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<p>I'm guessing that, this would be someone in a rocket or something... When they hit their top speed, at what fraction of $c$ are they traveling?</p> | g7592 | [
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<p>I want to study SUSY QM. I found some excellent physically motivated articles on Arxiv. Despite, I am especially interested in the mathematical structure behind SUSY QM.
Does anybody know whether there is a particularly good reference to start studying SUSY QM from a rigorous mathematical point of view. The reference should cover Spectral analysis and a wide range of all the algebraic properties concerned with the topic. </p> | g7593 | [
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<p>For N non interacting spinless particles in a volume, we have 3N degrees of freedom and we can divide the phase space into 6N dimensional cells of volume h raised to power 3N. </p>
<p>And each cell represents a state of the system. That means the system can be in any of those cells. </p>
<p>How can a cell be visualized? Is it combination of many volumes of the individual particles where the particles might be in? Fixing one particle in its one of the individual states (i.e., in one cell when the system is only one spinless particle) and all the possible combination of the other particles in their cells, does this represent one cell for the N particle system? </p> | g7594 | [
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<p>Why is the criteria for fusion represented as a triple product nτT instead of the n,τ,T individually? i.e saying the density has to be above this value, temperature above this value? What are the advantage we gain from representing it this way? </p> | g7595 | [
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<p>It strikes me that the recent announcement of data from BICEP2 contains two really Big Deals:</p>
<ul>
<li>the first evidence of gravitational waves</li>
<li>the first evidence of inflation.</li>
</ul>
<p>Is there also a third?</p>
<ul>
<li>the first observation that will require quantum gravity to explain?</li>
</ul>
<p>Will the BICEP2 data, or data from any other experiment, require quantum gravity to explain? (I'm thinking here of other unexplained phenomena, like dark matter, etc )</p>
<p><strong>Update, two days after OP:</strong></p>
<p>Today Lawrence Krauss, Alan Guth, and John Kovac appeared on NPR's Science Friday. Krauss called the event a triple discovery, and a trifecta, providing first direct evidence of all three of these things. Guth said that he agreed. But I understand all the comments and answers; it seems what constitutes "direct evidence" is in the eye of the beholder.</p> | g7596 | [
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<p>Hi I wanted to know what is spin half in lattice site means? Is it electron or atom or total spins half of electrons in a atomic 1d chain or 2d? </p> | g7597 | [
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<p>Surely someone has found the solutions to the hard sphere collisions (in $n$ dimensions) of two bodies of mass $m_1$ and $m_2$, respectively--that is the resultant velocities (or momenta) of the two bodies after a hard sphere collision given $\vec{p}_1$ and $\vec{p}_2$. I have a solution (both for elastic and inelastic collisions), but I wonder whether or not it's correct.</p>
<p>FYI, here are my solutions for elastic, hard-sphere collisions:</p>
<p>$$
\vec{p}_{1f} = \vec{p}_1 + 2\frac{\left(m_1\vec{p}_2 - m_2\vec{p}_1\right)\circ \hat{r}}{m_1 + m_2}\hat{r} \\
\vec{p}_{2f} = \vec{p}_2 - 2\frac{\left(m_1\vec{p}_2 - m_2\vec{p}_1\right)\circ \hat{r}}{m_1 + m_2}\hat{r}
$$</p>
<p>wher $\hat{r}$ is in the direction of the "hard sphere" (i.e. the unit vector connecting the two radii of the spheres). You can see that my formulation trivially conserved momentum--the question is whether or not it conserves energy as well.</p> | g7598 | [
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<p>Being a grad student in math, and a rather pedantic one indeed, I was unable to accept many of the things taught to me in undergrad physics courses. I am now trying to learn the applications of geometry to string theory and the applications of probability theory, my main field, to statistical physics. Are there other prominent interfaces between abstract math and theoretical physics? </p>
<p>Where can I find these topics explored in a way that would be accepted by a mathematician? (I.e. every object mentioned is a legitimate object or logical statement in ZFC, and every nontrivial claim is proven, no use of unproven conjectures for anything but motivation, and wherever necessary to actually talk about physics of the real world, assumptions that link mathematical ideas (which are merely logical symbols and sets) to what they intend to model are stated in logically precise ways.)</p>
<p>In other words I am looking for a "Bourbaki" approach to physics, and wouldn't mind if the book started even as pedantically as to say, for instance, what a physical unit represents in set theory.</p> | g185 | [
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<p>I am reading the first few pages of Nakahara and refreshing my memory on physics I learned a while ago as a physics math undergrad. Nakahara defines a field $F$ to be conservative if it's the gradient of some potential $V(x)$. (standard) Then he defines the total energy as $1/2mv^2+V(x)$. He then states that $E$ is "often" the kinetic+potential energy, hence deserving the name "total energy." I was taught that kinetic is defined as $1/2mv^2$. So what does he mean here?</p>
<p><strong>Addum:</strong> The exact quote of Ref. 1 is: </p>
<blockquote>
<p><em>The function $E$, which is often the sum of the kinetic energy and the potential energy, is called the <strong>energy</strong>.</em></p>
</blockquote>
<p>References:</p>
<ol>
<li>M. Nakahara, <em>Geometry, Topology & Physics,</em> 2nd edition, 2003, Section 1.1.1.</li>
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<p>From Griffith's <em>Introduction to Electrodynamics</em></p>
<blockquote>
<p>The principle of superposition may seem obvious to you, but it did not have to be so simple: if the electromagnetic force were proportional to the <em>square</em> of the total source charge, for instance, the principle of superposition would not hold, since $\left(q_1+q_2\right)^2\ne q_1^2 + q_2^2$ (there would be cross terms to consider). Superposition is not a logical necessity, but an experimental fact.</p>
</blockquote>
<p>I am confused as to why it is important that electromagnetic force must depend linearly on charge for the superposition principle to hold. Suppose it <em>was</em> the case that electromagnetic force depended on the square of charge. Then, defining, a new quantity "squarecharge" $k = q^2$, electromagnetic force would depend linearly on "squarecharge", and therefore does superposition not hold?</p>
<p>Put another way, every object with charge $q$ has an associated quantity $m = q^{1/3}$. Suppose that $m$ is more naturally measured than $q$, therefore it is used in place of $q$ in all formulas. Then, even though electromagnetic forces are proportional to the cube of $m$, superposition still holds.</p> | g7600 | [
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<p>I know it does not because it emerges out of denser medium at 300,000 KM per second, but according to E=MC square and given that speed of light decreases inside denser medium with refractive index greater than 1, does not it suggest that energy of light inside denser medium is less?</p> | g7601 | [
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<p>According to Landau's symmetry breaking theory, there is a symmetry breaking when phase transition occurs. </p>
<ol>
<li><p>What is the symmetry breaking of superfluid-Mott insulator transition in <a href="http://en.wikipedia.org/wiki/Bose%E2%80%93Hubbard_model" rel="nofollow">Bose-Hubbard model</a>? </p></li>
<li><p>Why metallic state to <a href="http://en.wikipedia.org/wiki/Mott_insulator" rel="nofollow">Mott insulator</a> state transition in <a href="http://www.google.com/search?q=Fermi+Hubbard+model" rel="nofollow">Fermi-Hubbard model</a> is not a phase transition, but a crossover.</p></li>
</ol> | g7602 | [
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<p>As you know, impedance is defined as a complex number.</p>
<p>Ideal capacitors:
$$
\frac {1} {j \omega C} \hspace{0.5 pc} \mathrm{or} \hspace{0.5 pc} \frac {1} {sC}
$$</p>
<p>Ideal inductors:
$$
j \omega L \hspace{0.5 pc} \mathrm{or} \hspace{0.5 pc} sL
$$</p>
<p>I know that the reason why they 'invented' the concept of impedance is because it makes it easy to work with circuits in the frequency domain (or complex frequency domain).</p>
<p>However, since in real-life circuits both voltages and currents are real numbers, I'm wondering if there is any actual physical meaning behind the imaginary component of impedance.</p> | g7603 | [
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<p>How has CMBR temperature dropped as function of time? A graph would be nice, but I'd be happy with times (age of universe) when it cooled enough to not be visible to human eye, became room temperature equivalent, or reached some interesting temperatures regarding matter in the universe.</p>
<p>If there is a nice formula giving the temperature as function of time, that would be great too.</p> | g7604 | [
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<p>I know G.R. change our vision of space and time as a unique surface than can bend.
