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<p>The inspiration for this question is <a href="http://cooking.stackexchange.com/questions/17529/surface-tension-in-food">over on cooking.stackexchange</a>, asking more about actual measurements for commonly consumed liquids, but I'm interested more generally as well.</p>
<p>What determines the behavior of surface tension for solutions and mixtures with respect to concentration? Of course, I expect that the answer depends on the liquid, since different liquids have different causes of cohesive forces. I would be interested both in quantitative answers (very approximate/general, probably) and qualitative ones.</p>
<p>Additionally, what is the dependence of surface tension on temperature? Does that have any interaction with dependence on solution/mixture concentration?</p>
<p>(I know this question borders on chemistry, but there's no chemistry stackexchange, and besides, I'm sure at least some surface tension properties admit explanations from statistical mechanics!)</p> | 6,280 | [
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<p>The neutron decay is a spontaneous process. After isolating neutrons the mean lifetime is approx. 15 minutes. The real moment when the neutron decays is not affected by us. That's why, it is allowed to speak about <a href="https://en.wikipedia.org/wiki/Hidden_variable_theory" rel="nofollow">hidden parameters</a>?</p> | 6,281 | [
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<p>What is the difference between $\tau_{xy}$ and $\tau_{zy}$; because as far as i know the first character of subscript represents the direction to which the stress is perpendicular and other the actual direction.</p>
<p>So a vector perpendicular to $x$ along $y$ and another perpendicular to $z$ along $y$, shouldn't they be the same?</p> | 6,282 | [
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<p>Consider the product of two left Weyl spinors in the notation commonly found in supersymmetry,
\begin{equation}
\chi ^\alpha\eta_\alpha = \chi ^\alpha \epsilon _{ \alpha \beta } \eta ^\beta
\end{equation}
This is equal to,
\begin{equation}
\left( \begin{array}{c}
\chi ^\alpha \\
0
\end{array} \right) ^T\left( \begin{array}{cc}
\epsilon _{ \alpha \beta } & 0 \\
0 & \epsilon ^{ \dot{\alpha} \dot{\beta} }
\end{array} \right) \left( \begin{array}{c}
\eta ^\beta \\
0
\end{array} \right) = \bar{\eta} _L ^\ast \gamma _0 C \chi _L
\end{equation}
where I have used some common spinor identites and defined, $ \eta _L \equiv P _L \eta, \chi _L \equiv P _L \chi $ ($\eta $ and $ \chi$ are now four component spinors). I also use the defintion, $C \equiv i \gamma_0 \gamma _2 $. While I don't think anything is particularly wrong with this derivation, I have never seen a term like this in normal quantum field theory. It there a simpler way to reformulate this to correspond to common expression for such mass terms or is my uncomfort with this term due to my ignorance?</p> | 6,283 | [
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<p>I am trying to find out the <a href="http://en.wikipedia.org/wiki/Uninterruptible_power_supply" rel="nofollow">UPS</a> capacity in amp-hours for my HP UPS system.
I've already done some calculations based on the UPS information from the HP Power Manager software.</p>
<p><img src="http://i.stack.imgur.com/rdvd0.png" alt="HP UPS Parametars"></p>
<p>Bellow are my calculations but somehow I doubt them and I think I am making a mistake somewhere:</p>
<p>Output Power: <strong>1160W</strong><br>
Output Voltage: <strong>235V</strong><br>
Run time remaining: <strong>12min</strong> - Converted to hours that is <strong>0.2h</strong></p>
<p>First I am converting the W to A:<br>
1160W / 235V = <strong>4.936A</strong></p>
<p>Now to find the amp-hours for 12min that are specified in the run time remaining:</p>
<p><strong>4.936A * 0.2h = 0.987Ah</strong></p>
<p>Can someone more experienced in batteries, current and UPS Systems tell me if my calculations are correct?</p>
<p>I am not sure that I have taken the correct values into consideration since <strong>my calculations are based upon the output values from the UPS.</strong><br>
Also as a side note I must tell you that I am not very fond of current and all that stuff and I have only basic knowledge about amps, volts and watts from college.</p> | 6,284 | [
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<p>The hydrogen atom contains 1 proton and 1 electron. The radius of the proton is approximately 1.0 fm (femtometers), and the radius of the hydrogen atom is approximately 53 pm (picometers).</p> | 6,285 | [
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] |
<p>For an electron in its rest frame, we have an entropy
$$
S = \log 2,
$$
which comes from the 2 possible spin directions along z-axis. </p>
<p>If the measurement $S_z$ changes its state to $\left| + \right>$, the entropy goes to zero.</p>
<p>Does this violate the second law of thermodynamics?</p> | 6,286 | [
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<p>Pioneer space probe moving at a speed of $30km/s$.
Assuming its heading for Proxima Centauri, which is situated at $4.2ly$ from earth, calculate how long it would take to get there in years, to the nearest year?</p>
<p>Could you please help.</p> | 6,287 | [
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<p><img src="http://i.stack.imgur.com/MbcF9.gif" alt="enter image description here"></p>
<p>This is my opinion about what we will see. When the pipe arrive at the bar, we will be unable to see some part of it anymore (the pipe will absorb the light emitted by the bar), even if the pipe and the bar didn't appear to us superposed yet. We will not see the white background, because the bar is not transparent. So, we must see nothing (black), even if we know the bar is there. Am I right or wrong? </p> | 6,288 | [
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<p>This question is coming from someone who has very little experience with M-Theory but is intrigued by the AdS/CFT correspondence and is beginning to study it.</p>
<p>Why is the gauge/gravity duality discussed almost always in the context of anti-deSitter space? What is unique about it? What are the difficulties in studying it in Schwarzschild, deSitter, etc.? References to work done on the gauge/gravity duality in these more physical spacetimes would be much appreciated.</p> | 6,289 | [
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<p>I was recently watching a show that say we need at least 5 Higgs Boson to prove the existence of the dark matter because it will strengthen the concept of symmetry.</p>
<p>Why is that so? Because, I am not getting what it says.</p> | 6,290 | [
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<p>What is the Noether charge associated with Kahler invariance of <a href="http://en.wikipedia.org/wiki/Supergravity" rel="nofollow">supergravity</a> (SUGRA)? As the question is rather tangential to what I need to do, I have not tried explicitly calculating it myself, but I'm sure that I'm not the first one to wonder.</p> | 6,291 | [
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<p>Suppose I want to know what the universe looks like from the perspective of a frame of reference moving at $c$ relative to my current frame. As discussed at length in various other questions on this forum, from the perspective of the current established theory of special relativity, the notion of such a frame is more or less nonsense.$^{[1]}$</p>
<p>However...</p>
<p>Is it possible to modify the setting of special relativity, by adding dimensions to space-time, or any other hereto unobserved features, such that the restriction of the theory to our 4-D slice of space-time matches special relativity, and such that there is a meaningful way to describe the frame of a photon?</p>
<p>[1] In partiucular, the transformation we get by shoving $v=c$ into the usual formulae is not in the Lorentz group (it doesn't preserve volume of space-time and is not invertible).</p> | 6,292 | [
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<p>This question is an outgrowth of <a href="http://physics.stackexchange.com/questions/15402/regarding-voltage-and-emf">regarding voltage and emf</a> where @sb1 mentioned Faraday's law. However, Faraday's law as part of Maxwell's equations cannot account for the voltage measured between the rim and the axis of a Faraday generator because $\frac {\partial B} {\partial t} = 0$. It would've been a different story if the derivative were $\frac {dB} {dt} $ but it isn't. A palliative solution to this problem is given by invoking the Lorentz force. However, Lorentz force cannot be derived from Maxwell's equation while it must be if we are to consider Maxwell's equations truly describing electromagnetic phenomena. As is known, according to the scientific method, one only experimental fact is needed to be at odds with a theory for the whole theory to collapse. How do you reconcile the scientific method with the above problem?</p> | 6,293 | [
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<p>Electron as an example has a de Broglie wavelength and could diffract.
If it has a single wavelength the time extent of the particle's pulse duration would be infinite ..
