Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Which way do black hole jets spin? The centers of black holes and quasars often have jets coming out the two poles of an accretion disk, say north and south. Is it known if the two jets spin in the same direction or opposite directions to each other?
| The Blandford-Znajek process and variants are leading contenders for explaining black hole jets. The driving energy for the jets is extracted from the black hole spin and transferred to the outgoing plasma by twisted magnetic fields. Along with energy, the jets must contain the lost angular momentum from the black hole... | {
"language": "en",
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A question about the coupling between string and gauge field $A_{\mu}$ I have a question about deriving the coupling term of string and the gauge field on brane. According to David Tong's lecture note p184/(191 in acrobat), the coupling is given by
$$ S_{\mathrm{end-point}}=\int_{\partial M} d \tau A_{a}(X) \frac{d X^a... | There is no 2-D metrics here, because we are working with the boundary $\partial M$
You could imagine a standard action $S_0 = \int_{\partial M} d\tau A_a \frac{d X^a}{d \tau}$, where $A_a$ is constant.
With a small perturbation, we will have : $A_a(X) = A_a + \epsilon_a(X)$, and we have an action $S = \int_{\partial M... | {
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What is the difference between the Balmer series of hydrogen and deuterium? In my quantum mechanics textbook, it claims that the Balmer series between hydrogen and deuterium is different. However, I was under the impression that the Balmer series
$$H_\alpha, H_\beta, H_\gamma$$ is related by the equation $$\lambda=C\fr... | $$
\frac{1}{\lambda} = \frac{4}{C_M}\left(\frac{1}{4} - \frac{1}{n^2}\right) = R_M\left(\frac{1}{4} - \frac{1}{n^2}\right),
$$
where $R_M = 4/C_M$ is the Rydberg constant for the particular atom:
$$
R_M = R_\infty\left(1+\frac{m_\text{e}}{M}\right)^{-1},
$$
with $m_\text{e}$ the electron mass, $M$ the mass of the atomi... | {
"language": "en",
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Feynman's subscript notation Consider this vector calculus identity:
$$
\mathbf{A} \times \left( \nabla \times \mathbf{B} \right) = \nabla_\mathbf{B} \left( \mathbf{A \cdot B} \right) - \left( \mathbf{A} \cdot \nabla \right) \mathbf{B}
$$
According to Wikipedia, the notation $\nabla_\mathbf{B}$ means that the subscrip... | First of all, I always tell every student who asks me about such expressions to stop remembering all these infinite rules and learn to do that with Kronecker delta and Levi-Civita symbols. For example your initial expression looks like this:
$$\mathbf{A}\times[\nabla\times\mathbf{B}]=\varepsilon_{ijk}A_j\varepsilon_{kl... | {
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Surface gravity of Kerr black hole I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand.
Firstly, the metric is given by
$$\mathrm{d}s^2=\left(\frac{\Sigma}{\rho^2}\sin^2\theta\omega^2-\frac{\rho^2\Delta}{\Sigma}\right)\ma... | The calculation can be done in this coordinate system just fine, even though it doesn't extend across the horizon. Surface gravities are very commonly computed in coordinate systems which go bad at the horizon. For example, the surface gravity of Schwarzschild
$ds^2 = -f dt^2 + f^{-1} dr^2 + r^2 d\Omega_2^2, \qquad f= ... | {
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Why doesn't Bernoulli's Principle apply to Current and Resistors in a circuit? Bernoulli's principle makes sense when you apply it to fluids. If you decrease the diameter of a pipe then the velocity of the fluid increases because it needs to keep the same rate of fluid moving through the pipe.
So my question is:
If Vo... | So you can apply Bernoulli's theorem but not according to your analogy take velocity of fluid as electric field at that position now electric flux is conserved since no charge enclosed in it so as diameter is large electric field will be less.
| {
"language": "en",
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Spinor and Scalar Bose-Einstein condensate I read about an order paramater that describes a Bose-Einstein condensate. But I don't understand, the classification into "scalar" condensate and "spinor" one. Is it linked with spin of atoms that take part in condensation? Or is it a property of the condensate?
Does anyone h... | You call the condensate 'scalar' when the atoms are spin-0. When instead atoms have a non trivial spin you talk about 'spinor condensates'.
| {
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Adiabatic filling of a container Suppose a thermally insulated container is filled with atmospheric air until the pressure reaches 5000 psi. This could represent the filling of a diving cylinder, before thermal dissipation becomes significant.
Initially, then, some mass of air has atmospheric temperature $T_1$ and $p_... | I think you forget that when you fill the tank, you add mass to it. Your relations assumes that the mass in the system is constant.
| {
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Period $T$ of oscillation with cubic force function How would I find the period of an oscillator with the following force equation?
$$F(x)=-cx^3$$
I've already found the potential energy equation by integrating over distance:
$$U(x)={cx^4 \over 4}.$$
Now I have to find a function for the period (in terms of $A$, the am... | Starting from
$$ \frac{1}{2} \left( v(x)^2 - v_0^2 \right)= - \frac{c}{m} x^4 $$
with initial velocity $v_0$ when $x=0$, the time relationship is
$$ t = \int_0^x \frac{1}{v(x)}\,{\rm d} x $$
I use in intermediate variable $\xi$ for distance $x = \sqrt[4]{\frac{2 m v_0^2}{c}}\, \xi $ .
I integrate the energy relations... | {
"language": "en",
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when we rub objects together, what determines which material will pick up electrons? For example We know glass when rubbed by silk will become positively charged while the silk will be charged negative.
What exactly makes glass appropriate for losing electrons in that experiment? (
| Each object has a certain value that defines whether it will lose electrons when rubbing against an object with a higher value, and vice-versa. Glass can loose electrons much more easily than other objects, making it a useful tool for teaching about static electricity. Electrons are held in place by the positive balanc... | {
"language": "en",
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Distribution of point charges on a line of finite length How will $N$ freely moving charges confined to a line with length $L$ be distributed? What are their equilibrium positions?
| This is a more down-to-earth answer as opposed to the fancy mathematics in the other one. This problem is easily solved numerically. The equations are easily stated: inverse-square forces to the right from the particles to the left and to the left from the particles to the right. Thus, for a system of $n+2$ charges whe... | {
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$\pi/2$ phase shift in RC circuit I just recently learnt Alternating Current and RCL circuits and I also learnt about phasers and various graphs. Now I also know that current lags in an LR circuit. My intuitive understanding of this is according to Lenz Law, the inductor will oppose the current and hence slow it down. ... | When a resistance $R$ is put in series with some other impedance $Z$, by Ohms law you have $U=(R+Z)\cdot I$, or
$$I=U\cdot \tfrac{1}{R+Z}=U\cdot \tfrac{1}{R+Z}\tfrac{\overline{R+Z}}{\overline{R+Z}}=U\cdot \tfrac{(R+\mathbb{Re}(Z))-i\ \mathbb{Im}(Z)}{|R+Z|^2}.$$
If $Z$ has an imaginary part, then $I$ and $U$ differ by... | {
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On Einstein's equivalence principles There are two foundative Equivalence Principles in General relativity:
Weak Equivalence Principle (WEP): the dynamics of a test particle in a gravitational field is independent of its mass and internal composition.