We can associate the curvature of the space-time as the gravity created by the mass of planets, stars... But how can we measure the <a href="http://en.wikipedia.org/wiki/Curvature">curvature</a> of the space-time for calculate, as an example, the position of a star? </p> | g7605 | [
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<p>In many presentations of statistical mechanics where we have a system of particles having mass, such as the molecules of an ideal gas, the temperature is often equated to the average relative velocity of the particles. However no such velocity can exceed that of light. Is there therefore an absolute upper bound to temperature as well as an absolute zero?</p> | g7606 | [
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<p>Is photosynthesis more efficient than solar panels? If so, by how much?</p> | g7607 | [
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<p>Is it correct that for a motion in a <a href="http://en.wikipedia.org/wiki/Central_force" rel="nofollow">central force</a> field, e.g. a gravitational field, the absolute value of the total angular momentum of the particle and the component of the perpendicular to the plane of motion are conserved, but the other components of the angular momentum in general not?</p> | g7608 | [
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<p>I understand the reason that bicycle pedals are oppositely threaded on either side. What I don't understand is why it works because I'm missing something.</p>
<p>Take the right pedal for example. It's threads are right-handed, so it would be tightened by turning it clockwise (if the pedal were in between you and the bike). Now imagining this from the same perspective, a person pedaling makes the right pedal constantly turn counter-clockwise, relative to the crank. If there's any friction between the pedal and the bolt attaching it to the crank, I would imagine that it would create a force that would try to turn the bolt counter-clockwise along with the pedal.</p>
<p>This is the opposite of what happens, and I've seen the bolts unthread after pedaling backwards a lot myself. What am I missing?</p> | g7609 | [
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<p>Here is a video of a GoPro falling from a plane: <a href="http://www.youtube.com/watch?v=QrxPuk0JefA" rel="nofollow">http://www.youtube.com/watch?v=QrxPuk0JefA</a></p>
<p>Any idea what is happening when the image "stabilizes" around 0:35? I think it is because the camera's tangential velocity approaches the speed of the GoPro's rolling shutter.</p>
<p>Follow-up question: </p>
<ul>
<li>Why is the image skewed with the left side skewed "up" and the right side skewed "down?"</li>
</ul>
<p>A challenge: </p>
<ul>
<li>Find the axis of rotation (with supporting diagram and explanation of how it was computed).</li>
</ul> | g7610 | [
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<p>Here and on many other forums and blogs people ask the question <a href="http://physics.stackexchange.com/questions/6438/what-if-the-lhc-doesnt-see-susy">"What if LHC does not find SUSY?"</a>. I would like to ask the opposite. What if it finds it? What would the implications be? Is it going to just confirm something understood and expected or is it gong to bring something new? Will there be implications for string theory? String theorists will take it as a good sign, but by itself it is not a confirmation of string theory. </p>
<p>I do realize this is more that one question, but they are on the same topic.</p>
<p>p.s If this question is not suitable for this site, please delete/close </p> | g7611 | [
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<p>In optics it is widely mentioned real images are projectable onto screens whereas virtual ones can only be seen by a person. Isn't that contradictory? I mean in order to see the virtual image it has to be <em>projected</em> onto the retina (ultimately acting as a screen). </p>
<p>So, why can you see <a href="http://en.wikipedia.org/wiki/Virtual_image">virtual images</a> in the first place?</p> | g209 | [
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<p>Together with colleagues we got this question. Imagine to take small mirrors, the size for example of a dentist mirror, and stick them to a wooden frame with a parabolic shape. Each mirror is flat, and once set of the frame it can be aligned properly with screws so that it redirects its reflection towards the focus of the parabola. All the parabolic surface is covered with these small mirrors.</p>
<p>Now, if you build a Newtonian telescope out of this system, would you get a decent telescope? I expect it to be affected by various aberrations, but would it work ? </p> | g7612 | [
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<p>I have a graph that i drew and i got all the point and a question came up that what is SI Unit for intercept of a graph.</p>
<p>I have no idea what the answer is. (I'm a total newbie in Physics)</p> | g7613 | [
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<p>I've heard from a physics professor that there's no stationary platform to observe and analyze a body in motion.Why did he mention that? Is it because even seemingly stationary objects like a parked car on a road moves along with the earth's rotation? </p>
<p>As per my intuition there is a stationary platform.If you or your car is at rest then that becomes a stationary platform and you can study the kinematics of other objects.Am i right??</p>
<p>Also what is a frame of reference? Which one is intertial and non inertial?</p>
<p>(I might have not framed the question correctly.appologize for that)</p> | g7614 | [
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<p>Assume that the air pressure and the amount of water in the air stay constant. How can I figure out how much a change in temperature affects the relative humidity?</p> | g7615 | [
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<p>Consider a charge distribution $ρ_1(r)$ and the potential $φ_1(r)$ due to it. Consider another charge distribution $ρ_2(r)$ and $φ_2(r)$ due to it. Both distributions have finite extent, but are otherwise arbitrary and need not have anything to do with each other. Show that the $$∫ρ_1(r) φ_2(r) dv = ∫ρ_2(r) φ_1(r) \; dv$$ where the integrals are taken over all space. Solve this in two different ways as follows.</p>
<p>a) Consider the two collections of charges to be rigid objects that can be moved around. Start with them initially located very far apart, and then bring them together. How much work does this require. Imagine moving collection 1 toward collection 2, and then the other way around.</p>
<p>b) Consider the integral of $∫E_1 E_2 \; dv$ over all space, where $E_1$ and $E_2$ are electric fields due to the two distributions. By using the vector identity $∇ \cdot (E_1φ_2) = (∇ \cdot E_1)φ_2 + E_1 \cdot ∇φ_2$ (and similarly with the $1$'s and $2$'s switched), rewrite the integral $∫E_1 E_2 \; dv$ in two different ways.</p>
<p>This is a homework question, and I have no idea where to start. If someone could show me how to set this equation up to solve, then I would deeply be thankful. </p> | g7616 | [
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<p>This might be little of the track but my question is more on possibility of application of principle of center of mass.<br><p>
The probability of a vehicle overturning depends more on the level of center of mass of the body above the ground, the higher it is and smaller is the base to support it, the easier it is to tumble it.<br>
In case of vehicles on the road, how much is the possibility that lives can be saved to some extent if the driver or some intelligent system in car can let go the tires to bring the center of the mass of body closer to the ground and preventing it from deviating in the traffic to a great extent.<br>
I can fully understand the momentum of the body but it might be helpful in preventing it from crossing over the divider to the other side of the road.<br>
This question is amateur but seeing these horrific videos of road accident, this thought came to me. </p> | g7617 | [
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<p>It is well known that a <a href="http://en.wikipedia.org/wiki/SQUID" rel="nofollow">SQUID</a> can detect an extremely small magnetic flux.</p>
<p>What if the flux is time-dependent? E.g. a slow varying sinusoidal magnetic flux</p>
<p>$$\Phi=\Phi_0\sin(\omega t).$$</p>
<p>Can I still perform a real time measurement of the slow varying flux considering the induced EMF?</p>
<p>By "slow" I mean $\omega$ is smaller than Josephson frequency (AC Josephson effect due to the EMF).</p> | g7618 | [
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<p>We know that there is a relativistic version of Schrodinger equation called Klein-Gordon equation. However, it has some problems and due to these problems, there is Dirac equation that handles these problems. </p>
<p>So, the question is, if there is a solution that is allowed by Klein-Gordon, but not by Dirac, can this solution be considered valid?</p>
<p>Also, can Dirac equation be used for spin-0 particles? </p> | g7619 | [
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<p>Every wavefunction of a form $\Psi(x)$ can be described as a superposition of multiple free particle solutions.
We can see the following Fourier transform:
$$ \psi(x) = \int e^{ik\cdot x} \psi(k) dk $$</p>
<p>We can make it time dependent by replacing $e^{ik\cdot x}$ with $e^{ik\cdot x - i E_k t}$ where $E_k = \sqrt{k^2 + m^2}$. The result gives the positive energy time evolution of any initial wavefunction data. </p>
<p>The question is,</p>
<p>A. This may violate locality, as $E_k$ can be set as we want to, as $k$ can be set as we want to. Is this correct?</p>
<p>B. Why is this related to requiring a multi-particle theory to fix formalism in Klein-Gordon equation? (Context: <a href="http://physics.stackexchange.com/q/39323/2451">Complete set and Klein-Gordon equation</a>) </p>
<p>C. How is adding negative energy preserve locality? </p> | g7620 | [
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<p>During a transition of a molecule from one state to another, it pass through a transition state. This transition state, mathematically speaking, is a saddle point. That means, the second derivative along all the coordinates, except one, is greater than zero. I have two questions: </p>
<p>1) Is it possible for a molecule to have a transition state at a maximum if there is no saddle point on the potential energy surface?</p>
<p>2) In the case of a diatomic molecule, there is no saddle point on the potential energy surface. So the transition state should be at a maximum right?</p> | g7621 | [
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<p>I have been wondering why a fluid in a rotating container has a parabola shape? Is it possible to prove this mathematically? </p> | g7622 | [
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<p>In an analogy to the neutron, which decays rapidly as a free particle, but when bound in a nucleus it is stable, would it be possible to crease a structure that permits the stability of muons - be it muonic atoms, some sort of muonic lattice, etc.?</p>