If it carries a broadband will be finite in time .. my question is how is it determined the duration in time of the electron or it is assumed to be the classical diameter and what is its spectral content ?</p> | 6,294 | [
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<p>Just a quick check: If given a time-independent wavefunction of the form $$\psi(x) = e^{ikx}f(x)$$, where $f(x)$ any arbitrary function of $x$ but one can't factor out another $e^{i\alpha x}$, $\alpha\in\mathbb R$.</p>
<p>Could I then immediately conclude that $k^2= \frac{2mE}{\hbar^2}$? Is there a name for this quantity? It seems to creep up a lot.</p>
<p>Suppose the wavefunction is $$\psi(x) = e^{ikx}(\tanh{x}-ik)$$. Am I justified to conclude by inspection that there is no reflection (since there is no $Re^{-ikx}$ term)? What else can I conclude by inspection?</p>
<p>Thanks!</p> | 6,295 | [
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<p>Experimentally, I have seen how hooking up a battery to a simple circuit just with a high-resistance voltmeter raises the voltage reading (allegedly to a level equal to the EMF of the battery).</p>
<p>However, I find the explanation for why the reading rises, much less to an EMF, very unconvincing. We were told that the internal resistance and the necessary potential drop is ignored, because there is no current in the said circuit, hence why the voltmeter measures an EMF. How can this make sense? There clearly must be some current, albeit very little, flowing, for the high-resistance voltmeter to even have a reading, and that little current will still experience resistive forces from the internal resistance of the cell - so the EMF should not be attainable. Or is there a mechanism by which, when there is very little current, resistors are ignored, hence no work has to be done to traverse them?</p>
<p>Clearly I am wrong, as experimentally I saw the voltage rise in that super simple cell. My point of view suggests that there shouldn't be a difference between the reading in said circuit and the potential difference in a circuit consisting of 3 resistors (the voltmeter in this case measures the drop between these 3 resistors, note there is no other significant source of resistance other than the internal resistance). Really, in my theoretical understanding they should produce an equal reading, but they don't.</p>
<p>So, to be honest, not only do I believe that the reading we saw shouldn't have been the EMF, but not even any different from the reading in a normal circuit, as described (the latter belief clearly conflicts with reality). </p>
<p>I an eager to know what I am thinking wrongly about. Please ask if I can help clarify anything! </p>
<p>Thank you very much :)! </p> | 6,296 | [
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<p>We always assume that all the voltage, in no matter what type of (basic, I guess) circuit we are dealing with, is used up. I can see why this is true. Imagine a circuit with low resistance - and correct me if I am wrong, but from electrostatics, we know that an electric field, similar to magnetic fields, accelerates charges. </p>
<p>Now mustn't it be that some charges arrive at the end of the circuit (into the positive charge reservoir) with some velocity, higher than that with which they began. </p>
<p>Essentially, if seems to me what we always assume that the electrons always do the maximum that they could, no matter what the conditions. </p>
<p>Is it my misunderstanding that such an assumption exists or are there some ideas I am completely oblivious of? </p>
<p>Please ask if you want any clarifications.</p> | 6,297 | [
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<p>Suppose a man falls into very cold water and gets their foot stuck under a heavy rock. Fortunately, his head is above water and someone is able to call for help. The paramedics want to keep him warm while they work on freeing his foot. They put a hat on his head. Should they also wrap him in a blanket?</p> | 6,298 | [
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<p>Where can a good treatment of the <a href="http://en.wikipedia.org/wiki/Adiabatic_theorem#Diabatic_passage" rel="nofollow">'sudden' perturbation approximation</a> be found?</p>
<p>A lot of quantum mechanics books have very brief discussions of it but I want to see it in some detail and preferably with as many examples as possible. </p>
<p>Is there a book, paper, or some other place that details this approximation?</p> | 6,299 | [
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<p>I'll try to be clear: example: If you send the ISS far enough for it not to undergo the Earth's gravity anymore, then you turn it and the—sleeping—astronauts in it upside down, when they wake up, will they know/feel that they're not the right way up? How?</p> | 6,300 | [
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<p>How can one show that $\int_{-\infty}^{\infty}\psi^*(x)(d/dx+\tanh x)(-d/dx+\tanh x)\psi(x) dx=\int_{-\infty}^{\infty} |(d/dx+\tanh x)\psi(x)|^2 dx$, where $\psi$ is normalized? </p> | 6,301 | [
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<p>I know that parallel light beams hitting a parabola will be focused at the focus of the parabola (<code>f = 1/4a</code>) and a light source at the focus of the parabola will produce parallel light. What will happen if the light was not parallel but came from a light source shorter then the focus of the parabola and at an angle to the axis of symmetry? More general how will dispersement of the light from the parabola be affected with the light source at different angles and lengths from the parabola.</p> | 6,302 | [
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<p>A classic example for the method of images is the following, quoted from Griffiths's Introduction to Electrodynamics, page 121:</p>
<p>"Suppose a point charge $q$ is held a distance $d$ above an infinite grounded conducting plane. Question: What is the potential in the region above the plane?" </p>
<p>Griffiths continued on solving the example using the method of images setting V=0 on the plane as one of the boundary conditions saying "since the conducting plane is grounded".</p>
<p>Now, of course there will be an induced surface charge density. My question is, how can this be since the plane is grounded? </p>
<p>Does the word grounded have different meanings? sometimes it means not charged and the others it means the potential there is 0?</p> | 6,303 | [
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<p>Consider two stationary charges, one positive the other negative. Their potential energy is clearly negative. So you would expect that the energy density of the associated electric field would also be negative. But it isn’t. It’s the square of the electric field and therefore positive. Why isn’t the energy density negative like the potential energy?</p> | 6,304 | [
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<p>Reading an interesting article on a recent ArXiv paper by Carlo Rovelli and Francesca Vidotto on so-called Planck stars, at</p>
<p><a href="https://medium.com/the-physics-arxiv-blog/6cf7ec0ed28b" rel="nofollow">https://medium.com/the-physics-arxiv-blog/6cf7ec0ed28b</a></p>
<p>I was struck by the observation that time travels so slow "at" a black hole singularity of the structure these authors propose that light, assuming it was unimpeded, barely has time to cross it.</p>
<p>Couldn't the same observation be made generally, within the scope of General Relativity, i.e. without having to assume the existence of Planck stars (or at least mass concentrations whose lifetime was "out of sync" with the black hole so to speak), to conclude that despite its unimaginably colossal lifetime to an outside observer (10^70 years or more), a black hole was "internally" at its deepest level no more than a split-second bounce?</p>
<p>From that intrinsic standpoint a singularity would (literally) have no time to form, and one could even argue that being in effect "frozen" (albeit inaccessible) from an external standpoint might be a means of somehow preserving all its information.</p> | 220 | [
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<p>I understand the mechanism how <a href="http://en.wikipedia.org/wiki/CHSH_inequality" rel="nofollow">CHSH Inequality</a> works. One thing bugs me is why $\pi/8$. </p>
<p>I can also take $\pi/100$ for example and $\cos^2(\pi/100)> \cos^2(\pi/8)$ so much better probability and it doesn't contradict with the explanation of setting up states to suit $\pi/100$. </p>
<p>there is nothing special about $\pi/100$ infact i am guessing i can have the angle </p>
<p>0 < angle < $\pi/4$ but we want to get as close to zero as possible to get the highest probability </p>
<p>is this correct if not why </p> | 6,305 | [
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<p>Does reactive force require the two force involved have to have two medium for reactive force to occur?</p>
<p>I know the fuel-thruster is working on vacuum space, but we human could not use arm to swim in space?</p>
<p>For example, two baseball hitting together have two medium</p> | 6,306 | [
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<p>I have some confusion between with resolving the following situation.</p>
<p>I know that no measurable quantity can have a value of infinity. For example, I just wrote something out, but clearly this doesn't work, since infinity is not really a number and thus measurable entities can't be quantified as being of infinite amount.</p>
<blockquote>
<p>I own an infinite amount of coins scattered on the ground. I give you
all of them so I have none left and you have an infinite amount. </p>
<p>With the same infinite amount of coins, you then give me all coins
showing heads, and keep all coins that are tails. Now we both have an
infinite amount of coins. </p>
<p>I then keep £100 worth of coins for myself and give the rest back to
you. </p>
<p>Does that then mean that you have made a net gain of coins, or do you
have the same amount of coins as you had before?</p>
</blockquote>
<p>I can understand that the above doesn't make sense, however, what if you were to use the same concept with time. </p>
<p>For example, if I ask this question:</p>
<blockquote>
<p>Is time infinite?</p>
</blockquote>
<p>I can't understand how the answer to that can be either <code>Yes</code> or <code>No</code>. Both answers must be wrong. </p>
<p>If you respond saying <code>yes</code>, and say that time is in fact infinite, then it would mean that up until the writing of this question, that an infinite amount of time has past, and that an infinite amount of time is still yet to pass. However, the fact that I am writing this post now, must mean that time is not infinite, because how can an infinite amount of time have already past, if I am writing this now?</p>
<p>Put simply, "now" cannot exist, if time is infinite. </p>
<p>Equally, if you were to respond and say "no" time is not infinite, then that would mean that the big bang started time, but then that must also mean that time needs to stop at some point. Otherwise, time would be again be infinite, meaning that "now" could never exist.</p>
<p>(Someone feel free to change the title of this question to something more suitable). </p> | 6,307 | [
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<p>I have a <a href="http://en.wikipedia.org/wiki/Hammock" rel="nofollow">hammock</a> that I want to hang using a tree on one end and a wooden post set in a bucket of cement on the other end.</p>
<p>How would I determine how heavy the cement needs to be so that it would support the weight of a 250lbs person in the hammock?</p>
<p>Any ideas would be appreciated.</p> | 6,308 | [
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<p>We have the famous equation $E = mc^2$, and we also believe that matter is made of particles.</p>
<p>Then, What is the energy made of? If the two are interchangeable, there must be some common building block to both for sure. Isn't it?</p>
<p>If energy is made of "Nothing", how could it be converted to matter?</p> | 6,309 | [
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<p>I am reviewing some old material I learned years ago and am having trouble figuring this one out. Can somebody confirm that I have done my math correctly, and tell me how I can recover the field of view from these parameters?</p>
<p>I have a $3.6$(height) by $4.8$(width) mm sensor, which displays as $640\ by\ 480$ pixels. I take an image of some item that I want to be 50px large in my image. It is $10 m$ away, and $10 cm$ tall in real life.</p>
<p>I compute the size of a pixel on the sensor as $\frac{3.6}{640}\ by\ \frac{4.8}{480} mm$ to get $0.006\ by\ 0.01 mm$.</p>
<p>I compute the magnification by $\frac{image\_size}{actual\_size}$, so I compute that the image size of $50px$ with a pixel height of $0.006mm$ takes up $0.3 mm$ of the sensor. Thus, magnification is $\frac{0.3}{100} = 0.003 mm$.</p>
<p>Magnification can also be viewed as $m = \frac{f}{u - f}$, so $0.003 = \frac{f}{100 mm - f}$, which will give us $f = 0.299 mm$. </p>
<p>From here, I know that it's possible to calculate the field of view, but how can I do it? I imagine the equation will use the image sensor size and the focal length.</p>
<p>Thanks!</p> | 6,310 | [
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<p>Yesterday I asked whether the Schroedinger Equation could possibly be nonlinear, after reviewing the answers and material given to me in that thread I feel like my question were adequately answered.</p>
<p>However could there still be nonlinear dynamics underneath quantum mechanics that could potentially explain the "weirdness" of quantum mechanics?