(WEP is equivalent to say that the ratio between the gravitational m... | I agree that in the textbook you considered, explanation is not clear. First, please check my answer here:
graviton and principle of equivalence
Personally, I prefer to unify WEP and EEP, but let's distinguish them as in your textbook. The example you provided for WEP is definitely mechanical, so not-gravitational expe... | {
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Open problem? Square of the wave function $\Psi(x)_{x_o} = \delta(x-x_0)$ of a particle localized at a point $x_0$? Does anybody know the status of the problem to define the wave function (non-relativistic Quantum Mechanics) of a particle localized at a definite point?
Landau-Lifshitz says in chapter 1 that this funct... | Most scientists agree there are still some interpretational issues in QM, so it is hard to make unequivocal statements. IMO, point-like single quantum pure states (i.e., Hilbert space "rays") are not physically measurable or even physically realizable. They are idealizations of zero entropy and thus not realizable by t... | {
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Entropy of the Sun
*
*Is it possible to measure or calculate the total entropy of the Sun?
*Assuming it changes over time, what are its current first and second derivatives w.r.t. time?
*What is our prediction on its asymptotic behavior (barring possible collisions with other bodies)?
| The entropy of the sun is roughly $10^{35} \mathrm{J} /\mathrm{K}$ (see http://dx.doi.org/10.1103/PhysRevD.7.2333 where the entropy of the sun is given as $10^{42}\mathrm{erg}°\mathrm{K}^{-1}$)
It can be calculated using Boltzmanns law ( $S = k_B \ln{W} )$ where $W$ is the disorder parameter of the sun (depends on the... | {
"language": "en",
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How does humidity affect the path of a bullet? Background
Last night, I was reading the FM 23-10 (The U.S. army official field manual for sniper training), and I've noticed that they're potentially teaching snipers incorrect information.
Generally speaking, when we say "impact goes up" it means that the bullet was eith... | Today I have noticed that our humidity is extremely high compared to yesterday. The temp is about approx 5degrees F warmer today than yesterday. I just shot 30 rounds and noticed without any bias on this subject (no previous opinion) that my rounds were landing .125" higher than yesterdays 30 rounds. Hence why I am ... | {
"language": "en",
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How does a pressure suit work? I recently learnt that a suit called pressure suit is worn by fighter plane pilots to prevent red-outs and black-outs. And it seems to be work by -
"..applying pressure to selective portions of the body."
How do these suits work; i.e. by what means, selective portions of the body are pr... | If the body is subjected to high accelerations directed towards the feet the heart is unable to pump blood to the brain and unconsciouness results. There are no end of TV programmes showing such experiments in centrifuges, for example a quick Youtube search found this.
The type of pressure suit you mention compresses t... | {
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Why does a laser beam diverge? I was wondering why a laser beam diverges. If all the photons are in the same direction, I would imagine that it would stay that way over a long distance. I am aware that a perfectly collimated beam with no divergence cannot be created due to diffraction, but I am looking for an explanati... | Electromagnetic waves are diffracted, so a plane wave can only exist at a single location along the axis of propagation (in a uniform homogeneous medium) . In a semiconductor laser, the end mirrors might be planar crystal faces; but they aren't always; for example they aren't in VCSELs; where Bragg mirrors are often u... | {
"language": "en",
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"source": "stackexchange",
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Does a different opposing force affect work? Suppose a man exerts $10~N$ as he lifts a $1~kg$ box a distance of $2~m$ against Earth's gravity.
To determine work we can use the following equation:
$$
W = F \cdot d \\
W = (10~N) \cdot (2~m) = 20~J
$$
The work in this case is $20~J$.
Would work be the same if the man perf... | the fault is in the assumption that work done on the box only goes towards gravitational potential energy. take note that if the applied force exceeds the weight of the box at any time, the box will accelerate and also attain kinetic energy.
assuming $g_{earth}$ = $10N/kg$, then the box never accelerates, and the full ... | {
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Determing time to complete known distance with constant acceleration Answer: $a=v^2/d$ is the formula I needed.
This is a problem in a programming assignment, I haven't taken physics.
I have a starting speed (0 m/s), an final speed (208.33m/s) and the distance it took to reach that speed (200km). I need to get the ti... | According to the question while the car travels from 0 to 200 m/s with constant acceleration it covers a total distance of 200km.
Applying the formula $$2as=v^2-u^2$$ where v is the final speed,u is the initial speed and s is the distance. Here u=0m/s,v=208.3m/s and s=200km.Putting the values we get $$a=0.1085034 m/s$... | {
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Is it possible to find the ground state of generalized Ising models? Is there a general solver (or a theoretical algorithm) for obtaining the ground state configuration of the extended Ising model, which involves an arbitrary lattice, arbitrary coordination number (i.e. $n$-body interactions for arbitrary $n$), arbitra... | As in your question the stress was on the word general, I have some bad news:
an efficient "general solver (or a theoretical algorithm) for (...) extended Ising models, which involves an arbitrary lattice" does not exists.
Of course, one can invent algorithms that, in principle, could find the ground state. The most t... | {
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Deriving the condtion for spontaneity using gibbs free energy While deriving the condition for spontaneity, $\Delta$G$\leqslant$0,
we start by saying that
$\Delta S_{tot}$ $\ge$0 $\Rightarrow$ $\Delta S_{sys}$ + $\Delta S_{surr}$ $\ge0$
If $Q$ is the heat transferred to the system from the surroundings, then $−Q$ i... | There is an asymmetry between the system and the surroundings. In fact, at constant temperature $T$, we are in a canonical or grand-canonical situation (depending on cases), where the "surrondings" is a heat reservoir, with Energy, Number of Particles,etc... much greater than the system. When we modify some external da... | {
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Is it possible for the entropy in an isolated system to decrease? As far as I can tell, the concept of entropy is a purely statistical one. In my engineering thermodynamics course we were told that the second law of Thermodynamics states that "the entropy of an isolated system never decreases". However, this doesn't ma... | If you consider the case of different configurations of the gas in question will get a number of microstates. With them you can define an equivalence relation that form a macrostate. All this microstates share the general characteristics of the system (as the gas pressure exerted on the walls of the container).