<p>Granted, the energetic benefit of the neutron $\beta$ decay is only about 0.08% of its rest mass, while the muon is roughly 200 times as massive as the electron, thus having much more to gain from decaying - making this proposition seem somewhat unlikely. </p> | g7623 | [
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<p>Just a quick question: In high energy experiments, the fundamental forces are thought to merge into a single force. My question is, in very low energy experiments (very low), do the forces we know about split up even more/is this possible or likely?</p>
<p>Thanks</p> | g7624 | [
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<p>Hi all what is the definition of pressure derivative of <a href="http://en.wikipedia.org/wiki/Bulk_modulus" rel="nofollow">bulk modulus</a> if it is a pressure derivative of bulk modulus at zero pressure. if the pressure is zero how it is derivative by pressure? </p> | g7625 | [
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<p>When a sensor registers electromagnetic radiation, such as that used for the transmission of communication like light or radio waves, does this radiation "abrade" or "erode" the material of the sensor?</p>
<p>Are there any traces of the received radiation that can be detected, even if only theoretically?</p>
<p>An example from a biological background would be that high energy light (such as that in the UV range) destroys the pigments in the eyes, which is why animals that live longer than a few years cannot see in the UV range. Maybe something similar happens with man made sensors for different wavelengths of electromagnetic radiation.</p> | g7626 | [
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<ol>
<li><p>My question is why are we colliding particles in LHC to produce new ones? </p></li>
<li><p>And these particles that they sometimes say live for a fraction of a second, how in space they exists then? </p></li>
<li><p>In space all these particle exist without smashing to each other, why do we need to smash them to produce them?</p></li>
</ol> | g7627 | [
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<p>I'm curious about how to calculate the 2-point function of graviton, but there are no textbooks of general relativity covering this problem. </p>
<p>So how to calculate it? In which book can I find the answer?</p> | g7628 | [
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<p>I have a relatively complex (for me anyhow) situation which I would like to capture in bra-ket notation, rather than in words. However, I've not been able to find a source which will help me understand better how to do so, and I was hoping that one of you might help me out. I'll first describe exactly what I want to express, so that it's a little more clear what I mean. Note that this is not a homework question or something, it has to do with an experiment that I came up with, so chances are that it might be somewhat impossible to actually write it out the way I want to.</p>
<p>I have a system that lives on the <a href="http://en.wikipedia.org/wiki/Bloch_sphere" rel="nofollow">Bloch sphere</a>, like this one, but with $\left|\uparrow\right>$ instead of $\left|0\right>$ and $\left|\downarrow\right>$ instead of $\left|1\right>$</p>
<p><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Bloch_Sphere.svg/256px-Bloch_Sphere.svg.png" alt="Bloch Sphere"></p>
<p>Now, initially I am able to fully initialize something, say a spin, into 1 state, being $\left|0\right>$. Then, I rotate the state by pi/2 around the x-axis, and I wait a time t. In this time t, some more complex stuff happens. Depending on the state of a second spin, stuff will happen. This second spin can be in either of three states, $\left|-1\right>$, $\left|0\right>$ and $\left|1\right>$.</p>
<p>Now, during this time $t$, the state of the first spin will precess about the Bloch sphere depending on the state of the second spin. If the second spin is in state $\left|-1\right>$ the first state will rotate around the z-axis clock wise, if the second spin is in state $\left|0\right>$ the first spin will not change, and if the second spin is in state $\left|1\right>$ the first spin will rotate about the $z$-axis counterclockwise. </p>
<p>So, after this time $t$, I will rotate the first spin again, but this time by $\pi/2$ around the $y$-axis. This means that if I choose t such that it is exactly a quarter of the period in which the spin makes a full circle, the two spin states will be entangled. I can use this to establish what the second spin state is by reading out the first spin state:</p>
<p>If $\left|-1\right>$, then I will readout $\left|\uparrow\right>$ with $P=0$, if $\left|0\right>$, then I will readout $\left|\uparrow\right>$ with $P=0.5$, and if $\left|1\right>$, then I will readout $\left|\uparrow\right>$ with $P=1$.</p>
<p>I understand that this probably might be a little confusing, which is of course also the primary reason why I would just want to write this in nice, clean bra-ket notation. If there's anything in particular that's not clear, please let me know. And if someone could help me get started (possibly by pointing me to a similar example) I'd be very grateful.</p>
<p><strong>Edit:</strong>
Alright, I've done a little bit of reading on what I could find, and this is how far I get now</p>
<p>Initially:
$\left|\psi\right>$ = $\left|\psi_1\right> \otimes \left|\psi_2\right> = \left|\uparrow\right> \otimes \frac{1}{\sqrt{3}}\left( \left|-1\right> + \left|0\right>+ \left|1\right> \right)$ </p>
<p>Rotate first spin by $\pi /2$ around x-axis</p>
<p>$\left|\psi\right>$ = $R_x (\frac{\pi}{2}) \left|\psi_1\right> \otimes \left|\psi_2\right> = \frac{1}{\sqrt{2}} \left( \left|\uparrow\right> -i \left|\downarrow\right> \right) \otimes \frac{1}{\sqrt{3}}\left( \left|-1\right> + \left|0\right>+ \left|1\right> \right)$ </p>
<p>But here I get stuck again, as it is here that the rotation conditional on the second spin has to happen, and that I don't know how to do.</p> | g7629 | [
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<p>I have come to know the electrostatic potential energy in vacuum is given by
$${\frac{1}{2}} \epsilon_0\int d^3x {E^2} $$ and this energy is due to the mutual electrostatic coulomb potential energy.</p>
<p>So only a single point charge in space also contributes to some electrostatic potential energy according to $${\frac{1}{2}} \epsilon_0 \int d^3x {E^2} $$ as due to a single point charge also we have electric field at every point in space. </p>
<p>Now I am not getting it physically why should there be any Coulomb energy in this case as there is no another charge to provide the electrostatic coulomb potential energy?</p> | g7630 | [
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<p>What are the results of fusing an electron neutrino and a muon neutrino? If you have an answer, then why? I looked this up and searched for stuff on Google, Wikipedia and a few other sites, but all the results say are stuff on nuclear fusion and neutrinos.</p>
<p><b> BONUS QUESTION: </b>
<br>
What happens if you put another muon neutrino into the mix?</p> | g7631 | [
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<p>When an coil rotor is moving around a magnetic field there is -V induced to resist the input V.</p>
<p>Let's take an example, a 12 V DC motor induces -10V, and the actual running voltage is 2V.</p>
<p>If there we're no -V in the process, the motor would preform a lot better?
What is the advantages and disadvantages of counter EMF? Is it wasting energy?</p>
<p>I understand the concept, but I can not fathom how initially, the motor runs at 12V then drops to 2V(actual) and still preforms the same?
Are all current motors today lose 70%+ of their input voltage due to counter EMF?</p> | g7632 | [
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<p>The question relates to <a href="http://physics.stackexchange.com/questions/53148/in-qft-why-does-a-vanishing-commutator-ensure-causality">this post</a>.</p>
<p>As shown in Peskin and Schroeder's introduction to quantum field theory p. 28.,</p>
<p>$$[\phi(x),\phi(y)] = 0 \;\;\mathrm{if}\;\; (x-y)^2<0$$,</p>
<p>which implies the measurements between two spacelike places do not affect each other. However, in the EPR paradox, even two experiments are spacelike separated, once experimentalist $A$ obtained $+$ result of $S_z$, $B$ has to obtain $-$.</p>
<p>Though at this stage of EPR, no information is delivered. It still seems to me, actually, that the two measurements affect each other. Is there any further reasoning to reconcile this inconsistency?</p> | g7633 | [
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<p>If something crossed the horizon of the observable Universe, does this mean that all information about it is lost forever? If yes (or no), how this fits with the information-cannot-be-lost law? </p>
<p>Also, does it mean that the energy of our observable Universe is constantly decreasing? If yes, what are the consequences of that?</p> | g7634 | [
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] |
<p>There is a surprising number of papers seriously discussing the "<a href="http://focus.aps.org/story/v13/st3" rel="nofollow">feigel effect</a>" This has been linked to the <a href="http://peter.mapledesign.co.uk/writings/physics/2005_dissertation_The_Abraham-Minkowski_Controversy.pdf" rel="nofollow">Abraham-Minkowski controversy</a> also <a href="http://en.wikipedia.org/wiki/Abraham%E2%80%93Minkowski_controversy" rel="nofollow">here</a>. Although there are good discussions picking apart the feigel effect calculations, there does not appear to be a conclusive refutation of the effect under certain experimental circumstances. Much of this is linked to when the Poynting vector vanishes in the vacuum. Is there a legitimate possibility for seeing the Feigel effect? What would that mean about the nature of the poynting vector in physics?</p>
<p><a href="http://www.esa.int/gsp/ACT/doc/ARI/ARI%20Study%20Report/ACT-RPT-PHY-ARI-041201-Grenoble_Feigel.pdf" rel="nofollow">The Feigel Process: Lorentz invariance, regularization, and experimental feasibility Final Report</a></p>
<p><a href="http://www.esa.int/gsp/ACT/doc/ARI/ARI%20Study%20Report/ACT-RPT-PHY-ARI-041201-Koln_Feigel.pdf" rel="nofollow">Lorentz-invariant description of the Feigel Process for the Extraction of Momentum from a
vacuum Final Report</a></p>
<p><a href="http://arxiv.org/PS_cache/arxiv/pdf/1008/1008.3656v2.pdf" rel="nofollow">Alternative derivation of the Feigel effect and call for its experimental verification</a></p> | g7635 | [
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<p>We learn that the quantum wave function $\Psi$ <a href="http://en.wikipedia.org/wiki/Wave_function_collapse" rel="nofollow">collapses</a> when it interacts with a classic object (measurement). </p>
<p><strong>My question is:</strong><br> Why are there <em>classic</em> objects after all, how did it all start? In a <em>quantum universe</em> (and I understand we live in one) there should only be <em>superposition</em>, how did these <em>classic</em> beings came into existence (which "decohere" the others) in the first place? Is it a statistical necessity like <em>entropy</em> - or doesn't, quite simply, anybody know the answer to that riddle? </p> | g7636 | [