I know of atleast one serious physicist who is developing an approach in this direction, Tim Palmer with his <a href="http://www.physorg.com/news169725980.html">Invariant Set Postulate</a>.</p>
<p>Just like the Liouville equation is linear, but there are "deeper" nonlinear dynamics beneath it, couldn't the Schroedinger Equation be the same?
This is atleast one of Tim Palmers motivations for developing his approach and is also what Dirac said way back in the days.</p>
<p>I suspect this is what David Zaslavsky meant yesterday when he responded to my other thread (Could the schroedinger equation be nonlinear) when he said: </p>
<blockquote>
<p>That being said, there's no reason that the "true" theory underlying QM would have to be linear. In fact, for exactly the reason you pointed out (i.e. that general relativity is nonlinear), it's commonly believed that we will need some kind of nonlinear theory to properly explain the universe at its most basic level.</p>
</blockquote>
<p>Any views / opinions / thoughts / theories ?</p> | 6,311 | [
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<p>I can't solve a problem:</p>
<p>$ A= 0.5 (ms)^{-1}$, $ x_0 = 0.5 m $, $v(t)= A \cdot x^2 $, I have to compute the position at $t=3$ ($x_0$ is the initial position). </p>
<p>So my guess is that I should be able to compute the $x(t)$ formula by integrating $v(t)$: </p>
<p>$$ \int^t_0 A \cdot x^2 dt = x_0 + A \cdot x^2 \cdot t $$</p>
<p>So I get: </p>
<p>$$ x^2 \cdot At -x + x_0 = 0 $$</p>
<p>Which is a 2nd grade equation with a negative discriminant: </p>
<p>$$ \Delta(x) = (-1)^2 - 4 \cdot Atx_0 = 1 -4 \cdot 0.5 \cdot 3 \cdot 0.5 = 1-3=-2$$</p>
<p>My book includes just the solution, but it doesn't say how to get it. The solution is: </p>
<p>$$ x(t) = \frac{x_0}{1 - x_0At} $$ </p>
<p>If I study it I get: </p>
<p>$$ x = \frac{x_0}{1 - x_0At} $$
$$ x \cdot \big( 1 - x_0At \big) = x_0 $$
$$ xx_0 \cdot At -x + x_0 =0 $$</p>
<p>Which is different from the one I got ($x^2 \cdot At -x + x_0 = 0$).</p> | 6,312 | [
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<p>The sun pulls on the moon with a force that is more than twice the magnitude of the force with which the earth attracts the moon. Why, then, doesn’t the sun take the moon away from the earth?</p> | 6,313 | [
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<p>How can I see, using group theoretic arguments, that a the quantum of a gravitational wave has spin 2? </p>
<p>How can one show that it is described by a 5 dimensional representation of $SO(3)$?</p>
<p>I know the argument from Carroll's book on General Relativity: from looking at the perturbation on the geodesics followed by a perfect fluid, which are invariant under 180 degrees. But that doesn't seems very convincing.</p> | 6,314 | [
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<p>I have derived the energy conservation equation:</p>
<p>\begin{equation}
\frac{\partial}{\partial t} \left [ \frac{1}{2} \rho v^2 + \varepsilon + \rho \phi \right ] + \frac{\partial}{\partial x_j} \left [ \frac{1}{2} \rho v^2 v_j + \rho h v_j + \rho \phi v_j \right ]=0
\end{equation}</p>
<p>where $\varepsilon$ is internal energy and $\rho \phi$ is the gravitational energy.
I was trying to derive the <a href="http://en.wikipedia.org/wiki/Bernoulli%27s_principle" rel="nofollow">Bernoulli equation</a> from the above equation for time independent flow. It is not clear to me which term is Bernoulli equation term. How can derive the Bernoulli equation? </p> | 6,315 | [
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<p>We have 2 EPR experiments running in parallel, with Alice having one leg of each (a1,a2) and Bob the other leg of each (b1,b2). Thus (a1,b1) are anticorrelated, as are (a2,b2). Thus also (a1,a2) are uncorrelated as are (b1,b2). Now Alice locally entangles (a1,a2), and Bob measures b1 and b2. After repeating the entire experiment (including setting up the initial entanglements) many times, does Bob see consistent correlation or anticorrelation between his measured b1 and b2?</p>
<p>How Alice accomplishes this final entanglement (a1,a2) is either via entanglement swapping, or via the method described in Yurke and Stoler, Phys. Rev. A46, 2229 (1992): "Bell’s-inequality experiments using independent-particle sources".</p>
<p>Put another way, it's clear that b1 and b2 will show no correlation if Alice does not entangle (a1,a2), since the two EPR experiments are independent. Will this situation change for Bob as a result of Alice's entanglement of (a1,a2)?</p> | 6,316 | [
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<p>I'm reading the section on scattering in Goldstein's Classical Mechanics, and I have a rather basic question about this. </p>
<p>It says that scattering in the laboratory is a two-body problem because of the recoil of the scatterer. Therefore, we convert the obtained data into center of mass coordinates in order to find the true scattering angle, the angle that we would get if the scatterer didn't recoil. However, I'm having a hard time understanding what exactly this center of mass system is. The figure (3.25) below shows the path of two particles moving towards each other, but it looks like it is simply the laboratory problem shown in the frame of reference where the center of mass is not moving. </p>
<p>My question: It still looks like a two-body problem to me, especially since the scatterer is deviating from its path. How does this simply the situation? Figure 3.25 still doesn't show a situation where the scatterer's position is fixed. Neither does figure 3.24.</p>
<p><img src="http://i.stack.imgur.com/9OSm9.jpg" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/Fl79e.jpg" alt="enter image description here"></p> | 6,317 | [
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<p>Why is the magnetic flux not quantized in a standard <a href="http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect" rel="nofollow">Aharonov-Bohm</a> (infinite) solenoid setup, whereas in a superconductor setting, flux is quantized?</p> | 6,318 | [
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<p>I have started reading the book Connectivity and Superconductivity which gives an introduction to the ideas of de Gennes-Alexander theory. My question is: how is this theory regarded experimentally? Besides the sophisticated math approach,does it give good experimental results?</p> | 6,319 | [
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<p>[<b>Update:</b> Thanks, everyone, for the wonderful replies! I learned something extremely interesting and relevant (namely, the basic way decoherence works in QFT), even though it wasn't what I thought I wanted to know when I asked the question. Partly inspired by wolfgang's answer below, I just <a href="http://physics.stackexchange.com/questions/35118/can-the-montevideo-interpretation-of-quantum-mechanics-do-what-it-claims">asked a new question</a> about Gambini et al.'s "Montevideo interpretation," which (if it worked as claimed) would provide a completely different sort of "gravitational decoherence."]</p>
<p>This question is about <i>very</i> speculative technology, but it seems well-defined, and it's hard to imagine that physics.SE folks would have nothing of interest to say about it.</p>
<p>For what follows, I'll assume that whatever the right quantum theory of gravity is, it's perfectly unitary, so that there's no problem at all creating superpositions over different configurations of the gravitational metric. I'll also assume that we live in de Sitter space.</p>
<p>Suppose someone creates a superposition of the form</p>
<p>(1) $\frac{\left|L\right\rangle+\left|R\right\rangle}{\sqrt{2}},$</p>
<p>where |L> represents a large mass on the left side of a box, and |R> represents that same mass on the right side of the box. And suppose this mass is large enough that the |L> and |R> states couple "detectably differently" to the gravitational field (but on the other hand, that all possible sources of decoherence <i>other</i> than gravity have been removed). Then by our assumptions, we ought to get <i>gravity-induced decoherence</i>. That is, the |L> state will get entangled with one "sphere of gravitational influence" spreading outwards from the box at the speed of light, and the |R> state will get entangled with a <i>different</i> such sphere, with the result being that someone who measures only the box will see just the mixed state</p>
<p>(2) $\frac{\left|L\right\rangle\left\langle L\right|+\left|R\right\rangle\left\langle R\right|}{2}.$</p>
<p>My question is now the following:</p>
<p><b>Is there any conceivable technology, consistent with known physics (and with our assumption of a dS space), that could reverse the decoherence and return the mixed state (2) to the pure state (1)? If so, how might it work? For example: if we'd had sufficient foresight, could we have surrounded the solar system with "gravity mirrors," which would reflect the outgoing spheres of gravitational influence back to the box from which they'd originated? Are exotic physical assumptions (like negative-energy matter) needed to make such mirrors work?</b></p>
<p>The motivation, of course, is that if there's <i>no</i> such technology, then at least in dS space, we'd seem to have a phenomenon that we could justifiably call "true, in-principle irreversible decoherence," <i>without</i> having to postulate any Penrose-like "objective reduction" process, or indeed any new physics whatsoever. (And yes, I'm well aware that the AdS/CFT correspondence strongly suggests that this phenomenon, if it existed, would be specific to dS space and wouldn't work in AdS.)</p>
<p>[Note: I was surprised that I couldn't find anyone asking this before, since whatever the answer, it must have occurred to lots of people! Vaguely-related questions: <a href="http://physics.stackexchange.com/questions/18595/is-decoherence-even-possible-in-anti-de-sitter-space">Is decoherence even possible in anti de Sitter space?</a>, <a href="http://physics.stackexchange.com/questions/24354/do-black-holes-play-a-role-in-quantum-decoherence">Do black holes play a role in quantum decoherence?</a>]</p> | 6,320 | [
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<p>The kinetic energy of a particle is a periodic function in time. Does it imply that the particle is in a conservative force field and there are no dissipative forces acting on it at any instance of time ?</p>
<p><strong>EDIT</strong> (in view of comment by Willie)</p>
<p>Please consider the question as "Is the force acting on the particle conservative ?" Also consider the kinetic energy to be periodic with non zero period.</p> | 6,321 | [
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<p><img src="http://i.stack.imgur.com/L5thM.png" alt="enter image description here"></p>
<p>The image above shows the distribution of the surface charge in a current carrying wire. The surface charges distributes themselves to make sure the field inside the wire is always perpendicular to the surface of the wire. </p>
<p>Why is exactly half of the wire covered in negative surface charges and the other half with positive surface charges? I've noticed this in every surface charge distribution I've seen. </p> | 6,322 | [
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] |
<p>COG: The lower the center of gravity, the more stable and object is.