These ... | {
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Circumference of a circular path Suppose a car moves with a constant speed of $20 \text{m/s}$ a quarter of a circle, and completes the quarter in $5$ seconds. One way to calculate the circumference is simply $20 \cdot 5 \cdot 4 = 400 \text{m}$. However, I know that $a=\frac{v^2}{R}$ and the circumference is $2 \pi R$. ... | Acceleration is the derivative of velocity with respect to time, which is not the same as just dividing the difference in velocity by the difference in time.
$$a=\frac{dv}{dt}\neq \frac{\Delta v}{\Delta t}$$
$dv$ and $dt$ can be thought of as infinitely small $\Delta v$ and $\Delta t$. So if your $\Delta v$ and $\Delta... | {
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Do orbitals overlap? Yes, as the title states: Do orbitals overlap ?
I mean, if I take a look at this figure...
I see the distribution in different orbitals. So if for example I take the S orbitals, they are all just a sphere. So wont the 2S orbital overlap with the 1S overlap, making the electrons in each orbital "me... | An orbital is essentially a wave function from which a probability distribution of the location of an electron upon measurement can be inferred. What is depicted will be something like the region within which the probability is 50% (shaped in a way that depends on a decomposition of the state function in a radial part ... | {
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Why does voltage remains same over Parallel Circuit Why does voltage remains same over parallel circuit. If a resistor is connected in the circuit some of the charge should be transformed into heat and make a lack of charge after the resistor (in my sense). So, what's the reason in it?
| Two points:
1) The voltage across the two resistors is the same. The definition of a perfect conductor is that there is no voltage drop along it's course. Of course nothing is perfect but copper is a very good conductor and it would be difficult to measure the voltage drop across relative short segments. In a parallel... | {
"language": "en",
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Vanishing of the Ricci tensor in higher spacetime dimensions I understand how, if the Riemann tensor is 0 in all its components, since we construct the Ricci tensor by contracting the Riemann, Ricci tensor would be 0 in all components as well.
I've read that vanishing of the Ricci tensor in 3 spacetime dimensions impli... | So, let's take your formula, and set $n=3$. This gives you $N = \frac{9\cdot 8}{12} = 6$. Well, how many independent components of the Ricci tensor do you have? Well, since it's a 3x3 symmetric tensor, you've got six independent components. Therefore, there is no room in the Riemann tensor to have additional compon... | {
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Why 3 dipole terms in a multipole expansion? As can be seen on this page http://en.wikipedia.org/wiki/Multipole_expansion when we take a multipole expansion without assuming azimuthal symmetry we end up with $2l+1$ coefficients for the $l^{th}$ moment in the expansion. So the dipole moment has 3 terms, the quadrupole h... | The spherical multipole expansion arises from the solution of the Laplace equation in spherical coordinates. We try to solve by separation of variables and a eigenvalue equation appears .
The number 3 in the second term is caused by the degeneracy of certain eigenvalue (the are 3 linearly independent solutions for the ... | {
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Why is moment dependent on the distance from the point of rotation to the force? The formula for moment is:
$$M = Fd$$
Where F is the force applied on the object and d is the perpendicular distance from the point of rotation to the line of action of the force.
Why? Intuitively, it makes sense that moment is dependent o... |
I understand how when I am turning a wrench, if the wrench is shorter its harder to turn it but I don't understand WHY.
Suppose a bolt can be unscrewed with one turn, and the process consumes $E$ Joules. Then since $w=F d$, we have
$$E=2\pi rF.$$
Thus
$$F=\frac{E}{2\pi r}.$$
That's why it's harder to unscrew a bolt u... | {
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Quantum randomness and brownian motion in biological systems, e.g., fertilization I am looking for examples of physical indeterminacy impacting the macroscopic world. By physical indeterminacy, I mean physical sources of randomness such as quantum indeterminacy or brownian motion.
One example is of particular interest ... | Some kinds of mutation provide an example of this kind of indeterminacy. UV light can be bad for our health. One of the reasons is that, when we are exposed to sunlight, UVB photons are absorbed by double bonds in pyrimidines, which break open, become reactive, and dimerize (photo-dimerization). This damages the DNA... | {
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Why do same/opposite electric charges repel/attract each other, respectively? I know plus pushes another plus away, but why, really, do they do that? On the other hand, molecules of the same type are attracted to each other. I find that weird.
I do know some stuff about four universal forces. But why in general the gen... | It's all about the energy, in the sense that everything is positive or negative energy. Opposite charges attract each other in order to complement the lack or surplus of energy.
| {
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Is the uniqueness theorem correct in superconductivity? There is an uniqueness theorem in electromagnetism. It says that the solution of Maxwell's Equations is determined uniquely by boundary conditions.
We can treat superconductivity as a completely diamagnetic material with magnetic susceptibility $\chi=-1$.
I think ... | I think you have missed a step in the uniqueness theorem. After all, the fields in a ferromagnet are governed by non-superconducting E&M, but internal magnetization depends on the history and state of a system.
The uniqueness theorem applies to regions of space where the boundary fields and all charges and currents ar... | {
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Are quantum decoherence and Everettian approaches to the measurement problem necessarily distinct? As I understand it, there is a large contingent of physicists who believe that the measurement problem is "solved" by decoherence, without, for example, needing to postulate the existence of "many worlds." Yet at the same... | Decoherence and collapse/MWI are actually complementary, since they address completely different aspects of the classical limit. Decoherence explains what happens with interference terms on macroscopic systems, but it doesn't address the problem of individual measurements. The classical probability distribution of a mi... | {
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Do objects rotate around the torque vector or its center? If a sphere has a torque vector coming out of it at point A, would the sphere rotate about its center or the axis of the torque vector?
| If a body moves only because of the influence of a torque, then it will rotate about the center of mass.
There is no location for torques, only directions. You you take the equations of motion as seen here (https://physics.stackexchange.com/a/80449/392) you will see that the location of the torque does not enter into t... | {
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Why can't batteries be charged quickly? Charging of laptops, cell phones take so much time. Why can't we make such batteries easily/commercially which are charged more quickly? What's the thing behind this limiting?
| Heat. Batteries have internal resistance and so produced heat when current flows through them (Joule heating). Also, the heat generated increases by the square of that current. E.g, doubling the charging current causes the heat produced to be increased 4 times.
Ultracapacitors are a different technology that can be use... | {
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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?
|
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?