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<p>A <a href="http://prl.aps.org/abstract/PRL/v104/i7/e070401" rel="nofollow">paper</a> was published in 2010 claiming to resolve the <a href="http://en.wikipedia.org/wiki/Abraham%E2%80%93Minkowski_controversy" rel="nofollow">Abraham-Minkowski controversy</a>. Is this paper viewed as definitive by physicists?</p> | g7637 | [
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<p>This was my engineering viva question and I couldn't think of any example, for I am totally convinced that there cannot be drag in a inviscid flow. It also bothers me whether it is possible, a tricky scenario in fluid mechanics or gas dynamics. </p> | g7638 | [
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<p>How can one make sense of the idea of extremizing a Hamilton-Jacobi equation?</p>
<p>In Schrödinger's paper "Quantisation as a Problem of Proper Values I" (<em>Annalen der Physik</em> (4), vol. 79, 1926, p. 1, available e.g. in <a href="http://einstein.drexel.edu/~bob/Quantum_Papers/Schr_1.pdf" rel="nofollow"><em>Collected papers on wave mechanics</em>, AMS publishing</a>) he begins with the classical time-independent Hamilton-Jacobi equation </p>
<p>$$H(q,\frac{\partial S}{\partial q}) = E$$</p>
<p>and instead of assuming an additive solution for separation of variables he assumes a multiplicative solution thus defining $S = K\ln(\psi)$ to get</p>
<p>$$H(q,\frac{K}{\psi} \frac{\partial \psi}{\partial q}) = E.$$</p>
<p>Instead of solving it he talks about how this last equation "can always be transformed so as to become a quadratic form (of $\psi$ & its first derivatives) equated to zero", neglecting the relativistic variation of mass.</p>
<p>(I'm assuming that transforming this to a quadratic form means a Taylor expansion in powers of $\psi$, though I'm not sure about that).</p>
<p>Then he seeks "a function $\psi$, such that for any arbitrary variation of it the integral of the said quadratic form, taken over the whole of coordinate space (I am aware this formulation is not entirely unambiguous), is stationary, $\psi$ being everywhere real, single-valued, finite, and continuously differentiable up to the second order."</p>
<p>In other words, he basically extremizes</p>
<p>$$I = \iiint\left(\frac{K^2}{2m}\left[\left(\frac{\partial \psi}{\partial x}\right)^2 \ + \ \left(\frac{\partial \psi}{\partial y}\right)^2 \ + \ \left(\frac{\partial \psi}{\partial z}\right)^2\right] + (V - E)\psi^2\right)\,\mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z$$ </p>
<p>and ends up with the time independent Schrödinger equation, but the issue is extremizing the Hamilton-Jacobi equation. Where is the justification for this?</p>
<p>I can only find a reference to it <a href="https://www.google.ie/search?q=extremizing%20the%20hamilton-jacobi%20equation&ie=utf-8&oe=utf-8&rls=org.mozilla%3aen-US%3aofficial&client=firefox-a&gws_rd=cr&ei=b8kxUvrZMoiV7AaLooCQDg#psj=1&q=%22variation%20of%20the%20hamilton-jacobi%20equation%22&rls=org.mozilla%3aen-US%3aofficial" rel="nofollow">here</a> (in the ps.gz link), so it does seem to be something more than one person has done, but what is the theory behind this? Does it function as another method of solving Hamilton's equations? If so, why?</p> | g7639 | [
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] |
<p>The ability to manipulate light spectra (as in mercury lamps, sodium lamps, infra red) is within the ambit of contemporary technology. Stars are said to be unique in the spectrum they emit ; </p>
<p><a href="http://skyserver.sdss.org/dr1/en/proj/basic/spectraltypes/" rel="nofollow">http://skyserver.sdss.org/dr1/en/proj/basic/spectraltypes/</a> writes to say</p>
<blockquote>
<p>The best tool we have for studying a star's light is the star's spectrum. A spectrum (the plural is "spectra") of a star is like the star's fingerprint. Just like each person has unique fingerprints, each star has a unique spectrum.</p>
</blockquote>
<p>with my limited understanding of physics, I may have understood wrong!!</p>
<p>Can contemporary technology simulate the spectrum of a star? </p> | g7640 | [
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<p>I am trying to get a clear picture of the valence band, conduction band, and the band gap. Now I've been researching it for a little while now and understand most of what's going on. I'm still a little confused about some specifics though, so if you could please address the following, that would be great!</p>
<p>My favorite description thus far has been</p>
<p><em>"The most important aspect of semiconductor bandstructure may be summarised as follows; at absolute
zero the highest completely filled band (the valence band) is separated from the lowest empty band (the
conduction band) by an energy gap or band gap Eg of forbidden states. Therefore the material does
not conduct electricity at T = 0."</em></p>
<p>So from this description I have a pretty clear idea of what the valence band is (with the supplement of a few diagrams). Also, I know the conduction band is above the valence band in terms of energy, and is where electrons are free to roam the material as conduction electrons. My problem is where this "conduction band" is physically. It seems like there should be some allowed state, where if you just excite one electron you pass into that new state. From the above description, it seems to say some of these states are "forbidden", and that is my main question resides. Where is this conduction band, what determines its range (an example would be fantastic), and how do we determine what is necessarily a "forbidden" state?</p>
<p>Thanks =)</p> | g7641 | [
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<p>I'm having a problem following a derivation of <a href="http://en.wikipedia.org/wiki/Bloch_wave" rel="nofollow">Bloch's theorem</a>, looking at a one dimensional lattice with $N$ nodes and spacing a, we impose periodic boundary conditions, meaning that the wave-function of a single electron $\psi(x)$ can be decomposed in the following modes:</p>
<p>$$\psi(x)=\sum_{q}\phi(q)\text{e}^{iqx},$$ </p>
<p>where </p>
<p>$$q = \frac{2\pi m}{N a}\; m\in \mathbb{Z}.$$ </p>
<p>Otherwise it would be multivalued.</p>
<p>Schrodinger's equation gives:$$(\epsilon - \frac{\hbar^2q^2}{2m})\phi(q)=\sum_{k \in B}\tilde{V}(k)\phi(q+k)$$
where $\epsilon$ is the energy eigenvalue of $\psi$, $B$ is the reciprocal Bravais lattice ($k=\frac{2\pi n}{a}$ with $n\in \mathbb{Z}$), $\tilde{V}$ is the Fourier transform of the potential.
So the $\phi$ modes separated by a vector belonging to the reciprocal Bravais lattice are coupled but I don't see how it implies that only $q$ vectors that are in this class of equivalence (whose difference belongs to $B$) should appear in the first sum (the expansion of $\psi$ in modes).</p> | g7642 | [
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<p>Here's the conundrum I have been facing. Yesterday I asked the question: how can batteries constantly motivate electrons to complete a circuit? (<a href="http://physics.stackexchange.com/questions/126971/what-maintains-constant-voltage-in-a-battery">What maintains constant voltage in a battery?</a>)
After some thought I realized that the concept is that of an energy source. The batteries are a source of energy, and regardless of the mechanism, they will constantly 'push' for a goal. My solution finally came when I realized that speaking about someone's 'motivation' was identical to the constant push of the battery. Here's the issue:</p>
<p>My sister wanted to get me coffee yesterday for my birthday. She was attempting to give it to me before my class started. Unfortunately, she had difficulty with traffic, and so was able to deliver only after my class started. I realized when she told me that she tried as hard as she could, and that what really mattered was her motivation. The push she gave was constant regardless of the resistance she encountered. The parallel here to the constant push of a battery was strong; voltage didn't matter in respect to resistance for a given battery. </p>
<p>Now I have a different issue. The voltage drop is described as the per-capita potential energy difference of electric charges at points a and b right? The total energy would then be the amount of 'capitas' multiplied by this per capita potential energy difference. More capitas mean more total energy. </p>
<p>Here's the problem. If the motivation of a battery is described by voltage, then if we look at a circuit with a resistor and compare it to another circuit with an equal-length resistor but with a wider surface area, the potential difference is supposed to stay the same in both cases. However, in taking the charge from one surface to the other, more energy is required for the resistor with larger surface area! The amount of energy supplied is different in either case, yet from the same 'constant' energy source. This seems so wrong to me right now. </p>
<p>Yet I know that Power=Voltage*(Current)^2, so this actually makes sense in terms of the equation. I wonder what is lacking in my fundamental understanding of the potential difference in comparison to the idea of motivation/constant energy source. I'm really fundamentally misunderstanding something complex here that I don't quite have my finger put on yet. Please help clear up my view of a battery as a constant pusher to line up with this changing energy ouput a battery can give. </p> | g7643 | [
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<p>I have been given this formula from optics here, with no background:
$$\vec\nabla{n} = \frac{d(n\hat{u})}{ds}$$</p>
<p>Where $n$ is the refractive index and $\hat{u}$ is a unit vector tangent to the path $s$ that light takes inside a medium.</p>
<p>Does anyone know if this formula has a name? I am looking specifically for a derivation of it. I have looked through the optics book by Hecht with no luck - I assume it comes from fermats principle of least time in some form.</p>
<p>Any help greatly appreciated.</p> | g7644 | [
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<p>Yesterday I looked underwater with my eyes open (and no goggles) and I realized I can't see anything clearly. Everything looks very, very blurry. My guess is that the eye needs direct contact with air in order to work properly. With water, the refraction index is different, and the eye lens are not able to compensate for correct focalization on the retina.</p>
<p>Am I right ? If so, what lenses should one wear in order to see clearly while under water ?</p> | g7645 | [
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<p>Consider a theory of one complex scalar field with the following Lagrangian.
$$
\mathcal{L}=\partial _\mu \phi ^*\partial ^\mu \phi +\mu ^2\phi ^*\phi -\frac{\lambda}{2}(\phi ^*\phi )^2.
$$
The potential is
$$
V(\phi )=-\mu ^2|\phi |^2+\frac{\lambda}{2}|\phi|^4.
$$
The classic stable minimum of this potential is given by $\phi =\frac{\mu}{\sqrt{\lambda}}e^{i\theta}=:v$ for any $\theta \in \mathbb{R}$.</p>
<p>We then define a new field $\psi: =\phi -|v|$, rewrite the Lagrangian in terms of the new field $\psi$, et voilà: out pops the mass term
$$
2|v|^2\lambda \psi ^*\psi .