Rotational Inertia: The farther the concentration of mass from the defined axis of rotation, the more resistance the object has to movement.</p>
<p>I'm quite confused between these two statements. </p> | 6,323 | [
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] |
<p>I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate calculations.</p>
<p>Regarding this I have a few questions:</p>
<ol>
<li>Why is it called a symmetry if it is not a symmetry? what about Noether theorem in this case? and the gauge groups U(1)...etc?</li>
<li>Does that mean, in principle, that one can gauge any theory (just by introducing the proper fake degrees of freedom)?</li>
<li>Are there analogs or other examples to this idea, of introducing fake degrees of freedom to facilitate the calculations or to build interactions, in classical physics? Is it like introducing the fictitious force if one insists on using Newton's 2nd law in a noninertial frame of reference? </li>
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<p>So, the quantum path integral is a generalization of the classical principle of least action- but here we know that all paths contribute something finite to the probability density. What confuses me is that this doesn't seem to involve the quantization of energy (action) at all. How does this come into play? Is it a separate assumption, only coming into play when we worry about the non-commutativity of certain operators?</p> | 6,325 | [
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<p>I have a question in Srednicki's QFT textbook.
In order to compute the vacuum to vacuum transition amplitude given by :
$$\left \langle 0|0 \right \rangle_{J}~=~\int \left [ d\varphi \right ]e^{i\int dt ~L\left ( \varphi ,\partial _{\mu }\varphi \right )},$$</p>
<p>one has to Fourier transform the field to the momentum space </p>
<p>$$\varphi \left ( x \right )~=~ \int d^{4}k~e^{ikx}\phi \left ( k \right ).$$</p>
<p>But what is the motivation to do so? And what other methods that could be used to compute $\left \langle 0|0 \right \rangle_{J}$ in the path integral formalism? I feel that although I understand the derivation, many steps are done in many places in this book but I don't understand what are the motivations for taking them.</p> | 6,326 | [
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<p>I have been reading the stackexchange questions on enhanced symmetries in string theory, the Leech lattice, monstrous moonshine, etc. , and I have a question to ask.</p>
<p>An astute commentator pointed out with enhanced symmetries, massless vector bosons have to couple in the Yang-Mills fashion. Only if the massless vectors come in a Lie algebra will that be possible.</p>
<p>Imagine bosonic string theory. Compactify 24 spatial dimensions over the Leech lattice or odd Leech lattice. With respect to the uncompactified dimensions (one spatial and one timelike), we get 196560 massless vector bosons, but they can't be part of any Lie algebra. But that's OK because massless vector bosons in 2 dimensions have zero norm.</p>
<p>Let's try again. Compactify 23 spatial dimensions over the shorter Leech lattice. There are 2 spatial and one timelike uncompactified dimensions. Over this space, we have 4600 massless vector bosons, but they're not part of any Lie algebra either. But that's also OK because massless vector bosons in 3 dimensions are physically indistinguishable from massless scalar bosons. The reason for this is there is no helicity.</p>
<p>If we try to find a similar example over at least 4 uncompactified dimensions, where massless vector bosons exist for certain and aren't equivalent to anything else, we discover all unimodular lattices in 22 dimensions or less are part of a root system. Thus, we always have a Lie algebra.</p>
<p>What is the magical mechanism in string theory enforcing this sort of self-consistency? Is string theory only self-consistent because of accidental coincidences?</p> | 6,327 | [
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<p>See the pictures below. A pair of sunglasses I recently purchased has the polarization axis in one lens offset about 20 degrees (by eyeball estimation) from the other. I don't have much experience with other polarized sunglasses, but this seems very obviously wrong to me. And it's very noticeable while wearing the glasses. When facing into glare from certain directions, one eye filters our considerably more glare than the other, which is very distracting and uncomfortable.</p>
<p>I can see arguments for making the polarization axis angle just about anything (though horizontal or vertical seem most logical), but what I cannot see is any argument for having it different in each lens on the same pair of glasses.</p>
<p>Thoughts?</p>
<p><img src="http://i.stack.imgur.com/TIu4z.jpg" alt="enter image description here">
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<p>The mass of an elementary particle in string theory is related with the way the string vibrates. The more frantically a string vibrates the more energy it posses and hence the more massive it is. My question is how is the electric charge of a particle is described in S.T. How is the opposite charges described? More specifically, I would like to know how a particle and its antiparticle are conceptualized?</p> | 6,329 | [
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<p>I'd like to make a comparison of prices, availability and properties of semiconductor substrate layers like Si, Ge, GaP, AlN etc. I wonder what are the problems related to getting such data, what are the leading companies that sell such things, what's the quality, waiting time and so on. I'm not going to buy one, It's just a little research, that's why I ask here and not the companies directly. Your own experiences (what problems you've encountered and maybe some sample prices or company names?) are much appreciated.</p> | 6,330 | [
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<p>I thought that it was valid for very low temperatures since for it to be valid I think that it is necessary to be in the non-degeneracy condition, which requires $E_G >> k_B T$ (with $E_G$ being the energy gap), that it is satisfied at very low temperatures... But maybe at too low temperatures the non-degeneracy condition breaks for some other reason. And the Ashcroft and Mermin's book only helps to increase my confusion! Could someone help me figuring it out, please? Thanks!</p> | 6,331 | [
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<p>I've just finished a Classical Mechanics course, and looking back on it some things are not quite clear. In the first half we covered the Lagrangian formalism, which I thought was pretty cool. I specially appreciated the freedom you have when choosing coordinates, and the fact that you can basically ignore constraint forces. Of course, most simple situations you can solve using good old $F=ma$, but for more complicated stuff the whole formalism comes in pretty handy.</p>
<p>Then in the second half we switched to Hamiltonian mechanics, and that's where I began to lose sight of why we were doing things the way we were. I don't have any problem understanding the Hamiltonian, or Hamilton's equations, or the Hamilton-Jacobi equation, or what have you. My issue is that I don't understand why would someone bother developing all this to do the same things you did before but in a different way. In fact, in most cases you need to start with a Lagrangian and get the momenta from $p = \frac{\partial L}{\partial \dot{q}}$, and the Hamiltonian from $H = \sum \dot{q_i}p_i - L$. But if you already have the Lagrangian, why not just solve the Euler-Lagrange equations?</p>
<p>I guess maybe there are interesting uses of the Hamiltion formalism and we just didn't do a whole lot of examples (it was the harmonic oscillator the whole way, pretty much). I've also heard that it allows a somewhat smooth transition into quantum mechanics. We did work out a way to get Schrödinger's equation doing stuff with the action. But still something's not clicking.</p>
<p>My questions are the following: Why do people use the Hamiltonian formalism? Is it better for theoretical work? Are there problems that are more easily solved using Hamilton's mechanics instead of Lagrange's? What are some examples of that?</p> | 6,332 | [
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<p>I'm not a physicist but I'm interested in <a href="http://en.wikipedia.org/wiki/Theory_of_everything" rel="nofollow">unified theories</a>, and I do not know how to start learning about it. What would be a good book to read to start learning about this topic?</p> | 726 | [
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<p>If I had a piece of metal and i wanted it to be negatively charged.
How can I do that?</p> | 835 | [
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<p>Is it true that all static solutions in GR are also spherically symmetric? Is there a proof of this?</p>
<p>Similarly, are all stationary solutions axisymmetric? </p> | 6,333 | [
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<p>i have an incident plane wave and a dipole, consider that plane wave incident on dipole. at this moment what happen for dipole ? we know that after incident of plane wave on dipole, the radiation have occurred, and i want derive the <strong>phase difference between radiation field and incident plane wave field</strong> ?
