'? Coherent states of light, defined as
$$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle
$$
for a given complex number $\alpha$ and where $|n\rangle$ is a Fock state with $n$ photons, are usually referred to as the most c... | Coherent states are quantum states, but they have properties that mirror classical states in a sense that can be made precise.
To be concrete, let's consider coherent states in the context of the simple harmonic quantum oscillator which have precisely the expression you wrote in the question. One can demonstrate the... | {
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Asteroid collision debris calculation I wonder how to determine the directions, in which the collision debris is launched when 2 asteroids collide.
I am aware of: m1*v1 + m2*v2 = m*v = m3*v3 + m4*v4 + m5*v5 + ...
and this works just fine for the masses and valocity, however I find it difficult to determine the boundari... | I think that this problem doesn't have an exact answer. Some time ago, I talked about this with the astrophysicist Paolicchi (this is the asteroid named after him) who works on the field. The conclusion is that debris are produced at random and you can only impose some ("few") constraints globally, say on big branches ... | {
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Is Dark Matter evenly spread out in the universe? Is Dark Matter evenly spread out? If no, could we ever find a correlation between the amount of dark matter and matter in a specific place?
| The existence of dark matter comes primarily from gravitational evidence - in other words, we predict some behavior because of the force of gravity, but we don't observe that behavior and infer that dark matter is to blame. Thus, most predictions for dark matter come from locations in the universe where there are massi... | {
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Momentum conservation problem Lets a plastic ball of mass m which is collided with steel. After collision the ball is coming back with the half initial speed. If the steel doesn't move then how can I interpretate this ?
Let the initial speed of the ball is $u_1$ and mass $m_1$ and mass of steel $m_2$ speed of stee... | If $m_2 < \infty$ this is impossible. If $m_2 = \infty$ it is possible because $\infty \times 0$ is any number.
| {
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Mixed quantum states and "complete knowledge of the system" I ran across this statement in a professor's notes and I think it's just a typo, but I wanted to take the opportunity to check my understanding. So in his notes it says:
even if we have complete knowledge
of quantum systems, they still can be in the[a] mixe... | The other thing that I can think of, is when you are not interested in some parts of your system(i.e. environment), so you trace it out. Now if the environment is not separable from the rest of the system, which is usually the case; what you are left with(the reduced state) is a mixed state.
Note that in this case:
$$\... | {
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Centrality and collision parameter b Can someone tell me what does it 20-30% collision centrality mean in terms of impact parameter b?
| The most general relationship is
$$c(b) = \frac{\int_0^b \frac{\mathrm{d}\sigma}{\mathrm{d}b}\mathrm{d}b}{\int_0^\infty \frac{\mathrm{d}\sigma}{\mathrm{d}b}\mathrm{d}b} = \frac{1}{\sigma_\text{inel}}\int_0^b \frac{\mathrm{d}\sigma}{\mathrm{d}b}\mathrm{d}b\tag{1}$$
(source, one of many).
In practice, we usually use the... | {
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How can one see that the Hydrogen atom has $SO(4)$ symmetry?
*
*For solving hydrogen atom energy level by $SO(4)$ symmetry, where does the symmetry come from?
*How can one see it directly from the Hamiltonian?
| I wanted to complement the answers above.
For (1) $so(4) = so(3) \times so(3)$, one $so(3)$ is from the geometric 3D symmetry of the Hamiltonian, and the other $so(3)$ is from the potential term of $\frac{k}{r}$.
For (2). the second $so(3)$ symmetry is a dynamic symmetry and only holds when potential term is inversel... | {
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How would I explain Ohm's Law in terms of Electrical Fields and Force? In terms of current, resistance, and voltage, it's easy: Ohm's Law is the relationship between current, voltage, and resistance of a circuit. Boom, simple as that. How could I put this in terms of $E$ and $F$? I can sort of see a way to do it by rel... | Imagine at the face of the resistor that $N$ electrons each with charge $q$ are collected and move along it with a constant average drift velocity $v$. So in time $dt$ a charge $dQ$ of $N q vdt$ moves past any point, that is, the current $I = \frac {dQ}{dt} = N q v$.