$$
People usually explain that this shows the existence of a field whose quanta are particles of mass $|v|\sqrt{2\lambda}$. In this sense, the original field has $\phi$ acquired a mass.</p>
<p>I don't buy it. I don't see where this argument has actually used the fact that $v$ is the vacuum expectation value of the field. Yes, it is natural to expand about the classical minima, but why not do something stupid instead and define a new field $\psi :=\phi -7$. Once again, after rewriting the Lagrangian in terms of the new field, you should find that it has indeed acquired has a mass term. Playing this trick over and over, by picking a number different than $7$, you should be able to find a mass term with any mass you like. Obviously, this doesn't make any physical sense.</p>
<p>There is something special about the substitution $\psi :=\phi -|v|$. There must be more to it than a tedious algebraic manipulation, but what is it? Why does nature possess particles of the mass that this substitution yields, as opposed to any other substitution?</p>
<p>On another note, what exactly does this have to do with the global $U(1)$ symmetry present. It seems that the only thing that has played a role so far is that the vacuum expectation value of the field is non-zero, but yet I've always seen this mass generation presented alongside symmetry breaking. What precisely is the relationship between the two?</p> | g7646 | [
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<p>My question is the following. Are there solutions to the Einstein field equations, which have the property that there is a hypersurface of constant time and to the past of that surface space is empty (Minkowski space-time) and to the future it is not (non-vanishing stress-energy tensor)? At first thought it seems strange to have nothing and suddenly something. On the other hand define $g_{\mu\nu}(x)$ to be the Minkowski metric for the past of the surface and any functions (sufficiently smooth) that match it on the surface and are different than the Minkowski for the future. There are many ways (infinitely many) to do this. Then one can define the stress-energy tensor using Einstein's equations. This would seem to work, but there are certain conditions on the tensor, for example positivity, or other restrictions for physical reasons that I am unaware of, so it may be there are no such functions. </p>
<p>So the questions is: does anyone know of an explicit example or a more convincing argument than "there are so many functions, there has got to be some that work"? Of course a reason why it doesn't work, if that is the case, would be good too.</p>
<p>Thanks. </p> | g7647 | [
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<p>In <a href="http://en.wikipedia.org/wiki/The_Adventures_of_Tintin_%28film%29" rel="nofollow"><em>The Adventures of Tintin</em></a>, an opera singer (the Milanese Nightingale) broke a bulletproof glass case using her voice. Is that scientifically possible?</p>
<p>From the <em><a href="http://en.wikipedia.org/wiki/Bulletproof_glass" rel="nofollow">Wikipedia</a></em> page, a typical bulletproof glass</p>
<blockquote>
<p>is usually made from a combination of two or more types of glass, one hard and one soft. The softer layer makes the glass more elastic, so it can flex instead of shatter.</p>
</blockquote>
<p>When they <a href="http://www.youtube.com/watch?v=IZD8ffPwXRo#t=2m05s" rel="nofollow">did it on Mythbusters</a>, the singer had to stand really close to the glass that is so thin for it to break.
Any thoughts on whether the movie scene is even humanly possible?</p> | g7648 | [
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<p>The Super-Symmetry operators reduce or increase helicity by a half unit. And this result in an algebra that where the fermions and bosons vacuum energy sums to zero. And it seems to generate gravity, when the upgraded to a local symmetry. But as yet, physicist seem to have found no good way to break super-symmetry, i.e. Supergravity. What other transformations can one do at the same time as applying a super-symmetry operator? And still keep the good properties of super-symmetry.</p>
<p>At first view, I think one could swap left and right handed particles/fields, and swap sets of particles from one group containing both fermion and boson to another. I.e. switch to the other one of a direct product group. Does mirror-symmetry commute and/or co-operate with super-symmetry?</p> | g7649 | [
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<p>I want to ask if anyone has gone through the derivation of the second equality in the following formula </p>
<p><img src="http://i.stack.imgur.com/okF7P.jpg" alt="enter image description here"></p>
<p>which comes from <a href="http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165102" rel="nofollow">http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165102</a>.</p> | g7650 | [
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<p>The uncertainty principle is listed in most textbooks and articles as
$$ \Delta E \Delta t \geq \frac{\hbar}{2}.$$
This can be derived in many ways in many different settings, most of them involving commutation relations with appropriate operators.</p>
<p>This is often interpreted such that $\Delta E$ is the amount of energy that can be "borrowed" and $\Delta t$ is the time for which it can be borrowed. The uncertainty principle is then used to argue that if $\Delta t$ is large (that is, if the energy is borrowed for long times), then
$$ \Delta E \sim \hbar/2\Delta t$$
is small, making this effect negligible on large time scales.</p>
<p>However, the uncertainty relation is an inequality. If $\Delta E$ is actually the amount of energy we can borrow, and if $\Delta t$ is the time for which it can be borrowed, then if $\Delta t$ is large, $\hbar/2\Delta t$ is small, and
$$\Delta E \geq \hbar/2\Delta t.$$</p>
<p>This puts no upper limit on $\Delta E$ at all, and in fact gives it a lower limit. $\Delta E$ must be <i> at least </i> $\hbar/2\Delta t$, but it could also be orders of magnitude larger and still satisfy the uncertainty principle. In fact, $\Delta E$ and $\Delta t$ can both be infinite and satisfy the uncertainty principle.</p>
<p>My question is, then, since this argument is so frequently cited in textbooks, what justifications are used for interpreting $\Delta E$ and $\Delta t$ as relating to energy nonconservation? Am I missing something? Is there a reason for the switch from $\geq$ to $\sim$ in the relation? Why don't we observe the infinite violations of conservation of energy (in time and energy) that are predicted by this interpretation of the uncertainty principle? Why are only the minimum-uncertainty cases used in the literature?</p>
<p>I'm assuming there is a reason, and trying to figure it out. Thanks in advance for clarification!</p> | g7651 | [
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<p>Does anyone have an intuitive explanation of why this is the case? </p> | g7652 | [
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<p>I have arm wrestled people with less strength than me who win simply because they have thicker wrists, or larger hands. It has nary to do with having better technique either, because their wrist size alone seems to be a big advantage.</p>
<p>I want to know why, as explained by physics, why the torque they produce is so much larger, even with less muscular force by the axis than with me having greater strength, but smaller wrists & hands?</p>
<p>For example, I have 7-inch wrists, and 7.2-inch hands.</p>
<p>My opponent has 8-inch wrists, and 8.2-inch hands.</p>
<p>They have been tested to have less physical power in every muscle group used in arm wrestling compared to me, yet, they win, and they have no technical advantage over me in the sport either.</p>
<p>I have noticed that this advantage goes beyond arm wrestling, but to ANY angular/torque-like position of some grasping another's hand/wrist outwards in front of their bodies:
<img src="http://i.stack.imgur.com/s0Fls.jpg" alt="enter image description here">
<img src="http://i.stack.imgur.com/aqkBc.jpg" alt="enter image description here"></p>
<p>Please tell me why this is.</p>
<p>EXTRA: This question, or a question of this nature, has never been asked on this site, so please cut me some slack here! I know the question is poor at best, but some insight would be nice!</p> | g7653 | [
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<p>It's easy to find the "magic" numbers of neutrons on the diagrams of alpha-decay energy: 82, 126, 152, 162. Such "magic" nuclei should be more stable than their neighbors.</p>
<p><IMG src="http://elementy.ru/blogs/u/i/2598.gif">
<IMG src="http://elementy.ru/blogs/u/i/2599.gif"></p>
<p>But why some nuclei with "magic" numbers of neutrons have a half-life less than their neighbor isotopes with odd numbers of neutrons?</p>
<p>Examples for "magic" number 126:</p>
<p>A half-life of "magic" Po-210 is <strong>138 days</strong>, whereas a half-life of neighbor isotope Po-209 is <strong>102 years</strong>.</p>
<p>A half-life of "magic" Ra-214 is <strong>2.46 sec</strong>, whereas a half-life of neighbor isotope Ra-213 is <strong>2.74 min</strong>. </p>
<p>Examples for "magic" number 152:</p>
<p>A half-life of "magic" Cm-248 is <strong>348 thousand years</strong>, whereas a half-life of neighbor isotope Cm-247 is <strong>16 million years</strong>!</p>
<p>A half-life of "magic" Cf-250 is <strong>13 years</strong>, whereas a half-life of neighbor isotope Cf-249 is <strong>351 years</strong>.</p>
<p>P.S. <a href="http://www.nndc.bnl.gov/masses/mass.mas03" rel="nofollow">Source</a> of the diagrams data</p> | g7654 | [
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<p>For example, let's assume a chair here: It can be "slid" across the force if we use minimal upwards force, but not enough to actually "lift" the chair. Why should it move?</p>
<p>Here's a better example: I have seen some strong people lift and slide the back of cars, however, the back tires of the car never elevate completely off the ground. With regards to friction, though, how is it possible to actually "move" something without lifting it completely? How does this work is a better question. This image should illustrate the car example:</p>
<p><img src="http://i.stack.imgur.com/foRJg.jpg" alt="enter image description here"></p>
<p>Is there enough space within it to allow the angular force to make it "slid" a pinch, or what else would explain its ability to move without being completely suspended in the air that would, say, differ from this with a human?</p> | g7655 | [
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<p>Is my understanding of this <a href="http://en.wikipedia.org/wiki/Mechanical_equivalent_of_heat" rel="nofollow">experiment</a> correct?