Interesting interpretation. I would put it exactly the other way around: in a noninertial frame, the first and second laws hold, but the third... | {
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What is the opposite of the Planck length? What "large size" unit of length could be considered at the opposite end of spectrum from Planck's length?
Is there a table of smallest and largest value for various physical quantities that can be defined from well-known constants?
Edit
I was teaching the exponential functio... | Graham's number is the only practicable answer I can think of to answer your question.
| {
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do lenses with curved focal planes exist I know about spherical, aspherical, cylindrical lenses, but are there lenses that could have a curved focal plane? for example, the retina of the eye is curved, and still we see sharp images of distant objects.
In a recent problem I studied, I wanted to have a lens that would tr... | Well ALL lenses have curved focal surfaces; there are NONE that have perfectly flat sharp focal planes over any finite angular field of view.
It is however theoretically possible to design a lens with a flat focal surface, but only for imaging one specific object plane onto one specific image plane.
The problem is a f... | {
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How can doped semiconductor be neutral? I have studied about the two types of doping which result in p and n type semiconductors. I also came to know that they are neutral. But, how can it be?
Is it that the positive charge(holes) in p-type and negative charge in n-type are negligibly small to affect the overall neutr... | An atom contains not only the electrons but also the nucleus which consists of an equal number of protons. Hence an atom is neutral.
The reason why your doped semiconductor carries a neutral charge is because it has equal number of electrons as there are protons, be it boron doped or phosphorous doped.
While the whole... | {
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Expansion of the Universe: Conversion of gravitational potential energy to kinetic energy? Suppose there is an object floating in space which over time begins to fall toward the source of a gravitational field. As it falls, its motion happens to be such that it gets locked in orbit around the source with a greater vel... | Energy is not conserved in GR, in the sense that there is no global, tensorial measure of energy that is conserved and can be defined in all spacetimes. See this question: Total energy of the Universe
However, if the system described in your example is sufficiently isolated, then we can describe that region of space as... | {
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Why are lab Magnets painted red? Wy are lab magnets painted red in color?
I tried searching everywhere but couldn't get a satisfactory answer.
| Isn't it just a convention ? And are all the laboratory magnets around the worle painted red ?
I would agree with you that mostly they are painted red as i once bought a lot of laboratory bar magnets made of AlNiCo all of them were painted red while same was not true when I bought some higher power loadstone magnets th... | {
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2 dimensional Coulomb's law equation We can notice that in the Coulomb's law equation,
$$\begin{equation}\tag{1}F=\frac{1}{4\pi\epsilon}\cdot\frac{q_1q_2}{r^2}\end{equation} $$
$4\pi r^2$ factor in the denominator expresses directly the surface of a virtual sphere with radius $r$. Actually we can look at this equation... | What is 2D charge? It is not a good definition, and you should be more carefully. The force will be proportional to the charge or the square of charge? 2D charge in the vortex is the topological charge? The thing in 2D makes different.
| {
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Can a very thin sheet of any material float inside a liquid? When a body is immersed in a liquid,buoyancy is the net force of all the forces acting on it.
Now the forces are equivalent to those which will act on the same volume of liquid.Rightly so,but considering the chaotic motion of the molecules of the liquid,for e... | If the density of the material of your sheet is higher than the density of the liquid, then, the situation will be unstable, and it will collapse immediately by gravitational forces.
The process you are describing is basically just diffusion. If your material is also a fluid, and basically dissolved in the fluid, then ... | {
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Is there a heat transfer equation that takes conduction, convection, radiation and dT/dt into account? I see equations that take 2 or 3 of the listed parameters into account but I haven't been able to find one that is that complete. I'm seeking to solve this equation using matlab for a simulation project to study how t... | The general form of the heat equation would be
$$ \frac{\partial T}{\partial t} + (\vec{u} \cdot \nabla) T =a \nabla^2T + S$$
The first term is the time derivative, the second term convection, the third term diffusion of heat and the last term is the source term, which can be anything.
However, normally I would expect ... | {
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Have we found a Higgsino? In supersymmetry, for each particle (boson/fermion), there is a symmetric particle which is a fermion/boson.
The MSSM predicts five Higgs bosons: two neutral scalar ones (H and h), a pseudo-scalar (A) and two charged scalars.
Does this mean that there are five higgsinos?
My question arises bec... | The Higgs field of the standard model is a complex SU(2) doublet. This means it has two complex-number-valued components which interact with the weak-force gauge bosons. Two complex-number-valued degrees of freedom, equals four real-valued degrees of freedom. Three of these degrees of freedom are absorbed into W+,W-,Z ... | {
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A question on Bernoulli's principle Which is more appropriate regarding Bernoulli's principle
*
*fast moving air causes low pressure or
*lower pressure causes fast moving air.
| Definitely the second, assuming that what you meant to say was "Relatively low pressure causes fast moving air." Bernhard is absolutely correct on this point, in that really it's the pressure gradient, not the pressure itself which causes local accelerations in the flow. The language I am using is very deliberate, sugg... | {
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Explicit time dependence of the Lagrangian and Energy Conservation Why is energy (or in more general terms,the Hamiltonian) not conserved when the Lagrangian has an explicit time dependence?
I know that we can derive the identity:
$\frac{d \mathcal{H}}{d t} = - {\partial \mathcal{L}\over \partial t}$
but is there a m... | I) If a system (and hence the Lagrangian) depends explicitly on time, it can often be physically interpreted as that the system is not an isolated system. In other words, that it interacts with the environment, and hence there is no reason that the energy of the system should be conserved.
Example: A non-relativistic 1... | {
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How important is mathematical proof in physics? How important are proofs in physics? If something is mathematically proven to follow from something we know is true, does it still require experimental verification? Are there examples of things that have been mathematically proven to some reasonable degree of rigor (eg s... | Mathematical proofs relate to exactly how a MODEL will behave. They don't have much to do with how the real world behaves. If the mathematics is carried out correctly, then one has "proven" how the model will behave.
The reason for experimentation, is to find out if the completely fictional MODEL that somebody simpl... | {
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Catapult vs. Trebuchet I have been looking at trebuchet designs lately, and I have noticed that most, if not all, have a sling attached to them. Without such a sling, the machine would be a catapult. In terms of the speed and energy of a launched projectile, what is the general difference between a catapult and trebuch... | Well ultimately the range depends on launch velocity. This is a combination of acceleration (applied force) and time or distance (during acceleration.)
