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<p>Suppose we have a symmetric wavefunction that composed of a two-particle system:</p>
<p>$$ \psi_s = \frac{1}{\sqrt 2} \left(|u,A\rangle|v,B\rangle + |v,A\rangle|u,B\rangle\right)$$</p>
<p>where $u_{(x)}$ and $v_{(x)}$ are wavefunctions corresponding to orthonormal bound states u and v.</p>
<p>Can I assume that the states with particle A sitting in u, and v are orthogonal? i.e.</p>
<p>Can I assume $$\langle u,A|v,A\rangle = \langle u,B|v,B\rangle = 0$$?</p>
<p>Thus is the overlap this:</p>
<p>$$\langle\psi_s|\psi_s\rangle = \frac{1}{2}\int \langle u,A|u,A\rangle\langle v,B|v,B\rangle + \langle v,A|v,A\rangle\langle u,B|u,B\rangle d^3r = \int 2|u|^2|v|^2 d^3r $$?</p>
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<p>I was looking at a plot of the parton distribution functions today and had a question. On the y axis, it seems like the value of x f(x) for gluons is greater than one at small x. I was under the impression that parton distribution functions are probability densities and cannot be greater than one. Also, x is a fraction of momentum and can also not be greater than one. Does anyone know why this is?</p>
<p><a href="http://www.google.com/imgres?um=1&hl=en&sa=N&biw=1920&bih=821&tbm=isch&tbnid=T1lUDiMsjtq3oM%3a&imgrefurl=http://en.wikipedia.org/wiki/File%3aCTEQ6_parton_distribution_functions.png&docid=6IDx1_-MUSW2_M&imgurl=http://upload.wikimedia.org/wikipedia/commons/0/0d/CTEQ6_parton_distribution_functions.png&w=1024&h=717&ei=pTYtUMTxMOXj0QHI9YHYDQ&zoom=1&iact=hc&vpx=158&vpy=138&dur=87&hovh=188&hovw=268&tx=129&ty=104&sig=101432623456645059726&page=1&tbnh=106&tbnw=144&start=0&ndsp=58&ved=1t:429,r:0,s:0,i:76" rel="nofollow">link to PDF image</a></p>
<p>Thanks!</p>
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/9290/why-does-the-moon-drift-away-from-earth">Why does the moon drift away from earth?</a> </p>
</blockquote>
<p>It seems to me that, due to conservation of energy, the moon would drift away from the Earth if humans began extracting large amounts of energy from the ocean due to the shift in water levels due to the tides. This would occur to decrease the gravitational energy in the system. Some have said that it would cause the rotation of the moon to slow down, but that doesn't seem right to me. </p>
<p>Edit: To make it certain that something must happen, assume that the energy extracted from the tides is 100% radiated outside of the closed system that includes all volume surrounding the moon and the earth. The inside of that system must lose energy somehow.</p>
<p>Edit: If your answer involves the rotation of the moon and/or earth, what would happen if neither were rotating?</p>
| 221 |
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<p>I was curious if antimatter could undergo nuclear fission/fusion with other antimatter. It makes sense, I was wondering if it would work?</p>
| 9,641 |
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] |
<p>Is the inflation speed of the universe accelerating or is it a constant speed of expansion proportional to distance between objects.</p>
| 9,642 |
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<p>I'm confused by the famous wave-particle duality mystery:</p>
<p>When a particle is left unobserved, it acts like a wave and can explore all classically available particle trajectories simultaneously. By looking at it, you force it to decide on a single trajectory, like going through the left or right slit, or like Schrödinger's cat that ends up being either dead or alive; the wave-like characteristics are lost.</p>
<p>Are there theories that actually <em>explain</em> this behaviour?</p>
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<p>Although the question stands for itself, I would like to know that if the answer has to be no then does any particular law forbids the existence of such forces; and if there are such forces then what are these and upon travelling under such forces in a closed loop where does the energy come from (as they are non conservative and non dissipative)?</p>
<p>Addendum : I would also highly appreciate it if someone could give an example of force fields which could be set up and left undisturbed by movement of particles under their influence. For example a charged non conducting fixed sphere provides an approximately fixed static field under which if particles move the cause is not disturbed. Since we know about induced electric field, but motion of charged particles under induced electric field, disturb its cause and then we have to supply more energy to maintain the field at original state. </p>
<p>I would hasten to add that although this would be highly appreciated, its not a necessity for the original question.</p>
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<p><strong>Chaos</strong> is defined as an aperiodic long-termed behavior, that is very sensitive to initial conditions.</p>
<p>Now from this definition I can only conclude that the adjective 'chaos' is a <em>mere analogy</em>, since there is nothing aperiodic (or periodic) during inflation. The inflaton follows a nice, smooth (often taken to be a quadratic) potential.</p>
<p>Furthermore the initial conditions are essentially that
$$\ddot{\phi}\approx 0 \quad \text{and}\quad \dot{\phi}\text{ is small},$$
shows that these are not very stringent wrt to the final result: at whatever 'speed' you begin, as long as it small enough it is ok....</p>
| 9,645 |
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<p>When studying supersymmetry breaking, people often use a spurion chiral superfield to study the soft SUSY breaking terms which enter the Lagrangian ($X=\theta^2 F$). Since we let the spurion couple to every field and assume that the messengers are at the Planck scale this is used to parametrize gravity mediated SUSY breaking. For example we can get scalar masses through,
\begin{equation}
\int d^4\theta \frac{X^\dagger X}{M^2} Q^\dagger Q
\end{equation}</p>
<p>Recently I've seen papers using <a href="http://acfahep.kek.jp/acfareport/node104.html" rel="nofollow">anomaly mediated SUSY breaking</a> in their theories instead (one such paper can be found <a href="http://arxiv.org/abs/1203.5340" rel="nofollow">here</a>). Is there a way to parametrize the SUSY breaking terms in the anomaly medaited scheme analogously to the typical gravity mediated scenario?</p>
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<p>The question goes like this:
If we push a body shortly uphill and it gets a starting velocity of $v \ ms^{-1}$,the coefficient of friction between the body and the surface is constant, represented by $k$, . Which graph shows the movement of the body correctly?</p>
<p>The answer on the back of the book is a graph that looks like A but I think it should be like B. Because the acceleration is the same (so if $y$ is the line, $y=kx+l$, $k$ should stay the same) and nothing else is mentioned. Am I right? </p>
<p>A:</p>
<p><img src="http://i.imgur.com/FnPYreC.jpg" alt="Graph A"> </p>
<p>B :</p>
<p><img src="http://i.stack.imgur.com/ddA6a.jpg" alt="Graph B"></p>
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] |
<p>I have recently come to know that the electric and magnetic field contain both the translational and angular momenta in it given by some particular formulas at any given instant of the space....But I don't understand how? PLEASE EXPLAIN.....
