Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
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 assuming that the same average force will be able to lift your object to the same height on earth and in moon. Suppose, we consider lifting an object with zero speed to a height of $x$ meter on earth. Then the force required would be the gravitational force on the object ($mg_{earth}$). But on the moon, sa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/79486",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is Ohm's law obeyed in power transmission? We learnt in high school that according to Ohm's law $V/I=R$.
We also learnt that during power transmission in an electric line $P=VI$ and that in order to minimize loss voltage is raised. As a consequence current is reduced. This contradicts with the Ohm's law which states th... | If you use high voltage for long distances, you'll need a transformer to connect your household load. A transformer not only changes the voltage, but also the current, hence the R (impedance) with the square of the voltage ratio. On either side of the transformer Ohm's law will hold.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/79573",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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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... | Yes there is. Such Ising models are called 'Potts models' (due to the arbitrary number of possible spins). This can be mapped exactly to a graph or network, for which partitioning algorithm or 'community detection' algorithms are useful. For appropriate choices of objective function, the optimal partition will correspo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Dynamics of counter-rotating flywheels I've wondered about this for ages. If we create a pair of flywheels that rotate in the opposite direction with the same angular momentum, but are co-located and have the same mass and inertial moment (one can imagine various ways to accomplish this, at least approximately) -- it ... | I think that in case of two flywheels the angular momenta point in opposite directions and thus cancel each other. Therefore no nett torque will be required to change the angular momentum of the pair which is not the case if there is only one flywheel.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/79699",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 2,
"answer_id": 1
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Does the heat produced in an inductor affected by the total current in the resistance in the circuit? The energy stored in an inductor depends on the inductance of the inductor and the current flowing through it. But, assume that the switch is opened. Then, does the heat generated in the inductor dependent on the total... | It depends on the total resistance (including the winding resistance of the inductor, not shown in your circuit). Once the switch is opened, no current flows through the battery, so the battery does not affect the rest of the circuit then, after the switch is opened. Basically at that time, when the switch is opened,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/79771",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Rate of effusion in kinetic molecular theory? According to the kinetic molecular theory obeying Maxwell-Boltzmann distribution of speeds, the rate of effusion through a pinhole of area $A$ is
$$R=\frac{PA}{\sqrt{2\pi M R T}}$$ where $M$ is the molecular weight, $R$ is the gas constant and $T$ the absolute temperature. ... | If your Maxwell-Boltzmann distribution is $\mu(\vec v) = \mu(v) = (\frac{m}{2 \pi k T})^{3/2} e^{- \frac{m v^2}{2 k T}}$, then, if I am not mistaken, you should have to perform an integral with $\theta$ limited between $0$ and $\pi/2$ of kind $ I = nA \int_{0 \le \theta \le \pi/2} d^3 \vec v \mu(\vec v) (\vec v.\vec ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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 $2 \pi R$. ... | Why are you using Pythagoras' theorem? a triangle of two sides $R$ and one side hypotenuse $vt$ is a wrong depiction of $v$. you are essentially tracing a square path for the car with its 4 vertices on a circle of radius $R$. geometrically, $vt$ is the arc length $\theta R$, and shouldnt be chord length $R \sqrt{2-2\co... | {
"language": "en",
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How does interaction of a system with the environment lead to the damping of interference terms? A general way to describe a system $S$ that is entangled with an environment $E$ is
$\rho_{S}=Tr(\rho_{SE})=\sum\limits_{m,n}c_mc^*_n |s_m\rangle \langle s_n| \langle e_n|e_m\rangle$
with $\psi_S=\sum\limits_n c_n|s_n\rangl... | The situation depends on the specification of "system" and "environment", and the detailed form of the interaction Hamiltonian. Clearly, if your environment has only a few degrees of freedom then the Poincare recurrence time is finite, and the assertion that the coupling results in decoherence is false at certain point... | {
"language": "en",
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calculating the solar declination I was looking at this page
http://www.illustratingshadows.com/www-formulae-collection.pdf
and found the equation used for estimating the solar declination (sun declination). One problem, though, I wish to cite this equation in my work and was hoping there would be a textbook that shows... | A simple Google-book search of "solar declination" lead me to this Google-book preview of Solar Energy Engineering: Processes and Systems
by Soteris A. Kalogirou. This book gives the Spencer formula as Equation (2.6), on page 55.
| {
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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?
| As the battery forces charge through the resistor, indeed that energy is converted into heat. An ideal battery has enough power so that it can supply the current without any voltage drop.
With a real battery, you have to make allowance for the battery's internal resistance. This resistance is inseries with the resista... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/80103",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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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... | For the $l$-th term you take totally symmetric tensors of rank $l$ which are totally traceless under contractions of each index. This comes because that is how the multipole moments, or rather the spherical harmonics, are built from the cartesian coordinates. For example $l=2$ has $5$ components that look like $x_i x_j... | {
"language": "en",
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Why is the voltage drop across an ideal wire zero? I'm having trouble conceptualizing why the voltage drop between two points of an ideal wire (i.e. no resistance) is $0~V$. Using Ohm's Law, the equation is such:
$$
V = IR \\
V = I(0~\Omega) \\
V = 0$$
However, conceptually I can't see how there is no change in energy ... | The key thing is that there is NO electric field within the perfect wire. So, there is no force acting on the electron, and thus no work done on it (while it's in the perfect wire).
This goes back to the definition of a perfect conductor (which the perfect wire is). Within a perfect conductor, there is no electric fiel... | {
"language": "en",
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"source": "stackexchange",
"question_score": "10",
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Entropy Maximization using undetermined multipliers This is from Problems in Thermodynamics and Statistical Physics by P.T. Landsberg
A system can be in any one of N states. Using the method of undetermined multipliers to show that for the maximum entropy, $S = -k \sum_i p_i \ln p_i$ where $p_i = 1/N$, $$S = k \ln N\,... | Since $p_j$ is same for all $j$, we have for the normalisation $\sum_j p_j = N*p_j = 1$. This implies $p_j = 1/N$.
