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<p>This question is motivated by <a href="http://physics.stackexchange.com/questions/98067/does-natural-unit-of-information-and-entropy-nat-play-special-role-in-the-free">this one</a>.</p>
<p>Suppose $l$ is the minimum measurable unit of length. What is entropy of a spinless particle contained in this interval?</p>
<p>We know that entropy of a two-level system depends on the probabilities of the respective levels, if the probability of the state 0 is $p_0$, then the entropy (in <a href="http://en.wikipedia.org/wiki/Nat_%28information%29" rel="nofollow">natural units</a>) is:</p>
<p>$$S= -\sum_{i=0}^1 p_i \ln p_i = -p_0 \ln p_0 - (1 - p_0) \ln (1 - p_0)$$</p>
<p>So if $p_0=1/2$ then $S=\ln 2\: \mathrm{nat}$, equal to $1\: \mathrm{bit}$. A particle which has the maximum in the middle has entropy of $1\: \mathrm{bit}$ (it is equally likely to be measured to the right and to the left of the middle).</p>
<p>Since we cannot measure intervals smaller than $l$, we cannot make guesses about where the maximum of the probability for the particle is located. As such, if we assume that the particle is equally likely have the maximum of the probability in any point on the interval $x\in[0,l]$, the total entropy becomes
$$S=\int_0^l \frac{-(1-\frac xl) \ln (1- \frac xl)-\frac xl \ln (\frac xl)}{l} \, dx=\int_0^1 -(1-x) \ln (1-x)-x \ln (x) \, dx=\frac12$$</p>
<p>An entropy of a similar particle contained in a square area with side $l$ will be twice more, that is $1\: \mathrm{nat}$.</p>
<p>Now if we assume that $l=2l_p$ where $l_p$ is the Planck length, we arrive that such spinless particle has entropy of $1\: \mathrm{nat}$ per 4 square Planck length or $1/4\: \mathrm{nat}$ for one square Planck length.</p>
<p>Thus from the only assumption that double Planck length is the minimum measurable interval, and double Planck length squared is expected to contain 1 particle on average we arrive at the standard value of the Black Hole entropy in nats:</p>
<p>$$S=\frac{A}{4l_p^2}=\frac14 A_p$$</p>
<p>Where $A_p$ is the area in Planck units.</p>
<p>Sometimes I encountered a claim that the fundamental unit of information is 1 bit. From the above considerations it follows that possibly the fundamental unit is 1/2 (or 1 or 1/4) nat.</p>
<p><strong>UPDATE</strong></p>
<p>Note that the distance of $2l_p$ between two particles is natural if we assume that the particles are <a href="http://en.wikipedia.org/wiki/Planck_particle" rel="nofollow">planckons</a>, whose radius is Planck length $l_p$. Thus densely packed planckons will have average distance exactly $2l_p$.As such, the Black Hole can be viewed as a spherical shell consisting of one layer of planckons.</p> | 6,565 | [
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<p>Let's say you are in the air 500 meters above flat land and you have no parachute. Which pose - forming a sphere or spreading all extremities to make yourself as wide as possible or other - is the most appropriate to cause the highest likelihood of survival?</p>
<ol>
<li>in the air</li>
<li>right before impact</li>
</ol>
<p>In other words: which body position causes the least amount of negative acceleration in this context?</p>
<p>PS: As a side-question: Which body position enables you to control the direction of flight to control your angle of impact and make it as flat as possible?</p>
<p>My take: In the air make yourself as wide as possible and control direction by weight displacement. Right before impact, form a sphere when having a flat angle of impact and let rolling take care of the change of kinetic energy into heat and potential energy.</p> | 6,566 | [
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] |
<p>What is the formula we use to calculate average speed?</p> | 225 | [
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<p>In multi-electron atoms, the electronic state of the optically active "subshell" is often expressed in "term symbols" notation. I.e. $^{2S+1}L_J$. This presumes that the system of electrons has definite $L^2$, $S^2$ and $\mathbf{J}$ eigenstates.</p>
<p>In order to determine all the possible electronic states compatible with the Pauli's exclusion principle, the technique is to assign to each electron its $m_s$ and $m_l$ and to see what states can be found in terms of eigenvalues of $L^2$, $S^2$, $J^2$ and $J_z$.</p>
<p>What justifies this procedure? In other words, the assumption so far was: </p>
<ul>
<li>heavy nucleus -> the Hamiltonian is spherically symmetric -> total $\mathbf{J}$ is conserved</li>
<li>spin-orbit is negligible to some extent -> total $S^2$ and $L^2$ are conserved</li>
</ul>
<p>What justifies, apart from intuitiveness, returning to the single electron picture (assigning to every electron its spin and angular momentum) to find what states are allowed or not according to the requirement that the total wavefunction should be antisymmetric? And could be there exceptions?</p> | 6,567 | [
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<p>In an assignment I am given a random car with a random suspension system, and told that it is sufficient to test the safety of the car with regards to the suspension on three different sinusoidal roads.</p>
<p>The first road has an amplitude of 5 centimeters and a period of 20 meters, the second road has an amplitude of 2.5 centimeters and a period of 2 meters and the third road has an amplitude of 1 centimeter and a period of 20 centimeters.</p>
<p>I can't figure out why a test on these three roads would be sufficient to conclude that the car can handle any random other road, and I am given no other information.</p>
<p>Could anyone please tell me why it is sufficient to test the suspension on only these three roads?</p> | 6,568 | [
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<p>Say there was some situation where you have a lot of subatomic particles interacting with each other and decided to draw (say, by joining Feynmann diagrams) those interactions- so that you got some sort of (?directed) graph... what kind of network would you obtain? Would it be scale-free? Would it be a complex network similar to a social network? What properties would it have?</p> | 6,569 | [
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<p>Imagine a bar </p>
<p>spinning like a helicopter propeller,</p>
<p>At $\omega$ rad/s because the extremes of the bar goes at speed</p>
<p>$$V = \omega * r$$</p>
<p>then we can reach near $c$ (speed of light)
applying some <strong>finite</strong> amount of energy
just doing </p>
<p>$$\omega = V / r$$</p>
<p>The bar should be long, low density, strong to minimize the
amount of energy needed</p>
<p>For example a $2000\,\mathrm{m}$ bar</p>
<p>$$\omega = 300 000 \frac{\mathrm{rad}}{\mathrm{s}} = 2864789\,\mathrm{rpm}$$</p>
<p>(a dental drill can commonly rotate at $400000\,\mathrm{rpm}$)</p>
<p>$V$ (with dental drill) = 14% of speed of light.</p>
<p>Then I say this experiment can be really made
and bar extremes could approach $c$.</p>
<p>What do you say? </p>
<p><strong>EDIT</strong>:</p>
<p>Our planet is orbiting at sun and it's orbiting milky way, and who knows what else, then any Earth point have a speed of 500 km/s or more agains CMB.</p>
<p>I wonder if we are orbiting something at that speed then there would be detectable relativist effect in different direction of measurements, simply extending a long bar or any directional mass in different galactic directions we should measure mass change due to relativity, simply because $V = \omega * r$</p>
<p>What do you think?</p> | 121 | [
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<p>Assume we have a conveyor scales. Which consists of scales, and motor with conveyor belt placed above, so that the boxes can be measured (weight) while moving above. What I want is to create the model of the oscillations of that scale.
The equation of the oscillations of the spring is well known for everybody.
How to include the influence of the motor, conveyor and other important effects to the system? Is there any papers (articles) about this thema?