Is it related to photons being emitted by the accelerating charges or with Abraham Lorentz force....??</p>
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<p>Was reported <a href="http://xxx.lanl.gov/abs/1208.3829">here</a>. Of course if this is real it is very exciting. It leads me to the question: given that it took so long to find this resonance at a meager 38 MeV, is it possible that all SUSY particles are hiding down in the MeV or KeV range (or lower)?</p>
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<p>The question is about <strong>experiments</strong> (and references) that demonstrate interference patterns of neutral (chargless) particles (fermions), especially neutrons.</p>
<p>Like <strong>double-slit experiments for neutrons</strong> (or equivalent).</p>
<p>Searching around did not yield sth (or maybe i did not notice it). </p>
<p>My understading is that similar experiments have only been done for charged particles (i.e electrons, protons) or bosons (i.e photons).</p>
<p>Is this correct?</p>
| 9,650 |
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] |
<p>Dirac argues on page 17 of his book, The Principles of Quantum Mechanics, that multiplication of a ket by a complex number shouldn't change the state this ket represents. But then concludes:</p>
<blockquote>
<p>Thus a state is represented by the direction of a ket vector, and any
length one may assign to the ket vector is irrelevant.</p>
</blockquote>
<p><strong>Bearing in mind that he has only stated that we need to make a generalization of vectors in a space of an infinite number of dimensions</strong>, how is he able to conclude this?</p>
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] |
<p>I'm looking for existing papers studying a variation to Einstein equation that does not rely on the annoying matter conservation identity:</p>
<p>$$ T_{\mu \nu; \nu} = 0 $$</p>
<p>And instead tries to equate the divergence-free Einstein tensor with a sum of $T_{\mu \nu}$ plus some gravitational energy tensor $Y_{\mu \nu}$:</p>
<p>$$ G_{\mu \nu} = 8 \pi G (T_{\mu \nu} + \theta Y_{\mu \nu}) $$</p>
<p>Where the $\theta$ factor is a parameter of the ansatz.</p>
<p>Let me explain why this ansatz should be physically interesting: because the vanilla version of Einstein equation is based on the assumption that conversion between gravitational and non-gravitational energy does not happen never, ever. If you cherry-pick the gravitational energy tensor to be, say, the Landau Lifshitz <strong>tensor</strong>:</p>
<p>$$ Y^{\mu \nu} = (\sqrt{-g}_{; \alpha \beta}) ( g^{\mu \nu} g^{\alpha \beta} - g^{\mu \alpha} g^{\nu \beta} ) $$</p>
<p>(notice this is not the pseudo tensor variant; those derivatives are covariant)</p>
<p>this tensor is zero in the weak-field limit, is non-zero only after second order corrections in the metric, so it would match most astronomical observations that match GR in the weak field limit. Would be interesting to see what predictions does this produce in the nonlinear regime. In fact, the above argument applies just as well to any meaningful gravitational tensor that has only second order (or smaller) non-zero corrections.</p>
<p>Any thoughts?</p>
| 9,652 |
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<p>I'm having trouble with the explanation that a standing wave in a string is the superposition of traveling waves.</p>
<p><img src="http://www.physicsclassroom.com/Class/waves/u10l4c5.gif" alt="standing wave"></p>
<p>The nodes in the diagram above are points where the particles of the string's medium undergo zero displacement, i.e. they do not move at all. But if they do not move, <em>how is the disturbance of (any internal traveling wave) propagated past the node</em>?</p>
<p>The usual explanation for how a wave is propagated is that when one particle is disturbed (say, moved up), it exerts a pull on another, which in turn exerts a pull on the next one, and so on. In other words, to exert a pull or push on the next particle there must be some movement/disturbance of the previous one. But the particle(s) at the node point do not move at all, so how does the disturbance of a traveling wave propagation pass through them? (I'm trying to understand the picture in terms of the mechanical forces between particles).</p>
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<p>I'm having some trouble finding an expression for the probability to find the particle outside the classical area in the harmonic oscillator.</p>
<p>I have a wavefunction defined as:</p>
<p>$\psi \left( x,\,t \right)=\frac{1}{2}\left( \sqrt{3}i{{\phi }_{1}}\left( x \right){{e}^{-i{{E}_{1}}t/\hbar }}+{{\phi }_{3}}\left( x \right){{e}^{-i{{E}_{3}}t/\hbar }} \right)$</p>
<p>I'm supposed to give the expression by $P(x,t)$, but not explicitly calculated.</p>
<p>My thought was to use:</p>
<p>${{\int_{a}^{b}{\left| \psi \left( x,t \right) \right|}}^{2}}dx$,</p>
<p>but then I pretty ran into the wall.</p>
<p>So anyone who could give me a hint of what to do ?</p>
<p>Thanks in advance.</p>
| 9,654 |
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] |
<p>The planetary motion equations are written in the ellipse equation format, i.e. $x^2/a + y^2/b = 1$.</p>
<p>Can anyone please tell me where I can find the list of all the planetary motion equations, (Mercury, Venus, Mars, Earth, and so on) in the form of $(x(t)-c)^2/a + (y(t)-d)^2/b = 1$? (Both $x$ and $y$ are functions of $t$.)</p>
| 9,655 |
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<p>Is there a simple way to understand why phonon-phonon-interaction is described by higher order terms in the potential?</p>
<p>I mean: Having a quadratic potential is essential for the definition of the phonons as excitations of an harmonic oscillator. How can you suddenly talk about (interacting) phonons when you don't have a simple quadratic potential anymore...</p>
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] |
<blockquote>
<p><em>A compound flywheel is to be constructed in the form of a circular disc with a radius of 0.25m, a thickness of 0.05m and a moment of inertia about its axis of 2Kgm2. the flywheel is to have a central circular disc of aluminium alloy, density 2800kgm-3, and a steel outer rim, density 7900kgm-3. denoting the radius of the junction between the alloy central disc and steel outer rim by r, find expressions for the moments of inertia of
a) the alloy central disc about its axis
b) the steel outer rim about the same axis
hence determine the value of r.</em></p>
</blockquote>
| 9,657 |
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] |
<p>In <a href="http://www.youtube.com/watch?v=BcLk7jEQfx0" rel="nofollow">this</a>, in my opinion, intriguing speech, Rupert Sheldrake, tells the story of the drop between the measured valued of $c$ in 1928 and 1945. When he goes to visit the Head of Metrology of the Physics Lab in Teddington, he says (I resume):</p>
<blockquote>
<p>$c$ cannot change, it is a constant! We explain the drop you are
talking about with "intellectual phase locking". Anyway, we have now
solved the problem. We fixed the speed of light by definition in 1972.