The trebuchet seems to give a much longer "casting stroke" , so reaches a greater launch velocity. Very clever gadgets.
| {
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"source": "stackexchange",
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Lorentz transformation of the Spinor Field I'm reading chapter 3 of Peskin and Schroeder and am stuck on page 43 of P&S. They have defined the Lorentz generators in the spinor representation as:
\begin{equation}
S^{\mu \nu} = \frac{i}{4}[\gamma^\mu,\gamma^\nu]
\end{equation}
such that a finite transformation is given b... | The mistake you are making is in "daggering" the object $\omega_{\mu\nu}$. For each $\mu, \nu = 0,\dots 3$, the symbol $\omega_{\mu\nu}$ is a real number, so its dagger (which is really just complex conjugation in this case) does nothing; $(\omega_{\mu\nu})^\dagger = \omega_{\mu\nu}$.
When we say that $\omega_{\mu\nu}... | {
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Could velocity be taken as fundamental instead of time? In physics time and length are taken as fundamental in the SI system and, as it seems, in the thinking of physicists. Could one instead take velocity, with c as its unit, together with length as fundamental and then understand time by dimensional analysis in terms... | From the point of view of dimensional analysis alone, this can be done. It would not give mathematically inconsistent results. Mathematically, any quantities $A$, $B$, $C$ can be chosen as 'fundamental', as long as no relationship of the form $f(A, B, C) = 0$ exists between them.
However, from the point of view of phys... | {
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What is the depth in meters of the pond? A small spherical gas bubble of diameter $d= 4$ μm forms at the bottom of a pond. When the bubble rises to the surface its diameter is $n=1.1$ times bigger. What is the depth in meters of the pond?
Note: water's surface tension and density are $σ= 73 \times 10^{-3} \mbox{ N}$ a... | The surface tension of the bubble would help you to find out how much work the bubble is doing while it increases its volume.
| {
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Do atoms get created or are they recycled? Basically, are the atoms that make up my body right now something that has existed since the big bang?
| Watch out, though, because particles can be indistinguishable. Roughly, you can't write a label on an atom, even in principle, so to say that your hydrogen atoms are this old and my hydrogen atoms are that old is not very well defined. What is closer to reality is that there are this many atoms in this state, and that ... | {
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Dimensional regularization - integral How can I derive the following formula?
$$\int d^{d+1} k \frac{e^{i K X}}{K^2} = \frac{\Gamma (d-1)}{(4\pi)^{d/2} \Gamma (d/2) |X|^{d-1}}, \quad K^2 = k_0^2 + \vec k^2, KX = k_0 \tau + \vec k \vec x$$
What I tried so far:
*
*Integrate over $k_0$ while promoting $k_0$ to complex ... | The second route should work, look up the form of $d \Omega$ and note that it has a $d \cos \phi$ term that appears in it. From there, a quick change of variables and some research on gamma functions and solid angle integrals and you should be home free.
| {
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Is the uncertainty principle valid? The uncertainty principle says that the product of the uncertainties in position and momentum can be no smaller than a simple fraction of Planck's constant $h$.
Several articles lately suggest this is not true.
Today in Physicsworld.com
Looking at the position and momentum of spin-... | "Can we safely throw out the Heisenberg uncertainty principle and start to view physics with more certainty?"
No, you definitely can not throw out the HUP. If you have two operators $A$ and $B$, and define $\Delta A = A - \langle A \rangle $, it is easy to prove that (see, e.g., Sakurai's QM book, section 1.4)
\begin{e... | {
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Does antimatter curve spacetime in the opposite direction as matter? According to the Dirac equation, antimatter is the negative energy solution to the following relation:
$$E^2 = p^2 c^2 + m^2 c^4.$$
And according to general relativity, the Einstein tensor (which roughly represents the curvature of spacetime) is linea... | Here's a naive argument for expecting antimatter and matter to both have "attractive" properties under gravity. General relativity describes gravity in terms of a valence 2 tensor $g_{\mu\nu}$. Upon quantization one would therefore expect a spin $2$ particle. The propagator might look something like
$$(g_{\mu\rho}g_{\n... | {
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Are there models/simulations of antigravitational antimatter-galaxies? In the comments to another question's answer, I started wondering:
Assuming antimatter possessed negative gravitational mass§ (which is not proven impossible to date, though deemed unlikely), basically entire galaxies consisting of antimatter could ... | There are strong constraints on antigravitating antimatter, because it could, in principle, be used, to create a perpetual motion machine.
1) Use energy $E$ to create a particle/antiparticle pair at height $h_{i}$
2) Raise the particle/antiparticle pair to a height $h_{f}$. This takes zero work, because the antipart... | {
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"source": "stackexchange",
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Normal force of ball sliding on concave surface Imagine a ball is sliding along a surface shaped like $y=x^2$. Like ,
but please ignore the fact that the center of the ball is on the surface instead of the edge.
When the ball is stationary, I can calculate the normal force fairly easily. $F_\text{net}$
in the direction... | When a particle follows a path then at any instant there is tangential vector $\vec{e}$ and a normal vector $\vec{n}$ allowing for the velocity to be defined as $$\vec{v} = v \vec{e}$$ and the acceleration $$ \vec{a} = \dot{v} \vec{e} + \frac{v^2}{\rho} \vec{n} $$ where $\rho$ is the radius of curvature of the path.
Fo... | {
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How does energy transfer between B and E in an EM standing wave? I'm trying to understand how an electric field induces a magnetic field and vice versa, its associated energy, as well as relating it to my understanding of waves on a string.
Using a standing wave as an example, I came up with the equations
$\vec{E}=A\si... | Ah, but there is energy stored in the field: recall that the energy density is given by
$$
u(t,x)=\frac12\left(\varepsilon_0\vec{E}\cdot\vec{E}+\frac{1}{\mu_0}\vec{B}\cdot\vec{B}\right)
$$
which is clearly non-zero at $t=0$. Surely there are zeroes in the energy at $t=0$, but for $t>0$, the energy is transferred from t... | {
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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,... | The moon DOES affect weather but not significantly.
Just like it affects ocean tides, it affects the atmosphere in a similiar way. When the moon is full or new for example, it creates a "bulge" in an ocean, which is why we have tides. A similar thing happens with the atmosphere; it attracts the atmosphere to itself.
Wh... | {
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B3LYP vs PBE functionals for conjugated organic systems Two of the most popular (exchange and correlation) functionals for density functional theory are B3LYP and PBE. Out of the people I've worked with / learned from, mostly the computational chemists were using B3LYP, and the physicists were using PBE.