Now, $S_{max} = -k \sum_j p_j \ln p_j = -k N * (p_j \ln p_j) $. Now substituting $p_j = 1/N$ should give the expression you are looking for.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Signs in proof of gravitation potential energy (GPE) Proof of gravitational potential energy.
Work done by gravity in bringing mass from infinity to a distance of $r$ between masses.
When we use the integration formula and arrive at the answer we get $-GMm/r$ taking lower limit as infinity and upper as $r$.
But this ... | Maybe the confusion arises from the fact that the potential energy in a point $P$ can be interpreted as the work needed to bring a particle from a reference point $O$ to $P$, without altering its kinetic energy. Due to the fact that $\Delta K = W$ this is exactly minus the work done by the conservative forces.
In this... | {
"language": "en",
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"source": "stackexchange",
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What determines the form of the intensity curves in Laser-Induced Fluorescence (LIF) measurements? What determines the form of the intensity spectra of different particle species in Laser-Induced Fluorescence (LIF) measurements? See e.g.
I figure that bigger particles have more ways to get excited and so the intensiti... | In short: the spectra can be explained by considering vibronic transitions, the Franck-Condon principle (http://en.wikipedia.org/wiki/Franck%E2%80%93Condon_principle), and the uncertainty principle. The explanation is as follows:
The intensity of a transition is determined by its probability amplitude $P$
\begin{equati... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | Well the mutual repulsion of like particles, such as electrons (for example) is commonly explained as being due to "exchange particles" that mediate the four standard forces of the standard model. For the Electro-magnetic force (Coulomb) between like charges (electrons) the exchange particle is the Photon.
Two electr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/80807",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "97",
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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?
| Edited answer to answer the question
If we define a rest-frame such that
$$
\mathbf{r} = \mathbf{R}_0 + \mathbf{r}' \\
\mathbf{v} = \mathbf{V}_0 + \mathbf{v}' \\
\mathbf{a} = \mathbf{A}_0 + \mathbf{a}'
$$
where $\mathbf{R}_0$ represents the distance from the rest-frame origin to the moving-frame origin (and similarly ... | {
"language": "en",
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What is the opposite of the Planck length? What "large size" unit of length could be considered at the opposite end of spectrum from Planck's length?
Is there a table of smallest and largest value for various physical quantities that can be defined from well-known constants?
Edit
I was teaching the exponential functio... | Planck's constant is not at one end of a spectrum, so it has no "opposite" in this sense. In particular, it's not a minimum length. There is an argument for a minimum measurable length that is on the order of the Planck length, but that's different.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Stress-energy tensor. Why this general form? How is the stress energy tensor obtained? In most textbooks, it's simply stated as
$$T^\mu{}_\nu=(\rho+P)U^\mu U_\nu-P\delta^\mu{}_\nu$$
I can see why this makes sense for a comoving observer at rest wrt. the perfect fluid. But I don't understand how the general case is arr... | The answer to this depends on what you're starting from. If you know the Einstein tensor, then you can find the stress-energy tensor from the Einstein field equations. If you know the Lagrangian density, then you can find the stress-energy tensor by variation with respect to the metric. If you know the rate at which en... | {
"language": "en",
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"source": "stackexchange",
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Why are all force particles bosons? All of the force-particles in the standard model are bosons, now my question is pretty short, namely:
Why are all force particles bosons?
This can't be a coincidence.
| The simplest Feynman diagram for an interaction between two particles looks like a letter "H". The cross-bar is a force-carrier being exchanged. At each vertex, you have a particle either emitting or absorbing a force-carrier. If the force-carrier has a half-integer spin, then you can't emit or absorb it without violat... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | If semiconductor is doped with both n- and p- dopants equally - electrons and holes "annihilate", and you are getting almost "neutral" material.
Of course high level of such "neutral" doping will degrade semiconductor specs (like electron/hole mobility).
If there will be more n-type dopants than p-type ones - you will ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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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... | One may view both (i) the infinite wall
$$\tag{1} V(x)~=~\left\{\begin{array}{ccc}\infty & \text{for} & x>0, \\ 0 & \text{for} & x\leq 0, \end{array} \right. $$
and (ii) the delta function potential
$$\tag{2} V(x)~=~A\delta(x),$$
as an appropriate limit of a finite barrier wall
$\tag{3} V(x) ~=~ V_0 1_{[0,a]}(x)=\le... | {
"language": "en",
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Confusion about the probability cloud What is the meaning of the electron probability cloud?
I understood it to mean that the electron has a probability to be found in a certain postion before measurement, but now after reading experiments involving Schrödinger's cat type states (with bonding and antibonding gaps in $... | I don't think the term electron probability cloud has a precisely defined meaning. It's more of a metaphor meant to show that the electron does not have a well defined position.
Like any quantum particle the electron does not have a position until you interact with it e.g. scatter another particle off it. The interacti... | {
"language": "en",
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How to get Hamiltonian of QED from lagrangian? I have the QED lagrangian:
$$
L = \bar {\Psi}(i \gamma^{\mu }\partial_{\mu} + q\gamma^{\mu}A_{\mu} - m)\Psi + \frac{1}{16 \pi}F_{\alpha \beta}F^{\alpha \beta} .
$$
I tried to get hamiltonian by getting zero component of energy-momentum tensor:
$$
T^{\mu}_{\quad \nu} = i\ba... | You can only find the Hamiltonian if you do a so-called 'gauge fixing' procedure, since the Dirac field couples (minimally, but uniquely) to a gauge field. To get the Hamiltonian (density) you need to perform the full Dirac constraint analysis and at the end 'gauge fix'. See the books by Sundermeyer or Henneaux+Teitelb... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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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... | Subtle question. Here's my take.