please introduce me a reference </p> | 6,334 | [
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<p>Why Magnifying glass(convex lens) produces heat when placed in front of sun? </p> | 6,335 | [
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<p>The problem asks me to find the density of gas in a cylinder of radius $R$ and length $l$ rotating about its axis with angular velocity $ω$, there being a total of $N$ molecules in the cylinder.</p>
<p>What I have done is shown as following:</p>
<p>I choose to look this scenario in a static frame with the cylinder, which is rotating at an unchanging angular speed $ω$. Then we can consider the field is a centrifugal field.</p>
<p>Thus the energy of a particle can be written as</p>
<p>$$E = E_0 - \frac{1}{2}m\omega^2 r^2\tag{1}$$</p>
<p>I haven't determined $E_0$ yet as I'm not sure about the thermal energy of the particle and the energy caused by the centrifugal field differs with the choosing of zero potential point.</p>
<p>After that, I wrote the probability as</p>
<p>$$\mathrm{d}P = \frac{\rho \mathrm{d}V}{N} = \frac{\rho \cdot 2\pi r\mathrm{d}r\cdot l}{N}\tag{2}$$</p>
<p>where $\rho \mathrm{d}V$ is what I want to find.</p>
<p>My goal is to convert all $r$ and $\mathrm{d}r$ into $E$ and $\mathrm{d}E$ and finally compare it with Boltzmann distribution</p>
<p>$$P(E)=C\cdot e^{-E/kT}\tag{3}$$</p>
<p>where $C$ is a constant.</p>
<p>However, I have met with some problems doing this.</p>
<p>From (1), it can be derived</p>
<p>$$dE=-m\omega^2 r dr\tag{4}$$</p>
<p>After I plug this into (2), I find $P(E)$ in $\mathrm{d}P=P(E)\mathrm{d}E$ is always negative. Thus is cannot be compared with the Boltzmann distribution.</p>
<p>How can I fix this?</p> | 6,336 | [
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<p>Let's say you have a traffic light with the well known red, yellow, and green tinted glasses. </p>
<ul>
<li>Setup 1: Each glass has a white light bulb behind it.</li>
<li>Setup 2: Each glass has a colored bulb behind it which matches the tint on the glass. So there is a red light behind the red glass, a yellow light behind the yellow glass, and a green light behind the green glass.</li>
</ul>
<p>Assuming all the light bulbs -white and colored- have the same power specs, which setup would appear to be brighter to the human eye?</p> | 6,337 | [
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<p>I understand that a reversible computer does not dissipate heat through the Landauer's principle whilst running - the memory state at all times is a bijective function of the state at any other time.</p>
<p>However, I have been thinking about what happens when a reversible computer <em>initializes</em>. Consider the state of the physical system that the memory is built from just before power up and initialization. By dint of the reversibility of underlying microscopic physical laws, this state stay encoded in the overall system's state when it is effectively "wiped out" as the computer initialized and replaces it with a state representing the initialized memory (set to, say, all noughts). </p>
<p>So it seems to me that if $M$ bits is the maximum memory a reversible algorithm will need to call on throughout its working, by the reasoning of <a href="http://en.wikipedia.org/wiki/Landauer%27s_principle" rel="nofollow">Landauer's principle</a>, ultimately we shall need
do work $M\, k\,T\,\log 2$ to "throw the excess entropy out of the initialized system".</p>
<p><em><strong>Question 1: Is my reasoning so far right? If not, please say why.</em></strong></p>
<p>Now, specializing to quantum computers, this seems to imply some enormous initialization energy figures. Suppose we have a system with $N$ qubits, so the quantum state space has $2^N$ basis states. Suppose further that, for the sake of argument, the physics and engineering of the system is such that the system state throughout the running of the system only assumes "digitized" superpositions, $i.e.$ sums of the form:</p>
<p>$$\frac{1}{\sqrt{\cal N}}\sum_{j\in 1\cdots 2^N} x_j \,\left|\left.p_{1,j},p_{2,j},\cdots\right>\right.$$</p>
<p>where $x_j, \;p_{k,j}\in{0,1}$ and ${\cal N}$ the appropriate normalization. To encode the beginning state that is wiped out at power up and initialization, it seems to me that the Landauer-principle-behested work needed is $2^N \,k\,T\,\log 2$. This figure reaches 6 000kg of energy (about <a href="http://en.wikipedia.org/wiki/World_energy_consumption" rel="nofollow">humanity's yearly energy consumption</a>) at around 140 qubits, assuming we build our computer in deep space to take advantage of, say, 10K system working temperature.</p>
<p><em><strong>Question 2: Given that we could build a quantum computer with 140 qubits in "digital" superpositons as above, do we indeed need such initialization energies?</em></strong></p>
<p>One can see where arguments like this might go. For example, Paul Davies thinks that similar complexity calculations limit the lower size of future quantum computers because their complexity (information content) will have to respect the <a href="http://en.wikipedia.org/wiki/Bekenstein_bound" rel="nofollow">Bekestein Bound</a>. P.C.W. Davies, "The implications of a holographic universe for quantum
information science and the nature of physical law", <em>Fluctuation and Noise Lett</em> <strong>7</strong>, no. 04, 2007 (see also <a href="http://arxiv.org/abs/quantph/0703041" rel="nofollow">http://arxiv.org/abs/quantph/0703041</a>)</p>
<p>Davies points out that it is the Kolmogorov complexity that will be relevant, and so takes this as an indication that only certain "small" subspaces of the full quantum space spanned by a high number of qubits will be accessible by real quantum computers. Likewise, in my example, I assumed this kind of limitation to be the "digitization" of the superposition weights, but I assumed that all of the qubits could be superposed independently. Maybe there would be needfully be correlations between the superpositions co-efficients in real quantum computers. </p>
<p>I think we would hit the Landauer constraint as I reason likewise, but at a considerably lower number of qubits. </p>
<p><strong>Last Question: Am I applying Landauer's principle to the quantum computer in the right way? Why do my arguments fail if they do?*</strong></p> | 6,338 | [
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<p>Without reducing the energy more than necessary due to the frequency decrease? And if this happens/works, is there an index of such materials and their optic properties?</p> | 6,339 | [
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] |
<p>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 $h$. </p>
<p>Several articles lately suggest this is not true.</p>
<p>Today in <a href="http://physicsworld.com/cws/article/news/2013/nov/01/uncertainty-reigns-over-heisenbergs-measurement-analogy" rel="nofollow">Physicsworld.com</a></p>
<blockquote>
<p>Looking at the position and momentum of spin-polarized neutrons, they found that, as Ozawa predicted, error and disturbance still involve a trade-off but with a product that can be smaller than Heisenberg's limit.</p>
</blockquote>
<p>and earlier work in <a href="http://physicsworld.com/cws/article/indepth/2013/mar/07/in-praise-of-weakness#comments" rel="nofollow">Toronto, Canada</a></p>
<blockquote>
<p>Aephraim Steinberg and colleagues at the University of Toronto conducted an optical test of Ozawa's relationship, which also seemed to confirm his prediction. Ozawa has since collaborated with researchers at Tohoku University in another optical study, with the same result.</p>
</blockquote>
<p>Can we safely throw out the Heisenberg uncertainty principle and start to view physics with more certainty?</p> | 6,340 | [
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<p>The fundamental question is</p>
<blockquote>
<p>Why is Hall conductance quantized?</p>
</blockquote>
<p>Let's start with the Hall bar, a 2D metal bar subject to a strong perpendicular magnetic field $B_0$. Let current $I$ flow in the x-direction, then the y-direction develops a voltage $V_H$. The Hall conductance is $\sigma_H = I/V_H$ <img src="http://i.stack.imgur.com/0bhnE.gif" alt="Hall bar (http://members.home.nl/skoric/quantum/setup.gif)"> </p>
<blockquote>
<p>To make Laughlin's charge pump, how should we wrap the Hall bar? Identify the left and right, or top and bottom sides?</p>
</blockquote>
<p>Based on my understanding, we should paste top and bottom side together. (correct? Figure 1. left of the Paper maybe a little confusing.)</p>
<p>Laughlin assumes the Fermi level is in the middle of the gap, so that the ring is an insulator. But the changing flux will induce an current by taking "adiabatic derivative" of total energy w/r flux
$$I = c\frac{\partial U}{\partial \Phi}$$
which flows in y-direction and where $c$ is speed of light.</p>
<p>Following Laughlin's calculations, as one threads one flux quantum, there will be $p$ (number of filled Landau levels) electrons transported. Then
$$U=peV$$ where $V$ is the potential difference of two edges. From the current formula, we find the quantized Hall conductance.</p>
<p>The heart of the problem is </p>
<blockquote>
<p>What is an adiabatic derivative? Why is ${\bf j} = \partial {\cal H}/\partial {\bf A}$ valid?</p>
</blockquote> | 6,341 | [
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<p>I know Fermi's Golden Rule in the form</p>
<p>$$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$</p>
<p>where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition matrix elements.</p>
<p>I'm struggling to do a derivation based on the density of states. I know that under certain circumstances it's a good approximation to replace $\sum_f$ with $\int_F \rho(E_f) \textrm{d}E_f$ to calculate the transition probability, for some energy range $F$. </p>
<p>Doing this calculation I obtain</p>
<p>$$\Gamma_{fi} ~=~ \int \rho(E_f) \frac{2\pi}{\hbar}\delta (E_f - E_i) |M_{fi}|^2\textrm{d}E_f.$$</p>
<p>Now assuming that the $M_{fi}$ are constant in the energy range under the integral we get</p>
<p>$$\Gamma_{fi} ~=~ \rho(E_i) \frac{2\pi}{\hbar} |M_{fi}|^2.$$</p>
<p>Now this is <strong>absolutely not</strong> what is written anywhere else. Other sources pull the $\rho(E_f)$ out of the integral to obtain <a href="http://en.wikipedia.org/wiki/Fermi%27s_golden_rule" rel="nofollow">Fermi's Golden Rule</a> of the form</p>
<p>$$\Gamma_{fi} ~=~ \rho(E_f) \frac{2\pi}{\hbar} |M_{fi}|^2$$</p>
<p>for any $f$ with $E_f$ in $F$ which makes much more physical sense. But why is what I've done wrong? If anything it should be more precise, because I have actually done the integral! Where have I missed something?</p> | 6,342 | [
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<p>I've been discovering recently the concept of noise spectrum, defined as:
$$S_{xx}[\omega] = \int dt<x(t)x(0)>\text{e}^{-i\omega t}$$
Roughly the Fourrier transform of the two-point function.