He might still change, but since we define the meter from $c$, we
would never know.</p>
</blockquote>
<p>Is that true? If $c$ changed, would we be able to see it? And how does official science explains really the famous drop in the measures of $c$?</p>
| 9,658 |
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<p>I've noticed that if you take a full glass of water and look from above, through the water, you can't see through the glass sides - instead, you see a reflection. I tried with a laser pointer and the case was the same, the beam was just reflected from the water-glass interface. Even when looking from a variety of angles the case is the same. With no water in the glass, you can see through it fine.</p>
<p>Why is this?</p>
<p>I thought maybe <a href="https://en.wikipedia.org/wiki/Total_Internal_Reflection" rel="nofollow">TIR</a>, but then $n_{\text{water}} \approx 1.3$ and $n_{\text{glass}} \approx 1.5$. So the light is going from a lower to high <a href="http://refractiveindex.info/?group=LIQUIDS&material=Water" rel="nofollow">refractive index materia</a>l, which shouldn't give TIR.</p>
<p>A little research (Wikipedia) suggests that you can get Frustrated TIR from tightly grasping the glass, so photons can tunnel through from inside the glass of water, get reflected by skin and then tunnel back to get to your eye (again, I <em>think</em> this is right).</p>
<p>However, I wonder what physical mechanism prevents light from escaping a glass of water?</p>
| 9,659 |
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<p>In the paper <em>Markov Fields</em> by Edward Nelson the introduction section claims that analytically continuing a Markov process with appropriate symmetry properties yields the solution of the Schrodinger equation. </p>
<p>What is the appropriate symmetry required by a Markov process to solve the Schrodinger equation? Is the symmetry that of the Euclidean group? </p>
<p>Furthermore, how would you show a Markov process with appropriate symmetry is a solution to the Schrodinger equation?</p>
<p>Link to the paper: <a href="http://www.mathunion.org/ICM/ICM1974.2/Main/icm1974.2.0395.0398.ocr.pdf" rel="nofollow">http://www.mathunion.org/ICM/ICM1974.2/Main/icm1974.2.0395.0398.ocr.pdf</a></p>
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<p>Roughly speaking, in condensed matter systems, spin waves and spin density waves are both low-energy states with spin that varies spatially. What precisely are their differences?</p>
| 9,661 |
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<p>From a statistical mechanics point of view, the <em>extensivity</em> of thermodynamics arises from the fact that we can neglect interaction terms in the Hamiltonian. This allows us to infer that when we put two systems in contact, the total energy is approximately equal to the sum of the individual systems' energy. If the systems are in thermal equilibrium it follows that the entropy is extensive as well.</p>
<p>However, it is well known that if the interaction terms cannot be neglected then these extensivity results do not follow. In theory, this should typically be the case for very small systems. (It should also be the case for systems with very long range interactions, such as gravitational systems, but for this question I'm more interested in systems that are made of atoms and interact electromagnetically.)</p>
<p>I'm interested in whether there has been any experimental work designed to measure this effect experimentally. In principle it could be done with calorimetry, but I'm not sure how sensitive the measurements would need to be. There might be ways to multiply the effect into a larger one, such as letting a very large number of tiny particles come into contact, rather than just two. Indeed, it might be a well-known effect that just isn't usually explained in these terms.</p>
<p>I'd be particularly interested in work that measures the non-extensivity of <em>both</em> internal energy <em>and</em> entropy, in the same system, using independent measurements. However, any empirical work that addresses this issue is of interest.</p>
<p>From searching Google I did come across a few experimental papers that mention non-extensivity. However, they seem to be concerned with testing the predictions of Tsallis entropy maximisation, which isn't what I'm interested in here. I'm really looking for calorimetric measurements of the non-additivity of the Hamiltonian in small systems, and the resulting changes in thermodynamic properties.</p>
| 9,662 |
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<p>I have been trying to reason why energy packets (i.e. <a href="http://en.wikipedia.org/wiki/Photon">photons</a>) are assumed to be quantized. I know this originated from Max Planck, but may someone explain why energy couldn't be emitted continuously rather than in packets?</p>
<p>Also:</p>
<p>Planck said he didn't understand the reason for this, but it happens. So, how did he arrive at the assumption?</p>
<p>Thanks for any clarification!</p>
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<p>Events in relativity[SR or GR]are marked by coordinate values and not by physical values.We write a metric for motion along the x-axis:
$$ds^2=g_{00}dt^2-g_{11}dx^2$$ ----------- (1)</p>
<p>For physical values we may write:</p>
<p>$$ds^2=dT^2-dL^2$$ ------------ (2)</p>
<p>Where $dT^2=g_{00}dt^2$ and $dL^2=g_{11}dx^2$</p>
<p>For the null geodesic $ds^2=0$</p>
<p>From (1) we have for the null geodesic,</p>
<p>$$\frac{dx}{dt}=\sqrt{\frac{g_{00}}{g_{11}}}\ne1$$ [Generally speaking]-----(3)</p>
<p>Relation (2) provides a SR picture in the local context.