Mathematically in 2D the flux will be through a line bounding the charge $\lambda$ (let's assume it is a charge for now). Using symmetry arguments, Gauss says
2$\pi$$r$$E$=$\lambda/c$, hence we get $E$=2$K\lambda$/r, where $c$ and $K$=1/(4$\pi c$) are analogous to the vacuum diel const... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/81883",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | Let's assume your sheet is a disk of height $h$ and radius $r$, and we'll consider what happens when we take the height down towards zero.
The pressure at some depth $d$ is given by:
$$ P = \rho g d $$
where $\rho$ is the liquid density and $g$ is the acceleration due to gravity. So the pressures on the upper and kowe... | {
"language": "en",
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What are orbifolds and why are they useful and interesting for physics? Just what the title says.
*
*What's the basic definition of an orbifold?
*How do they arise in physics and why are they interesting?
| Orbifolds are spaces of the type $O = M/G$ where $M$ is a manifold and $G$ is a group acting nonfreely on $M$. That is there are fixed points (or more generally submanifolds of this action); i.e., points $x \in M$ such that $G.x = x$ for all $G$. These fixed points are called singular points, they have the property tha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/82101",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Simple photon recoil question Imagine two charges A and B separated by some distance.
Charge A emits a photon which is absorbed by charge B.
Is the recoil momentum received by charge A always equal and opposite to the momentum gained by charge B?
Is this true both for static Coulomb fields and radiation fields from acc... | The momentum and mass-energy of a quantum system are together conserved. So a classical notion of recoil momentum is only partly true. The electron can absorb or emit photons but photons are quantized so will not conserve momentum classically like your question implies. Nor will it behave as a classic inelastic collis... | {
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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.
| Neither of your two statements have any validity to them and are therefore not applicable to understanding Bernoulli's principle, let alone more appropriate than the other. Pressure is a relative quantity that has little meaning by itself. Changes in pressure have meaning and can cause fluid motion. For situations w... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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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... | The time dependent hamiltonian also implies, that the volume element in the phase space is not conserved under time evolution.
| {
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"url": "https://physics.stackexchange.com/questions/82404",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Confusion about a lemma on the time constraint of an adiabatic evolution (arXiv:quant-ph/0604077) I am going through the paper Quantum adiabatic evolutions that can't be used to design efficient algorithms by Zhaohui Wei and Mingsheng Ying. On the second page they prove a lemma. The statement goes as follows.
Lemma 1 ... | I'd say you are missing the "hat", i.e. they write $|\hat{0^n}\rangle$ instead of $|0^n\rangle$ and never really define what they mean by that before the lemma. If, however, you look at eqns (19)-(21), you'll find a definition that the hat indicates the Hadamard basis - and then the two definitions should be equivalent... | {
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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... | Both operate on the same principle: the velocity of a point on a rigid body undergoing rotation is proportional to its distance from the pivot.
The sling is simply an ingenious way to extend the distance of the the projectile from the pivot without extending the rigid arm. As the trebuchet arm moves in an arc, the slin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/82635",
"timestamp": "2023-03-29T00:00:00",
"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 last step you performed is incorrect.
$$\begin{equation}
\begin{aligned}
\psi^\dagger & \rightarrow \psi^\dagger \left(1-\frac{i}{2} \omega_{\mu \nu}S^{\mu \nu} \right)^\dagger \\&
= \psi^\dagger \left(1+\frac{i}{2} (\omega_{\mu \nu})^\dagger (S^{\mu \nu})^\dagger \right) \\&
= \psi^\dagger \left(1-\frac{i}{2} \ome... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/82704",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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Quantum operator catastrophe Assume we look at an interaction between 2 fermions
$V \sum_{k_i,k_j,k_m,k_n} c_{k_i}^\dagger c_{k_j}^\dagger c_{k_m} c_{k_n} \delta_k $
where $\delta_k$ conserves momentum. We can directly write down a few terms from the sum
$ ... + \underbrace{c_{k_1}^\dagger c_{k_2}^\dagger c_{k_3} c_{k_... | As an addition an example to Adam's answer, consider the action for the superfluid normal transition in liquid helium-4:
$$
F = \int dx \left( \frac{\hbar^2}{2m}|\nabla \phi(x)|^2 - \mu |\phi(x)|^2 + \frac{V_0}{2}|\phi(x)|^4 \right)
$$
Fourier transforming the latter interaction term (which by the way comes from assumi... | {
"language": "en",
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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... | There's two rational reasons why this would be a bad idea for everyday life:
*
*most speeds we encounter are significantly smaller than $c$.
*it would change our units system entirely
For the first point, I'd be traveling down my street at 0.00000037 instead of 25 mph (40 km/h). Airplanes would travel at about 0... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Neutrons reflective materials in nuclear reactors Nuclear reactors are driven away from criticality with the use of control rods which absorb neutrons. In case of overheating and melting of the core, the control rods may not be inserted any more leading to a disaster.
A subcritical mass can be made critical by placing ... | The size of the core plays a large role in the feasibility of controlling a reactor through reflection. In small cores, the surface area is large relative to the volume, which, in the absence of a reflector, leads to high neutron leakage out of the core. As core size increases, the ratio of surface area to volume decre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/82919",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
"answer_id": 3
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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?
| Not exactly. Fusion of atoms in Supernova nucleosynthesis is thought to be responsible for the various atoms that make up the periodic table. While there hasn't been one in our part of the galaxy for quite some time, plenty of Supernova are occurring through out the universe right now. So, while you are made of old s... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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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$$
What I tried so far:
*
*Integrate over $k_0$ while promoting $k_0$ to complex ... | Hint:
$$ \int_{\mathbb{R^{d+1}}}\! \frac{d^{d+1}r}{{\rm Vol}(S^{d-1})} \frac{e^{ik\cdot r}}{r^2}
~=~\int_{0}^{\infty}\! dr~r^{d}\int_{0}^{\pi}\!d\theta~ \sin^{d-1}\theta \frac{e^{ikr\cos\theta}}{r^2}$$
$$~=~\int_{0}^{\infty}\! dy~y^{d-1}\int_{-\infty}^{\infty}\!dx~ \frac{e^{ikx}}{x^2+y^2}
~=~\int_{0}^{\infty}\! dy~y... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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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-... | To start with, quantum mechanics was not postulated. It grew from observations of quantized states including the study of the effects of Heisenberg's uncertainty principle.