I think that the influence of the motor in simle case can be modelled as the force:
$F(t) = A sin(\Omega t)$ Where $A$ is a constant and $\Omega$ is the parameter which depends on the motor (frequency), which is also constant (depending on the speed of the motor). How to add the ocsillations created by conveyor belt and may be some other oscillations such as box moving above can create additional vibrations?</p>
<p>EDIT 1:
I want to crate the model. I have created one for a scales, but without conveyor and motor. It seems that they do not match. The data of the model and the real data of the conveyor with scales. So there sems to be a big influence of a motor, conveyor belt etc. And what I want is to identify what has a big influence and include it inside the system. So that my model will match the real system. I don't care of some influences which do not make big difference. It is difficult to identify what makes a big influence. And It is more difficult to model for example the moving of the conveyor with or without a box above. How to do it?</p> | 226 | [
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<p>I'm reading an article about bi layered membranes which state that for the free energy function<br>
$f(\theta) = \theta \ln \theta + (1-\theta)\ln(1-\theta) + \chi \theta (1-\theta)$</p>
<p>Where $\phi_i$ is the mole fraction of certain types of lipids in layer $i$ and $\chi$ is the energy of interaction between two lipids molecules composing the layer. The article states that a critical point exist at $\chi=2$ and $\theta=0.5$. Reading in <a href="http://en.wikipedia.org/wiki/Critical_point_%28thermodynamics%29">wikipedia</a>, I concluded that removing the layers interaction part, I simply need to take the second and third derivative of the free energy of the membrane. How do I do this with the interactions? Where can I read about this?</p> | 6,570 | [
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<p>Argument: Buckling is an engineering concept that can only be applied to <strong>thin columns</strong> with <strong>compressive</strong> loading.</p>
<p>(Is it possible to) Prove the above sentence right or wrong with mathematical formulation. Emphasis on cellular and solid materials that have no concept of "thin". </p>
<p>Also, why can you use buckling to describe crack growth experiments in thin sheets:
out-of-plane deformation of sheets = buckling? => deformation in perpendicular direction respect to force is buckling? => 3D solids can experience buckling ? => example of this kind of material is...</p>
<p>Good references, rigorous treatment and mathematical approach are more than welcome.</p>
<p><strong>edit:</strong> In other words, what is the mathematical definition for buckling?</p>
<p><strong>edit2:</strong> So, buckling is the bifurcation of static equilibrium (see annav's comment below). And thus:</p>
<blockquote>
<p>More technically, consider the continuous dynamical system described
by the ODE</p>
<p>$\dot x=f(x,\lambda)\quad
> f:\mathbb{R}^n\times\mathbb{R}\rightarrow\mathbb{R}^n.$</p>
<p>A local bifurcation occurs at $(x0,λ0)$ if the Jacobian matrix
$\textrm{d}f_{x_0,\lambda_0}$ has an eigenvalue with zero real part.</p>
</blockquote>
<p>This also happens to coincide with ASTM E-9 standard, section 3.2.1 that says: </p>
<blockquote>
<p>bucklig -- (3) a local instability, either elastic or inelastic, over
a small portion of the gage length</p>
</blockquote> | 6,571 | [
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<p>When Einstein started to think about gravitation, he completely created a new theory that no experiment supported. He based his reasoning, as he explained it later, on small thought experiments (Gedankenexperiment) that led him to formulate the equivalence principle. From this equivalence principle, he used the principles of physics and understood that a new space-time geometry was necessary and after years of effort he obtained the Einstein's equation. It is only when he used this equation to compute the anomalous perihelion advance of the planet Mercury that he knew his theory had something to do with the real world (but one could not call this a prediction). Since then, many predictions of General Relativity have been successfully checked experimentally.</p>
<p><strong>Edited question</strong></p>
<p>A thought experiment is an experiment that has not been realized, but that was imagined. The results of such experiment are based on well established physical principles but have never been observed physically. A second example of a thought experiment considers a frictionless movement of a vehicle on a road (see Einstein and Infeld, <em><a href="http://en.wikipedia.org/wiki/The_Evolution_of_Physics" rel="nofollow">The Evolution of Physics: The Growth of Ideas From Early Concepts to Relativity and Quanta</a></em>, chapter 1 on the Galilean relativity). Another example in particle physcis is described in <a href="http://physics.stackexchange.com/questions/93839/are-there-correct-physical-predictions-made-only-from-thought-experiments-other?noredirect=1#comment192225_93839">one of the above comments</a>. Thought experiments only draw conclusions from physical considerations, not from mathematical derivations, and can therefore be used as illustrations destined to non-physicists.</p>
<p>Does anyone think of other thought experiments which results have been proved relevant later by physical experiments, either because the thought experiment has been realized or because its results had physically testable consequences ?</p> | 6,572 | [
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<p>In the literature (<a href="http://openlibrary.org/books/OL6927036M/Vorlesungen_u%CC%88ber_mechanik" rel="nofollow">Kirchhoff G. - Mechanic (1897), Lecture 18</a> or Lamb, H. - Hydrodynamics (1879)) one can find the following analytical closed form expression for the gravitational potential of homogeneous ellipsoid of unit density, whose surface is given by
\begin{equation}
\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1 \;.
\end{equation}
Gravitational point for internal points is
\begin{equation}
\Omega=\pi abc\int_0^\infty\left(1-\frac{x^2}{a^2+\lambda}-\frac{y^2}{b^2+\lambda}-\frac{z^2}{c^2+\lambda}\right)\frac{d\lambda}{\Delta}
\end{equation}
and for external points
\begin{equation}
\Omega=\pi abc\int_u^\infty\left(1-\frac{x^2}{a^2+\lambda}-\frac{y^2}{b^2+\lambda}-\frac{z^2}{c^2+\lambda}\right)\frac{d\lambda}{\Delta} \;,
\end{equation}
where
\begin{equation}
\Delta=\sqrt{(a^2+\lambda)(b^2+\lambda)(c^2+\lambda)}
\end{equation}
and $u$ is the positive root of equation
\begin{equation}
\frac{x^2}{a^2+u}+\frac{y^2}{b^2+u}+\frac{z^2}{c^2+u}=1 \;.
\end{equation}</p>
<p>The expressions in these formulas appear similar to <a href="http://mathworld.wolfram.com/ConfocalEllipsoidalCoordinates.html" rel="nofollow">confocal ellipsoidal coordinates</a>.</p>
<p>How can these formulas be derived? (perhaps something more readable than the <a href="http://openlibrary.org/books/OL6952302M/Ueber_die_anziehung_homogener_ellipsoide." rel="nofollow">original papers</a>)
Can they be derived in terms of <a href="http://mathworld.wolfram.com/LaplaceEquationConfocalEllipsoidalCoordinates.html" rel="nofollow">ellipsoidal harmonics</a>?</p> | 6,573 | [
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<p>I am reading a physiology book chapter (<a href="http://rads.stackoverflow.com/amzn/click/0387983813" rel="nofollow">Mathematical Physiology, by Keener</a> --Respiration chapter) about the gas exchange between capillaries and alveoli. It seems that this gas exchange can be modeled after some simple physical relationships. Since I am not usually studying physics, I do not fully understand some concepts that the author uses to derive a conservation law and I would appreciate any help. </p>
<p>I do admit, however, that this question may be off-topic since it could be a mathematical lapsus rather than a physics question. </p>
<p><strong>Preliminaries</strong></p>
<p>First, the author indicates that if a gas with partial pressure $P_g$ is in contact with a liquid, the steady-state concentration $U$ of gas is given by:
$$
U = \sigma P_s
$$</p>
<p>where $\sigma$ is the solubility of the gas in the liquid. I assume that this is a particular version of Henry's Law.</p>
<p>Then, it explains if there is a difference between the partial pressure of the gas ($P_g$) and the partial pressure on the fluid ($\frac{U}{\sigma}$), then there should be some flux between the gas and the fluid and the simplest model would be to assume that this flux is linearly proportional to the pressure difference:
$$
q = D_s \left(P_g - \frac{U}{\sigma}\right)
$$</p>
<p><strong>Problem</strong></p>
<p>The author then considers a segment of a capillary (a cylindrical tube) of length $L$, constant cross-sectional area $A$ and perimeter $p$, that is in contact with a gas with partial pressure $P_g$. The fluid moves through the tube with a velocity $v(x)$. Finally, they say that since mass is conserved:
$$
\frac{d}{dt} \left( A \int_{0}^{L} U(x,t) dt \right) = v(0)AU(0,t) - v(L)AU(L,t) + p \int_{0}^{L} q(x,t) dx
$$</p>
<p><strong>Question</strong></p>
<p>How is the relationship below derived? </p>
<p>I understand that $A \int_{0}^{L} U(x,t) dt$ is in fact the total amount of the dissolved gas in the tube at a given time. I also understand how $\int_{0}^{L} q(x,t) dx$ represents the total flux of gas across the whole capillary wall. However, I fail to see what the two first elements of the right-hand represent and why is the left-side derived with respect to $t$.</p> | 6,574 | [
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<p>Or would it be acceleration voltage? Acceleration sounds like it makes more sense, but my paper says accelerating.</p>
<p>What are possible ways you could go about calculating it?</p> | 6,575 | [
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<p>My question is vague, so I'm hoping the answers will help me ask more concrete questions and maybe produce some interesting discussion.</p>
<p>In mean field theory, say for the Ising model, we treat the magnetization $m$ as a parameter and derive the equation
$$
\langle\sigma_i\rangle = \tanh (\beta J dm),
$$
where $J$ is the neighbor coupling, $\beta$ is the inverse temperature, and $d$ is the spatial dimension. Self-consistency requires
$$
\langle\sigma_i \rangle = m,
$$
from which can be derived all the ordinary mean field theory conclusions.</p>
<p>However, we don't have to impose this equation by hand if instead we minimize the mean field free energy with respect to $m$.</p>
<p>In string theory something superficially similar happens. Consistency conditions on the world-sheet theory are equivalent to equations of motion of the target-space theory. I have always wondered why this is the case, and it would be interesting to see a correspondence like mean field consistency $\simeq$ world-sheet consistency, mean field equilibrium for liberated $m$ $\simeq$ target-space vacuum.</p>
<p>An observation: mean field theory maps a physical system with site-to-site interactions to a single site problem, where the other sites are treated as creating the background magnetization $m$.</p>
<p>An analogous observation for the string: to derive Einstein's equations, we consider a string propagating in a background metric (which would be emergent from a sea of strings) and show that the background metric gets renormalized according to the Einstein-Hilbert action.</p>
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<p>If you "disobey" the constraints of the <a href="http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations" rel="nofollow">Kramers-Kronig relations</a>, what happens? Do you get non-physical results?</p>
<p>I am simulating reflection and transmission off/through a slab of material. I specify the complex index of refraction $n = n_r + i n_i$ of the material, assume it has vacuum on either side, and then use the transfer-matrix method to find the reflection and transmission for some given wavelength range.</p>
<p>As I was messing around, adjusting $n_r$ and $n_i$ to see what happens, I found that with certain combinations of $n_r$ and $n_i$ I could get seemingly impossible results -- e.g., reflection going above 1 (which represents more power coming reflecting off of the material than went into it!).</p>
<p>But I was pretty arbitrarily choosing my $n$'s, and I realized that in real life one of $n_r$ or $n_i$ determines the other, from the Kramers-Kronig relations. So was I getting these bizarre results as a result of (probably) "disobeying" the K-K relations, is it more likely my simulation is broken?</p> | 6,577 | [
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<p>My question is mainly an engineering question. Assume I have a turbine in which I adiabatically expand compressed air. The air cools down and does work to its surroundings, which is captured by the blades of the turbine and then is transformed into rotational energy/electricity. </p>
<p>When instead I let the compressed air flow through a nozzle into open space (no vacuum) and it expands adiabatically, it also cools down. But where is the internal energy of the air going? It does work to its surroundings, but where does this work end up? Does the surrounding heat up? Does it produce wind, i.e. kinetic energy in the surrounding air?</p>
<p>Feel free to replace adiabatic with polytropic. Whenever the gas cools down, I ask: Where does the energy end up, when I do not capture it with a turbine?</p> | 6,578 | [
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<p>We know about some events that happen very quickly. For example, the <a href="https://en.wikipedia.org/wiki/Dielectric" rel="nofollow">dielectric</a> relaxation time is about $10^{-14}\, \mathrm{seconds}$. </p>
<p>I'm interested in other processes that switch extremely fast or or could be use as a very short tick in a clock.</p> | 446 | [
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] |
<p>Immediately prior to becoming a supernova the core of some types of stars may suffer gravitational collapse. </p>
<ul>
<li><p>What happens to any planets in orbit around the star at the instant the mass is fully collapsed? </p></li>
<li><p>Assuming this sudden change would cause some perturbation ; how large/distant would a planet in the system have to be to be relatively immune to such perturbation?</p></li>
<li><p>Could unexplained perturbation serve as an indicator of a historic supernova in the vicinity?</p></li>
</ul> | 6,579 | [
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<p><strong>(1)</strong> As we know, we have theories of second quantization for both bosons and fermions. That is, let $W_N$ be the $N$ identical particle Hilbert space of bosons or fermions, then the "many particle" Hilbert space $V$ would be $V=W_0\oplus W_1\oplus W_2\oplus W_3\oplus...$ , and further we can define creation and annihilation operators which satisfy commutation(anticommutation) relations for bonsons(fermions).</p>
<p>So my first question is, do we also have a "second quantization theory" for anyons like bosons and fermions?</p>
<p><strong>(2)</strong> Generally speaking, anyons can only happen in 2D. Is this conclusion based on the assumption that the particles are <strong>point-like</strong>? </p>
<p>In <a href="http://arxiv.org/abs/quant-ph/9707021" rel="nofollow">Kitaev's toric code model</a>, the quasiparticles are <strong>point-like</strong> due to the <strong>local operators</strong> in the Hamiltonian. My question is, in 3D case, whether there exists a simple model whose Hamiltonian contains <strong>local operators</strong> and <strong>spatially extended operators</strong>, so that it has both poit-like quasiparticles(say, $\mathbf{e}$) and knot-like quasiparticles(say, $\mathbf{m}$), then the $\mathbf{e}$ and $\mathbf{m}$ particles have nontrivial mutual statistics in 3D? </p> | 6,580 | [
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<p>I read some where that there are three types of UV and infrared rays namely UV-A, UV-B, UV-C and near infrared, mid infrared and far infrared. Which is the most abundant among the the three in Ultraviolet and infrared radiation from sun? I mean there is a total of 1000 W per unit area illumination by sun among which more than 500 watts is infrared, around 450 watts in visible and the rest part is ultraviolet so in the infrared rays which are the most abundant means which contribute to most of the 500 watts?