Apparently it represents, the probability that the system has to absorb (or emit) energy for positive (negative) $\omega$. I am not familiar with this new object to me, but let's say that I look at composite system, for example an oscillator in a bath. The Hamiltonian pictures says that the exchange of energy between both are caused by the existence of an interacting Hamiltonian:
$$H_{int} = g\;\hat{F}.\hat{x}$$
quantum in this example. From what I said about the noise spectrum, I would say that the exchanges of energy would be motivated by an overlap of the two noise spectrum functions $S_{xx}$ and $S_{FF}$. However, I don't see yet how to conciliate these two points?</p> | 6,343 | [
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<p>I have read that we can charge a capacitor using a battery, but can the vice versa happen? My project needs to show a battery being charged through a fully charged capacitor.</p> | 6,344 | [
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<p>I recently used an oscilloscope in X-Y mode to draw the phase ellipsis of two voltages. I then used the formula phi = arcsin(2y/B) where y is the value of the ellipsis at x = 0 and B is the total distance from the highest point of the ellipsis to the lowest.</p>
<p>Now I really want to know why this works, thank you.</p> | 6,345 | [
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<p>Are tidal power plants slowing down Earth's rotation to the speed of the orbiting moon? (1 rotation per 28 cca days) </p>
<p>Are they vice versa increasing the speed of moon orbiting by generating some waves in gravitation field?</p>
<p>If yes, can you calculate how much energy must be produced by how many tidal power plants (compare it to average nuclear plant please) to slow down the Earth's rotation to 25 hours / day?</p> | 349 | [
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<p>When the focal length of a camera gets further, the object projected on the image gets larger. But would more or less of the object be projected on the image?</p>
<p>I know the answer is that less of the object would get projected on the image because just try it on a camera and I could see the effect. But I don't understand how is this so. I drew a quick diagram below to illustrate my thoughts:</p>
<p><img src="http://i.stack.imgur.com/9MFT1.png" alt="enter image description here"></p>
<p>The $f_1$, $f_2$ and $f_3$ are 3 different lengths of focal length from the the camera lens denoted by the small circle in the centre. The projected object on the image are the arrows. So it looks like the further the focal length, the larger the projected image gets. But this doesn't put on any restriction as to how much of the projected object on the image could be shown. In other words, it appears like whatever the lens could see of the object could be enlarged into the image if the focal length is increased without having the projected object being truncated on the image. What have I missed out?</p>
<p>I am assuming that the lens is a normal camera lens.</p> | 6,346 | [
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<p>The phrase "speed of light" is commonly used for the constant c =3E8 m/s, a feature that's "hardcoded" into the structure of spacetime. All massless waves and particles move at this speed, and it's a key concept in all fundamental theories in physics.</p>
<p>Light, in vacuum, is one fine example. But light in air or glass, or microwaves in a waveguide, move slower than c. The speed of actual light isn't the "speed of light". And of course there are plenty of other things besides electromagnetic quanta whose behavior is described by equations involving c.</p>
<p>The letter "c" alone isn't good for general writing and conversation, especially with non-scientists. It is fine as a mathematical symbol in equations, but isn't catchy or self-descriptive (albeit misleading) as "the speed of light".</p>
<p>EDIT: I have an impression I'm not asking this question in quite the right way. It's not at all about light, or phase or group velocities of light, but about our spacetime geometry having a fundamental constant speed "built in" - what to call it? </p>
<p>Historically it was discovered in connection with light, but c isn't specific to electromagnetism. It's important in all the fundamental forces, and in all situations with high energy particles flying about. </p>
<p>"Universal spacetime speed constant" would be an answer, but for that it's long and clumsy to repeat often in writings about physics. I'm looking for some name or phrase shorter and easier than that, but not so brief as just "c" which is okay in equations and tables of physical contants.</p> | 6,347 | [
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<p>I have this question related to the the Noether's Theorems.
I want to know a rigorous enough enunciation of this theorem, the context is Classical Field Theory without fancy geometrical structures but the usual stuff you need to know to do QFT and the use of Lie Groups(without being too abstract, I need a sensible connection with particle physics). </p>
<p>For what I read around in standard classical mechanics texts, Peskin, <a href="http://arxiv.org/abs/hep-th/0009058" rel="nofollow">Brading and Brown</a> and <a href="http://www3.nd.edu/~kbrading/Research/PhD%20Thesis/PhD%20thesis.html" rel="nofollow">the thesis of one those authors</a>,it is not really clear to me what a symmetry transformation and Noether's theorems are if viewed with a group theoretic perspective and the knowledge constraints mentioned above. </p>
<p>For what I read in other posts on the site, the group that acts on the Lagrangian and gives the conservation of currents(conservation law) and Noether's theorems is the group of transformations on the space of fields $ \mathfrak{F(\mathcal{M})}$ that is $\mathcal{G} = \{ \Lambda: \mathcal{M} \rightarrow G \} $ where $\mathcal{M}$ is a manifold(for now let just say Minkowski space or Euclidean ), $\Lambda(x)$ is the transformation and $G$ is a group usually compact as $SU(N)$ or Poincare/Galileo. But the problem is that there is a big distance in understanding between this fact and what I have read about Noether's theorems using the literature mentioned above .</p>
<p>Following what they do in the paper, lets define the total variation of the action as $\hat{\delta}S\equiv S(\phi'(x'), \partial_{\mu},\phi(x'),x') -S(\phi(x),\partial_{\mu}\phi(x),x) $. They also define a generic transformation of the action as $\Delta S \equiv \tilde{S}(\phi'(x'), \partial_{\mu},\phi(x'),x') -S(\phi(x),\partial_{\mu}\phi(x),x) $. The transformations that give both variations are "infinitesimal"(what are they more rigorously?). <strong>Question a)</strong> Are these elements of $\mathcal{G}$? I think they are.</p>
<p>In the thesis they define a symmetry as the transformations (I suppose elements of $\mathcal{G}$) that give $\hat{\delta} S = 0$. Here I think they are again talking about the action of some infinitesimal transformations of $\mathcal{G}$. Then they proceed to derive the so called Noether relations without imposing the Lagrange Euler conditions. Those are:
\begin{equation}
\sum_{i=1}^{N} \left( \partial_{\mu}\frac{\partial \mathcal{L}}{\partial(\partial_{\mu}\phi_i)} - \frac{\partial \mathcal{L}}{\partial \phi_i} \right)\delta \phi_i= \sum_{i=1}^N \partial_{\mu}\left( \frac{\partial \mathcal{L}}{\partial (\partial_{\mu}\phi_i)}\delta \phi_i + \mathcal{L}\delta x^{\mu} \right)
\end{equation}
Then they do following. To enunciate Noether's First Theorem they restrict to "finite dimensional continuous group of transformations depending smoothly on $\rho$ independent
parameters $\omega_{i}, (i= 1, \cdots, \rho)$ " that give $\hat{\delta}S = 0$. Then they proceed to expand $\delta \phi$ around the parameters and impose Lagrange Euler equations and get the conservation theorem. For what I understand is that they restrict to the "infinitesimal group action" of some group of transformations that depends on finite parameters. <strong>Q b)</strong> This is not a Lie group, right? What is the relation with the usual physicist defnition of global symmetries as "the infinitesimal action of a finite dimensional Lie group that leaves $S$ invarant"</p>
<p><strong>Question c)</strong> Are they talking about a subgroup of $\mathcal{G}$ that is finite? how is that if $\mathcal{G}$ is infinite dimensional? Are they talking about $G$? or is that the subgroup of $\mathcal{G}$ is somehow isomorphic to G? They seem to act the same way.</p>
<p>In the paper they just refer to transformation that do not act on coordinates ("they defined them as gauge transformations") but in the thesis the same approach is done with one that changes coordinates. </p>
<p>For Noether's second theorem they consider the infinite dimensional group of transformations with finite parameters that depend on x (i.e. functions). I really don't understand this. How is that having the parameters depending explicitly on spacetime changes your the dimension of the group of transformations. How this Second Theorem relates to usual local symmetries as defined in textbooks of physics is even muddier at least for me. </p>
<p>Thanks in advance.</p> | 6,348 | [
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<p>We don't get eigenstates of momentum when we operate momentum operator in the wave function of particle in a 1D box problem yet we say momentum is quantized in this situation. Why is it so?</p> | 6,349 | [
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<p>Could we still use Newtonian mechanics in a frictionless world?</p> | 6,350 | [
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<p>I remember reading about all chicken at a poultry farm being violently sick/dying for apparently no reason. It turned out the culprit was machinery at a nearby factory that emitted sound at a frequency equivalent to the resonant frequency for brain cavity of the chicken. </p>
<ul>
<li>Could the story be true?</li>
<li>Could sound be used to purify water of bacteria/viruses (preferably filter, else cull)?</li>
</ul> | 6,351 | [
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<p>What is the period of the pattern from the double slit experiment? It varies along the pattern right?
Namely I'm confused because when considering two point sources (See:
<a href="http://physics.stackexchange.com/questions/87287/period-of-interference-pattern-on-a-substrate">Period of Interference Pattern on a Substrate</a>) this should be like the double slit, at least along the x-axis. That being said, it gives the period as $\frac{\lambda}{2 \sin(\theta)}$ at the origin. I don't know how to calculate the period in the double slit experiment though, so I don't know if this agrees.</p> | 6,352 | [
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<p>I understand how mathematically is possible to have one object with elliptical or circular orbit around another object in space.</p>
<p>so can I think of it as a limit cycle? If yes, then is it stable or unstable? and why?</p>
<p>The intuition behind my question is to know if due to friction we will have a Moon-Earth collision or not.</p> | 221 | [
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<p>Why the ratio of a circle's circumference to its diameter is always the constant $\pi$?
Moreover many of you know better than me about <em>golden ratio</em> $\phi$, <em>Euler's number e,</em> and many other constants. How explain this while everything seems to be in chaos? Is there any explanation for this kind of questions in physics?</p> | 6,353 | [
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<p>In a nozzle, the exit velocity increases as per continuity equation $Av=const$
as given by Bernoulli equation (incompressible fluid). Pressure is inversely proportional to velocity, so we have lower pressure at the exit of the nozzle. But as per definition of pressure, $P=F/A$, i.e., pressure is inversely proportional to the area which contradicts the above explanation on basis of continuity and Bernoulli equation.</p>
<p>Which is true?