Now we have a consistent theoretical framework for quantum mechanics which in principle allows us to predict by computation, the probabilities of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/83169",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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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... | Antimatter has the same mass as normal matter, and its interaction with gravity should be the same according to GR and QM.
That said, antimatter has only been created in tiny amounts so far and only few experiments have been performed to confirm there is no new physics involved.
The gravitational interaction of antima... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "28",
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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 ... | Astrophysicists have been looking at electron positron annihilations in the cosmos
The Universe viewed trough INTEGRAL: the first complete map of the sky
at the electron-positron annihilation energy (Credits J. Knödlseder - CESR - September 2005).
If there existed regions in the sky where antimatter was aggregatin... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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Fundamental Constants in a theory of everything (TOE) Do physicists ever expect to be able to derive the fundamental constants of nature from theory? For example, if string theory or some other theory unites the four forces, would the theory be considered complete if it relies on these measured constants, or would a t... | The following constants might vanish (e.g., place-dependent behaviors along a dimension, built-in identifiers that assign access along a string [ push-forward ], carrier-entropy) or transform--as in a qubit (a decision) flinching characteristically from dimensional memory, where the amount of the flinch is just the car... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/83562",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why does the counterterm's propagator have inverse units of the propagator? $\phi^4$-theory According to Peskin & Schroeder (page 325), the Feynman rule for the counterterm
------(x)-----
for
$$ \frac12 \delta_Z(\partial_\mu\phi_r)^2-\frac12\delta_m \phi_r^2$$
being $\phi_r$ the renormalized field, is given by
$$i... | I also found it hard to find a rigorous explanation. By dimensional analysis and explicit checking you indeed find that this is the correct Feynman rule for the counterterm.
The closest thing I have to a derivation is that we can include the counterterm in the kinetic term and expand this full propagator for small $\d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/83711",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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does light experience time? If we positioned a mirror 1 light year away from earth and shot a particle of light at the mirror so that it would reflect and come back to earth, how long would it take for us to receive that particle of light back to earth and if I jumped on this particle of light for the trip how would it... | at Light speed change in Proper Time will be zero:
$$d\tau=dt\sqrt{1-(\beta^2=1)}=0$$ that means light observer do not experience time.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/83919",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Electric field inside a conductor I would like to clear things up:
How exactly the electric field inside a conductor is zero? Let a really "powerful" electric field be outside of it, how can the "few" charges in a conductor balance the field? From my point of view, it's the conductor surface which stops their movement... | Metal being a crystal structure of atoms being locked in position,an electric field would have a net zero in relation to itself unless it is varied.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/85974",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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"answer_id": 2
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Peskin and Schroeder Equation 2.56 In Peskin and Schröder's QFT, equation 2.56, could anyone give a list of all the arguments necessary in order to make all the transitions mathematically rigorous?
I tried composing such a list myself and I came up with:
*
*$\frac{d}{dx}\theta(x)=\delta(x)$
*$\theta(x)\delta(x)\equ... | Probably not a complete answer. However, your item 1. is correct but
1'. $\partial^\mu\theta(x^0)=g^{\mu 0} \delta(x^0)$ is better for this purpose. And then $\partial_\mu\partial^\mu\theta(x^0) = \partial_0\delta(x^0)=\delta'(x^0)$.
Your item 2. is incorrect, the distribution on the l.h.s. is not defined as far as ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is water a gas at critical density, room temperature? I am quoting Chaikin, Lubensky, Principles of Condensed Matter Physics, p. 4.
Now suppose we have a closed container of water vapor at a density of 0.322 g/cc at room temperature. As the temperature is lowered...
It then proceeds to describe condensation, and says... | If this state is prepared at room temperature (somehow), condensation will happen immediately, and the temperature will rise so much that the water will be boiling hot (some water will stay in the vapor phase), although it will still be less hot than the critical point.
Yes, it is a mistake. You can only prepare/mainta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/86127",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What is the definition of particle-hole symmetry in condensed matter physics? People often talk about particle-hole symmetry in solid state physics. What are the exact definition and physics picture of particle-hole symmetry? How to define the density of particles and holes?
| We find particle hole symmetry (PHS) for example in superconductors, where you can consider the Bogoliubov-de Gennes (BdG) Hamiltonian as a mean-field approximation. This is the only experimental example I know. There maybe other systems with particle hole symmetry but I don't know about them. Here, I will use supercon... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/86293",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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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:
... | flux is not a vector. hence you have to calculate E.dA . write the electric field with direction and then take its dot product with area vector and then do the double integral.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/86387",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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"answer_id": 1
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Hall effect with similar positive and negative carriers? The Hall effect includes the transverse (to the flow of current) electric field set up by the charges which accumulate on the edges, to counter the magnetic component of the Lorentz force acting on them to move towards the edges. These charges can be both positiv... | We should consider about the mobility of electrons and holes. Intrinsic semiconductors have a negative hall coefficient such as in metals. If we consider the mass action law , we can find the carrier densities when the hall coefficient is equal to zero.
http://physics111.lib.berkeley.edu/Physics111/Reprints/SHE/11-Ha... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"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... | Actually, one wave and its 180 flip phase image can be seen as two waves with the same phase but with opposite amplitude (when one is positive the other is negative).
The reason you cannot hear the difference between the two is that your ear (or microphone) is not sensitive to the amplitude but rather to the intensity... | {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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Electron Wave Interference In the double slit interference pattern for the wave of an electron, what will happen if I make the slits to be smaller than the size of an electron ? Will I still observe an interference pattern on the opposite side of the screen or no electron will be able to cross the slit?