Start with Peltio’s first equation above assuming th... | {
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Why do solar cells have a window layer on top of the absorber layer and not below it? In solar cells there is a p-n junction. P-type semiconductor (for example CdTe) is often absorber layer because of its carrier lifetime and mobilities. In case of CdS/CdTe,* CdS is n-type window layer and everywhere it is said that it... | I can't speak directly to this design, but can offer two general reasons for an overlayer. First, it may be necessary to protect or passivate the junction material. Second, a layer of appropriate thickness and index of refraction will reduce the overall reflectance, thus improving the collection efficiency of the dev... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If time isn't continuous, what is the best-known upper bound on the length of time intervals? There have been several questions about whether time is continuous or not and it seems like the answer isn't currently known. I know quantum mechanics treats time as continuous and any mathematics that involves integrating ov... | The lifetimes of the W and Z boson and top quark are each on the order of $10 ^ {-25}\,\rm{s}$ .
The Z-boson lifetime is $2.64 \times 10^{-25}s$ from a decay width of $2.495 \pm 0.0023 \, \rm{GeV}$. Decay width for the W-boson is $2.085 \pm 0.042\, \rm{ GeV}$
If time were not intervals of less than this order of magni... | {
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What is the symmetry associated with the local particle number conservation law for fluid? According to Noether's theorem, every continuous symmetry (of the action) yields a conservation law.
In fluid, there is a local particle number conservation law, which is $$\partial{\rho}/\partial{t}+\nabla \cdot \vec{j} ~=~0,$$ ... | Noether's theorem in its usual form assumes that the system (in this case a fluid) is governed by an action principle. We assume for simplicity that the fluid consists of just one type of fluid particles.
I) In the Lagrangian fluid picture, the (local) conservation of fluid particles is manifest from the onset, since t... | {
"language": "en",
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Would a black hole created on the surface burrow through the crust? If scientists created a microscopic black hole with an initial mass of one ton on the surface of the earth, would the gravitational attraction to the center be enough for it to "burrow" until it eats its way through the crust? It seems like there would... | As dmckee said in his comment, the black hole would fall towards the center of the Earth.
To specifically answer this portion of your question:
How dense would rock have to be to form a barrier?
There is absolutely no density of rock or anything else that would stop or even slow it down. Even if you created this mic... | {
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Resonance Raman spectroscopy vs fluorescence In Resonance Raman Spectroscopy we often want to avoid the fluorescence. But what is the problem with fluorescence . What we want is a shift between exciting line and emitted radiation and both can show the vibration energy difference??
also from "What is the difference bet... | Let's put it clear first: for Raman scattering there is no excited state at all, the light just bounces of a molecule. If the photo has the right energy, it can bring the molecule to an excited state. Different things can happen to a molecule in this state - in most of the cases the energy will be dissipated through co... | {
"language": "en",
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an Abelian complex statistical phase from exchanging non-Abelian anyons? We have some discussions in Phys.SE. about the braiding statistics of anyons from a Non-Abelian Chern-Simon theory, or non-Abelian anyons in general.
May I ask: under what (physical or mathematical) conditions, when we exchange non-Abelian anyons... | If you put a non-Abelian anyon and its anti particle on a sphere, then moving
the non-Abelian anyon around its anti particle only induces an Abelian phase.
Also, twisting a non-Abelian anyon by 360$^\circ$ only induces an Abelian phase as well, which define the (fractional) spin of the non-Abelian anyon.
| {
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Why Inox Steel doesn't interact with magnets? My dad has a HUGE magnet on his workshop.
I love magnets, and when I saw it, I asked him what it was for.
His reply was: "I don't know why, but inox steel bolts don't get attracted to it, so I use it to identify them."
Thus I got curious, why a magnet don't attract inox ste... | The are various crystal forms that iron and steel can adopt, the common ones being ferritic, martensitic and austenitic. The ferritic and martensitic forms are ferromagnetic (or just magnetic in everyday terms) while the austenitic form is not. So it isn't simply that iron is magnetic and steel isn't, it is specifical... | {
"language": "en",
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What kind of energy does superfluidity use? Liquid helium (and other similar fluids) can "climb up" the walls of their containers. Who does the work in this case, and what kind of energy does it use? I'm sure we can't make a perpetuum mobile out of this, so I guess some kind of energy must somehow be expended to make t... | Courtesy of the book Carl found we have an answer!