since,
$$\frac{dL}{dT}=1$$ ------------ (4)</p>
<p>[c=1 in the natural units]</p>
<p><em>Since events are marked by coordinate values</em> our light cone in GR should correspond to equation (3). It should be a flickering one in a time varying field[ and one with a distorted surface in a stationary field] since the metric coefficients go on changing in a time varying field.</p>
<p>As I advance long the time axis the distorted surface of my light cone goes on changing.Points which I expect to be at space-like separation in the future are now at a time-like separation[or vice versa]</p>
<p>Query:Does this relate to changes in the causal structure of the light cone?</p>
| 9,664 |
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<p>In popularizations, people tunnel through walls or doors. But what can really tunnel through a graphene sheet without tearing it? </p>
<p>According to Wikipedia, a single layer of graphene absorbs 2.3 % of white light, but 97% makes it through. It conducts electrons well enough to make a transistor. </p>
<p>I doubt that a baseball tunnels through a sheet of graphene without harming it.<br>
But what about a Buckyball? or a smaller molecule? A helium atom? A bare proton? </p>
<p>This looks deceptively like the one dimensional finite barrier problem in elementary QM textbooks. Can we calculate the probability of a given projectile at a given velocity tunnelling through the graphene sheet? Is there any experimental data?</p>
| 9,665 |
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<p><img src="http://img696.imageshack.us/img696/7078/gaussl.jpg" alt="">!</p>
<p>Why does it say that the flux due to q_2 and q_3 through S is 0? Doesn't it contain a nonzero charge q_1? </p>
<p>Does anyone also know the difference between "no charge" vs "net charge is 0"? My book differentiates it.</p>
| 9,666 |
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<p>While answering <a href="http://physics.stackexchange.com/a/71912/6634">another question</a> about heat in an atom, the discussion in the comments led to the question of how heat is related to thermal radiation picked up by infrared cameras. The answer is that molecules undergoing translational motion (which therefore have a temperature) emit energy in the IR range and the intensity of the radiation in that range is related to the temperature. </p>
<p>What is the actual mechanism for the emission of this energy? What is it about translation that causes the emission? Does it require collisions with other atoms/molecules to cause a change in momentum and the emission of thermal energy (thereby slowing down/cooling the bodies involved in the collision)? </p>
<p>Does that mean in rarefied conditions where the mean-free-path is relatively large, the rate of IR emissions decreases (while the intensity is still only dependent on the temperature)? </p>
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<p>When a charged particle moves in an electric field, the field performs work on the particle. Thus, the energy of the field decreases, turning into kinetic energy of the particle.</p>
<p>Does the magnetic field of a permanent magnetic similarly lose energy and perform work when moving a conductor with a current?</p>
| 9,668 |
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] |
<p>Minkowski space time is defined in terms of a flat pseudo-Riemannian manifold. I have wondered if it can be redefined as Riamannian manifold and in the case what type of curvature would there appear.</p>
<p>Formally:</p>
<p>Let M be a semi-Riemannian manifold of dimension 4, corresponding to the Minkowski space, and let g be the metric tensor (non positive definite), T be the Riemann curvature tensor and P a generic point of M.</p>
<p>Question 1</p>
<p>Which (if any) of the following is true?</p>
<p>a. at every P there exists one system of coordinates for which the metric g becomes Riemannian (positive definite) in a ball of radius R non infinitesimal centred in P</p>
<p>b. there exists one system of coordinates for which g is Riemannian (positive definite) at all P of M</p>
<p>Comment: in words, can we, with a change of coordinates, get rid of semi-Riemannianity – either in finite region or globally? </p>
<p>If this is the case, how do we pay it in terms of curvature? This the next question:</p>
<p>Question 2</p>
<p>c. if previous a) is true,
is it true that T cannot be null in the entire ball? And what type of curvature T "displays"?</p>
<p>d. if previous b) is true,
is it true that T cannot be null in the entire ball? And what type of curvature T "displays"?</p>
<p>Thanks a lot</p>
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<p>Currently working through a practice preliminary examination problem. I have your standard charge situated a distance d from a infinite conductor(lets say in the $\hat{z}$ direction and neglecting gravity). The question asks when $v = 0$ at $t = 0$, determine the equation of motion of the electron.</p>
<p>We know the charge induces a oppositely charged particle a distance 2d from the original charge. The electric field due to this charge at the point of the original charge is</p>
<p>$$\vec{E} = - \frac{1}{4 \pi \epsilon_0} \frac{q}{(2d)^2} \hat{z}$$
giving a force of $\vec{F} = q \vec{E}$</p>
<p>Therefore $\ddot{z}(t) = -\frac{1}{16 \pi \epsilon_0} \frac{q^2}{m d^2} $ and straightforward integration gives $z(t) = - \frac{1}{32 \pi \epsilon_0} \frac{q^2 t^2}{m d^2} + d$</p>
<p>Now here's where I'm getting confused. The question then asks a "You know a moving electron produces a magnetic field, does this magnetic field vary with time?"</p>
<p>Intuitively I would say yes because as the speed increases we will have two $\vec{B}$ fields created in the new moving frame from the acceleration of the charges(one original charge and one image charge)</p>
<p>The force felt on the original charge will now have to be the Lorentz force law, but I'm not sure how to include the velocity terms in here. </p>
<p>Thanks.</p>
<p>EDIT I - (7/23/13): I think if I was to see the precise equations of motion for the entire range of the motion as the charge eventually comes to the plate. I would understand what I'm missing.</p>
<p>EDIT II - (7/26/13):</p>
<p>Since we are looking at an image charge that is also in motion(accelerating and moving at some instantaneous velocity) A poster here has given an idea to use the Leinard-Wiechert expression for the Lorentz force and then calculate the EOM from here. The expression of the LW Lorentz force is quite complicated. See for example 10.67 in Griffiths EM in SI units. Where is the acceleration of the test charge in this expression? </p>
<p>This question and differential equation seem entirely too complicated for a qualification examination but it has sparked some interest. Is it even possible to write down the EOM for this situation?</p>