Also, what are the sources of infrared at night and what is the power density of infrared rays at night!.</p> | 6,581 | [
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<p>In spherical coordinates the flat space-time metric takes:</p>
<p>$$ds^2=-c^2dt^2+dr^2+r^2d\Omega^2$$</p>
<p>where $r^2d\Omega^2$ come from when the signature of metric $g_{\mu\nu}$ is (-,+,+,+)?</p>
<p>what is signature of spherical metric?</p>
<hr>
<p>this is signature of spherical coordinates:
$(1,r^2,r^2\sin^2\theta$)</p>
<hr>
<p>let me ask in this way,
Isn't it metric of spherical coordinates?</p>
<p>$$g_{\mu\nu}= (-1,+1,+r^2,+r^2\sin^2\theta)$$</p> | 6,582 | [
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<p>If light is passed through two polarizing filters before arriving at a target, and both of the filters are oriented at 90° to each other, then no light will be received at the target. If a third filter is added between the first two, oriented at a 45° angle (as shown below), light will reach the target.</p>
<p>Why is this the case? As I understand it, a polarized filter does nothing except filter out light--it does not alter the light passing through in any way. If two filters exist that will eliminate all of the light, why does the presence of a third, which should serve only to filter out additional light, actually act to allow light through?</p>
<p><img src="http://i.stack.imgur.com/OogSm.png" alt="Image of three polarizers, target is at the right"></p> | 6,583 | [
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<p>New question: In string theory and QFT, do particles travel back in time? Not related to antimatter: Do they travel back and forth in time in reality or are these just interpretations of mathematical formulas used to make sense of calculations?</p>
<p>This is a different question (<a href="http://physics.stackexchange.com/q/58101">from this one</a>) as it concerns strings and not antimatter...</p> | 6,584 | [
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<p>The first <a href="http://en.wikipedia.org/wiki/Chern_class" rel="nofollow">Chern number</a> $\cal C$ is known to be related to various physical objects.</p>
<ol>
<li><p>Gauge fields are known as connections of some principle bundles. In particular, principle $U(1)$ bundle is said to be classified by first Chern number. In terms of electromagnetic field, ${\cal C} \neq 0$ is equivalent to the existence of monopoles. </p></li>
<li><p>In the case of integer quantum Hall states, Chern number is simply the Hall conductance up to a constant.</p></li>
</ol>
<p>In both physical problems, Chern number is related to vorticity -- a quantized value (first case, Dirac's string argument and second, vortices in magnetic Brillouin zone).</p>
<p>Then my questions:</p>
<ol>
<li><p>What was the "physical" picture in Chern's mind when he originally "dreamed up" the theory? (Maybe knots, but how?)</p></li>
<li><p>If I want to learn how Chern classified $U(1)$ bundles using integers (first Chern number), which books or papers should I refer to?</p></li>
</ol>
<p>Notes: </p>
<p>My point is that mathematical theorems are not God-given but arose from concrete problems. I was asking what was <em>the original problem</em> that Chern solved, from which he codified the general theorems? And Chern number seems related to vorticity and then what are the corresponding vortices in his problem?</p> | 6,585 | [
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<p>In the special relativistic action for a massive point particle, </p>
<p>$$\int_{t_i}^{t_f}\mathcal {L}dt,$$</p>
<p>why is the Lagrangian </p>
<p>$$\mathcal {L}=-E_o\gamma^{-1}$$</p>
<p>a negative number?</p> | 924 | [
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<p>The question concerns <a href="http://www.theepochtimes.com/n3/739183-former-nasa-physicist-disputes-einsteins-relativity-theory/?photo=2" rel="nofollow">this video</a>: </p>
<p>It says that the <a href="http://en.wikipedia.org/wiki/Gravitational_lens" rel="nofollow">Gravitational Lens</a> effect is an illusion, meaning it's not caused by gravity but by change in density of a plasma atmosphere. It claims further that this gravitational lens effect is not present with other massive objects that aren't made of, or surrounded by, plasma. </p>
<p>Does this mean general relativity is invalid, somewhat invalid, or still luckily valid? What is the merit of claim that bending could be caused by plasma and not by gravity? </p> | 6,586 | [
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<p>I have a ball of metal about an inch in diameter and a concave disc of another metal (which is magnetic) around the ring of the disc (about $12 {\rm mm}$ in diameter). I don't know which metals they are. The ball is not magnetic on its own. That is <a href="http://en.wikipedia.org/wiki/Paramagnetism" rel="nofollow">paramagnetism</a>, right?</p>
<p>The magnetic ring is strongly attracted to the surface of the ball, '<em>sticking</em>' to it. However, I can stick a paperclip on the opposite side of the ball as if it has become magnetic itself, until I remove the magnetic ring from the ball.</p>
<p>When I wave the paperclip the same distance from only the ring itself, I feel no force at that distance.</p>
<p>Has the strong magnetic field of the ring caused a temporary magnetic alignment through the metal of the ball, allowing the paperclip to be attracted to it while the ring remains?</p> | 6,587 | [
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<p>If we are travelling with the speed of light, can we see whats behind us(like if we are moving away from earth can we able see the earth)? And how we see the things that we are approaching with speed of light? Does the things look like fast forwarding because we are moving and the source also sending photons with the same light speed.</p> | 6,588 | [
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] |
<p>Pioneer <a href="http://en.wikipedia.org/wiki/Pioneer_10">10</a> & <a href="http://en.wikipedia.org/wiki/Pioneer_11">11</a> are robotic space probes launched by the NASA in the early 1970's. After leaving our solar system, an <strong>unusual deceleration</strong> of both spacecrafts has been measured to be approximately $$\ddot{r}_p = -(8.74±1.33)×10^{−10} \frac{m}{s^2}$$ with respect to our solar system.</p>
<p><a href="http://en.wikipedia.org/wiki/Pioneer_anomaly#Proposed_explanations">Several attempts</a> were made to <strong>explain this tiny effect</strong>, called the <a href="http://en.wikipedia.org/wiki/Pioneer_anomaly">Pioneer anomaly</a>, but none was fully accepted in the scientific community so far.</p>
<p>Two months ago, <a href="http://arxiv.org/abs/1103.5222v1">Frederico Francisco et al</a> have proposed another solution to the problem. They assume, roughly speaking, that the <strong>thermal radiation</strong> of the spacecraft caused by plutonium on board along with the actual structure of the probes is responsible for this mystery of modern physics.</p>
<p>Here an image of Pioneer 10 taken from Wikipedia along with a sketch of the <strong>radiation model</strong> employed in the paper:
<img src="http://i.stack.imgur.com/Ukwcx.png" alt="Pioneer 10 and heat model"></p>
<p>Hence my question:</p>
<blockquote>
<h3>Is the Pioneer anomaly finally explained?</h3>
</blockquote>
<p>Sincerely</p> | 6,589 | [
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<p>In all the literature I've seen the turbulent energy spectrum described as $E(k)$ instead of $E(L)$, i.e. as a function of a wave number not eddy size. The connection via $k=2\pi/\lambda$ is clear, but exactly what wave process is meant here. Is the idea that turbulent flow can be viewed as a superposition of waves? Waves of what? Or is this just a common notation used for energy spectra? </p> | 6,590 | [
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<p>I've seen many science popularisation documentaries and read few books (obviously not being scientist myself). I am able to <em>process and understand</em> basic ideas behind most of these. However for general relativity there is this one illustration, which is being used over and over (image from Wikipedia):</p>
<p><img src="http://upload.wikimedia.org/wikipedia/commons/2/22/Spacetime_curvature.png" alt="Spacetime curvature (from Wikipedia)"></p>
<p>I always thought that general relativity gives another way how you can describe gravity. However for this illustration to work, there needs to be another force, pulling the object down (referring to a direction in the attached image). If I put two non-moving objects in the image, what force will pull them together?</p>
<p>So where is my understanding incorrect? Or is general relativity not about explaining gravity and just describes how heavy objects bends spacetime (in that case the analogy is being used not correctly in my opinion)?</p>
<hr>
<p><strong>UPDATE</strong> Thank you for the answers and comments. Namely the XKCD comics is a spot on. I understand that the analogy with bent sheet of fabric pretty bad, but it seems that it can be fixed if you don't bent the fabric, but just distort the drawn grid. </p>
<p>Would you be so kind and answer the second part of the question as well - whether general relativity is explaining gravitational force. To me it seems that it is not (bending of spacetime simply can not affect two non-moving objects). However most of the time it is being presented that it does.</p> | 6,591 | [
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] |
<p>On a quantum scale the smallest unit is the <a href="http://en.wikipedia.org/wiki/Planck_scale">Planck scale</a>, which is a discrete measure.</p>
<p>There several question that come to mind:</p>
<ol>
<li>Does that mean that particles can only live in a discrete grid-like structure, i.e. have to "magically" jump from one pocket to the next? But where are they in between? Does that even give rise to the old paradox that movement as such is impossible (e.g. <a href="http://en.wikipedia.org/wiki/Zeno%27s_paradoxes">Zeno's paradox</a>)?</li>
<li>Does the same hold true for time (i.e. that it is discrete) - with all the ensuing paradoxes?</li>
<li>Mathematically does it mean that you have to use difference equations instead of differential equations? (And sums instead of integrals?)</li>