Consider the element of the liquid helium at a height $h$ above the fluid surface and distance $y$ from the wall. To raise that element above the fluid surface costs an energy $mgh$, but because there is a Van der Waals attraction between the helium atoms and the wall... | {
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Quantum mechanics problem? I had a test on Quantum mechanics a few days ago, and there was a problem which I had no clue how to solve. Could you please explain me?
The problem is:
Let's look at the $\hat H=E_0[|1 \rangle \langle 2| + |2 \rangle \langle1|]$ two-state quantum system, where $E_0$ is a constant, and $\lan... | Part 1
The state vector can be written in terms of the two states at time $t$ as
$$
\left|\psi\left(t\right)\right> = c_1\left(t\right) \left|1\right> + c_2\left(t\right) \left|2\right>
$$
and at time $t=0$ as
$$
\left|\psi\left(0\right)\right> = c_1\left(0\right) \left|1\right> + c_2\left(0\right) \left|2\right>.
$$
W... | {
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Gravity on the International Space Station - General Relativity perspective My question is an extension to this one: Gravity on the International Space Station.
If all the outside views of the ISS was sealed, then the crew inside would not be able to tell whether they were in orbit around the earth in orbital speed or ... | Not only the position in the gravitational field is important, but also the velocity. Consider the Schwarzschild metric
$$
\text{d}\tau^2 = \left(1 - \frac{2GM}{rc^2}\right)\text{d}t^2 - \frac{1}{c^2}\left(1 - \frac{2GM}{rc^2}\right)^{-1}\left(\text{d}x^2 + \text{d}y^2 +\text{d}z^2\right),
$$
where $\text{d}\tau$ is th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Estimating the number of atom/nuclei in a single quantum dot I often read in introductions about quantum dots that depending on the fabrication method, a single dot contains about 100 - 100000 atoms.
Assuming a self-assembled dot of lens or pyramid (cone) shape, I did some rough estimation by considering the volume (o... | The most accurate way to assess this number is by counting the relevant lattice sites with TEM;
(from Chamard et al. Phys. Rev. B 69 (2004) 125327.)
But it is ambiguous which sites at the edge of the dot to include, so the number of atoms is not well defined, at least in these self assembled dots.
One could perhaps as... | {
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Photons traveling backwards in time? Imagine that two widely separated charged particles $A$ and $B$ exchange a photon.
Because they are far apart one can imagine that there is a major contribution to the photon propagator that travels at the speed of light from $A$ at a time $T_0$ to $B$ at a time $T_1$ where $T_1 > T... | Its impossible for a photon to travel backwards in time sense it keeps disappearing because it keeps giving up its energy to other particles like an electron, either part of it or all of it which means it wont have enough energy to warp space time or even have enough energy to create closed time like curve and travel b... | {
"language": "en",
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The origin of contact noise? I was trying to measure the noise of a device with metal probes. I was not sure whether I should trust the results because I was told contact noise might contribute to some degree.
I am a little confused about the notion of "contact noise". Is it because of the contact resistance (every res... | The noise observed at a contact is known as chattering. A stronger mechanical contact should impart a steadier electrical contact resistance (ECR) [1].
However the structure and cleanliness of the surface should also be considered in the design of this setup to minimise the presence of varying passivating layers. It sh... | {
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The geodesic line on Poincare half plane I was calculating the geodesic lines on Poincare half plane but I found I somehow missed a parameter. It would be really helpful if someone could help me find out where my mistake is.
My calculation is the following:
Let $ds^2=\frac{a^2}{y^2}(dx^2+dy^2)$, then we could calcula... | You say $C,\lambda$ are constants of integration, but that gives $\ddot{x}-\lambda\dot{x} = 0$ instead. Since your followup would be inconsistent, I will assume you meant $C,\omega$ are constants of integration.