Now, different... | For static polarizability calculations it seems that both B3LYP and PBE functionals do a pretty good job; for benzene and napthalene I am getting numbers within a few percent of experimental values. What is much more important is the basis set. In particular, it's absolutely necessary to include diffuse functions. Fo... | {
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Is false vacuum bubble nucleation possible in our universe?
*
*Is it possible that a false vacuum bubble to nucleate into our universe rather than a true vacuum one?
*If yes, it will expand at speed of light within our spacetime or what?
| If there is another metastable point below the energy our universe lives in but above the true vacuum level then yes (a nice description on page 3 here). The information within it would travel at the speed of light and any photons that may be within but I am unsure if it might experience an inflationary period or not.
| {
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Classical Wave Equation - Approximations I don't understand the derivation of the wave equation given below -
$$T \sin (\theta _1) - T \sin (\theta ) = T\tan (\theta _1 )-T\tan (\theta ) = T \left. \left(\frac{\partial f}{\partial z} \right|_{z + \Delta z} - \left. \frac{\partial f}{\partial z}\right| _z \right) = T \f... | As we can see from the previous answers, we have the following approximations:
$tan(\theta) = \frac{opposite}{adjacent} = \frac {rise}{run} = gradient = \frac {∂y}{∂x}$
and we can say, still through approximation:
slope(z+∆z)=slope(z)+slope_variation_tax*∆z, which mathematically means:
$$\frac{\partial f(z+∆z)}{\partia... | {
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How much extra distance to an event horizon? How much extra distance would I have to travel through space to get from Earth to a stellar mass event horizon?
(compared to the same point in space without a black hole)
| I suspect you're not asking the question you're really interested in, because the answer to your question is really boring. If you jump into a black hole you'll see the event horizon retreating before you, and you'll never cross it. The distance you've travelled is an ambiguous quantity since of course in your frame yo... | {
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Chinook Helicopter Torque The Chinook Helicopter has 2 rotors to counteract the torque generated by spinning the blade.
Theoretically, could you use a smaller "back" rotor that is farther away from the main rotor to achieve the same result, ie no twisting?
| The separation between the rotors does not actually matter. What matters is that the torque exerted by each of the motors on the respective rotor be the same and in opposite directions. Those torques then add vectorially and cancel out to give zero net torque on the helicopter.
It's not clear to me exactly what you mea... | {
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One way insulation? I know from basic physics lessons that a box painted black will absorb heat better than a box covered in tin foil. However a box covered in tin foil will lose heat slower than a black box.
So what is the best way to conserve the temperature of a box? (aiming for 0 degrees Celsius inside the box whe... | If your box (at 0-20°C) starts out hotter than the environment (at -60°C) then your best strategy is to prevent any heat flowing out of the box into the environment i.e. insulate the box.
Using foil will reduce radiative energy transfer, however in most cases the cooling is dominated by convection rather than radiation... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
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Electric flux for a rectangular surface? I have the following homework problem:
A line of charge $\lambda$ is located on the z-axis. Determine the
electric flux for a rectangular surface with corners at coordinates:
$(0, R, 0)$, $(w, R, 0)$, $(0,R, L)$, and $(w, R, L)$.
This is what I have come up with so far:
... | I think the integral would simply be $Φ=(λ/L2πε0)\sin^{−1}(w/R)$ and not $\sinh^{-1}$.
| {
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"source": "stackexchange",
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What is fundamental difference between wave and its 180 flip phase? I'm studying property of sound wave and I was wondering what is difference between two waves (one is original and one is 180 flip phase of original) ?
Amplitude and frequency remains same and also wavelength is same, so are they same?? I could not dete... | If you play them simultaneously then they will destructively interfere provided they arrive at the listener at the same time (no additional phase difference). This is the basis of noise cancellation.
| {
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"source": "stackexchange",
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Uncertainty principle in atomic clocks? How does the uncertainty principle limit the accuracy of atomic clocks. I know line width and measurement time are important but not exactly why?
| A caesium clock generates a microwave signal that it tunes to match the absorption peak in the Caesium spectrum. A counter counts every oscillation of the generated microwave, and every 9,192,631,770 counts = 1 second. That's how the clock counts the seconds and keeps time.
But if the peak in the caesium spectrum is br... | {
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Why are high voltage lines “high voltage?” If I have two spheres of the same size and one sphere has a small amount of charge compared to the other that has a lot more charge, then clearly the sphere with the larger charge has a larger voltage (relative to the ground). My question is do high voltage power lines have a ... | For an analogy, you should consider voltage more like a "pressure" than an amount of charge. It just so happens that in your sphere example, with a fixed number of charges (electrons), you get this nice correlation between charge and voltage.
But in a conductor, the pressure can come from far away so to speak - from th... | {
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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 ... | I believe this is essentially what happens in gilding, owing to the special properties of gold (malleability and lack of corrosion).
Extremely flat surfaces can get stuck together due to Van der Waals forces as well as air pressure. I once accidentially stuck two quartz optical windows together, and had a hell of a tim... | {
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"url": "https://physics.stackexchange.com/questions/87107",
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Why force $F$ is $ma$ but not $md$ or $mv$? How can I observe and understand "force" in real life? As a layman, i can calculate approx "displacement" just by observing the moving object. And accurately by using a simple "scale". Similarly, again, I can calculate angle from origin by using displacement in $x$ and $y$ di... | A force is something that can modify the state of motion of a system.
If a system has a constant velocity (it means it doesn't accelerate : $\vec{a}=\vec{0}$), then no force is applied to the system ($\vec{F}=m\vec{a}=\vec{0}$).
If the system has a velocity that changes (it accelerates or turns) then the acceleration ... | {
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Atwood machine problem
Sorry for the bad drawing, but I hope that this will help you get a hold of the problem.
Consider an Atwood Machine with a total of two blocks, a mass less pulley, ideal string. One block rests on the floor, while the other one is at a height (H). Now, the string near the block that rests on the... | The answer is that both mechanical energy conservation and linear momentum conservation are not valid.
Linear momentum can't be conserved because there will be an impulse exerted on the system by the pulley. This impulse will be in the upward direction because notice how the tensions in the string on the pulley are dow... | {
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Difference between primitive unit cell and the associated basis? As I understand it, the basis is the group of atoms whilst the primitive unit cell is the unit space that fits the total space without any gaps, and only containing one lattice point? How do the two relate to each other? Thanks.
| I'm going to maximally disagree with P3trus and say that they're exactly the same thing: "A crystal can be categorized by its lattice and the atoms that lie in a primitive cell (the basis)" (source).
| {
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Is there a theoretical maximum for refractive index? May there be materials yet to be discovered which may have a higher refractive index than today's known materials (for wavelengths within the visible range)?