There is the quantity $MC\delta \theta$ associated to the heat which I think is not an absolute value to be compared with $mgh$ since the $\delta \theta$ could be defined arbitrarily. So this experiment does not prove : thermal energy = $mgh$ it could however show a linear relation between $\delta \theta$ and $h$. </p> | g7656 | [
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<p>I know they have accurate means of measuring the distance of the planets in the Solar System from the Sun. I'm skeptical how can they use the same tools or techniques for other systems so far away as 22 light years.</p>
<p>According to this <a href="http://www.dailygalaxy.com/my_weblog/2012/02/newsflash-habitable-zone-earth-like-planet-discovered-22-light-years-away.html">link</a> the planet GJ667Cc resides in the "habitable zone". How are they able to measure the distance of something from something while observing it from a distance of 22 light years?</p> | g7657 | [
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<p><img src="http://i.stack.imgur.com/0dOhU.jpg" alt="enter image description here"></p>
<p>In this picture if the only parts of an object in contact with a surface are the lines AB and CD am I right in saying that the centre of mass has to be in the area enclosed by ABCD (as shown). I think this is correct as if the mass lies outside this region taking moments about e.g.an axis AC would lead to a resultant moment. If this is true please can you also give me a more generalised rule. thanks</p> | g7658 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/2175/is-it-possible-for-information-to-be-transmitted-faster-than-light">Is it possible for information to be transmitted faster than light?</a> </p>
</blockquote>
<p>I mean by using a perfect solid stick long enough and moving it forward and backward can I send information fastest than light ? Can you imagine a solid stick long enough to reach the moon and using it to comunicate with the lunar base. Will be information faster than light? What are the theoretical reason other than technical reason for rules this as impossible?
We should rule that a perfect unelastic solid exist ?</p> | g4 | [
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<p>In a recent answer (here: <a href="http://physics.stackexchange.com/questions/20944/the-equipartition-theorem-in-momentum-space/20981#20981">The equipartition theorem in momentum space</a> ), I suggested that if you have an appropriate first order equation (in the answer I used a second order equation, but it is more likely to be true for a first order equation) of the form:</p>
<p>$$ i\partial_t \phi = (\nabla^2)^N \phi + \lambda \phi^3 + f + D $$</p>
<p>(EDIT: I first had $|\phi|^2\phi$, which is the nonlinear Schrodinger equation, but this has the same frequency shifting property as the relativistic version--- the frequencies are not completely perturbatively decoupled even with a resonance condition. The only reason I went to first order was to fix this annoying problem, and there is no condition of being physical. Although this will not conserve the total $|\phi|^2$, it has a conserved energy.)</p>
<p>Where f is a driving force with only long-wavlength components, and D is a damping force which only affects short wavelength components. The field $\phi$ is a complex scalar. Then if N is large and $\lambda$ is sufficiently small (by scaling, $\phi$'s magnitude can substitute for $\lambda$, so the limit of small $\lambda$ is really the limit of small $|\phi|$), the cascade due to the nonlinear term is a thermal gradient draining energy from the hot low frequency modes to the cold high-frequency modes.</p>
<p>I don't know if this model is in the literature, of if the thermal analysis is accurate (I am pretty sure it is correct, because the resonance matching does lead to local flow of energy in |k|, but I am not sure if there isn't a block to thermalization due to some problem with mixing in each |k| modes separately).</p>
<p>In the original answer, I used a second order equation, which has frequencies of both signs. This allows some extra mixing between distant modes, which shifts the frequency of low modes based on the occupation of high modes. While I don't think this changes the cascade significantly, I wanted a clean example, so I used a first order equation here. (EDIT: The clean example does not use the absolute value, so that the frequencies have to strictly additively combine.)</p>
<p>Is this model analyzed in the literature? Does it thermalize into a thermal gradient cascade?</p> | g7659 | [
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<p>Higher velocity implies low pressure. So in whirlpool the velocity of water have to decrease with radius in order to have force towards its center.</p>
<p>My question is how is explained whirlpool formation in simple words.</p> | g7660 | [
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<blockquote>
<p>A man pulling sled of his daughter by a massless rope, climbing a snowy hill whose slope is equal to 15 °. Considering that the mass of the sled is $4Kg$, the girl's $26Kg$ and $\mu _c = 0,25$, calculate the work done by the tension of the string after walking with constant speed a distance of $130m \Delta x$</p>
</blockquote>
<p>So, I know:</p>
<p>$\varphi=15°; \alpha =30°; m_d=26Kg; m_s=4Kg; \mu _c =0,25; d=130m$</p>
<p>So, the equations will be:</p>
<p>Weight in Y:</p>
<p>$P_y=P.\cos\varphi $</p>
<p>Weight in X:</p>
<p>$P_x=P.\sin\varphi$</p>
<p>Tension in Y:</p>
<p>$T_y=T.\sin\alpha$</p>
<p>Tension in X:</p>
<p>$T_x=T.\cos\alpha$</p>
<p>Normal force:</p>
<p>$P_y-N-T_y=0 \implies N = T_y-P_y$</p>
<p>Newton's 2nd law:</p>
<p>$\sum F = m_t.a \implies T_x-F_r-P_x=m_t.a$</p>
<p>Frictional force:</p>
<p>$F_r=\mu _c.N$</p>
<p>work definition:</p>
<p>$W=m_t.a.d$</p>
<p>Total mass:</p>
<p>$m_t=m_d+m_s \implies m_t =30Kg$</p>
<p>I want to get the acceleration of the object and then replacing $a$ I can get the string tension, so (...)</p>
<p>$a={{T_x-F_r-P_x}\over m_t}$</p>
<p>Now, ${T_x-F_r-P_x} = \sum F \implies {T_x-F_r-P_x} = W =m_t.a.d$</p>
<p>But again, If such replacement, the unknown $a$ appears again.</p>
<p>¿How can I solve this?</p> | g7661 | [
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] |
<p>how to define electric charge ? How to explain this term ? As learned by me
electric charge is an intrinsic property of atoms like mass of different atoms. </p> | g253 | [
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<p>Let's have the spherical spinors:
$$
\mathbf {Y}_{j, m, l = j \pm \frac{1}{2}} = \frac{1}{\sqrt{2l + 1}}\begin{pmatrix} \pm \sqrt{l \pm m +\frac{1}{2}}Y_{l, m - \frac{1}{2}} \\ \sqrt{l \mp m +\frac{1}{2}}Y_{l, m + \frac{1}{2}} \end{pmatrix}.
$$
How to prove the relation
$$
(\hat {\sigma} \cdot \mathbf r )\mathbf {Y}_{j, m, l = j \pm \frac{1}{2}} = -r\mathbf {Y}_{j, m, l = j \mp \frac{1}{2}}?
$$
I tried to rewrite the $(\hat {\sigma} \cdot \mathbf r )$ as
$$
(\hat {\sigma} \cdot \mathbf r ) = r\begin{pmatrix} \cos(\theta ) & \sin(\theta )\,e^{-i\varphi } \\ \sin(\theta )\, e^{i \varphi } & -\cos(\theta ) \end{pmatrix},
$$
but it's hard to use recurrence relations for associated Legendre functions after that. Is there some hint which simplifies the proof?</p>
<p>Maybe, I can first show that $(\hat {\sigma} \cdot \mathbf r )\mathbf {Y}_{j, m, l = j \pm \frac{1}{2}} = -ra\mathbf {Y}_{j, m, l = j \mp \frac{1}{2}}$,
because the parity of the left side is opposite to the parity of $\mathbf {Y}_{j, m, l = j \pm \frac{1}{2}}$, and $(\hat {\sigma} \cdot \mathbf r )$ commutes with rotation operator, because refers to the scalar pdoduct?</p> | g7662 | [
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<p>I have searched around the web and looked at Wiki entries and I am overcome by the number of catalogs available. What I want is a catalog that includes all objects you might conceivably see with equipment under $500k (I hope that captures all backyard astronomers).</p>
<p>Apart from that the main requirements are that it is up to date, machine readable (CSV is relatively easy. SQL might be too much to hope for?) and free to use. </p>
<p>Can anyone say which catalog would be best for that purpose and where I can get it?</p>
<p>(Is there one numbering system used for stars? I'm seeing HDE, SAO and Gliese numbers, Bayer and Flamsteed designations and proper names e.g. Rigol. If there isn't a universally identified system there must be some kind of cross reference? Thinking like a programmer - what's my primary key?)</p>
<p>While Physics isn't my first choice for this question the SE Astronomy site didn't make it through beta, and its page now directs users here.</p> | g7663 | [
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<p>(Rest) mass of proton = (rest) mass of neutron (approximately) = $1.67 \times 10^{-27}$ kg.</p>
<p>let $m$ be the mass of nitrogen atom then $m = 2.32 \times 10^{-26}$ kg.</p>
<p>$c = 3 \times 10^8$ m/s (approx).</p>
<p>Energy $E = mc^2$.</p>
<p>$E = 2.32 \times 10^{-26} \times 3 \times 10^8 \times 3 \times 10^8$ Joules.</p>
<p>$E = 20.88 \times 10^{-26+16}$ Joules.</p>
<p>$E = 20.88 \times 10^{-10}$ Joules.</p>
<p>Energy required to propel a nitrogen atom at the speed of light is very less. Is my calculation wrong?</p>
<p>Because even if we take a cluster of 10000 atoms of nitrogen we can make them cross the speed of light easily.</p> | g7664 | [
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<p>I have a question regarding the <a href="http://en.wikipedia.org/wiki/Holstein%E2%80%93Primakoff_transformation" rel="nofollow">Holstein-Primakoff representation</a>.</p>
<p>In the HP-representation we define the spin operators in terms of bosonic creation and annihilation operators.</p>
<p>$$
S_j^+ = \sqrt{2S - n_j} a_j \\
S_j^- = a^\dagger_j\sqrt{2S - n_j} \\
S^z_j = S - n_j
$$</p>
<p>Where $a_j$ and $n_j$ are operators. When we derive the magnon dispersion relation, we make the assumption that</p>
<p>$$
\frac{\langle n_j \rangle}{\langle S^z \rangle}\ll 1
$$</p>
<p>which is fine. As far as I understand this only means that we assume that most of the spins are pointing along the z-direction. However, when we go further in the derivation, we do a series expansion in $n_j/S$, so that i.e.</p>
<p>$$
S_j^+ = \sqrt{2S}\sqrt{1- \frac{n_j}{2S}+...} \approx \sqrt{2S}\sqrt{1- \frac{n_j}{2S}}
$$</p>
<p>This is where I don't understand. Say that we are in a spin $1/2$-system. In that case we can for one site have at most 1 magnon excitation and $S=\pm 1/2$, so for each individual site $n_j/2S$ is not much smaller than one. </p>
<p>My question is then, how can we justify that the series expansion makes sense in the operators at each individual site? Will the contributions from each site when summed up not contribute because</p>
<p>$$
\frac{\langle n_j \rangle}{\langle S^z \rangle}\ll 1
$$</p>
<p>or have I misunderstood something?</p>
<p>Any thoughts would be much appreciated.</p> | g7665 | [
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<p>One of the quantities appearing in the integral form of Maxwell's Equations is the line integral of the magnetic field around a closed loop. (The relevant equation states that this is equal to the current through any surface bounded by that loop, plus the displacement current in the case of changing electric fields, with some constant coefficients possibly thrown in, depending on how you manage your units. This is usually called Ampère's Law, with Maxwell's correction for the displacement current.)</p>