You should not have three components to the geodesic equation, but rather two:
$$\ddot{y} + \Gamma^y_{xx}\do... | {
"language": "en",
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Festive physics: gold flake vodka I have a bottle of vodka that has a load of gold flakes suspended in it. It has been sat still for over 24 hours and the flakes are all still suspended within the liquid: they have not risen to the surface or sunk to the bottom. Any ideas as to the physics behind this?
| I'd imagine the viscosity of the vodka is pretty high, and this is why the gold flakes are not rising or sinking within the bottle. Moreover, the viscosity of Vodka has no absolute numerical value as brands vary, but it's pretty high.
Here's an useful link on the viscosity of alcohols.
| {
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Is the spin 1/2 rotation matrix taken to be counterclockwise? The spin 1/2 rotation matrix around the $z$-axis I worked out to be
$$
e^{i\theta S_z}=\begin{pmatrix}
\exp\frac{i\theta}{2}&0\\
0&\exp\frac{-i\theta}{2}\\
\end{pmatrix}
$$
Is this taken to be anti-clockwise around the $z$-axis?
| The three generators of right-handed spinor rotations are given by $\left\{- i\sigma_x,-i\sigma_y,-i\sigma_z\right\}$, see for instance Peskin & Schroeder page 44, and the rotation matrix for a spinor rotation over an angle $\phi$ around a unit vector $\hat{s}$ is given by:
$R~=~ \exp\left(-i\frac{\phi}{2}~\hat{s}\cdot... | {
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Is there is a reason for Pauli's Exclusion Principle? As a starting quantum physicist I am very interested in reasons why does Pauli's Exclusion Principle works. I mean standard explanations are not quite satisfying. Of course we can say that is because of fermionic nature of electrons - but it is just the different wa... | I think that while these "explanations" are all dancing around the same pole, they aren't created equal. I think the meat is in the fact that nature has a local Lorentz symmetry, so we expect to be able to decompose things into representations of the group $SO(3,1)$. It's a mathematical fact that this group (or it's al... | {
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General relativity in terms of differential forms Is there a formulation of general relativity in terms of differential forms instead of tensors with indices and sub-indices? If yes, where can I find it and what are the advantages of each method? If not, why is it not possible?
| It is not sensible to write any theory - GR included - in terms of differential forms. Differential forms are just completely antisymmetric tensors. The antisymmetric tensors are just one kind of irreducible representation of the general linear group GL(m,C); the completely symmetric tensors are another irrep and so ar... | {
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Why did they used to make the mill chimneys so tall? Why did they used to make the mill chimneys so tall?
This question was asked in an Engineering Interview at Cambridge University.
| Two reasons - which matters more will depend on the context.
*
*making the chimney taller increases the flow through it due to the stack effect. This may be useful if you need to get rid of a lot of exhaust gases quickly as it avoids the cost of having to pump the exhaust gases.
*if the exhaust is environmentally u... | {
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How can space and time arise from nothing? Lawrence Krauss said this on an Australian Q&A programme.
"...when you apply quantum mechanics to gravity, space itself can arise from nothing as can time..."
Can you elaborate on this please?
It's hard to search for!
| Even going back to Newton, space and time are the consequences of measurement.
From the Principia's Scholium
Relative time is a measure of duration by the means of motion; Relative space is a measure of the absolute spaces determined by the senses.
So they came from measurement. Not from nothing.
| {
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Does a sound at 50dB at 1m have the same intensity of a sound of 51dB at 10m? Does a sound at 50dB at 1m have the same intensity of a sound of 51dB at 10m, and also the same intensity of a 52dB sound at 100m?
| This depends on things like the shape of the pressure wave. You're probably thinking of a point-source w/ an expanding spherical pressure wave, in which case the equations for energy per unit area as a function of radius are pretty straightforward (but keep in mind the log function involved in dB). As presented at W... | {
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Lax-Pair for principal chiral model This question concerns Eq. (2.10) of the paper https://arxiv.org/abs/hep-th/0305116 by Bena, Polchinski and Roiban.