| 9,670 |
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<p>If the physical world we know is made of matter stretched in time and space and some forces affecting it, what would be an Idea, pure Information or something similar.</p>
<p>Does those things don't exist in a physical model or did I just miss something.</p>
<p>If yes where to arrange it into the physical model? Is an idea just matter without time and Space?</p>
| 9,671 |
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<p>I am trying to figure out how an object could achieve a perfectly circular orbit. Given a mass for the planet or other body the object is orbiting and a distance from the center of mass, how fast would the object have to be moving perpendicular to the center of mass?</p>
<p>My initial assumption was it would have to be travelling horizontally (relatively speaking) as fast as it was falling towards to center of mass. Is this a correct assumption? I guess I am confused because it is easy to calculate the acceleration towards the center of mass given the distance and mass of the body, but I have no idea how you would go about calculating the velocity necessary.</p>
| 9,672 |
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<p>I was pointed out by a friend to <a href="http://hint.fm/wind/" rel="nofollow">this website</a> that shows live map of wind in US. It sometimes show interesting places where <a href="http://imgur.com/yEOjS" rel="nofollow">all the wind seems to converge and vanish</a>. </p>
<p>What's the origin of such "wind drains"? Do pure geological phenomena lead to simple cancellation of wind vectors or more complex effects? Is that (can that be) somehow explored in terms of wind energy?</p>
| 9,673 |
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<p>I've read that QM operates in a Hilbert space (where the state functions live). I don't know if its meaningful to ask such a question, what are the answers to an analogous questions on GR and Newtonian gravity?</p>
| 9,674 |
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<p>Is dark matter really a form of matter? We know it has a gravitional attraction and we know that everything that has a gravitional force is made by matter. But maybe this is an exception? </p>
<p>And if there are such theories, would there be theories on that dark energy is not really energy?</p>
| 9,675 |
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<p>In what ways can energy transform into matter and vice versa? Annihilation is one way to tranform matter to energy. Fission is another (when splitting and atom, what happens to its two parts?)</p>
<p>Are quantum fluctuations one way to transform energy to matter?</p>
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<p>If I have two containers filled with very hot water(~210F) with one in outer space and one on earth, which one has a higher rate of cooling initially? Imagine the containers are single wall metal containers that are able to withstand any pressure.</p>
<p>Intuitively I would assume the one in space would cool faster because the average temperature of space is 3K. However a vacuum flask is an extremely good insulator since the only way heat can transfer is through radiation. Space is an even more extreme vacuum then any flask so would that mean that it "insulates" even better?</p>
<p>If allowed to come to thermal equilibrium, the space container would certainly lose more energy overall, but is the rate affected by the temperature difference a la <a href="http://scienceworld.wolfram.com/physics/NewtonsLawofCooling.html" rel="nofollow">Newton's Law of Cooling</a> or does it lose energy at the same rate no matter what?</p>
| 9,677 |
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<p>Imagine a bullet fired at a series of partitions stacked one after the other. Given that the bullet looses half its velocity in crossing each partition, velocity of the same is a geometric progression(GP) with $a= v_0$ and $r=0.5$.</p>
<p>The question is, how many partitions is it supposed to successfully cross, or at what partition would the bullet be stopped?</p>
| 9,678 |
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<p>Someone claiming to have studied physics is telling me that spacetime is all that exists and that this fact is the basis of modern physics. When I said matter/energy also exists in its various forms, he said that energy is merely spacetime "waving/vibrating/acting", else what did I think was doing the waving: magical fairy dust? and has presented the following Einstein quote to support his claim:</p>
<p>"When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter."</p>
<p>Does Einstein's quote support what he's saying, that space-time is all that exists, and that matter/energy is spacetime waving?</p>
| 804 |
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<blockquote>
<p>Starting with the Boltzmann equation in terms of $f(t,\vec v,\vec x)$ or $f(t,\vec v)$</p>
<p><a href="http://en.wikipedia.org/wiki/Boltzmann_equation" rel="nofollow">http://en.wikipedia.org/wiki/Boltzmann_equation</a></p>
<p>$$\left(\frac{\partial}{\partial t} + \vec{v} \, \nabla_\vec{x} + \frac{1}{m} \vec{F}\cdot \nabla_\vec{v}\right) f(\vec{x},\vec{v},t) = \left.\frac{\partial f}{\partial t}\right|_\mathrm{collision}\,,$$</p>
<p>how to derive the "two-term approximation", which is expressed in terms of an energy-dependend $f(t,\varepsilon)$? </p>
<p>That one essentially looks like</p>
<p>$$\frac{\partial}{\partial t}f(t,\varepsilon)=\frac{\partial}{\partial \varepsilon}\left(\left(A\ \varepsilon + c\ B\right)\ f(t,\varepsilon)+\frac{\partial}{\partial \varepsilon}\left(B\ \varepsilon\ f(t,\varepsilon)\right)\right)\,.$$</p>
</blockquote>
<p>And I think a relatedkeyword is "<a href="http://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation" rel="nofollow">Fokker-Planck</a> type". </p>
<p>I have here the book "Mathematical theory of transport processes in gases", which discusses the Boltzmann equation in detail, but as far as I can see it never passes to the energy-representation. Searching the web, I found a version of such a $f(t,\varepsilon)$-reformulation described in the software manula for the "Comsol" software,
although no derivation of any kind:
<a href="http://www.comsol.com/model/download/31731/two_term_boltzmann.pdf" rel="nofollow">www.comsol.com/model/download/31731/two_term_boltzmann.pdf</a></p>
| 9,679 |
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<p>Can I use Newtonian laws of dynamics and kinematics applied to electrons (like $F = ma$ and $s = s_0 + v_0 t + at^2/2$)? If not, why not? </p>
<p>I know that everything in principle behaves in a quantum way, even macroscopic bodies, but is the level of precision of using classical mechanical on electrons acceptable?</p>