Is there a theoretical limit for the refractive index of a material?
| Since the refractive index is given by $\displaystyle{n_{12}=\frac{\sin \theta_1}{\sin \theta_2}}$, theoretically there is no limit at all on the value of refractive index. You could say that it must be positive, but then check this out: http://en.wikipedia.org/wiki/Negative_refraction
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is any apparent horizon a minimal surface? I faced "any apparent horizon is a minimal surface", but I don't know how I can relate a physical concept (apparent horizon) to pure mathematical concept (minimal surface). How can I prove it?
| I found the answer:
The apparent horizon $\mathcal{H}$ is defined as the outer boundary of the region of $\Sigma$ (a hypersurface of spacetime with induced metric $h_{ab}$ and extrinsic curvature $K_{ab}$) which contains trapped or marginally trapped surfaces. $\mathcal{H}$ itself must be a marginally trapped surface, ... | {
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Does changing the electric / magnetic field cause self-reinforcing induction of the other? I understand that changing electric field produces magnetic field and changing magnetic field produces electric field.
Are these produced magnetic and electric field produced due to one defined to be constant or variable?
If thes... | Instead of thinking about one field changing in response to the change of the other, it is more correct to say that
whenever the magnetic field is changing, so is the electric field, and vice versa.
The way these fields change is governed by Maxwell's equations. This way, we do not arrive at the confusion OP has.
| {
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Symmetries of a Uniform Magnetic Field Simple question. A system with a uniform electric field everywhere in space has translational invariance in the directions perpendicular to the electric field but no translational invariance parallel to it. This system also has rotational invariance in the plane perpendicular to... | Your hamiltonian is still gauge invariant because the canonical momentum, that is the generator of translations, is $m \dot{\vec{x}} - q \vec A$. In other words, your Hamiltonian is still $H = \frac{1}{2m}\Pi^2 - q \Phi$, where $\vec \Pi = m \vec{ \dot{x}}$ is the mechanical momentum.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Detecting a photon without changing it: Does it break conservation laws? This is about an article published on ScienceMag: Nondestructive Detection of an Optical Photon. I don't have access to full text, but you can see a brief transcription in this link.
Basically, it says that a photon causes a phase shift in another... | There exists elastic scattering where only directions are changed , momentum is conserved and energy is conserved.
There exists elastic scattering of photons:
In Thomson scattering a photon interacts with electrons.
Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, a... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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?
| The only stars you can reliably see are ones that are spewing enough photons at your eyeballs to appear stable.
Any star which is so dim that photons entering your eye can literally be counted one by one, simply will not register in your vision, because your eye's retina is not sensitive enough.
So your question is bas... | {
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"url": "https://physics.stackexchange.com/questions/87986",
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"source": "stackexchange",
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Predominant light frequency over the day? I'm not well-versed in physics, so I hope you'll forgive me if this question is significantly off the mark.
I'm interested in the predominant frequencies of light over the course of one day. My understanding is that as the sun rises and falls, the atmosphere absorbs differing a... | I found a good paper that can help you. However, due to copyright issues I cannot put the spectra here.
Try to get this article:
"The Distribution of Energy in the Visible Spectrum of Daylight". A. H. TAYLOR and G. P. KERR. J. Opt. Soc. Am. 31 no. 1, pp. 3-8 (1941)
. Also available here (pdf).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/88071",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Effective mass of a black hole? Suppose a black hole forms from a given mass of particles such as the core of a star going supernova. The black hole formed will have an effective mass due to the curvature of space time induced. Such a mass is presumably the inferred mass deduced from the effect of the black hole on the... | Answer: slightly less mass.
In general relativity, mass/energy of any system is conserved from the point of view of a distant observer (I forget the name of this theorem). We use this mass when we talk about how heavy a black hole is because we are (very) far away.
If you start with particles that are stationary, the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/88143",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Faradays law for a falling magnet If experimentally it can be proven that the velocity of a falling magnet through a coil is proportional to the emf induced, has it also been proven that dB/dt is proportional to the emf induced and how so ?
| For slowly moving magnets, you can measure the strength of the magnetic field using another magnet mounted on a torsion balance. The degree of deflection would be proportional to the field strength. For fast moving magnets, you run into difficulties with your apparatus "lagging behind" and it is more properly the case ... | {
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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:
$$ 0=\overrightarrow{F}_{ext}=\frac{d\overrightarrow... | There's another way to do this also, more akin to how spacecraft actually do it:
Take a weight on a string, hold it up and spin it. You'll turn in the opposite direction. When you stop it you also stop turning.
Of course this will produce an off-axis force that will be a real pain to deal with. Real spacecraft do it... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is it easier to walk diagonally upstairs Try it yourself on a set of wide steps! Work is given by
$$\int_C \mathbf{F} \cdot d\mathbf{x}$$ where $C$ is a path integral. In this case I think $\mathbf{F}$ is a rotational vector field because the stairs are essentially a set of discontinuities. This would mean that the... | It's because of how the body is oriented when going up diagonally which allows for the lateral thigh muscles to contribute to the effort, versus only the frontal muscles when going straight up. Since the effort is spread over more muscle areas, it feels less strenuous.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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A naive question about the Second Quantization? Let's consider a single-particle(boson or fermion) with $n$ states $\phi_1,\cdots,\phi_n$(normalized orthogonal basis of the single-particle Hilbert space), and let $h$ be the single-particle Hamiltonian. As we all know, the second quantization Hamiltonian $H=\sum\left \l... | The entirety of the modern quantum mechanics literature uses inner products that are linear in the second argument, and antilinear in the first one. Mathematicians often use the other convention, but I've never seen it used in physics. This is of course pure convention, but you will find grief, at least when you try t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Physics of the inverted bottle dispenser
When you invert a water-bottle in a container, the water rises and then stops at a particular level --- as soon as it touches the hole of the inverted bottle. This will happen no matter how long your water-bottle is. I understand this happens, because once the water level touch... | Your mistake is to assume that the water will stop "no matter how long a bottle you take". It will not - you just need a longer bottle than you expect. To be precise, you need a column of water 10 meters high to counteract atmospheric pressure.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/88669",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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"answer_id": 1
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Quantizing the Dirac Field: which commutation relations are more fundamental? When quantizing a system, what is the more (physically) fundamental commutation relation, $[q,p]$ or $[a,a^\dagger]$? (or are they completely equivalent?)
For instance, in Peskin & Schroeder's QFT, section 3.5, when trying to quantize the Dir... | Firstly, note that they postulate those commutation relations in the beginning of section 3.5 in order to show that they are wrong, which they demonstrate in the ensuing pages. The ultimate point is to show that one needs to impose anti-commutation relations on fermionic fields.