In section 2.1 they are showing that the infinite number of conserved quantities for the principal chiral model
\begin{equation}
L = \frac{1}{2\alpha_0} \mathrm{Tr}(\p... | Defining the Wilson loop without the minus sign in the exponent gives
\begin{align}
\partial_t U(y,t;z,t)
& = \partial_t \mathrm{P} \, e^{\int_{(z,t)}^{(y,z)} dx^\mu a_\mu} \\
& = \partial_t \mathrm{P} \, e^{\int_z^y dx a_1} \\
& = \int_z^y dx \, U(x,t;z,t)\dot{a}_1(x,t)U(y,t;x,t) \\
& = \int_z^y dx \, U(x,t;z... | {
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Without apparatus can we say that the system is measured(decohered) by the environment? "Einselection" and "tridecompositional uniqueness theorem" seem to resolve the preferred basis problem. But the premise is that there are three parts in discussion.(system, apparatus, environment)
However, it seems that in many situ... | At least to me, it is unclear what it means to be "measured by the environment". As far as decoherence is concerned the situation is however quite clear.
Already the original "einselection" framework of Zurek is applicable to bipartite system/environment scenarios.
Let $(| p\rangle)_p$ be a "pointer basis" for the syst... | {
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How do I show that the eigenstates of a Hamiltonian can be made orthonormal? I've been tearing my hair out over this all evening. It should be simple but I must be missing something somewhere. Can someone show me how to prove that the eigenstates of a Hamiltonian can be made orthonormal, please?
| *
*We first prove orthogonality of non-degenerate eigenvectors of the
Hamiltonian. Consider the braket and act with the Hamiltonian in
both directions,
$ \left\langle\alpha | H |\beta\right\rangle =
E_\alpha\left\langle\alpha |\beta\right\rangle = E
_\beta\left\langle\alpha |\beta\right\rangle $
If the state... | {
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The famous drop of $c$ In this (in my opinion) intriguing speech, Rupert Sheldrake tells the story of the drop in the measured value of $c$ between 1928 and 1945. When he goes to visit the Head of Metrology of the Physics Lab in Teddington, he says (I summarize):
$c$ cannot change, it is a constant! We explain the dro... | *
*The speed of light was defined at its present value in 1983, not 1972.
*We could know that $c$ because $\alpha\propto1/c$ (fine structure constant) and we have better ways of determining $\alpha$ than $c$
*
*Not actually true: we cannot determine if physical constants change, cf. this Physics.SE Q&A
*"Officia... | {
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How to treat differentials and infinitesimals? In my Calculus class, my math teacher said that differentials such as $dx$ are not numbers, and should not be treated as such.
In my physics class, it seems like we treat differentials exactly like numbers, and my physics teacher even said that they are in essence very sma... | With the objective of keeping complexity to a minimum, the best "unifying" solution, is to think of differentials, infinitesimals, numbers, etc. as mathematical symbols to which certain characteristics, properties, and mathematical operations (rules), are applicable.
Since not all rules are applicable to all symbols, y... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Negative sign in the Dirac term from the SUSY Kahler potential I want to calculate the Dirac term from the canonical Kahler potential,
\begin{equation}
K = \Phi ^\ast \Phi \tag{1}
\end{equation}
but I'm coming across a pesky negative sign in the final result. I am finding (see derivation below),
\begin{equation}
- i... | The final sign $- i \bar{\psi} \bar{\sigma} ^\mu \partial _\mu \psi$ seems correct if we look at Matteo Bertolini, formula $5.2$, page $72$, just notice that the order of $\psi$ and $\bar \psi$ is inverted in the formula and apply $\frac{i}{2}\partial_\mu \psi \sigma ^\mu \bar{\psi} = -\frac{i}{2} \bar{\psi} \bar{\sigm... | {
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Would a three wheeled vehicle be faster than a four wheeled vehicle of the same weight? If I have a four wheeled vehicle (small wooden block with metal nail axles and plastic wheels) and apply a force X to it, would it be made faster by keeping one wheel off the ground in order to reduce friction? My thought is that t... | Friction is what keeps the wheels from spinning (i.e. traction), the friction that you want to reduce in order to gain speed, is air resistance. Removing a wheel adds more strain (friction) to the axes, probably making the car slower (keep in mind that the 4rth wheel still has some friction even though it is removed).
| {
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"timestamp": "2023-03-29T00:00:00",
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Different definition of SL(2,R) algebra? I'm looking into $SL(2,\mathbb{R})$ group and it's algebra. I found on line that the $sl(2,\mathbb{R})$ algebra is given by the two by two real matrices of trace zero. This Lie algebra has dimension three; a standard basis is given as
$$X=\begin{pmatrix}1 & 0\\ 0 & -1\end{pmatri... | Given Lie Algebras $\mathfrak{g}$ and $\mathfrak{g'}$ structure constants need not to be the same in order for $\mathfrak{g}$ and $\mathfrak{g'}$ to define the same Lie Algebra.