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<p>In the context of the 3 + 1 decomposition of spacetime needed for a Hamiltionian formulation of general relativity, quantities with so called internal indices are introduced (in the <a href="http://rads.stackoverflow.com/amzn/click/0199590753" rel="nofollow">book</a> I am reading on p.43). For such quatities $G^i$ , some kind of a "covariant derivative" is defined:</p>
<p>$D_aG^i = \partial_a G^i + \Gamma _{aj}^iG^i$ </p>
<p>Using this derivative, a corresponding "curvature tensor" $\Omega_{ab}^{ji}$ is then calculated by</p>
<p>$D_aD_b - D_bD_a = \Omega_{ab}^{ji}G^i$</p>
<p>My quastions about this are:</p>
<p>1) Why is $\Gamma _{aj}^i$ called <strong>spin</strong> connection; it has to do with the spin of what ...?</p>
<p>2) How is the so called curvature of connection $\Omega_{ab}^{ji}$ related to the "conventional" curvature tensor ?</p>
| 9,681 |
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<p>Consider some positive charge that is distributed uniformly over a very long line along the z-axis.</p>
<p>If I am stationary with respect to the line then there is only static electric field which has cylindrical symmetry.</p>
<p>Assume now that I am moving with some constant velocity which has only a (positive) component along the z axis. With respect to me there is now current running down the (negative) z-axis, hence I expect to find a static magnetic field in my moving inertial frame. </p>
<p>My question is, do I still find (a static) electric field as well in this case? [Because on one hand I find the answer to be NO, since static electric fields should come only from static charges, and the charges here will not be static. On the other hand, although the line carries current, the line is still charged (which is different from currents running in conducting wires where the wires are neutral at all times). That means the answer is YES and one expects to see static electric field because the line is continuously charged.]</p>
<p>So is the answer yes or no (and why)? </p>
| 9,682 |
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<p>In lectures on effective field theory the professor wanted to find the correction to the four point vertex in massless $\phi^4$ theory by calculating the diagram,</p>
<p>$\hspace{6cm}$<img src="http://i.stack.imgur.com/JmHzE.png" alt="enter image description here"></p>
<p>We consider the zero external momentum limit and denote $p$ as the momentum in the loop. Then we get,
\begin{align}
\int \frac{ d ^d p }{ (2\pi)^4}\frac{1}{p ^4 } & = \frac{ - i }{ 16 \pi ^2 } ( 4\pi ) \Gamma ( \epsilon ) \mu ^\epsilon \\
& = - \frac{ i }{ 16 \pi ^2 } \left( \frac{1}{ \epsilon _{ UV}} - \gamma + \log 4\pi - \log \mu ^2 \right) \\
& = \frac{ i }{ 16 \pi ^2 } \left( \frac{1}{ \epsilon _{ UV}} - \frac{1}{ \epsilon _{ IR}} \right)
\end{align}
where we introduced $\mu$ as an IR cut-off and then take $\log \mu ^2 $ as a $\frac{1}{\epsilon_{IR}}$.</p>
<p>This is fine, however the professor then goes on to say that this diagram is zero since the two divergences cancel. Why would this be the case? The two divergences arise for completely different reasons. The UV divergence is due to a UV cutoff (possibly from new high energy particles arising at some high up scale) and the second is a consequence of studying a massless theory.</p>
<p>For more context the lecture notes are available <a href="http://pages.physics.cornell.edu/~ajd268/Notes.html">here</a> under Effective Field Theory (Eq. 4.17)</p>
| 9,683 |
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<p>I usually don't want to do this, but please go to this link, the solution is too big to post it here</p>
<p><a href="http://engineering.union.edu/~curreyj/MER-201_files/Exam2_2_26_09_Solution.pdf" rel="nofollow">http://engineering.union.edu/~curreyj/MER-201_files/Exam2_2_26_09_Solution.pdf</a> </p>
<p>And go to page 5 of the pdf. </p>
<p>Briefly, the problem say</p>
<blockquote>
<p>Determine the velocity of the 60-lb block A if the
two blocks are released from rest and the 40-lb block B
moves 2 ft up the incline. The coefficient of kinetic friction
between both blocks and the inclined planes is $\mu_k$ = 0.10.</p>
</blockquote>
<p><strong>Things I am confused with the solution</strong></p>
<p>1.First of all, I seriously thought lb was mass not force. after some googling, it turns out they are used interchangeably...</p>
<p>2.Where did they even get $2s_a + s_b = 0$ from? Why did they determine the change in distance this way? My first assumption was that if block B moved up 2ft, then block A should move down 2ft (the rope must "move" 2ft too right?). Then I wasn't sure, so I did a few triangles and found that the angle made a difference</p>
<p>3.Where did $2v_A = -v_B$ come from?</p>
<p>4 The FBD for block A is confusing, why is the friction force $F_A$ in the direction of the ropes? I thought it was block B that is going down? Am I the only one who had trouble deducting that the pulley and block A are the same object? </p>
<p>5.Look at the final answer, how could $v_b$ be negative? The problem says block B goes UP.</p>
<p>If you are wondering, this is not homework. I am just interested in this problem and it is out of curiosity and very confused with the concepts. </p>
<p>I've had at most introductory physics experience, but I think I should have been able to solve this still.</p>
<p>Thank you for reading</p>
| 9,684 |
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] |
<p>What is a <a href="http://en.wikipedia.org/wiki/Ergodic_theory" rel="nofollow">ergodic</a> system? What is Onset temperature of <a href="http://en.wikipedia.org/wiki/Ergodicity" rel="nofollow">ergodicity</a> breaking in super cooled liquids when we go towards lower temperature?</p>
| 9,685 |
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<p>Why is allowed decompose the spacetime metric into a spatial part + temporal part like this for example</p>
<p>$$ds^2 ~=~ (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b$$ </p>
<p>($N$ is called lapse, $N_a$ is the shift vector and $q_{ab}$ is the spatial part of the metric.)</p>
<p>in order to arrive at a Hamiltonian formulation of GR? How is a breaking of Lorentz invariance avoided by doing this ?</p>
<p>Sorry it this is a dumb question; maybe I should just read on to get it but I`m curious about this now ... :-)</p>
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<p>How is the <a href="http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation" rel="nofollow">Schrödinger equation</a> </p>
<p>$$\frac {\partial }{\partial t}\psi=-\frac {i }{\hbar }H{\psi }$$</p>
<p>being derived?</p>
| 9,687 |
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] |
<p>How to find the average value of several measurement results if we know their statistical and systematics uncertainties?