<li>From the point of view of the space metric do you have to use a discrete metric (e.g. the <a href="http://en.wikipedia.org/wiki/Manhattan_metric">Manhattan metric</a>) instead of good old Pythagoras?</li>
</ol>
<p>Thank you for giving me some answers and/or references where I can turn to.</p>
<p><strong>Update:</strong> I just saw this call for papers - it seems to be quite a topic after all: <em>Is Reality Digital or Analog?</em> FQXi Essay Contest, 2011. <a href="http://web.archive.org/web/20110504051348/http://www.fqxi.org/community/essay">Call for papers (at Wayback Machine)</a>, <a href="http://www.fqxi.org/community/forum/category/31417">All essays</a>, <a href="http://www.fqxi.org/community/essay/winners/2011.1">Winners</a>. One can find some pretty amazing papers over there.</p> | 114 | [
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<p>If a vibrating atom can produce light why can't an alternating current of electrons do the same?</p>
<p>EDIT: When I use the term "light" I mean all EMR</p> | 6,592 | [
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<p>consider object A with mass $m_{A}$ and positional vector $\overrightarrow{r_{A}}$</p>
<p>object B with mass $m_{B}$ and positional vector $\overrightarrow{r_{B}}$</p>
<p>object C with mass $m_{C}$ and positional vector $\overrightarrow{r_{C}}$</p>
<p>since reference frame is inertial (assumed) so</p>
<p>$m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{A}}=\overrightarrow{F}{}_{AB}+\overrightarrow{F}{}_{AC}$</p>
<p>$\Rightarrow$$m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{A}}=G\frac{m_{A}m_{B}}{\left|\overrightarrow{r_{B}}-\overrightarrow{r_{A}}\right|^{3}}(\overrightarrow{r_{B}}-\overrightarrow{r_{A}})+G\frac{m_{A}m_{C}}{\left|\overrightarrow{r_{C}}-\overrightarrow{r_{A}}\right|^{3}}(\overrightarrow{r_{C}}-\overrightarrow{r_{A}})$ ....[1]</p>
<p>for potential energy equation is to be integrated with a positional
vector and i am trying
hard to figure out what that vector could be, but still no success. please
help</p>
<hr>
<p>Potential energy of a object due to another object
$m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{A}}=\overrightarrow{F_{A}}=G\frac{m_{A}m_{B}}{\left|\overrightarrow{r_{A}}-\overrightarrow{r_{B}}\right|^{3}}(\overrightarrow{r_{B}}-\overrightarrow{r_{A}})$</p>
<p>assuming $\overrightarrow{r_{0}}=\overrightarrow{r_{B}}-\overrightarrow{r_{A}}$</p>
<p>$\Rightarrow m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{0}}=-(1+\frac{m_{A}}{m_{B}})(G\frac{m_{A}m_{B}}{r_{0}^{2}}\hat{r_{0}})$</p>
<p>$\Rightarrow\intop_{\overrightarrow{r_{0i}}}^{\overrightarrow{r_{0f}}}\left(m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{0}}\right).d\overrightarrow{r_{0}}=-\intop_{\overrightarrow{r_{0i}}}^{\overrightarrow{r_{0f}}}\left((1+\frac{m_{A}}{m_{B}})(G\frac{m_{A}m_{B}}{r_{0}^{2}}\hat{r_{0}})\right).d\overrightarrow{r_{0}}$</p>
<p>$\Rightarrow\left.\frac{1}{2}m_{A}v_{0}^{2}\right|_{v_{0}(\overrightarrow{r_{0i}})}^{v_{0}(\overrightarrow{r_{0f}})}=\left.G\frac{m_{A}(m_{A}+m_{B})}{r_{0}}\right|_{\overrightarrow{r_{0i}}}^{\overrightarrow{r_{0f}}}$</p>
<p>So What positional vector should be integrated with equ [1] ?
How it is decided ? (i mean what kind of property(s) that vector should possess ?)</p>
<p>EDIT 1</p>
<p>$\int_{\overrightarrow{r_{i}}}^{\overrightarrow{r_{f}}}\left(m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{A}}\right).d\overrightarrow{r}=\int_{\overrightarrow{r_{i}}}^{\overrightarrow{r_{f}}}\left(G\frac{m_{A}m_{B}}{\left|\overrightarrow{r_{B}}-\overrightarrow{r_{A}}\right|^{3}}(\overrightarrow{r_{B}}-\overrightarrow{r_{A}})+G\frac{m_{A}m_{C}}{\left|\overrightarrow{r_{C}}-\overrightarrow{r_{A}}\right|^{3}}(\overrightarrow{r_{C}}-\overrightarrow{r_{A}})\right).d\overrightarrow{r}$
.....[2]</p>
<p>questions </p>
<p>a) what is $\overrightarrow{r}$ in terms of $\overrightarrow{r_{A}}$,$\overrightarrow{r_{B}}$or
$\overrightarrow{r_{C}}$ ?</p>
<p>b) solve equ [2].</p> | 6,593 | [
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<p>I am looking at the <a href="http://en.wikipedia.org/wiki/Poincare_sphere" rel="nofollow">Poincaré sphere</a> and I am trying to compute a <a href="http://en.wikipedia.org/wiki/Jones_calculus" rel="nofollow">Jones matrix</a> for a particular rotation. Specifically, I would like it to perform the following maps:</p>
<p>$O :|H \rangle \rightarrow |R \rangle$</p>
<p>$O :|V \rangle \rightarrow |L \rangle$</p>
<p>$O :|L \rangle \rightarrow |H \rangle$</p>
<p>$O :|R \rangle \rightarrow |V \rangle$</p>
<p>where $|R \rangle$, $|L \rangle$ are right circular and left circular light. Is this possible? I should mention that I would also accept the same equations with L,R replaced by linearly polarized light $|D \rangle$, $|A \rangle$. If it is possible, what would be common plates that could do it?</p> | 6,594 | [
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<p>How are the external magnetic field intensity H, magnetisation M and the entropy related to each other? i.e. if I change the magnetic field intensity by dH what will be the change in entropy dS in terms of M. </p> | 6,595 | [
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<p>An isolated system $A$ has entropy $S_a>0$.</p>
<p>Next, the isolation of $A$ is temporarily violated, and it has entropy reduced $$S_b ~=~ S_a - S,\space\space\space S\leq S_a.$$</p>
<p>Is it true to say: <strong>the process of lowering entropy of a system requires work and energy?</strong></p>
<p>I am not sure if energy of the system must be changed when entropy is reduced. However, energy certainly is required – changing entropy is work and uses energy?</p> | 6,596 | [
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<p>In <a href="http://en.wikipedia.org/wiki/Metric_expansion_of_space#Understanding_the_expansion_of_Universe" rel="nofollow">this wikipedia article</a> it is described how a beam of light, with its locally constant speed, can travel "faster than light". That is to say it travels a distance, which, from a special relativistic point of view, is surprisingly big. </p>
<p>I wonder if a gravitational wave on such a curved spacetime (of which the wave is actually part of) behaves equally. </p>
<blockquote>
<p>Does a gravitational wave also ride on expanding spacetime, just as light does? Do the nonlinearities of gravitation-gravitation interaction influence the propagation of a wave (like e.g. a plasma) such that light and gravity are effectively not equally fast?</p>
<p>If I want to send a fast signal in this expanding universe scenario, in what fashion do I decide to I send it?</p>
</blockquote> | 6,597 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/759/does-quantum-physics-really-suggests-this-universe-as-a-computer-simulation">Does Quantum Physics really suggests this universe as a computer simulation?</a> </p>
</blockquote>
<p>I know the title sounds far-fetched, but the idea was first brought to my attention by a comment by Prof. Jim Gates of the University of Maryland during the <a href="http://www.youtube.com/watch?v=lYeN66CSQhg" rel="nofollow">2011 Issac Asimov Memorial Debate</a>.</p>
<p>Google lead me to <a href="http://www.bottomlayer.com/bottom/argument/Argument4.html" rel="nofollow">this essay</a> which seems to argue that the universe/reality shares many analogues to how a modern Turing machine (a computer) does what we perceive it to do. It doesn't come out and state that <em>The Matrix</em> ought to be reclassified as a documentary, but it leaves that possibility open.</p>
<p>Not being a physicist, I'm wondering just how much water these ideas might hold. Is this an avenue that we really ought to explore or are these scientists abusing an (apparently uncanny) analogy?</p> | 227 | [
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<p>Say we have an expression of the form:
$$
\left<0\right|:\phi(x)^2: : \phi(y)^2:\left|0\right>,
$$
where $\phi$ is some scalar field. I have heard the claim several times, that in evaluating this expression using Wick contractions, one only has to contract terms between groups of normal ordered terms. In this example this would mean we only have to contract $\phi(x)$ with $\phi(y)$ but not $\phi(x)$ with $\phi(x)$. I have no clue how to derive this. Has anyone got an idea?</p>
<p>EDIT: And say we consider anticommuting operators, would we have:
$$
\left<:\Psi^{\dagger}(x)\Psi(x)::\Psi^{\dagger}(0)\Psi(0):\right> = (-1)^3\left<\Psi^{\dagger}(x)\Psi(0)\right>\left<\Psi^{\dagger}(x)\Psi(0)\right>,
$$
or with a plus sign?</p> | 6,598 | [
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<p>I am trying to make sense of <a href="http://arxiv.org/abs/physics/0210005" rel="nofollow">arXiv:physics/0210005</a>. I am confused with the concept of information bearing degrees of freedom of a system mentioned at the very beginning. To verify the arguments of the paper, I would like to start with a 1-D quantum simple harmonic oscillator. We know that it has two degrees of freedom, momentum and position. You can also use generalized degrees of freedom if you want. My question is which of these are the information bearing degrees of freedom?</p> | 6,599 | [
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<p>Google has not been very useful in this regard. It seems no one has clearly defined terms and Kittel has too little on this. </p> | 6,600 | [
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<p>Hey guys I really need help on this problem.</p>
<blockquote>
<p>A ceramic slab of dimentions 5cm x 10 cm x .25 cm has to be heated to $177\,^{\circ}{\rm C}$. The ceramic slab travels on a conveyor belt traveling at $.1 \frac{m}{s}$. The slab is initially at a temperature of $18\,^{\circ}{\rm C}$ when it enters a radiant heater on the conveyor belt. The heater surrounds the whole slab and emits heat as a black body at $1000\,^{\circ}{\rm C}$. Since the heat surrounds the slab, all the energy that leaves the heater is absorbed by the slab. The slab has an emissivity of .85. Find the amount of time it takes to heat the slab to $177\,^{\circ}{\rm C}$. The slab has properties $c_{p}=1500\frac{J}{Kg K}$ and $\rho=900\frac{kg}{m^{3}}$ and $k=1 \frac{W}{mK}$</p>
</blockquote>
<p>I started off by creating an energy balance on the slab as it's in the heater. I assumed convection that is caused by the conveyor belt traveling at such a slow speed to be insignificant to all calculations.