Since any Lie Algebra is by definition a vector space with a product (the commutator) that satisfies certain properties, it is indeed a linear... | {
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What is the difference between the words transparent and translucent? Merriam Webster defines transparent as:
Having the property of transmitting light without appreciable scattering so that bodies lying beyond are seen clearly.
And translucent as:
Transmitting and diffusing light so that objects beyond cannot be se... | Lenses and glass bottles are transparent. As you quoted above, the different has to do with diffusion.
Here is an example of an image through a transparent object:
Here is an example of a translucent object:
This is an example of how diffusion causes translucency:
As light passes through a translucent object, it ei... | {
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Field of moving charge / Lorentz; Liénard-Wiechert First question here. I'm really confused at the moment.
An electron moves at constant velocity, no acceleration
Wikipedia says here Lorentz:
$$\mathbf E=\frac{q}{4\pi\epsilon_0}\frac{1-v^2/c^2}{1-v^2\sin^\theta/c^2}\frac{\hat{\mathbf r}}{r^2},$$
which yields something... | Both equations (for the instantaneous field of a charge moving with constant velocity $v$) are correct. (Well, maybe the primes should be swapped in the second equation, so that the unprimed frame is that in which the charge is moving.)
The first figure is not an accurate representation of the first equation: as Jan ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/93390",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Physical motivation for differentiation under the integral I am thinking about the mathematical process of "differentiating underneath the integral", i.e. applying the theorem $$\partial_s \int_{-\infty}^\infty f(x,s)\,dx=\int_{-\infty}^\infty \partial_s f(x,s)\,dx$$ given some regularity assumptions. I was trying to t... | For example, consider some water flow in the space, in which the density $\rho(x,t)$ fluctuates in space and in time. You might be interested in how the mass inside some fixed volume $V$ changes over time. The mass is equal to
$$
M(t)=\int_V{\rho(x,t)\mathrm{d}x},
$$
therefore the "mass flow rate", using the rule you m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/93554",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
Beam power and electric field after a beam splitter Consider a beam with power $P_1$ and electric field amplitude $E_{01}$. It is sent through a 50/50 beam splitter that produces beams with power $P_2=P_3=P_1/2$. What are the electric field amplitudes of the split beams, $E_{02}$ and $E_{03}$?
From what I understand, ... | Your error is in how the electric fields are combined by a 50/50 beam splitter. If you have two entry ports $a$ and $b$ with electric field amplitudes $E_a$ and $E_b$, and exit ports $c$ and $d$ with electric field amplitudes $E_c$ and $E_d$, then the correct way to combine them is
$${E_c=\frac1{\sqrt2}(E_a+E_b),\\ E_d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/93669",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Why does dark matter form walls and filaments Related: How are galaxy filaments formed? And do they have any analogues in stellar formation?
But I want to come at this from a different angle. Like the user asking that other question, I was a bit surprised by the walls, filaments and nodes of the large-scale structure o... | Gravity is not attractive emanating from objects. It is repulsive emanating from voids, and objects result from congealed light pressed together in black hole whirlpools.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/93851",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 3,
"answer_id": 2
} |
Does any object placed in an electric field change the electric field? Lets say I have a point charge of magnitude $+q$, All around it I would have a symmetric radial electric field. Now if I place a neutral object lets say a sphere (doesn't matter insulating or conducting) in this field some distane away from the poin... | I'm not quite sure I understand why you have a problem with this - every static charge is a source or a drain of the electric field, depending on its sign. So obviously the field of a single charge at the origin will be different from the field of three charges or any other configuration.
The electric potential of such... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/93911",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
} |
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