In fact, the correct relations are post... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/88727",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Exciting Surface Plasmon-Polaritons with Grating Coupling I'm very new the topic of SPPs and have been trying to understand this particular method of exciting surface plasmons using a 1D periodic grating of grooves, with distance $a$ between each groove. If the light incident on the grating is at an angle $\theta$ from... | Yes light can change propagation direction when scattering off of a grating into pre-defined directions that depend on the angle of incidence and the grating period (as well as the refractive medium the grating resides in). This is just Bragg's Law. The change in direction (or momentum) is determined by the above par... | {
"language": "en",
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Bulk modulus of Liquid helium and first sound Does anyone know where to find the bulk modulus of liquid helium ?
I've been looking all over the internet but everywhere I get N/A. Any tips ?
I'd need it to estimate the speed of first sound in liquid helium which is given by:
$c_1=\sqrt{\left.\frac{\partial p}{\partial\r... | The best way is to use the inverse value, the compressibility, this one is more easilly found.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Calculate average speed with unknown variable accelaration I am in the middle of a vehicle tracking project where I have to calculate the distance traveled by the vehicle in a given amount of time.
Data I am getting:
Speed : 30.2 km/hr 12.7 km/hr 15 km/hr 21.8 km/hr
Time : 11:00:00 11:00:22 11:00:45... | Well, this is an easy problem in kinematics. "The rule" for solving it is drawing a graphic of the (differences of) time versus the speed. You will get some points. Join these points to obtain a trapezoid histogram. So, what do you think it is the area beneath this curve? It has the dimensions of a length, so... Now, y... | {
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"timestamp": "2023-03-29T00:00:00",
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Why do some beverages stay cold longer than others? For my daughter's science experiment, she placed six beverages (cola, diet cola, milk, chocolate milk, apple juice, and water) in the exact same amount in the exact same type and size of plastic cups, and placed all of the cups in a refrigerator at the same time and a... | It is mostly because different liquids have different Thermal conductivity and Heat capacity.
http://en.wikipedia.org/wiki/Heat_capacity
http://en.wikipedia.org/wiki/Thermal_conductivity
Of course viscosity of Liquid is effective but it is a secondary factor.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/89042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Dirac Lagrangian density in curved spacetime I'm trying to derive this form of the Dirac Lagrangian density in curved space-time:
$$ \mathcal{L}~=~\det\left(e\right)\bar{\Psi}\Bigg (\frac{i}{2}\gamma^{a}\partial_{a}-m+\gamma^{a}\gamma^{5}B_{a}\Bigg)\Psi $$
starting from this form:
$$ \mathcal{L}~=~\sqrt{-g}\Bigg (\frac... | What does B correspond to here? Is it related to the spin connection? The axial current?
Also the link you propose does not work anymore.
If you want a rather nice demonstration of the Dirac equation in curved space, you can try "Nonlinear spinor equation and asymmetric connection in general relativity" by Hehl and Da... | {
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"timestamp": "2023-03-29T00:00:00",
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What is the area in Faraday's law if we have only a piece of metal moving in a magnetic field? If a piece of metal of length $l$ is moving with a speed $v$ in a region where there is a uniform magnetic field $B$ perpendicular to it, there will be a potential difference across its terminals equal to $lvB$ which is known... | I think your question answers itself, indeed the area of what? Faraday's law is for a closed loop of wire, thus Faraday's law is inappropriate and we should look for an alternative, as you have done by considering the Lorentz force. If the metal were a closed loop of circumference $l$ then Faraday's law would be valid.... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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All objects radiate energy, but we cannot see all objects in the dark. Why? We claim that all objects radiate energy by virtue of their temperature and yet we
cannot see all objects in the dark. Why not?
| Cold bodies radiate mostly in the infrared zone (invisible to the human eye), but as the temperature increases the body will emmit higher frequencies with more intensity. So room temperature obects will not be seen due to black body radiation.
As you can see, hot bodies are visible because they emmit visible light mos... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/89477",
"timestamp": "2023-03-29T00:00:00",
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Why are roofs blown away by wind? Whenever there are high winds, such as in storms, thin metal roofs on sheds as well as concave roofs on huts are sometimes blown away.
One explanation provided to me said that the higher velocity of the air outside causes the air pressure above the roof to decrease and when it has decr... | Bernoulli to the rescue!
Does this answer the question?
Keep in mind, hurricane speeds are often twice small aircraft stall speeds, and typical aircraft wing loading is in the range of $50 kg/m^2$, so a roof could see 4 times that.
Roofing material would have to be really heavy not to be lifted by that.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/89570",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 1
} |
Heating metal with laser? Can a laser be used to heat metal's to the point they glow red?
How are laser cutters able to cut metal very easily?
How much heat can a laser generate?
| *
*Can a laser be used to heat metal's to the point they glow red?
Yes
*
*How much heat can a laser generate?
How big can it be? What laser are you talking about?
*
*How are laser cutters able to cut metal very easily?
Now that is a good question.
Some laser cutters will melt the object they are cutting ... | {
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What is quark transverse momentum? When you google my question you get something on the order of 400 000 results but none of them explains how it is defined (No I didn't check them all).
I know what the words quarks, transverse and momentum mean. But what is quark transverse momentum? Transverse with respect to what? ... | The only way we know that quarks exist is by a series of deep inelastic scatterings with leptons and with protons. This is a reconstructed event at LEP
quark antiquark at 12:00 o'clock and 4:00 o'clock gluon the third one.
The lepton colliders have the advantage that most of the energy taking part in the collision c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/89762",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
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How does air escape from a pneumatic tire? Obviously, it is caused by the difference in pressure between the inside of the tire and its surrounding environment; but how specifically is the air escaping?
| Air escapes via multiple mechanisms.
Diffusion through the material: Most materials have some permeability to air. Air molecules can fit between the rubber molecules. The N2 and O2 molecules are so few and far between that they don't interact. The average force on a molecule is zero as it randomly walks through the rub... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/89962",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
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As the universe ages, will we see more stars or less? After a very long time will we see more stars (due to the fact that more light is get to us) or less stars (as the universe expends and light have to pass larger distance)?
In general, can stellar objects go outside of the scope of the observable universe or is it o... | Star formation will slowly start to decrease in galaxies as the universe ages because of the conversion of gas, such as hydrogen, into heavier elements, such as carbon and iron. Essentially the universe is slowly running out of fuel. Stars have a hard time fusing heavier elements.
Eventually there will be no stars left... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/90024",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "18",
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