<p>Is there a name for this quantity? More generally, is there a name for the line integral of the magnetic field along an arbitrary non-closed curve? (Then this is not equal to any other named quantity or sum of quantities.) Ideally, I'd want a name for the integral of the H-field (rather than the B-field, when one distinguishes them) in amperes (or the equivalent in non-SI units), but I am not really picky about those details.</p>
<p>It seems that every other quantity in the integral form of Maxwell's Equations has a name (magnetic flux, electric flux, charge, etc), so I'd hope that this one does too. Of course, the term for the line integral of the electric field (electromotive force) is somewhat of a historical oddity, so maybe this quantity is too obscure to have a name. Still, you'd think that somebody would have given it one sometime!</p>
<p>ETA: A theoretical way to measure this quantity is to place a conductive tube (as conductive as possible, with as small diameter as possible) around the curve in question. The magnetic flux through the tube will induce a current running around (not along) the inside of the tube, which will in turn serve to cancel (or shield) the source of the magnetizing field, in accordance with Lenz's Law (in the broad sense). The current so induced, serving to completely cancel the magnetic field near the curve in question, should equal this quantity, if I'm thinking about this correctly. (Well, I'm having a little trouble getting the sign straight, but one way or the other it should work!)</p> | g7666 | [
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<p>I guess that everything that happens to me (or I do), happens before my shadow "records" the information. Is that right? Is it the same for any observer?</p> | g7667 | [
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<p>Does someone know simple model of energy loss in solid materials for a solid bullet?</p>
<p>For example: I want to estimate momentum transferred to a thin plastic plate given by a small bullet. No matter how difficult model is. But it should depend only on plate/projectile parameters?</p>
<p><strong>EDIT:</strong></p>
<p>No precise solution is needed. It is interesting to know order of energy transfer.
One simple model that i suggested was model of exponential suppression:
$$ {\delta E}(r) \approx E_{0} e^{ - \frac{r}{d} } $$
where $d$ is a "terminal length" - after crossing this length bullet loses $e$ units of energy. So, knowing max distance in material one can find parameter $d$</p>
<p>It is not obvious that this formula is close to reality, but it is first step. Also it is not clear if one can use this formula for thin plates.</p>
<p>I have no experience solving such problems, so i asked if someone can point me (links, books, ideas). </p> | g7668 | [
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<p>It is well known that you can trap water in a drinking straw by placing the tip of your finger over the top while the straw is in the water, and then lifting it out. The inner diameter of the straw is 0.5 cm; the height of the trapped water column inside the straw is 5.0 cm. Find the pressure in the air pocket between your finger and the water.</p> | g7669 | [
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<p>I read couple of similar question on this forum and few blogs on web, though I am still confused,I am determined to calculate object displacement using accelerometer data.</p>
<p>So, I tried using www.freescale.com/files/sensors/doc/app_note/AN3397.pdf , which gives nearly 20-50% error.</p>
<p>I also tried this equation on data and got some better results.</p>
<pre><code>V1 = V0 + ((a1) * t)
X2 = abs((V1 * t) + (((a1)/2)*t*t))
X2 = X0 + X2
V0 = V1
X0 = X2
</code></pre>
<p>Here
t is the time differance between two samples.
X0 is the final displacement.
V1,a1 current values.
V0 previous value.</p>
<p><a href="https://www.dropbox.com/s/qnux0f61mjbmaap/Idle_to_standing_sensor_readings.xls?dl=0" rel="nofollow">Here</a> is my graphs for the movement from Android sensors readings.</p>
<p>1)From Linear Acceleration Z axis graph, how do I calculate the distance?
2)Which values should I take and which should not? how many data samples I should use for calculation. For positive acceleration only or for an entire positive negative cycle of acceleration data?
3) What the Linear acceleration graph means. Please explain its values based on movement of object.</p> | g7670 | [
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<p>I need to know the consumption of a water tap in Liters. </p>
<p>I'm able to know the cross-sectional area of the pipe and how long the tap is open. With these data, how can I know the consumption/volume of water that pass through the water tap?</p>
<p>It can be rough estimation. I can assume a maximum volume of water...</p>
<p>Thanks in advance!</p> | g7671 | [
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<p>Are the stars in our galaxy spiraling inwards towards the center, or are they in a permanent orbit?</p>
<p>And if we are heading towards the center then what is the rate of this process?</p>
<p>I started wondering this while watching this documentary: <a href="http://www.youtube.com/watch?v=zKE4Bt8ylhM" rel="nofollow">http://www.youtube.com/watch?v=zKE4Bt8ylhM</a></p> | g1017 | [
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<p>While hiking through the Grand Canyon, I started wondering. Say we have a pipe for the purpose of transporting water across a canyon, with the bottom submerged in a pool of water. Like the blue line in this terribly drawn image:</p>
<p><img src="http://i.stack.imgur.com/7iVLE.png" alt="enter image description here"></p>
<p>Now let's seal the two ends of the pipe, which is full of water. What would happen if the pipe broke at the bottom of the U?</p>
<p>Note: It shouldn't matter whether the pipe is a U or a vertical line, I simply thought about this with a U-shaped pipe.</p>
<hr>
<p>If the ends of the pipe weren't sealed, the water inside the pipe would leak out until the height of the water outside the pipe was the same as the height of the water inside the pipe. But the ends are sealed.</p>
<p>A vacuum can support 10m of water, so perhaps the water will drain out of the pipe until it is 10m above the height of the water outside of the pipe, leaving a big near-vacuum behind. This would explain why the Grand Canyon's pipe has such a large number of valves.</p>
<p>On the other hand, we learn from <a href="http://what-if.xkcd.com/6/" rel="nofollow">http://what-if.xkcd.com/6/</a> that water boils into a vacuum. Does this leave a significant amount of water vapour behind?</p> | g7672 | [
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<p>Theorem 5.1 on page 80 of <a href="http://arxiv.org/abs/hep-th/0307199" rel="nofollow">this</a> paper says that </p>
<p><em>Assuming that the matter fields satisfy their equations of motion, the matter field action is locally Weyl invariant if and only if the corresponding energy-momentum tensor is traceless.</em></p>
<p>If I have understood this right, Weyl invariance reduces to scale invariance in flat spacetime, which is basically what I am up to at the moment.</p>
<p>My question now is:</p>
<p>If one has Weyl or scale invariance in accordance with this theorem, does this mean that global Weyl or scale invariance (such that the scaling parameter does not depend on position) is guaranteed too? If not why not?</p> | g7673 | [
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<p>I was reading about <a href="http://it.wikipedia.org/wiki/Mulinello_di_Joule" rel="nofollow">the experiment of Joule</a> (Italian wiki page). I'm not sure how it's called in English, since there is only an Italian and French version. In any case, in the page it is stated that (my translation):</p>
<blockquote>
<p>Through this experiment, Joule determined the <a href="http://en.wikipedia.org/wiki/Mechanical_equivalent_of_heat" rel="nofollow">mechanical equivalent of heat</a> to be equal to 4,186 J/cal, value of extraordinary precision for the time.</p>
</blockquote>
<p>Is the importance of this experiment "only" ascribable to the fact that the evaluation was really precise and exact for the time? Or are there other reasons? </p>
<p>I don't need a whole list of reasons, just the most exemplary/important<sup>1</sup> fact(s) will suffice. </p>
<hr>
<p><sup>1: Objectively considered as such by most researchers, experts, etc.</sup></p> | g7674 | [
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<p>In 2008, NASA astronaut Clayton Anderson <a href="http://www.space.com/6056-space-station-trash-burns-south-pacific.html" rel="nofollow">tossed a 635-kg tank of ammonia coolant</a> overboard from the International Space Station (ISS). Subsequently the tank burned up in earth atmosphere as planned.</p>
<p>Obviously in the 1-g environment on Earth's surface, no human could have lifted the tank let alone tossed it. The astronaut was only able to do so because the tank weighed much less in the microgravity environment of the orbiting (free-falling) ISS. </p>
<p>Because I was asleep in much of physics class in high school, I am unable to work out a formula for how much <s>weight</s> mass a human can chuck overboard from the ISS unassisted. In particular, I have only the vaguest notions of inertia and action/reaction. (What I mean is, I can look up Newton's laws of motion but I am unable to use them to solve my question.) </p>
<p>In the picture within the article that I linked to in my first paragraph above, we see that the astronaut appears to have his feet strapped into a footrest at the end of a robotic arm. </p>
<p>Am I right that this is vitally important because otherwise he would not have a backstop to push off from?</p>
<p>Anyway, can you give me a way to calculate, using simple arithmetic, what is the heaviest object that an average-strength human can toss overboard from the ISS? </p>
<p>Also, why is not all trash discarded from the ISS by being thrown overboard manually or using a device instead of being packed into a space-craft that will depart from ISS and burn up in the atmosphere?</p>
<p><sup><em>(A day later:)</em> Thank you to all three who took the time to reply so far, I upvoted each of your Answers. I could not for the life of me single out one for "acceptance" so no green checkmark from me this time :)</sup></p> | g7675 | [
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<p>Please note that I am very new on this website so have some difficulties in writings as required here but trying really hard to learn quickly. La-Tex is the main problem but please understand me that I am serious.</p>
<p>How do Vectors transform from one inertial reference frame to another inertial reference frame in [special relativity].</p>
<p>A bound vector in an inertial reference frame ($x$,$ct$) has its line of action as one of the space axis in that frame and is described by $x$*<em>i</em>*,then what would it be in form of new base vectors (<strong>a</strong>) and (<strong>b</strong>) in a different inertial system ($x`$,$ct`$) moving with respect to the former inertial system with $v$*<em>i</em>* velocity.Let (<strong>i</strong>) and (<strong>j</strong>) be the two bounded unit vectors with the line of action as co-ordinate axis($x$) and($ct$) respectively and senses in the positive side of co-ordinates and similarly (<strong>a</strong>) and (<strong>b</strong>) are defined for co-ordinates ($x`$) and ($ct`$) respectively.</p> | g7676 | [
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<p>What common household liquids / foodstuffs show Herschel-Bulkley fluid behavior?