$$\dot{E}_{in}- \dot{E}_{out}+\dot{E}_{g}=\dot{E}_{st}$$
$$A\alpha\sigma T^{4}_{heater}-A\epsilon\sigma T^{4}=\rho c_{p}V\frac{dT}{dt}$$
$$A\sigma(T^{4}_{heater}-\epsilon T^{4})=\rho c_{p}V \frac{dT}{dt}$$</p>
<p>I then plugged in the values and got:
$$44.185-1.428x10^{-11} T^{4}=\frac{dT}{dt}$$</p>
<p>I realized that this comes out to be a VERY nasty integral so I tried to use matlab and numerically integrate it using Euler's method. My graph for that came out to be linear which I knew was not right and I came here straight away to figure out what I was doing wrong</p> | 6,601 | [
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] |
<p>Reading about plasmonic nanoparticles I faced the term "localised light".</p>
<p>How can one localise light? What are applications of it?</p> | 6,602 | [
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] |
<p>How to calculate the area / volume of a black hole?
Is there a corresponding mathematical function such as rotating $1/x$ around the $x$-axis or likewise to find the volume? </p> | 6,603 | [
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<p>For a simulation, I want to compute the path that light follows near a black hole.</p>
<p>Non-relativistically, a massive point particle in a central newtonian gravitational field follows either an ellipse, a parabola, or a hyperbola. Is the same true relativistically for light around a black hole? A problem I see with this, is that while particles gain velocity when approaching a black hole, a photon gains energy instead. So do photons behave differently?</p> | 6,604 | [
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<p>I know there may be missing information, but my question is really simple and yet I haven't found an answer to it. To make things easy, let's assume we have a $40×40×40$ cm oven that we want to keep its temperature at $200$ degrees Celsius using natural gas. How much energy per second is consumed to achieve this?</p> | 6,605 | [
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<p>Imagine two laser beams A and B are released at the same moment to bounce between two mirrors, A was moving and B was at rest, doing the calculations I found that for a person at rest B would reach the upper mirror before A because in his frame of reference A travels less distance. but for another person in the same reference frame of A, A would reach the upper mirror first.
Is that OK in relativity!<img src="http://i.stack.imgur.com/MJn2B.jpg" alt="the upper is moving and the lower is constant"></p> | 6,606 | [
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<p>The <a href="http://en.wikipedia.org/wiki/Vis-viva_equation" rel="nofollow">proof</a> of the vis-viva equation of orbital mechanics found on wikipedia looks, in my opinion, somewhat convoluted and unenlightening. Considering the simplicity and importance of the vis-viva equation, is there a shorter or more insightful derivation?</p>
<p>The vis-viva equation states that for a Kepler orbit of a mass around a central mass $M$, the magnitude of the velocity at any distance $r$ from the center obeys $v^2 = GM(\frac{2}{r}-\frac{1}{a})$, where $a$ is the semi-major axis of the orbit.
It is equivalent to saying that the energy of a Kepler orbit with semi-major axis $a$ is $-\frac{GM}{2a}$.
This is a very natural generalization of the 'circular' case where the total energy is $-\frac{GM}{2r}$.</p>
<p>Because of the simplicity of the result, I guessed that there could be a relatively straightforward derivation. The derivation on wikipedia involves quite some algebra and, importantly, only holds for elliptical orbits.</p> | 6,607 | [
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<p>Lately I'm reading about surface enhanced fluorescence. In many articles I can see that <a href="http://en.wikipedia.org/wiki/Fluorophore" rel="nofollow">fluorophores</a> are called "dipoles". Is it because that they can be modelled by a vibrating electric dipole? Or maybe they are all chemical dipoles?</p> | 6,608 | [
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<p>I saw the following way of derivation of Maxwell equations: author starts from Lorentz transformations for the 3-vector of force, then he applies them for the Coulomb law, after that gets the Lorentz force law with expressions for $\mathbf E $ and for $\mathbf B$ fields, then he takes curl and divergence and, finally, he derives the Maxwell equation for the field of charge moving with constant speed. </p>
<p>After that he uses a few axioms: superposition principle and independence of equations on acceleration, and generalizes equations on all electrodynamical processes.</p>
<p>But I have some doubts about this method. The most problematic question is followIng: there are EM fields of electric and magnetic type. For the first one $\mathbf E^{2} - \mathbf B^{2} > 0$, for the second one - $\mathbf E^{2} - \mathbf B^{2} < 0$. But the author have started from the electric type, so he can't generalize final result on all EM processes. </p>
<p>The question: can we violate this argument against this methot of derivation by introducing some other argument?</p> | 6,609 | [
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<p>I am studying the Fujikawa method of determining the chiral anomalies in a $U(1)$ theory. As we know the basis vectors selected are the eigenstates of the Dirac operator. One of the reasons given is that the eigenstates diagonalize the action which is needed for determining an exact quantity such as Ward-Takahashi identities. Anyone care to explain? I am referring to <em>Path Integrals and Quantum Anomalies</em> by Kazuo Fujikawa and Hiroshi Suzuki.</p> | 6,610 | [
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<p>Through what I learned from school, frequency $f=\frac1T$ while $T$ is the period. However, things get harder in college where there are non-periodic signal. That means they have no period or their period is extended to infinity but they still have frequency. How can they have frequencies even there is no period to apply the formula $f=\frac1T$? Is there any definition of frequency in those cases.</p> | 6,611 | [
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<p>This theory has bugged me ever since my first physics class on the subject. If this (<a href="http://en.wikipedia.org/wiki/Kinetic_theory" rel="nofollow">http://en.wikipedia.org/wiki/Kinetic_theory</a>) is true, it leads me to a few weird conclusions.</p>
<p>Opening the rear window in a pickup truck at 10 m/s doesn't empty the cabin of all its air. This means that gas molecules can catch up with us from behind so we can conclude that gases move much faster than 10 m/s at normal temperatures.</p>
<p>Then, shouldn't gases mix almost instantaneously? For example, shouldn't a fart's smell reach us faster than a car on an highway and then dissapear almost immediately into such a large area that the concentration is too low for our noses to detect?</p> | 6,612 | [
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] |
<p><strong>If any equations are there ,for split the light particle, means
that i have a 1m length of light just consider that in that who can i
split the light particle into 1/2 m length Pls tell</strong> </p> | 6,613 | [
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<p>While watching a <a href="http://en.wikipedia.org/wiki/Schlieren_photography" rel="nofollow">Schlieren</a> video of a <a href="https://www.youtube.com/watch?v=4CR22kpG3ig" rel="nofollow">hand clapping</a>, I noted a very distinct difference between a sound wave and a puff of air, which were both created by a hand clapping. What is the difference between a puff of air and a sound wave regarding creation and propagation?</p>
<p>In the video, it appears that some of the energy goes into the sound wave and some of the energy goes into the puff. Is there a principle that governs the distribution of impact energy between oscillation (sound) and pushing (puff?) </p> | 6,614 | [
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<p>I am reading the original paper by Bondi, van der Berg and Metzner (<a href="http://rspa.royalsocietypublishing.org/content/269/1336/21" rel="nofollow">link</a>) regarding gravitational waves in asymptotically flat axisymmetric spacetimes. In the introduction, he makes the following comment - </p>
<blockquote>
<p>The conservation of mass effectively prohibits purely spherically symmetric waves and similarly, conservation of momentum prohibits waves of dipole symmetry. </p>
</blockquote>
<p>I know that Birkhoff's theorem tells us that spherically symmetric asymptotically flat solution to GR is necessarily static, and therefore contains a timelike Killing vector, which implies conservation of mass (energy). Bondi et. al. seem to be stating the converse of this theorem, whose validity I do not immediately see. How do we show this?</p>
<p>Also, what is the corresponding proof of the second statement made above?</p> | 6,615 | [
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<p>Suppose we have a material point. If it is moving from position $X_0$ with initial velocity $V_0$ and constant acceleration $A$, then from elementary physics course I remember that its movement is described by the equation</p>
<p>$$X(t) = X_0 + V_0t + At^2/2.$$</p>
<p>Now, my question is, what is the equation of the movement of the material point if its acceleration is an arbitrary function of $t$: $A(t)$. Is it simply:</p>
<p>$$X(t) = X_0 + V_0t + A(t)t^2/2,$$</p>
<p>or is it more complicated than that? From the looks of $At^2/2$ I have a suspicion that integrals may be involved. </p> | 228 | [
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<p>The light traveling a 3 lake km/sec, but Pls tell me how can a control the speed of light, means can limit the speed like 2 lake km/sec are 1 lake km/sec </p>
<p>Pls tell me equation</p> | 6,616 | [
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<p>Given a black hole of some size, say $10^8$ solar masses, how can the size of its sphere of influence of light be calculated?</p>
<p>To clarify, ultimately I'd like to be able to calculate the apparent angle of a black hole's lensing effects, as viewed from some distance.</p>
<p>(I'm no physicist, so I might be making incorrect assumptions about gravitational lensing. If this is the case, sorry!)</p> | 6,617 | [
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<p>How would I figure the needed pressure differential to freeze water inside a cooler using ambient air? I am assuming that the combined gas law would apply here and that the formula P1•V1/T1=P2•V2/T2 would provide the answer. My understanding is that by lowering the pressure I could effectively lower the temp as well. By this calculation I would need to reduce the air pressure from 1 bar to 313 milibar. Does this seem right on the math side?