What relation is true for compressible flow?</p> | 6,354 | [
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<p>It appears that in Japan, there is an old custom called Uchimizu. The name is a combination of words "road" and "water". The essence of it is moisturizing small parts of populated areas like sidewalks, streets, parks, gardens. A very nice diagram explaining how Uchimizu is performed can be found on <a href="http://www.uchimizu.jp/language/en/" rel="nofollow">this site</a>.</p>
<p>Apart from being a traditional and cultural thing, various sources (<a href="http://en.wikipedia.org/wiki/Uchimizu" rel="nofollow">Wikipedia</a>) claim that it helps reduce the heat in the surrounding area, but don't say by how much exactly.</p>
<p>They also say that it prevents dust particles from spreading, but this is a more obvious part of Uchimizu, as watering sandy ground should prevent the wet sand particles from flying around. I'm more interested in the cooling effect of Uchimizu here.</p>
<p>Let's say we have enough people watering everything in a small city, enough to make 1/2 of all the outside surfaces wet at all times. Potential harm to structures aside, by how much degrees Celcius will the average temperature in that city decrease? Let 30°C be the average summer temperature during the day.</p>
<p>What about watering only the area in immediate proximity? For example, everything around your house. Will that help reduce the summer heat?</p> | 6,355 | [
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<p>With degrees in Mechanical and Electrical engineering but no advanced education in physics, I submit a query based on ellipsometric macro photography of TEMS supplied by FDA/NIH. In one TEM a triangle of RNA/DNA indicates ionic activity.<br>
PHOTO 1. <img src="http://i.stack.imgur.com/mMdGD.jpg" alt="100nm RNA/DNA Traingle"> </p>
<p>This piqued my curiosity, so I photographed the 100nm size triangle with a macro lens in order to enlarge the 35-42,000x TEM further and obtained unexpected images upon which the question is based.</p>
<p>I angled the macro lens camera to the light source hoping to enhance the images within the photographic gel. The black-gray shades in TEMS are not ink but silver atoms crystallized in the original film negative by electron beams then projected into a silver-halide photographic gel. Electrons convert silver halide over 10,000 times more efficiently than photons. The biological samples, dark stained with nano-gold, provide a plethora of particle targets and possibly emit surface plasmon resonances that generate latent photon induced images hidden due to the shortened photographic development time required to form primary images with electron precipitated silver atoms.</p>
<p>Collisions between electrons and particles must have occurred as can be seen in the spiraling burst emanating from a point above the bottom angle of the triangle that impressed me as having ionic interactions. The triangle legs are about 2nm wide with 100nm between vertices. Microvilli sized ion channels appear to be in the picometer range and may be waves generated from electron collisions.</p>
<p>PHOTO 2. <img src="http://i.stack.imgur.com/djUBK.jpg" alt="Electron-particle collision erupts above lower angle"></p>
<p>An invisible clear cloud seemed to lie between the left two vertices and I took hundreds of photos in an attempt to illuminate it.</p>
<p><img src="http://i.stack.imgur.com/RFgEb.jpg" alt="A spiraling cloud illuminated"></p>
<p>PHOTO 3 is the result of those efforts. I assume the cloud to be one of those hypothetical latent images of energy associated with electron-particle collision. Unfortunately the color forces in QED do not relate to colors. </p>
<p>PHOTO 4 was taken in the same area as PHOTO 3 with a different lens-light configuration. <img src="http://i.stack.imgur.com/2407g.jpg" alt="Annihilation?"> </p>
<p>Might the simultaneous Lycurgus Cup-like red/green~emission/absorption seen in PHOTO 4 correspond to an electron travelling back in time (positron) colliding with an electron beamed or displaced in the TEM vacuum and depict an annihilation? </p> | 6,356 | [
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<p>When discussing the Schroedinger equation in spherical coordinates, it is standard practice in QM handbooks to point out that the radial part of the 3-dimensional wave equation bears a strong analogy to the corresponding 1-dimensional case. This is because the Laplace operator in spherical coordinates can be written in the form
$$L = \frac{1}{r}\,\frac{d^2}{dr^2}r.$$
Hence my making the substitution $\psi\to r\psi$, the 3D radial wave function $r\psi(r)$ satisfies exactly the same Schroedinger equation as the wave function $\psi(x)$ in the 1D case. </p>
<p>So far so good. However, at this stage some authors point out that this substitution is merely feasible, as long as the condition $r\psi\to0$ in the limit $r \to0$ is met. If not, then the wave function diverges at the origin, and this is unacceptable on physical grounds. [One may counter this argument, by pointing out that in the calculation of expectation values the square of the absolute value of the wave function is always multiplied by the spherical shell $4\pi r^2\,dr$. The factor $r^2$ neutralizes the above mentioned divergence.]</p>
<p>Indeed there appears to be a slight difference between the 3D and 1D case, when one observes the elementary case of a particle in a box. In both cases, outside of the box the wave function is exponentially decreasing. Inside, where the particle is "free", the solution is oscillatory. In the 1D case, the wave function can be written as $$\psi(x) = A\sin(kx) + B\cos(kx).$$ In the 3D case, the wave function is given by the zeroth order Bessel function $$\psi(r) = C\sin(kr)/r.$$ [Apparently the term $D\cos(kr)/r$ is omitted since it is considered unphysical, see previous paragraph.]</p>
<p>Now if the wave function inside the box has only one free parameter $C$, all one can really do is determine its value by demanding continuity of the wave function on the boundary of the box. On the other hand, QM textbooks claim that one should always seek a solution in which not only the wave function itself, but also its first derivative is continuous on a boundary! </p>
<p>All in all I find the omission of the $D\cos(kr)/r$ term on physical grounds confusing. First of all it creates a difference between the 3D and 1D case. This seems odd to me since the corresponding wave functions satisfy essentially the same Schroedinger equation. Secondly, by omitting this term one loses an adjustable parameter $D$, which plays an important role in meeting the full set of boundary conditions. </p> | 6,357 | [
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<p>So there has been talk in the news of a star named Methuselah that is <a href="http://www.space.com/20112-oldest-known-star-universe.html" rel="nofollow">"older than the universe"</a>. Moreover, this star happens to belong to our very own Milky Way. </p>
<p>The article mentions that Methuselah is consistent with universe age estimates if we consider the margin of error, but this would seem to imply (statistically-speaking) that this method of age estimation is biased towards overestimation. The article also mentions that other studies have put Methuselah's birth at pre-Big-Bang. This seems to indicate that many methods are overestimating its age. To me this seems to indicate a fundamental theoretical misunderstanding or some consistent problem in the measurement phase of the estimation.</p>
<p>I must admit that I only have a modicum of familiarity with stellar evolution, and so these incredible headlines have left me strapped with questions:</p>
<ol>
<li>How reliable is this research?</li>
<li>What method do they use to measure the age of such a star as Methuselah?</li>
<li>Which is more likely to be wrong, the age of Methuselah or the current estimate of the age of the universe?</li>
<li>Could relativistic effects account for some of the age?</li>
</ol> | 6,358 | [
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<p><img src="http://i.stack.imgur.com/Hgytn.jpg" alt="enter image description here"></p>
<p>This picture violates some laws of physics. Am I right?</p> | 6,359 | [
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<p>Is an excited atom more likely to emit a photon if there is a similar atom in the ground state nearby ready to absorb it?</p>
<p>When I say "nearby" I guess I mean that the absorber has an approximately zero <strong>spacetime</strong> separation from the excited atom.</p>
<p>I suppose there are a vast number of ground state atoms with zero spacetime separation from any given excited atom out in the Universe so that adding some more wouldn't significantly change the probability that the excited atom will emit a photon. </p> | 6,360 | [
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<p>In quantum field theory, we are looking for a Lagrangian that is, amongst other, renormalizable. But how do we determine whether or not a theory is renormalizable? Is this purely done by power counting due to Weinberg? <strong>This question is already answered in the a <a href="http://physics.stackexchange.com/questions/88884/semantic-problem-about-renormalizability">previous question</a>.</strong></p>
<p>My question result from the fact that the Yang-Mills Lagrangian was considered to be non-renormalizable, and thus non-physical, for a decade until Veltman and 't Hooft found a method to regularize the theory. Keeping this in mind, <strong>is it possible that there are theories that we today consider to be non-renormalizable, and thus non-physical, which actually <em>are</em> renormalizable but we haven't (yet) discovered a way to do this?</strong></p>
<p>I apologize in advance if my question is vague and if I'm using the wrong terminology, but I'm very new to the idea of renormalizability.</p> | 6,361 | [
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<p>While trying to actually understand the difference between <a href="http://en.wikipedia.org/wiki/Quantum_nondemolition_measurement#Description_from_the_literature" rel="nofollow">QND</a> and <a href="http://en.wikipedia.org/wiki/Complete_set_of_commuting_observables" rel="nofollow">CSCO</a>, I went and found the relevant reference doc, <a href="http://www.ligo.caltech.edu/docs/P/P960048-00.pdf" rel="nofollow">Quantum nondemolition measurements: The route from toys to tools</a>. The key example in the paper discusses can best be summarized by looking at equations (7) and (29). Equation (7) defines the uncertainty of energy in the Standard Quantum Limit (SQL) as:</p>
<p>$$\Delta E_{SQL} = \hbar\omega\sqrt{N}$$</p>
<p>Equation (29) is a modification of (7) that takes into account "a priori" information about energy of a large object and is:</p>
<p>$$\Delta E_1 = \hbar\omega\sqrt{N} \dfrac{1}{\sqrt{\omega\tau}} \ll \Delta E_{SQL}$$</p>
<p>The argument being for large periods of observation the uncertainty in energy becomes much less than the uncertainty of the standard quantum limit.</p>
<p>Equation (30) then tells us:</p>
<p>$$\Delta E_{QND} = \dfrac{\hbar}{\tau} \ll \Delta E_1$$</p>
<p>The arguments in general rely upon repeated measurements over large periods of time, and it is the effect of long observations over large systems that reduces uncertainty in the measurement. </p>
<p>In the discussion it isn't clear how this in any way shows Heisenberg, Schrodinger, Bohr et al are wrong in any way, shape or form. The mantra of quantum mechanics has consistently maintained that classical mechanics emerges in the large N limit of quantum mechanics, and certainly if you increase the number of observations of a system over a large period of time there is no contradiction that you would approach classical mechanics. It seems that at some level this is just a misinterpretation of <a href="http://en.wikipedia.org/wiki/Quantum_decoherence#Mathematical_details" rel="nofollow">decoherence</a>. </p>
<p>So what is new here and why do physicists and physics journalists have a hard time with this?</p> | 6,362 | [
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] |
<p>I've often seen the Casimir effect cited as a source of negative energy/exotic matter with regards to ideas like the Alcubierre drive. The articles then go on to note that the energy required by the Alcubierre drive is orders of magnitude more than that produced in theory by the Casimir effect.</p>
<p>Fair enough. What I <em>haven't</em> seen is numbers, or formulae: as far as I can see, nobody has put up the actual resulting stress-energy tensor online, nor an expression for "effective negative mass" produced. I can see in principle how to calculate it, but I don't yet have the education to do it myself, so I'm turning to StackExchange.</p>
<p>So: How do you calculate the curvature of spacetime due to a parallel-plate Casimir setup; and, if you were to replace the setup with a suitable amount of exotic matter, what is the mass (and optionally, geometry) of the matter required?</p> | 6,363 | [
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<p>How can I determine the needed initial velocity to make a 2d wind resistance free projectile (in computer simulation) reach maximum height at a certain x distance away, with launch position and target position on uneven ground?</p> | 6,364 | [
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<p>If I have a projectile shot in a vacuum-box that has no gravity or wind resistance inside it (lets say the box is 1000 units tall and 1000 units wide), with the only rule being that the projectile bounces off the sides of the box how do I solve for the angles that will hit any target inside the box from a projectile launched at any point inside the box, in less than or equal to 1 side-bounces?</p>
<p>Of course, shooting at any angle would eventually hit the target because the projectile would bounce around forever until finally meeting the target, I'm looking for the angles that result in a single side-bounce only.</p> | 6,365 | [
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<p>I just came from a class on Fourier Transformations as applied to signal processing and sound. It all seems pretty abstract to me, so I was wondering if there were any physical systems that would behave like a Fourier transformation.</p>
<p>That is, if given a wave, a purely physical process that would "return" the Fourier transform in some meaningful way. Like, you gave it a sound wave and you would see, "Oh, there are a lot of components of frequency 1kHz...a few of frequency 10kHz...some of 500Hz..."</p>
<p>I've seen things happening where, if you put sand on a speaker, the sand would start to form patterns on the speakers that are related to the dominant wavelengths/fundamental frequencies of the sound. Is this some sort of natural, physical fourier transform?</p> | 6,366 | [
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<p>When cooking pasta, some organic foam usually forms on the surface of the boiling water and the situation can be kept under control by adjusting the heat (and/or adding some oil).