If no, then ho... | Nothing teaches like experimental observation. So I would suggest to iota, that (s)he should do the experiment, then come back and report the observed result. so what is the size of an electron ?
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/86752",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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A commutation problem in Hubbard model Does the Hubbard Hamiltonian $$H=-t\sum_{\langle ij\rangle \sigma}c_{i\sigma}^{\dagger}c_{j\sigma}+h.c.+U\sum_{i}n_{i\uparrow}n_{i\downarrow}$$ commute with $\sum_{i}\mathbf{S}_i^2$? where $\mathbf{S}$ is the spin angular momentum.
| It is known that the Hubbard model possesses the global $SU(2)$ spin-rotation symmetry, which means that the Hamiltonian commutes with the total spin $\sum_i\mathbf{S}_i$(where $\mathbf{S}_i=\frac{1}{2}c_i^\dagger \mathbf{\sigma}c_i$), which is the generators of the global $SU(2)$ spin-rotation group, and it does not c... | {
"language": "en",
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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 ... | Two reasons:
*
*Oxides
*The roughness of the surface
If the surface is rough, then the majority of the surface is touching the air gap between the two, not the opposite surface. A bond may form at the touching "peaks", but it will be weak compared to the rest of the metal because a very small fraction of the surf... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... |
So exactly what is it in the real sense.
It is that which acts to change an object's momentum or quantity of motion.
| {
"language": "en",
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Could there have been two "Big Bangs"? A couple of years ago, I remember seeing a documentary on the big bang theory. The theory presented was that to explain the cosmic microwave background radiation, there needed to have been two big bangs. Is this theory legitimate? I've tried searching for details without success.
... | I believe you are referring to the phenomenon known as 'inflation'. It refers to the extremely rapid expansion of the universe shortly after the Big Bang. According to wikipedia (linked above) it
lasted from $10^{−36}$ seconds after the Big Bang to sometime between $10^{−33}$ and $10^{−32}$ seconds. Amongst other thing... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/87289",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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What is the origin of the factor of $-1/4$ in the Maxwell Lagrangian? I have seen numerous 'derivations' of the Maxwell Lagrangian,
$$\mathcal{L} ~=~ -\frac{1}{4}F_{\mu \nu}F^{\mu \nu},$$
but every one has sneakily inserted a factor of $-1/4$ without explaining why. The Euler-Lagrange equations are the same no matter w... | The factor is there so that once you add a source term, i.e. $J^\mu A_\mu, $ you get the correct equations of motion, namely Maxwell's equations:
$\partial_\nu F^{\mu\nu}=J^\mu.$
Furthermore, this convention produces the usual $1/2$ in front of the kinetic term of the gauge fields.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/87342",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
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"answer_id": 2
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Partition functions in $\phi^{4}$ theory The partition function in a $\phi^{4}$ theory is written
\begin{equation}Z[J]=\int D\phi \, e^{-\int d^{4}x \left(\frac{1}{2}\left[(\nabla \phi)^{2}+m^{2}\phi^{2}\right]+\frac{\lambda}{4!}\phi^{4}+J\phi\right)}\end{equation}
I'm confused on how the Fourier transform of this is d... | Let's define the fourier transform as $\phi(x)=\int_p e^{ipx}\phi(p)$. Plugging this expression in $\int_x \phi(x)^4$, you will get four integrals over the momenta, and one over position. This last integral will give the delta function, and the result is the one given by Wikipedia.
| {
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"timestamp": "2023-03-29T00:00:00",
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How long would it take a projectile accelerating twice as fast as another to catch up? Given a projectile with initial velocity $u$, and constant acceleration $a$, travelling in the one direction. How long would it take a second projectile the same as the first with the same initial velocity $u$ and twice the accelerat... | First of all, you're overloading your time variable. Let the delay of the launch of the 2nd projectile be $t_d$ while the time variable is $t$.
As you've already correctly written, the equation for the displacement of the 1st projectile is (for $t \ge 0$):
$$s_1 = ut + \dfrac{at^2}{2}$$
Now, for the 2nd projection, we... | {
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Is there a theoretical maximum for refractive index? May there be materials yet to be discovered which may have a higher refractive index than today's known materials (for wavelengths within the visible range)?
Is there a theoretical limit for the refractive index of a material?
| Theoretically, there is no limit to the refractive index. The reason is that, if you go by the definition, $n= c/v$, the more you can slow down light (short of stopping it completely), the higher you refractive index will be. And, mathermatically, we are looking at the following,
$$ n = \lim_{v \to 0^{+}} \frac{c}{v} ... | {
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"timestamp": "2023-03-29T00:00:00",
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Tension in vertical circular motion In vertical circular motion we conserve energy for calculating velocities at a point (if initial velocity given). But, energy can only be conserved when forces are conservative. Tension is not a conservative force. Does it not affect the particles velocity? Is the tension's role on... | By definition, the tension in the string can only supply a force towards the center of the circular motion, so in one sense the tension is a centripetal force.
However, at any moment, the force of gravity can be decomposed into radial and tangential components. It is the sum of the tension and the inward radial compon... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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The Weyl tensor and gravitational waves How exactly is the Weyl tensor is connected with information about gravitational waves? And what are physical reasons for that?
| The Weyl tensor is the trace-free part of the Riemann tensor. The latter describes the curvature of spacetime. In the absence of sources, the trace part of the Riemann tensor will vanish due to the Einstein equations, but the Weyl tensor can still be non-zero. This is the case for gravitational waves propagating in vac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/87737",
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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... | I dont now about this system but i have had a lecture about a similar non destructive measurement aperatus. they trap a photon in a cavity and have a atom move throw the cavity. right throw the destructive interference spot (there where the photon has low change of being so low change of destroying it) They trick lies ... | {
"language": "en",
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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?
| Although I agree with all three of the above answers let me present a slightly different perspective on the problem.