There might be that there is no such thing as best way to do it, but it would be helpful to know how is this done in different areas of physics/science.</p>
| 9,688 |
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<p>I think it was Feynman that suggested that you should always carry ten big problems around in your head, and when you encounter a new method, see whether this new method allows you to make progress on any of your problems. To prevent the answers becoming to unwieldy, I'll restrict the question here to condensed matter physics (if it proves useful, the same question can be asked for every branch of physics, or even physics in general).</p>
<p>So, what should be considered amongst the biggest outstanding problems in condensed matter physics today? </p>
<p>If possible, please accompany any answer with a short up-to-date technical review of the field.</p>
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<p>I am modelling gas combustion in porous media. Most contemporary models assume that the pressure drop from the porous media is small enough to disregard, but I want to include that in my investigation. Most studies alos assume that the gas is filtered through the media at a constant speed $u$.</p>
<p>I use Darcy's law to couple the velocity and pressure feilds:</p>
<p>$u=-\frac{k}{\mu}\nabla p$.</p>
<p>Plus we have the ideal gas euqation of state and the continuity equation:</p>
<p>$p=\rho RT/M_r$</p>
<p>$\frac{\partial \rho}{\partial t}+\nabla \cdot (\rho u)=0$.</p>
<p>Since we are talking about combustion the case is not isothermal, two energy euqations are also present. All the quations are solved with finite differences.</p>
<p>I first of all want to qualitatively reproduce the results obtained in previous studies to validate my model. <strong>The question is how do I simulate a constant velocity in the domain.</strong> It seems like the Darcy equation implues that I should apply a proper pressure drop, i.e first order boundary conditions on the pressure. This implies a big pressure drop if I want to obtain something around $u=0.5$ m/s in the camera. Moreover the velocity appears to be increasing rapidly towards the far end, where atmosperic pressure is prescribed. </p>
<p>I was thinking perhaps that I ran into this problem limitation as a payment for not solving a real Navier-Stockes. But I am not sure, so here I am :).</p>
<p>P.S. I do realize that I can through away the gasodynamical part of the model and just prescribe the speed in the energy equations as far as validation goes, I have indeed done that and got good results.</p>
| 9,690 |
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<p>My understanding is that gravitomagnetism is essentially the same relativistic effect as magnetism. If so, why is it that I've heard so much about magnetic monopoles, but never gravitomagnetic monopoles? Aren't each just as theoretically well-motivated as the other? In a similar vein, one always hears that "there is no independent existence of an electric or magnetic field, only the electromagnetic field" because E and B fields transform into each other under Lorentz boosts. Shouldn't the same statement apply to gravity and gravitomagnetism?</p>
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<p>When a quantum system have a double degenerescence at one point, the Hamiltonian should be proportional to Pauli matrices near this point (also known as <em>diabolic point</em>) [<a href="http://ajp.aapt.org/resource/1/ajpias/v78/i7/p661_s1?isAuthorized=no" rel="nofollow">Ref.</a>]. But, why the Hamiltonian have this form?</p>
| 9,691 |
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<p>Is it possible to get two atoms to opposite quantum states of one another so when I change the state of first one, the state of the other one changes too? Is it possible to move them to another place on Earth and communicate like this? I've seen it in a sci-fi game but am wondering if that is truly possible. </p>
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<p>I was pondering about the following 'experiment', and was curious about the formulae behind it. </p>
<p>Imagine having a glass filled with a liquid. On one side there is a sensitive receiver that records all the vibrations and is attached to the outside. If I would then tap on the opposite side I would in send an impulse to the glass side, which would transmit the waves to the liquid, which would travel to the opposite side and will be transmitted to the glass and finally the receiver. Of course the glass is higher density so some waves will reach the receiver earlier.</p>
<p>I have some questions here:</p>
<ol>
<li><p>I am used to dynamical mechanical systems involving eigenmotions and the likes. This is no different I presume? I am sending an impulse and recording the output, so in fact I have a transfer function. What I am wondering is is what the eigenfrequency of a solid/fluid is when being excited. Will this be the speed of sound through the solid/fluid?</p></li>
<li><p>What happens at the interface between the glass and the fluid? I can imagine the wave moving with $V_{glass}$ through the glass, however how is this transmitted to the fluid? What will $V_{fluid}$ be? Will it be equal to $V_{glass}$? I can imagine that the fluid will attenuate the higher velocity movement, because high frequency sound is attenuated by a fluid, but that is sound... and is this sound?</p></li>
</ol>
<p>Can someone point me into the right direction?</p>
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<p>$:\!\!\hat\phi(x)^2\!\!:$, for example, constructed from the real Klein-Gordon quantum field.</p>
<p>For a Wightman field, the Wightman function $\left<0\right|\hat\phi(x)\hat\phi(y)\left|0\right>$ is a distribution, which is certainly the case for the real Klein-Gordon quantum field --- call it $C(x-y)$ in this case. In contrast, the expected value $\left<0\right|:\!\!\hat\phi(x)^2\!\!:\,:\!\!\hat\phi(y)^2\!\!:\left|0\right>$ is a product of distributions, in fact for the real Klein-Gordon quantum field it's $2C(x-y)^2$, which seems to make this normal-ordered product of quantum fields not a Wightman field. $C(x-y)^2$ is well-enough behaved off the light-cone, but on the light-cone it has a $[\delta((x-y)^2)]^2$ component.</p>