In an open system lowering the pressure should also lower the volume and therefore keep the temperature from dropping. Is this correct as well.</p>
<p>I would assume an ambient temp of 100 F. </p> | 6,618 | [
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<p>I have measured the total activity from a radioactive sample during an experiment by counting the number of decays happening in 3 seconds intervals. I got data as:</p>
<p>Time bin: 0 1 2 3 4 5 6 7 ... <br>
Count number: 307 294 257 246 250 216 186 169 ...</p>
<p>Now I want to curve fit an exponential $ae^{bt}$ to the data to determine $b$ as the decay constant. But since I have measured during intervals of 3 seconds, how should I convert/scale this data to get a proper estimate of the decay constant that has units s$^{-1}$?</p> | 6,619 | [
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<p>I'm trying to calculate the initial velocity $v_0$ and angle $\theta$ for a given destination $(x, y)$ with a launch height of $y_0$. Obviously there will be a set of pairs of velocity and angle that will pass through the destination point. This set is given by
$$ \left\{(v_0,\theta) \middle|y = - \frac{g}{2 v_0^2 \cdot \cos^2(\theta)} \cdot x^2 + \tan(\theta) \cdot x +y_0 \right\} \ .$$</p>
<p>I have already looked at this questions:</p>
<p><a href="http://physics.stackexchange.com/questions/27992/solving-for-initial-velocity-required-to-launch-a-projectile-to-a-given-destinat">Solving for initial velocity required to launch a projectile to a given destination at a different height</a></p>
<p><a href="http://physics.stackexchange.com/questions/56265/how-to-get-the-angle-needed-for-a-projectile-to-pass-through-a-given-point-for-t">How to get the angle needed for a projectile to pass through a given point for trajectory plotting</a></p>
<p>So for example I could rewrite the set to
$$\left\{ (v_0,\theta) \middle| v_0 = \frac{1}{\cos(\theta)}\sqrt{\frac{\frac{1}{2} g x^2}{x \tan(\theta)+y_0}} \right\}\ .$$</p>
<p>Is there an easy way to compute this set for one given destination without iterating over all possible velocities or angles?</p> | 6,620 | [
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<p>I was laying on my bed, reading a book when the sun shone through the windows on my left. I happened to look at the wall on my right and noticed this very strange effect. The shadow of my elbow, when near the pages of the book, joined up with the shadow of the book even though I wasn't physically touching it. </p>
<p>I have posted a video of the event <a href="http://tinypic.com/player.php?v=6xw7tc%3E&s=5#.UtqZmbRFCM8">here</a>. <em>(Note: the video seems to be wrong way up but you still get the idea of what is happening)</em></p>
<p>What is causing this? Some sort of optical illusion where the light get's bent?
Coincidentally, I have been wondering about a similar effect recently where if you focus your eye on a nearby object, say, your finger, objects behind it in the distance seem to get curved/distorted around the edge of your finger. It seems awfully related...</p>
<p><em><strong>EDIT:</em></strong> I could see the bulge with my bare eyes to the same extent as in the video! The room was well light and the wall was indeed quite bright.</p> | 6,621 | [
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<p>I am trying to prove that the momentum $p_x$ operator is Hermitian, my approach is the following</p>
<p>$$<p_x>~=~\int \Psi^*(\vec{r},t)[-ih\frac{\partial}{\partial x}]\Psi(\vec{r},t)\, d^3r.$$</p>
<p>I try to do integration by parts but I cannot resolve the differential, as the integration is in respect to $\vec{r}$ and the partial is in respect to $x$.</p> | 6,622 | [
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<p>Please bear with this experimentalist trying to understand the subtleties of TIs in what may well be imprecise language. I appreciate that one can deduce the topological trivial or non-trivial nature of a filled band for particular crystalline structures by virtue of $(-1)^{\nu_0} = \Pi \delta_i$ taken over the <a href="http://en.wikipedia.org/wiki/T-symmetry" rel="nofollow">TR</a> symmetry points of the <a href="http://en.wikipedia.org/wiki/Brillouin_zone" rel="nofollow">BZ</a>. I also appreciate that the gap must close at the interface between topologically distinct insulating phases. In my naive understanding, I would expect that the surface state must "fix" the overall parity difference between the valence bands of the TI and trivial insulator and believe that $N_k = \Delta \nu$ mod 2, where $N_k$ is the number of Kramers pair edge modes implies this fix. I would have expected however that their would be some implication about the parity of the edge mode itself (i.e. that is must be odd). Why is there no statement about the edge modes parity? </p> | 6,623 | [
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<p>I want to know how a ceramic transparency is mostly affected by the pores, grain boundary, second phases etc. present inside of it, but the major contribution is due to the pores. </p>
<p>Let's consider the glass slab with an air gap between them. It is still transparent.</p>
<p>Hence: how can simple pores make ceramics opaque? I am after a theoretical description.</p> | 6,624 | [
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<p><strong>Edit 26/Sept/13: Fixed Typo in potential</strong></p>
<p>I'm solving the following (seemingly simple) quantum-mechanical problem in <em>four spatial dimensions</em>. In natural units ($\hbar^2/2m=1$), the Schrödinger equation reads:</p>
<p>$$
\Big[-\nabla^2-\frac{24 R^2}{(\mathbf{x}^2+R^2)^2}\Big]\psi(\mathbf{x})=E\,\psi(\mathbf{x})\,,
$$</p>
<p>where $R>0$ is a parameter simultaneously characterizing the depth and range of the potential.
The potential depends only on the distance away from the origin, so I can separate variables $\psi=R_{nl}(r)\,Y_l(\vec{\theta})$ and the radial equation then reads:</p>
<p>$$
\Big[-\frac{\partial^2}{\partial r^2}-\frac{3}{r}\frac{\partial}{\partial r}+\frac{l(l+2)}{r^2}-\frac{24 R^2}{(r^2+R^2)^2}\Big]\,R_{nl}(r)=E_{nl}\,R_{nl}(r)\,.
$$</p>
<p><strong>Problem:</strong> I seem to have found an <em>s</em>-wave ($l=0$) non-scattering state with zero energy $E_{nl}=0$ that appears to be localized:</p>
<p>$$R_{n,l=0}(r)=\mathcal{N}\frac{r^2-R^2}{(r^2+R^2)^2}\qquad E_{nl}=0.$$</p>
<p>But, I am unable to normalize this "bound" state since the integral $\int_0^\infty dr\, r^3 |R(r)|^2$ does not converge. What is the nature of this state? Or am I just totally screwing something up?</p> | 6,625 | [
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<p>I want to solve the TISE of a particle of charge $q$ and mass $m$ in a one dimensional triangular potential, with an infinitely high potential wall at $x = 0$, i.e.</p>
<p>$$\hat{H}=-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2}+V(x),$$
with</p>
<p>$$V\left(x\right)=\begin{cases}qEx&{\rm if}\,x>0 \\
\infty &{\rm if}\,x\leq0\end{cases}$$</p>
<p>For $x>0$, this gives the TISE
$$-\frac{\hbar^2}{2m}\frac{\partial^2\Psi_n}{\partial x^2}+qEx\cdot\Psi_n = E_n\Psi_n.$$
I know that the solutions of
$$\frac{d^2y}{dx^2} - xy = 0$$
are given by the Airy functions, however I don't know how I can transform the TISE to this form. I know it's possible, because I have the solution to the problem, but I don't know how I can myself come up with this, I don't see the aim which has to be reached in order for a substitution to be successful. Also, I don't know how the differential will transform under a substitution including $x$.