It's tempting to think of the light from the star as a flood of photons that behave like little bullets. However this is oversimplified because a photon is a localised object i.e. we observe a photon whe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/87986",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Charge of the muon In the Wikipedia article of Muon, it says
...with unitary negative electric charge of roughly -1 and a spin of 1/2,
What are they trying to convey with the "roughly"? Aren't the allowed values of charge discrete?
| I believe that the "roughly" term is applied because of the associated experimental error when measuring its charge.
The same cannot be said to the electron because "we" decided to make the electron the reference charge.
So, the reference charge is definitely -1. However the muon charge must be measured.
According to t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/88228",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Completing the square for Grassmann variables When working with path integrals of both bosonic and fermionic field variables, I'm a bit unsure of how to do the usual complete the square trick when an interaction between the two is concerned. Say you have a generic partition function like
\begin{equation}Z=\int D\phi D... | I don't think there are miracles here.
With an interaction term like $\lambda \bar \psi \psi \phi$, ou may always write something like :
$Z(j,\eta, \bar \eta) \sim e^{\large i\int d^4x ~\lambda~ {\frac{\delta}{\delta \eta(x)}\frac{\delta}{\delta \bar \eta(x)}\frac{\delta}{\delta J(x)}}} \int \mathcal{D\phi}\mathcal{D... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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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... | Basically, the answer is that you have to do more work when you go up a set of stairs vs going up a wheel chair ramp or like you mentioned, a smooth hill. I would think this is caused by the up and over pattern of stairs where you would have to go straight up against gravity and then over instead of moving your feet li... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Do heavier objects fall faster? This question has been asked multiple times here and all over the internet yet I can't find a conclusive answer:
*
*Some claim that heavier objects do fall faster: Don't heavier objects actually fall faster because they exert their own gravity?
*Others claim that all objects fall at... | In one sentence:
More mass means stronger attraction and less buoyancy (they fall faster), but the effect is negligible in most cases.
| {
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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... | The condition comes from "phase-matching" - or in other words that the wavevector of the SPP ($\beta$ in your example) is matched to the wavevector of the in-plane component of the incident light.
Now before the light hits the surface, this in-plane wavevector is given by $k \sin \theta$, but when it hits the grating, ... | {
"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... | A Google books search for "bulk modulus of liquid helium" turned up this result: Helium, edited by Paul Muljadi. On page 7, you will find the value of the bulk modulus as on the order 50 MPa. There is a reference linked to this value, but it is not part of the free preview, so I cannot tell you what it is.
| {
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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... | You first have to get a clear definition of what the speed samples mean. Are they the instantaneous speed at the time of the sample? Are they the low pass filtered result of recent signals? If so, how recent? What kind of filter? Are they the average speed during the last interval?
The best for your purposes would... | {
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Continuously feeding an evaporating micro-black hole? What would happen if you created a micro-black hole and could continuously feed it as quickly as it evaporates? Is it possible that it would remain relatively stable?
If so, how might such a thing be continuously fed?
| Yes, it would remain stable.
But these black holes are incredibly hot and there is no known matter that could feed them fast enough to balance the mass loss that they experience through evaporation. Assuming that with 'micro black hole' you mean a TeV-sized black hole, the mass loss is of the order of a TeV/fm. In add... | {
"language": "en",
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Can radioactive energies become electromagnetic I am trying to learn about radioactive energies and wonder if, because these also seem to come under the topic of radiation, can these energies become electromagnetic. I'm pretty much a beginner, so if you could keep the answer pretty simple, it would help.
| Radioactivity comes in three basic types. Gamma radiation is an electromagnetic wave just like light and radio waves but of higher energy, and is described using electrodynamics. Alpha and beta radiation is charged particles (helium nuclei and electrons respectively) and again the motion of charged particles is describ... | {
"language": "en",
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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... | The general Faraday law of emf formulated with magnetic flux is meant mostly for closed circuits made of thin wire, which can be assigned area without problem.
For other situations, magnetic flux may not have sense. Moving piece of metal is still subject to magnetic electromotive intensity, but it has to be calculated... | {
"language": "en",
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Can eigenstates of a Hilbert space be thought of as delta functions? Say we have an observable that describes a Hilbert space and that observable acts on state kets. Lets take the position observable for example. Then $\langle y|x\rangle = \delta(y - x)$. But can the eigenstates of the position observable be individual... | Okay, so a general observable acting on $|x\rangle$ won't give you $x' |x\rangle$. Only the position operator, acting on the state $|x'\rangle$ will give us $x'|x'\rangle$, where the x' is a label for the state, think of it as a number, not a variable. Just because the state $|x'\rangle$ is an eigenstate of the positio... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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?
| Any warm body radiates electromagnetic radiation with a spectrum that depends on the temperature. Above 500 degree centrigrade there is enough radiation in the visible part of the spectrum to be visible but at lower temperatures most of the radiation is at infrared frequencies or lower. Our eyes are not sensitive to in... | {
"language": "en",
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Acceleration and Newton's third law I am puzzled with the following problem.
A man starts to jump. First he will exert force on the floor and he starts accelerating upwards. Then he is off the floor. What is the relationship between the force exerted by him and the force of the floor towards him while he is still on t... |
However, the problem says that the floor pushes the man upwards with a stronger force than his legs.