Covering the pot with a lid, even loosely so, usually leads to the foam overflowing within a short time (removing the lid fixes the problem). Everybody knows that - the question is why?</p>
<p>It seems to me that the only variable that changes noticeably when adding the lid is the vapor pressure but I don't see how that should affect the foaming process.</p> | 6,367 | [
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<p>One of the experimental evidence that supports the theory of big bang is cosmic microwave background radiation (CMBR). From what I've read is that CMBR is the left over radiation from an early stage of the universe.</p>
<p>My questions are: </p>
<ol>
<li><p>Why are we able to detect this radiation at all? </p></li>
<li><p>As the nothing travels faster light, shouldn't this radiation have passed over earth long time ago? </p></li>
<li><p>Why is this radiation filling the universe uniformly?</p></li>
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<p>I have spent an unreasonable amount of time trying to plot $F(r,\theta,\phi)$ plane slices in MATLAB. I want to look at $x-y,y-z,x-z$ planes. Here's the function, specifically:</p>
<p>$$F(\rho,\theta,\phi)~=~4\pi\rho^{2}|\frac{\rho e^{\frac{-\rho}{2}}}{4\sqrt[]{2\pi}}\cos(\theta)|^{2}.$$</p>
<p>I certainly know about <code>contour()</code> and <code>imagesc()</code>in MATLAB. I would appreciate it if people would not respond "use <code>contour()/imagesc()</code>".</p>
<p><strong>Unnecessary backstory</strong>: There happens to be a lot of information out there about plotting in spherical coordinates, however it's not relevant for my specific case because generally people have functions like $\rho=\theta^{2}$ to plot.</p>
<p><strong>For the curious helper</strong>: This is Hydrogen's probability density function. The argument of the absolute value $|arg|$ is the $2P_{z}$ normalized wave function $\Psi(\rho,\theta,\phi)$. The $4\pi\rho^{2}$ accounts for the probability density conversion when working in spherical coordinates. People generally leave off the $4\pi$ portion since it is a constant.</p> | 6,369 | [
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<p>I'm a mathematics student trying to grasp some basics about wave propagation. A sentence I find very often in introductive physics textbooks is the following: </p>
<blockquote>
<p>In a wave, energy is proportional to amplitude squared.</p>
</blockquote>
<p>This is something I would like to understand better in the case of mechanical (linear) waves.</p>
<p>The simplest model is the vibrating string of mass density $\mu$ and tension $T$: here an element of string of rest length $dx$ and vertical displacement $y(x, t)$ possesses a kinetic energy $\frac{1}{2}\mu dx \left( \frac{\partial y}{\partial t}\right)^2$ and a potential elastic energy $\frac{1}{2}T dx \left( \frac{\partial y}{\partial x}\right)^2$. So we have the total energy </p>
<p>$$dE=\frac{1}{2}\mu dx \left( \frac{\partial y}{\partial t}\right)^2+\frac{1}{2}T dx \left( \frac{\partial y}{\partial x}\right)^2,$$</p>
<p>which completely explains the sentence. Can we obtain a similar formula for higher-dimensional waves? How should I modify the above formula for a (simplified model of an) elastic membrane, for example? I would expect something like </p>
<p>$$dE=\text{some constant}\left(\frac{\partial z}{\partial t}\right)^2+\text{some other constant}\left\lvert\nabla z\right\rvert^2,$$</p>
<p>where $z=z(x, y, t)$ is the vertical displacement. Am I right? </p> | 351 | [
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<p>Can cloud charge imbalance be used as an energy source?</p>
<p>First off quite some energy must be present in clouds: a lightning path is quite long, and electrical breakdown of air requires about 1MV/m. Most (many, smaller) electric discharges are not seen because they occur within clouds. The electric energy built up can also be lost in other ways (i.e. Lorentz force).</p>
<p>Some of it comes to ground and when it happens it has such large <em>peak</em> power (on average about a trillion watts) that it can not efficiently be harvested.</p>
<p>I assume that charges build up quite continuously during the lifetime of a cloud: if we knew what cloud to select for discharge we could control (by selecting the right cloud or part of a cloud) the power flux, though not easy its hard to rule out as impossible.</p>
<p>Now how exactly do I propose to do this?
Air can be made conducting through bruteforce electrical breakdown (not efficient), or by heating it (not efficient) or by an energy form encouraging with higher specificity the ionization of specific molecules present in air (be it oxygen or nitrogen or ...).</p>
<p>Apparently non-lethal weapons were designed which do not use projectiles:
a UV laser with 2 optical, parallel paths, each connected to an electrode at the weapon side can tetanize (stimulate at such a pulse rate as to keep the muscle contracted) with specificity any of the 3 broad muscle types (voluntary skeletal muscle, involuntary smooth muscle, and cardiac muscle all respond to different pulse patterns/frequencies). A weapon on same principle was designed to stop cars up to 2km by frying the control chip in the car.</p>
<p>According to <a href="http://hsvti.com/faq.html#t1" rel="nofollow">hstvi (not sure how credible this source is)</a> ionizing wavelengths with lasers can make a path of air conductive to 2km:</p>
<blockquote>
<p>"With an ultraviolet wavelength of 193 nanometers, the maximum
effective range is about 100 meters. The effective range increases to
two kilometers when a wavelength of 248 nanometers and a more intense
beam are used."</p>
</blockquote>
<p>Now for our clouds we would not need 2 optical paths to the laser.</p>
<p>Problems I envision: clouds heights are on kilometer scales, so possibly stages of such lasers would need to be mounted on weatherballoons, preferably locked by cable to a certain height/location.</p>
<p>Each laser would could be surrounded by a thick piece of transparent insulator (glass?) so as to allow UV to pass but not current to enter the setup. On the glass electrodes are placed which are connected to a similar electrode on say a retroreflector of this balloon (a lower one targets this balloon).</p>
<p>If forming a conductor with the lasers consumes more energy than would be got from the lesser charged clouds (or parts of them), we may need to allow electrical breakdown to occur at which point switching of the laser beam would not stop the lightning.</p>
<p>Problem lightning?</p> | 6,370 | [
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<p>Are there any good video lectures for learning quantum mechanics at the level of Griffith?</p> | 6,371 | [
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<p>I'm not well-versed in physics, so I hope you'll forgive me if this question is significantly off the mark.</p>
<p>I'm interested in the predominant frequencies of light over the course of one day. My understanding is that as the sun rises and falls, the atmosphere absorbs differing amounts of light, and that is responsible for the changing colour of the daylight, for example becoming more red as the sun sets.</p>
<p>I guess that there is some curve from (all but) absolute darkness, through to broadband white light during the middle of the day, back to darkness again over the course of twenty-four hours?</p>
<p>If so, is it possible to approximate the makeup of the light at a given point during the day? And if so, how? I appreciate that there are probably significant complicating factors, so any rough approximation would be fine.</p>
<p>Again, I'm coming from a layman position here, so I apologise if I've drastically misunderstood something.</p> | 6,372 | [
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<p>I've come across this article: <a href="http://pubs.acs.org/doi/abs/10.1021/nn4037706" rel="nofollow">Fluorescent Imaging of Single Nanoparticles and Viruses on a Smart Phone</a>.</p>
<p>And what is the theoretical limit for such smartphone extension? And how that limit can be computed (same as for microscope $\sim 1.22\,\lambda / D$)?</p> | 6,373 | [
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