Any help?</p>
<p>The substitution used in the solution is
$$u=\left(\frac{2mqE}{\hbar^2}\right)^\frac{1}{3}\left(x-\frac{E_n}{qE}\right).$$</p> | 6,626 | [
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<p>What I want:
I have a rubber rope which is $5m$ in length when not stressed and is able to stretch about $100\%$ (to $10m$ long). I want to accelerate a constant mass horizontally, which has negligible friction. I'd like to have a function that tells me the velocity of the mass dependent on time, so for instance velocity $1 s$ after releasing it.</p>
<p>What I did:
I've done some measurements of forces of the rope when pulling it to different lengths. Of course, when pulling $0cm$ (total length $5m$) I got a force of $0N$. Here is a graph of my results.</p>
<p><img src="http://i.stack.imgur.com/Mok8k.png" alt="http://i.imgur.com/vtEnACQ.png"></p>
<p>$x-axis$: displacement of one end of the rope</p>
<p>$y-axis$: measured force</p>
<p>I was also able to do a regression and found a function which describes how much force I get after I pull a given length.
I name this function $F(s)$ for Force dependent on displacement.
From this, it's easy to get the acceleration function, which is $a(s) = F(s)/m$ with $m = mass$ of the object I want to accelerate.
But now I'm stuck.
I somehow need to get $a(t)$ instead of $a(s)$, thus the acceleration by time, not by length, so I can then integrate that to get $v(t)$.</p>
<p>How do I convert the dependency of the function?</p> | 6,627 | [
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<p>In light-front QFT, in the Minkowski space, we define a hypersurface, $\Sigma_+ : x^3+ x^0 = 0 $. How can I write its parametric equations? </p> | 6,628 | [
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] |
<p>How much energy is derived from the full process from hydrogen-1 fused into helium-4? Including all the sub-reactions (H1 into Deuterium, etc).</p> | 6,629 | [
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<p>In a typical photon experiment the photon is depicted as moving across the page, say from right to left.
Suppose we were actually able to witness such an experiment, from the side (to position of reader to a page).
If the photon is actually moving from left to right can I, standing at 90 degrees to the motion, see the photon? </p> | 6,630 | [
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<p>What are the quantum mechanisms behind the emission and absorption of thermal radiation at and below room temperature? If the relevant quantum state transitions are molecular (stretching, flexing and spin changes) how come the thermal spectrum is continuous? What about substances (such as noble gases) which don't form molecules, how do they emit or absorb thermal radiation? Is there a semi-classical mechanism (with the EM field treated classically) and also a deeper explanation using the full apparatus of QFT?</p> | 6,631 | [
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<p><em>[insert obligatory statement of my lack of knowledge in physics]</em></p>
<p>Alright, so we have all seen the movies where someone gets blasted out of the airlock on their starship, or their suit decompresses while on a space walk. The poor schmoe usually either decompresses so violently that blood is oozing out of every orifice in their body, or they freeze instantly.</p>
<p>From this I have two questions:</p>
<ol>
<li><strong>Would the decompression really be that violent?</strong>
<ol>
<li>Clearly the drastic difference in pressure from a normal "earth" like environment to space would be bad, but would it be <em>that</em> devastating.</li>
<li>I vaguely remember that standard atmospheric pressure was something like 15 psi, which doesn't seem like enough to mess you up that bad.</li>
</ol></li>
<li><strong>Would you <em>actually</em> freeze instantly in space?</strong>
<ol>
<li>Heat, or lack thereof is a measure of internal energy, but in a vacuum there wouldn't be anything to have internal energy, so does space even have a temperature?</li>
<li>Wouldn't some form of matter have to be present in order to cool off? If there were no matter besides yourself and a few stray particles here and there, it seems like it would take a very long time to cool off.</li>
</ol></li>
</ol> | 6,632 | [
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<p>Given some observable $\mathcal O \in \mathcal H$ it is simple to construct a CP (completely positive) map $\Phi:\mathcal{H}\mapsto \mathcal{H}$ that conserves this quantity. All one has to observe is that
$$ \text{Tr}(\mathcal O \, \Phi[\rho]) = \text{Tr}(\Phi^*[\mathcal O] \rho).$$
Therefore, if we impose $\Phi^*[\mathcal O] = \mathcal O$, then $\text{Tr}(\mathcal O \, \Phi[\rho])=\text{Tr}(\mathcal O \rho), \; \forall \rho\in \mathcal H$. That amounts to impose that the Kraus operators of $\Phi^*$ should commute with $\mathcal O$.</p>
<p>I'd like, however, to construct a trace-preserving CP map for which the expectation value of $\mathcal O$ does not increase for any $\rho \in \mathcal H$. More explicitly, given $\mathcal O\in \mathcal H$, I want to construct $\Gamma:\mathcal H \mapsto \mathcal H$ such that
$$ \text{Tr}(\mathcal O\, \Gamma[\rho]) \le \text{Tr}(\mathcal O \rho), \; \forall \rho \in \mathcal H .$$</p>
<p>How would you go about that? Any ideas?</p> | 6,633 | [
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<p>I need to find the possible values of energies and impulses of virtual photon emitted by real electron. I don't understand how to compute it (look to the text below). </p>
<p>Let's introduce the free electron. Then let's use the frame in which it is at rest. </p>
<p>So the laws of energy-momentum conservation take the form
$$
E_{0} = E_{1} + E_{photon}, \quad 0 = p_{1} + p_{photon} .
$$
According to this, electron after photon emission must be virtual.
What to do after that? Formally I have only two equations for four unknown values. What to do next? To use energy-impulse relation $p_{\mu}p^{\mu} = m^2c^2$ for virtual particles?</p> | 6,634 | [
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<p>Quantization of gravity (general relativity) seems to be impossible for spacetime dimension D >= 4. Instead, quantum gravity is described by string theory which is something more than quantization (for example it introduces an infinite number of fields). More direct approaches to quantization of gravity have failed (my opinion; not everyone would agree on this).</p>
<p>However, gravity in dimensions D < 4 is special, because it is topological (carries no dynamic degrees of freedom locally). It is possible to quantize gravity coupled to other fields at D = 2: in fact perturbative string theory is exactly that! What about D = 3? Are there approaches to quantization of gravity (coupled to other fields) which have been more successful at D = 3 than at D = 4?</p> | 6,635 | [
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<p>Does the PV regulator breaks SUSY? </p>
<p>Take for instance the 1-loop (top/stop loops) correction to the Higgs squared-mass parameter in the MSSM, and you'll get something like, </p>
<p>$$\delta m^2_{h_u} = - 3Y_u^2/(4 \pi^2) m_{\tilde{t}}^2 ln (\frac{\Lambda_{PV}^2}{m_{\tilde{t}}^2})$$ </p>
<p>Where, $\Lambda_{PV}$ is the PV regulator/cutoff, and $m_{\tilde{t}}$ is the stop-quark mass. </p>
<p>In my mind, as the calculation is performed before ElectroWeak Symmetry Breaking (EWSB) (i.e. no mass for the top), but at the same time it's considering softly broken susy (i.e. there is mass for the stop-quark), therefore we don't get perfect cancelation. But I heard someone saying that there's no perfect cancelation because PV regulator breaks SUSY!</p>
<p>I don't see where the PV breaking SUSY argument fits. Can anyone enlighten me?</p> | 6,636 | [
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] |
<p>The traditional (not taking into account phasor addition or complex addition) application of Kirchoff Voltage law, i.e. $\Sigma\Delta V=0$ along a loop, does not work for AC circuits. We can sum the voltage drops to zero if we take into account their phase differences. But at some particular time, no matter what the phase differences in the general equation for the voltages across various components, there will be only one numeric value of $\Delta V$. </p>
<blockquote>
<p><strong>Why doesn't this sum to zero over the loop in case of AC circuits with
non-zero <a href="http://en.wikipedia.org/wiki/Electrical_reactance" rel="nofollow">reactance</a>?</strong></p>
</blockquote>
<p>Is this because there is some contribution to the $\oint E.dl$ due to changing magnetic flux? If it is, even in absence of any inductance, the voltage drops still do not sum to zero. why? </p> | 6,637 | [
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<p>I hope this is the right forum to ask this question. Is there a material (preferably thin, like a membrane) that changes its local conductivity (by that I mean the permeability for an electric field; I hope it's the right term) upon excitation with light or heat? I have no idea where to start my search for something like that. </p>
<p>Thanks a lot.</p> | 6,638 | [
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<p>It seems as though I've come across a rather unusual conclusion that could either simply be a misinterpretation or a contradictory discovery. I seem to have found a way to utilize the Heisenberg Uncertainty Principle (HUP) to our benefit to communicate faster than the speed of light (FTL). I am aware of many proposals that try to utilize entangled spin particles and try to communicate, but this schemes fail because the measurement outcome can NOT be controlled. Therefore, even if two people share an entangled pair of particles, and Alice measures spin up, although she knows Bob has a spin down particle, Bob didn't measure yet and has no way of knowing that Alice has measured her particle. Hence, FTL is impossible based on the reason that the measurement outcome can not be controlled.</p>
<p>This leads to my proposal of using position and momentum entangled pairs. Consider <strong>Alice and Bob hold an ensemble of entangled particles in position and momenta</strong>, where each particle is trapped in a separate harmonic potential. At some specified time agreed upon in the future, Alice measures all of her particles' position to high precision. <strong>Alice and Bob have synchronized clocks</strong> and Bob measures all of his entangled particle's momentum to whatever accuracy he chooses. Alice can calculate the average value and also the standard deviation of position. The standard deviation of position would be extremely narrow, i.e, the spread of her measurements would be very small.</p>
<p>From the entanglement relation, <strong>x1 = x2 and p1 = -p2</strong>, we know that when Bob measures his particle's momentum, the spread of momentum will be very large. This must be true because position and momentum cannot be measured to arbitrary accuracy at the same time. This is very similar to Einstein's proposal to violate the HUP, however I am exploiting HUP.</p>
<p>What this all means is that the if Bob measures a very large momentum spread, it must mean that Alice has made her measurements. If Bob measures a relatively moderate momentum spread, then he knows Alice did not measure her particles. <strong>Since the position measurement can be made to arbitrary accuracy, we are "controlling the spread or the standard deviation as the means to communicate."</strong> (MAIN RATIONALE)</p>
<p>Say Alice and Bob have multiple ensembles of entangled particles. Alice can relay a message by simultaneously measuring her first ensemble, meaning its a "1" and not touch her second ensemble meaning its a "0", and perhaps she chose to measure the third ensemble, "1", etc. Hence generating the series 101..., where <strong>each ensemble of entangled particles represents one bit of information.</strong></p>