This can not be true. The floor pushes the man upwards with as much force as his legs exert downwards. However, this happens to be more than his weight, which is why he accelerates upwards.
| {
"language": "en",
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How to obtain the field equations in Brans-Dicke theory from the action? The action for the Brans-Dicke-Jordan theory of gravity is
$$
\\S =\int d^4x\sqrt{-g} \;
\left(\frac{\phi R - \omega\frac{\partial_a\phi\partial^a\phi}{\phi}}{16\pi} + \mathcal{L}_\mathrm{M}\right).
$$
And the field equations of the gravitation ... | I have been in your situation. I agree with Andrew and I've found this helpful
http://arxiv.org/abs/1002.0617v4. Go directly to appendix B, There you will find the answer of an identical problem and you shall use appendix A, as well.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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The effect of dark lines in the Sun's spectrum on reflected paint/ color Its well known that the Sun's spectrum is not continuous, and that there are dark bands within the suns spectrum. Is it possible to produce a color of paint that is bright in, say, indoor lighting and dark in the sunlight?
| In theory, perhaps. It is possible, using multilayer dielectric coatings, to produce a surface which is reflective in very narrow bands (in this case, the Sun's dark lines)and transmissive (or absorptive) elsewhere. In practice, the spectral "blurring" caused by atmospheric transmission/absorption/re-emission effects... | {
"language": "en",
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Circularly polarized light incident at Brewster's Angle If a perfectly circularly polarized wave of light is incident on a dielectric medium (coming from air) at Brewster's Angle, what will the polarization state of the transmitted wave be? I am aware that the reflected wave will be linearly polarized, but will the tr... | If you split the circularly polarised light up into two perpendicular polarisations with a $\pi/2$ phase lag between them. You are free to choose which unit vectors to represent these perpendicular polarisations - so choose one in the plane of incidence and one parallel to it.
Upon reflection at the Brewster angle the ... | {
"language": "en",
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Actual meaning of "Gravitational Potential"? In a gravitational field, the gravitational force acting on a body (of mass m) at a point x metres away from the attracting body (of mass M) is $\frac{GMm}{x^2}$. Integrating this force from a point at infinity to x gives $-\frac{GMm}{x}$, or the work done by the gravitation... | I can explain about all your confusion with a simple example. Suppose, you go to a moneylender who charges no interest. Now, you lend some money like 5 dollars from him. If you do not take any further loan, the only possible transaction between you and moneylender is that you give him his 5 dollars back. This is what g... | {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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Wave function of a particle in a gravitational field
Suppose we have a particle with mass $m$ and energy $E$ in a gravitational field $V(z)=-mgz$. How can I find the wave function $\psi(z)$?
It should have an integral form on $dp$. Any help would be appreciated.
What I've tried
One way to solve the problem is use of... | The basic idea for this is to use the momentum space version of the Schroedinger equation:
$$
\hat{p}\to p,\quad\hat{x}\to i\hbar\frac{\partial}{\partial p}
$$
and then solve the system1,
$$
\left[\frac{p^2}{2m}+img\hbar\frac{d}{dp}\right]\phi=E\phi
$$
which should be solvable (e.g., complex exponentials). You can then... | {
"language": "en",
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1 Tesla electromagnet? Is it possible to create a powerful electromagnet at home?
With use of a ferromagnet it seems so...
Using the following formula: $B(Tesla)= k\mu_0nI$. I understand some ferromagnet's like iron could have permeability above 10,000? That would easily boost the field above a 1 Telsa?
Relative perme... | I find this all very intriguing..
Making an electromagnet requires you understand the formula shown here
hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html
You need to use thick wires and provide high amperage. Thicker the wire, lower the resistance and higher the current carrying capacity. You cannot keep on i... | {
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How to smooth the spectrum of a light source? Could somebody please tell me if there's a reasonably cheap substance or device can I use to smooth the spectrum of a light source?
For example, if the spectrum has spikes as in the blue graph below, is it possible to smear in terms of wavelength (not spatially, as in ordin... | When you scatter light off of a material there is a photon-phonon interaction which will shift the photon frequency depending on the phonon energy (Raman scattering, Brillouin scattering). The effect is quite small, however.
How much broadening do you need? Rayleigh scattering through a warm, high density gas will prob... | {
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Nuclear Spin of Sodium 23 I am actually calculating the nuclear spin of Sodium 23. Here we have 11 protons and 12 neutrons. Now both the nuclei are short of the magic numbers. When I use the shell model for protons and neutrons separately, I found 3 protons in the $1d_{5/2}$ sub-shell and 4 neutrons in the same $1d_{5/... | Neutrons provide nothing to nuclear spin due to even number, but uncouple proton in 1d5/2.To maximize the Iz (uncouple proton) it should be in 3/2 state because couple protons in 5/2.So I=5/2
| {
"language": "en",
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"source": "stackexchange",
"question_score": "6",
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Does the radius of the Universe correspond to its total entropy? I heard a claim that due to holographic principle, the surface area of the cosmic horizon corresponds to the universe's total entropy.
As such the initial state had zero surface area and later expanded.
Given this, I wonder whether any increase in entrop... | This is a very good question. But before I attempt to give you some of the details, the increase in the entropy is not what causes the universe to expand but is rather a consequence of the expanding universe. In fact, to understand why the entropy of the universe was so low before the inflationary epoch is an open ques... | {
"language": "en",
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Work in circular motions Suppose that a satellite circles around a planet that exerts $2000N$ of gravitational force on the satellite.
I understand the fact that since the circular motion and the centripetal force are always perpendicular to each other, the work done by gravity is 0.
However, the satellite is being m... | The work equals to the amount of energy added to the system (or subtracted if the work is negative) and since you don't need to add energy to the satellite in order for it to stay in orbit the total work is zero.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "9",
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Is it possible for bubbles to exist in vacuum? In the case of a bubble, the outside pressure is less then the inside pressure.
If that is the case can bubbles exist in vacuum? I am not sure but this should be true if vacuum has zero pressure
| Yes, a bubble can exist in vacuum. A bubble itself has surface tension which tries to minimize the surface area, i.e. tries to push inward. It is small compared with the atmosphere on Earth though. But in the vacuum, there is no pressure from the outside and very little pressure from the inside. Thus, the surface tensi... | {
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Is it possible to focus the sun in such way?
Imagine the sliding part of the mirror is controlled by computer and opens on intervals.
Is it possible to increase the power of the beam by making it bounce between the mirrors thus going through the lens and then releasing it resulting in beam with more power ?
|
Is it possible to focus the sun in such way?
Yes, as others have pointed out, all of the ideas in your sketch are already used in existing designs - perhaps excepting the shutter (which actually performs no useful purpose so far as I can see).