I assume tomato soup to be one, since when sloshing it around lightly on a spoon the visible surface moves as one (as can be seen by following the dots of black pepper that don't change relative position) - is this observation basically correct?</p>
<p>What are (other) easy and sure ways to identify yield-stress behavior (vs. other non-Newton flows)?</p>
<p>How can common states of flow (through a pipe/ open channel, discharge from a small source into a large standing volume of the fluid, mixing) be observed - not necessarily quantitatively?</p>
<p>Are there easy to produce transparent yield stress fluids?</p> | g7677 | [
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<p>When we derive Ohm's Law using the Drude Model, we assume at one point of time that $E=V/L$, when is fact, $E=dV/dL$, unless $E$ is constant, in which case the assumption $E=V/L$ is true. But I don't understand why the electric field in a conductor must be constant as current flows. Is there a convincing explanation that is perhaps related to the way atoms behave and orient themselves?</p>
<p>Also, if the assumption $V=E\cdot L$ makes sense, I can understand why Ohm's Law should work for a homogeneous electric circuit. However, I don't understand why it should work for a heterogeneous circuit - perhaps one with two different resistors connected in series. And please don't use the traffic jam analogy. Surely there must a more theoretical way to explain this (using Classical Physics).</p> | g7678 | [
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<p>To preface my question, I ask this as a mathematics student, so I don't have a very good sense of how physicists think.</p>
<p>Here is the historical context I'm imagining (in particular taking into account the development of differential geometry in the 19th century):</p>
<p>Classical mechanics is about Lagrangians of matter fields on $\mathbb{R}^3$ (with the flat metric)</p>
<p>Sometime in the 1820s Gauss speculated about replacing the flat metric on $\mathbb{R}^3$ by one with non-vanishing curvature</p>
<p>Special relativity is about Lagrangians of matter fields on $\mathbb{R}^{3,1}$ (with the flat metric). I'm taking this jump for granted since as I understand it, it was arrived at from experimental results on electromagnetism at the end of the 19th century.</p>
<p>Now in line with Gauss, it seems like it would be extremely natural to speculate about replacing the flat metric on $\mathbb{R}^{3,1}$ by one with non-vanishing curvature (and in the same spirit also considering more exotic topologies for the underlying manifold).</p>
<p>Given that then we would have to ask exactly which metric we are looking for, it seems natural to say that there should be a Lagrangian term corresponding to the metric. The Einstein-Hilbert functional is probably the simplest one to try. And so we get the Einstein equations.</p>
<p>Alternatively (as I heard from someone is the actual history) you could observe that the energy-momentum tensor is of course a 2-tensor, and so for an Euler-Lagrange equation the most natural metric-dependent expression would be $\operatorname{Ric}=T$. Since $T$ is always divergence free it would be natural to replace $\operatorname{Ric}$ by $\operatorname{Ric}-\frac{1}{2}Rg$ just from taking the contracted second Bianchi identity into account. And so again we get the Einstein equations.</p>
<p>I've often heard it said that if Einstein had not come up with special relativity, someone else probably would have in the next five or ten years. However if he had not come up with general relativity, it would have taken much longer to discover. <b>Why is this?</b> I feel that I must be missing something here.</p> | g7679 | [
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<p>Many of the most brilliant ideas of modern physics are very much unpopperian. In view of this, it has become more and more difficult to hold an orthodox Popperian attitude in physics. It simply looks like more of a philosophical dogma nowadays. My question is, should physicists abandon this criterion at least partially for good? If so, what criterion should replace it?</p> | g7680 | [
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<p>So, one thing has been annoying me ever since I learned about <a href="http://en.wikipedia.org/wiki/Orbital_hybridisation">orbital hybridization</a>: you explain the shape of molecules by postulating that the orbitals of multi-electron atoms are linear combinations of the orbitals of the hydrogen atom. Fine.</p>
<p>Here's what gets me, and I've asked several chemistry professors about this, and I haven't gotten an answer. If I measure the orbital angular momentum of an electron in a hydrogen atom, I get the value $L = \hbar \sqrt{\ell(\ell +1)}$, so an s orbital has angular momentum $0$ and a p orbital has angular momentum $\hbar$.</p>
<p>So, what happens when I measure the orbital angular momentum of a sp${}^{3}$ electron? Do I get $\frac{3\hbar}{4}$ with probability 1? Or do I get $\hbar$ with probability 0.75, and $0$ with probability 0.25? Are the original orbitals really the fundamental thing, and the hybridized orbitals fundamentally just quantum superpositions of these things? Or does the multi-electron potential create a state that just looks like a linear combination of one s and 3 p orbitals?</p>
<p>Or is the actual answer more complicated and this a heuristic picture that I'm taking too seriously?</p> | g7681 | [
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<p>If our universe comes from a flux compactification of string theory over 6 dimensions with a nonzero flux, then it can't be continually deformed to another compactification with zero flux as the total flux is a topological invariant. The cosmological constant of our universe is positive, which in string theory means it is a metastable state. The stable vacuum for a flux compactification in string theory is a BPS compactification with negative cosmological constant.</p>
<p>What if our metastable observable universe is actually embedded in a larger stable anti de Sitter background? An inflating metastable or slowly rolling or chaotically inflating patch of this asymptotically AdS universe inflates to our observable universe. By the AdS/CFT correspondence, our universe can be described by a superconformal field theory in 2+1D with no gravity.</p>
<p>Is there any flaw in my reasoning?</p> | g7682 | [
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<p>The WIKI Higgs boson site has an interesting diagram illustrating likely Higgs mass intervals that experiments (LEP & Tevatron) or indirect measurements have determined with a 95% confidence level. It posits that the feasible mass ranges are in the intervals of about 115-158 GeV or 175-185 GeV. The Tevatron confirmed the existance of the top quark (172 GeV) in 1995, so it had the energy and time to detect the Higgs in the 115-158 GeV ranges, but could not.
Given LHC's greater energy and luminosity, why haven't there been anouncements of the Higgs discovery? Do we understand enough about potential particle creation to definitively know they are Higgs decays? </p> | g7683 | [
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<p>It can be shown the sum over all Feynman diagrams in quantum field theory leads to a unitary S-matrix. Where can I find a proof that the sum over string worldsheets with varying genuses also leads to a unitary S-matrix?</p> | g7684 | [
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<p>The current zeitgeist here is on interpretations of quantum mechanics, so let me add my own two cents here. As you may know, consistent histories is an alternative interpretation proposed in a series of papers 1990-1994 by Gell-Mann and Hartle. In a shocking article, <a href="http://arxiv.org/abs/gr-qc/9412067" rel="nofollow">Dowker and Kent</a> proved there are many distinct consistent histories for most quantum systems. Even if we constrain ourselves to quasiclassical histories, i.e. those histories which are close to classical, being quasiclassical now does not guarantee being quasiclassical in the future, or in the past. This is disturbing. Do histories which are quasiclassical for all times exist? If they do, are they unique? Is the nightmare scenario of two everywhere quasiclassical consistent histories which are mutually incompatible possible? </p> | g7685 | [
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<p>There're some easy concepts which I don't get exactly in my mind. I've been studying these things for two years of my engineering but they still bother me. Battery is one of them. Can someone explain?</p>
<ul>
<li>Whether a battery store energy or simply it makes energy?</li>
</ul>
<p>I have searched it on Google and Yahoo but didn't find any helpful thing there (for me). So I will be glad if I got my problem solved here.</p>
<p>P.S. I hope that the question would not again be an off-topic, as it always does and moreover people don't suggest then where to go. It's a real sad thing.</p> | g7686 | [
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] |
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