<p>What is flawed in this proposal? Entanglement in position and momenta is well established. We can also choose to measure the position of a particle to arbitrary precision. The HUP must hold for Bob and everyone involved.</p> | 6,639 | [
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<p><a href="http://www.google.com/search?q=haldane+conjecture">Haldane's conjecture</a> states that the integer spin antiferromagnetic Heisenberg chains have a gap in the excitation spectrum. However, the dispersion relation of the antiferromagnetic spin wave is $\omega_k\sim k$ in the long wave length limit, meaning that the excitation energy could be zero. What is the matter?</p> | 6,640 | [
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<p>Relativity of Simultaneity seems to be about OBSERVING two events simultaneously (please correct me if I am wrong). </p>
<p>However, as long as the two events are separated by a distance (any distance) then two observers (in the same frame) cannot agree that they happen simultaneously unless they are equidistant from the two events within the frame.</p>
<p>Consider the example of A and B at rest with respect to another observer C. A and B are stationary in space but separated by 1 light second of distance.</p>
<p>An event occurs simultaneously at A and B, the time should be the same since they are at rest with respect to each other. However, A will OBSERVE event at A and exactly after 1 second, the event at B. B will OBSERVE the event at B and exactly after 1 second, the event at A.</p>
<p>C may observe A first, B first or A and B simultaneously (which is fine).</p>
<p>My questions are:</p>
<ol>
<li>Are A and B in the same inertial frame? And if so, if simultaneity is about OBSERVING an event, then how do we account for the different observation times within the same frame? An event can never be simultaneous for A and B unless they are at the same location.</li>
<li>If A and B are not in the same frame, then they are not in inertial frames as there is no motion with respect to each other.</li>
<li>If simultaneity is not about OBSERVING two events, then how do we separate the visual aspect (time taken for light to travel) from the temporal aspects (time at which the two events actually occurred.</li>
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<p>The water-gas phase transition is said to be similar to the ferromagnetic-paramagnetic phase transition (same set of critical exponents = same universality class). In the former case the order parameter is the difference in the densities, while in the latter it is the magnetization density.</p>
<p>In the magnetic case the $O(N)$ symmetry is broken spontaneously - hence we talk about two distinct phases as suggested by Landau, i.e. the ferromagnetic phase (which has $O(N-1)$ symmetry) and the paramagnetic phase (which has the full $O(N)$ symmetry). Now for the water-gas case, what symmetry is spontaneously broken? Both liquid water and gaseous water have translational and rotational symmetry..</p>
<p>Also, sometimes it is suggested that water and liquid should not be considered as distinct phases, since one can join the two phases by an excursion in the parameter space which does not encounter any singularities in the free energy. If so, then shouldn't we consider the paramagnetic and ferromagnetic phase to be just one phase as well?</p>
<p>How do we reconcile the concept of phases being characterized by symmetry (and their breakings), or being characterized by excursions in the parameter space, since they seem to give contradictory results? Thanks.</p> | 6,642 | [
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<p>According to <a href="http://www.ted.com/talks/jeremy_kasdin_the_flower_shaped_starshade_that_might_help_us_detect_earth_like_planets" rel="nofollow">this TED talk by Jeremy Kasdin,</a> Nasa is planning to spend $1bn on a "Starshade" project, where a giant flower shaped metal eclipser 20 meters wide is placed 50k kilometers in front of a space telescope, to fit the telescope diameter.</p>
<p>The idea is to occlude a star and photograph it's exoplanets.</p>
<p>The above solution is surreal. Why can't they control the diffraction of the light around the occlusion circle with a refractive material, to direct it outwards?</p>
<p>I suggest that they can design a round black occluder with soft edges overlaid with a refractive material that deflects the light away from the centre, similar to a lense.</p>
<p>Why do the angles and shapes at the edge of the flower shaped occluder have to be very precise in order to control diffraction?</p> | 6,643 | [
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<p>I currently have a very limited knowledge of how radiation works etc, but while sat in class the other day, one question occurred to me that even my teacher could not answer.</p>
<p>We have been learning about alpha, beta and gamma radiation. I know that alpha is positive and that makes perfect sense. However, when the neutron is broken down to form a β particle and this particle is then sent out of the nucleus, why is this negatively charged β particle not attracted (presumably by electromagnetic force) back into the overall positive nucleus of the atom? To me, at least, it does not make sense that it would not be attracted back the nucleus.</p>
<p>Sorry if this is simple stuff but even after some furious googling I haven't been able to find an answer.</p> | 6,644 | [
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<p>If I knew the exact value of constant centripetal force and the <strong>average velocity</strong> of an object travelling around a circle for time $t$, would that be enough information to determine the final positon of an object? What I mean is what if I had another object, at the same initial position and with identical centripetal force applied to it, which would have a different velocity function $f(t)$, but identical average velocity - would it eventually be in the same place as the first object after time $t$?
Deriving a formula answering this question was beyond my skills.</p> | 6,645 | [
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<p>My professor said that the $k_BT$ displacement in the energy levels of the band electrons is due to the space-thermal displacement of the potential of the ion host. I think that this displacement is due to the thermal fluctuations of the electromagnetic field coupled to the electron charge.</p>
<p>Who is right?</p> | 6,646 | [
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<p>Is there any phenomenon where the 'wave description' of the electron's motion is not applicable?</p>
<p>The reason for this question is to find out if there are any situations were quantum wave theories fail. If not, it seems that the Everett's multiworld analysis as described by Coleman, <a href="http://media.physics.harvard.edu/video/index.php?id=SidneyColeman_QMIYF.flv" rel="nofollow">http://media.physics.harvard.edu/video/index.php?id=SidneyColeman_QMIYF.flv</a> works.</p> | 6,647 | [
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<p><img src="http://i.stack.imgur.com/orT7X.png" alt="enter image description here"></p>
<p>In the left side example of cantilever brakes, how do I find the tension in strings DE and DC, in terms of T. According to me applying force balance equations, horizontal and vertical forces should be zero</p>
<p>i.e. $T_{DE} \cos(45) + T_{DE} \cos(45) = T$...</p>
<p>The answer given is $T/2$, which is against general understanding.</p>
<p><strong>SOURCE:- Mechanics of Materials by JM Gere Ed2009- Problem 1.2.3</strong></p> | 6,648 | [
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<p>As any light reflected or emitted from objects inside a black hole (if it is possible to be there) does not leave the event horizon and comes back inside, would it be like seeing yourself?</p>
<p>What I mean is that would the light we might emit/reflect return to our eyes and make us sort of look at ourselves? </p> | 6,649 | [
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] |
<p><a href="http://en.wikipedia.org/wiki/Turbulence" rel="nofollow">Wikipedia</a> states that </p>
<blockquote>
<p><em>Turbulent flow is chaotic. However, not all chaotic flows are turbulent.</em></p>
</blockquote>
<p>Someone give a picture for that?</p> | 6,650 | [
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<p>Assuming you have container with heat insulation (something like boiler).<br>
You can store water at any temperature <strong>below 100°C</strong>. At these conditions, you can drill a hole into container and <strong>store water at air pressure</strong>.<br>
But when you heat water to tempertature <strong>over 100°C</strong>, it starts to boil, increasing pressure in contailner. If you drill a hole, water will start to evaporate and that'll cause temperature drop. If you try to maintain constant temperature, after some time <strong>all water will evaporate</strong>.<br>
<strong>Water with temperature over 100°C can be stored only at high pressure?</strong><br>
If so, it'll reach some pressure (depending on temperature) and stop boiling?<br>
Are there any other risks besides high pressure to be aware when trying to store water at these conditions?</p> | 6,651 | [
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<p>Need help in understanding the direction of magnetic force in the magnetic field!Totally confused by directions.</p>
<p>Why is it that magnetic force is perpendicular to the direction of magnetic field and velocity of charged particle.
Why is it(force) not in the same direction as the magnetuc field</p> | 6,652 | [
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<p>I know that if two air bubbles which are formed inside a liquid are somehow joined using something (say a small tube), then, as the bubble with the larger radius has less pressure and the one with the smaller radius has more air pressure, air will flow to the larger bubble from the smaller bubble as the excess pressure inside the smaller bubble is greater.</p>
<p>But will we be able to quantitatively calculate the time taken for this to happen?</p>
<p>If so then what is the relation connecting time and every other variable?</p> | 6,653 | [
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<p>I do not have much experience on this but if an atom has some electrons around nucleus and the atom itself it is moving at some speed does that affect the distribution of electrons around?</p>
<p>I am presuming that the interaction between the nucleus and electrons has a constant speed $c$. Anything I found so far is a calculation for interactions that presume an infinite speed. </p>
<p>As an argument I am thinking of relativistic Doppler effect that does not change proportional with $v/c$. So I am thinking that maybe the speed does affect the distribution and so that is why the difference in the emission energy.</p> | 6,654 | [
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<p>Is the classical doopler effect for light shift equal to $1-v/c$ exact or an approximation of a classical formula? I know that it is an approximation of the relativistic formula, but what was the corresponding classical formula? I ask this because in Einstein's On the Electrodynamics of moving bodies he derives $\sqrt\frac{1-v/c}{1+v/c}$ and notes that it is different from the classical case. I'm not exactly sure what formula he is comparing it to. </p> | 6,655 | [
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<p>It's easy for me to imagine that if we brake the front wheel then there is a chance that I'll flip.</p>
<p>On the other hand if I brake the back wheel, there is no way it'll happen no matter how fast I brake.</p>
<p>But whether I brake the front wheel or back wheel, the force I've added is a backward force at the bottom of the wheel.</p>
<p>So why the different outcome?</p> | 6,656 | [
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