As Chris White commented - "this exact design (with the shutter permanent... | {
"language": "en",
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Is it possible to determine the universality class of phase transitions by just analysing symmetry? Since phase transition is closely connected with symmetry, I am wondering whether it is possible to determine the universality class of phase transitions just by symmetry?
Actually, I found it is quite boring to calcula... | In the simplest cases, yes, if you know the microscopic symmetries of the system, you know the universality class of the transition (if of course it's a second order phase transition). However, it does not have to be the case. Two examples: 1- emergent symmetries; 2- unexpected first order phase transition. Let me expl... | {
"language": "en",
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Derivation of normal shear stress I am self-studying this note and I am stuck in the derivation of the normal shear stress. Specifically I can't see how the relations (23) and (24) come about.
Specifically, what I don't understand is
$$
\tau'_{xx} = \frac{\tau_{xx}+\tau_{yy}}{2}+\tau_{yx} \tag{23}
$$
and
$$
\tau'_{yy} ... | Your use of the phrase "Normal shear stress" doesn't make a lot of sense. A more precise way to say it is the "principal components of the deviatoric stress". Once you recognize that this is the proper nomenclature, the formulas are easier to understand.
In an incompressible Newtonian fluid, the deviatoric stress tenso... | {
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What happens when a charged (negative or positive) object touches an insulator? I know that insulators do not conduct electricity because they do not allow the free movement of electrons. Let's assume the object that's going to touch the insulator is negatively charged. Does some charge get transferred to the the insul... | When a charged object touches an insulator there is usually no charge being transferred unless the field strength is so high that you get corona discharge.
For example, look at the electrophorus in this video. It shows that you can put a metal disk onto an insulating plate without any charge jumping over.
At the end o... | {
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Is it possible to "cook" pasta at room temperature with low enough pressure? It is known fact, that boiling point of water decreases by decreasing of pressure. So there is a pressure at which water boils at room temperature.
Would it be possible to cook e.g. pasta at room temperature in vacuum chamber with low enough p... | Well, I can share with you one experience from my high school. I wanted to boil coffee in my caffetier without a cooker. We had the vacuum pump in the physics room so there was the way to "boil" the water without getting it in 100°C. I did it... and coffee tasted horrible.
Never try it again.
| {
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"source": "stackexchange",
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How is the current for the Dirac equation derived? Why is it that the derivative of the current $j^\mu$ is the difference between the Dirac equation and its adjoint?
| The Dirac Lagrangian has what is commonly called an 'internal vector symmetry'; if we perform a transformation on the Dirac spinor field given by,
$$\psi \to e^{-i\alpha}\psi$$
the corresponding conserved current by Noether's theorem is given by, $j^\mu=\bar{\psi}\gamma^\mu \psi$. We can explicitly verify it is conserv... | {
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Increase in Mass with Velocity I just had a confusion. Does the mass of the body actually increase when it is moving with a certain velocity? Or does it only look like the mass has increase to another observer. How can the actual mass of the body increase. Please correct me if I am wrong but I feel that it only seems t... | There isn't a simple answer to your problem because it depends on what you mean by mass.
You've probably heard of Einstein's equation $E = mc^2$, and if you rearrange this equation you can use it as a definition of the mass:
$$ m = \frac{E}{c^2} $$
For a stationary object the mass we get is the rest mass or invariant m... | {
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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!
| The word "nothing" here is used somewhat loosely. What Krauss means by nothing is no particles. But, there is still the vacuum state of the quantum fields, which is something. And those vacuum states can give rise to phenomena out of "nothing".
| {
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What exactly is a bound state and why does it have negative energy? Could you give me an idea of what bound states mean and what is their importance in quantum-mechanics problems with a potential (e.g. a potential described by a delta function)?
Why, when a stable bound state exists, the energies of the related station... | Barry Simon writes:
One of the more intriguing questions concerns the
presence of discrete eigenvalues of positive energy (that is, square-integrable
eigenfunctions with positive eigenvalues) . There is a highly non-rigorous but
physically appealing argument which assures us that such positive energy “bound
states” ca... | {
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Why do high current conductors heat up a lot more than high voltage conductors? 120 volts x 20 amps = 2,400 Watts
However, if I increased the voltage and lowered the current, you can also use a smaller wire size (more inexpensive), also have less heat and achieve the same watt Power.
1,000 volts x 2.4 amps = 2,400 Wat... | In short, because the power drop across a circuit element is $P=IV$, and a resistor (or a piece of wire) experiences a voltage drop $V = IR$, which leads to $P = I^2 R$, or $P = \frac{V^2}{R}$. The first equation is relevant, which shows that for a fixed resistance, doubling the current quadruples the power loss throug... | {
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Which of these two different forms of spin-orbit interaction is correct? I am seeing the spin-orbit interaction in two different ways:
*
*$\lambda [\mathbf{p} \times \nabla V]\cdot \sigma$
*$\lambda [\nabla V \times \mathbf{p}]\cdot \sigma$
I don't see how these two expressions can be equivalent though; in (1) th... | Recall that (times $\lambda$)
$$\vec{\nabla} V \times \vec{p} =-\vec{p} \times \vec{\nabla} V$$
Call $\vec{a} = \vec{\nabla} V \times \vec{p}$. You can check that:
$$\vec{a} \cdot \vec{\sigma}=(-\vec{a})\cdot\vec{\sigma}$$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/92754",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Minimum acceleration so that mass $m$ falls freely A block of mass $m$ rests on a frictionless wedge of angle $\theta$ as in the figure. The wedge is given an acceleration $a$. What is the minimum value of $a$ so that the mass $m$ falls freely?
I have solved a similar problem, where the acceleration was in the opposit... | In addition to the correct answer, a little strategy to solve problems involving constraints that are unilateral, that is, given by a condition$$f(x,y,z)\geq 0,$$
as in this case: $$y\geq \tan \theta (x+\frac {1}{2} at^2).$$
You can imagine that the constraint is bilateral (that is, given by an equality) and look at t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/92842",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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