<p>If $:\!\!\hat\phi(x)^2\!\!:$ is not a Wightman field, then is it nonetheless in the Borchers' equivalence class of the free field? If so, why so? A (mathematically clear) citation would be nice!</p>
<p>Finally, if $:\!\!\hat\phi(x)^2\!\!:$ is not in the Borchers' equivalence class of the free field, because it isn't a distribution, is it nonetheless empirically equivalent to the free field at the level of S-matrix observables, as is proved to be the case for Borchers' equivalence classes (Haag, <em>Local Quantum Physics</em>, $\S$ II.5.5), even though it is manifestly not empirically equivalent to the free field at the level of Wightman function observables?</p>
<p>My reading of the Wightman fields literature of the late 1950s and 1960s is far from complete, which may be why I haven't so far found clear answers for these questions.</p>
| 9,694 |
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<p>In classical Newtonian mechanics, from what I understand, conservation of energy stems from the fact that all known forces are conservative forces,
and vector calculus tells us that they can be represented by a potential energy function.</p>
<p>I understand how Energy Conservation is derived by Noether's theorem, but
I'm trying to understand relativistic dynamics better in terms of four-vectors.</p>
<p>I know four-force can be written in special relativity as the derivative of the
four-momentum with respect to proper time.</p>
<p>Are four-forces still conservative?<br>
How do I write potential energy functions in SR?<br>
If I have a constant force in classical mechanics is it still constant in SR?<br>
(My guess abot the third question is not because four-momentum and three-momentum are quite different and four-momentum also depends on the relative velocity of the observer and the object)</p>
<p>My goal is to understand energy conservation is SR.</p>
<p>Thanx to anyone who answers!</p>
| 9,695 |
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<p>I am teaching myself Differential Equations from a website. In the website I am up to Direction Fields and an example of a differential equation is Newton's Second Law of Motion. It is written on the website like this:</p>
<p>$$m\frac{dv}{dt}=mg-\gamma v$$</p>
<p>I know that $m$ is the mass, $g$ is the gravitational acceleration, $v$ is the velocity, and $t$ is the time, but what does $\gamma$ stand for?</p>
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<p>I was wondering how gravity would behave on object of different shapes.</p>
<ol>
<li><p>If the Earth was squeezed into a thin disk what would the gravitional acceleration be at the center of the flat surface? Would it be really low because the amount of matter beneath me would be small? If I stood on the edge would the gravitational acceleration be enormous because the amount of matter beneath me was huge?</p></li>
<li><p>If an object is lowered into the Mariana trench will the effect of gravity increase because it gets closer to the center of the Earth?</p></li>
</ol>
| 313 |
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<p>I have a talk tomorrow in which <a href="http://en.wikipedia.org/wiki/Detailed_balance">detailed balance</a> is needed and I don't want to bore my audience with elaborate explanations for it so I'm looking for simpler explanations.</p>
<p>As far as I understood it detailed balance means, that for any given time the possibility to be in state $X$ and leave it equals the possibility to be in any state $Y\neq X$ and go from there to $Y$.</p>
<p>So if I draw a circle in (2 dimensional) state space around Y the "flow" in and out of that circle is zero ($\forall X$) - which leads to $div(S)=0$ ($S$ is the state space, also I think there is no need for a changing density ($\rightarrow \rho = const. \rightarrow \frac{\delta \rho}{\delta t} = 0$).</p>
<p>Is this correct? If yes, do you think, this makes understanding detailed balance easier?</p>
<p>If not - where's the mistake?</p>
| 9,697 |
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<p>usually when people want to quantize the string on flat background, they will try to find the the OPE of embeddings (by solving a green function in a 2D space) and use them to find the energy-momentum tensor OPE, central charge, Virasoro modes and their algebra and then, covariant quantization. </p>
<p>BUT
on a curved background (as one can expect in advance), for finding a the OPE of embeddings, you will reach to a non-linear differential equation with a point source! (I mean delta function). Im not sophisticated in GR, however I think it is possible to encounter such problems in GR. Does any one have any idea ? is there any more powerful approach for quantization (probably there is, but I'm not sure) for solving this problem?</p>
<p>Thanks </p>
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<p>I'm interested in teaching myself quantum mechanics, and I'm looking for a good goal to aim for. </p>
<p>I've got an undergrad maths degree and a graduate degree in probability theory and stochastic processes. I've worked fairly extensively with diffusion processes, so I understand how the Fokker-Planck equation works, for example. </p>
<p>As far as I understand, the Fokker planck equation is related to the Schrodinger equation via something called a Wick rotation. I'm a bit hazy on the details, but I think this may have been Feynman's approach to QM.</p>
<p>If anyone could recommend a text for someone with my background (linear algebra, group theory, ODE and PDE, probability), but with relatively little experience in physics, that would be very helpful.</p>
<p>The maths shouldn't be a problem, but there's a chance I'll just get bored unless I have a specific goal. Maybe deriving the emission spectra of various atoms, or understanding quantum computing. Any other suggestions?</p>
| 98 |
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<p>In a crystal, we don't have full translational symmetry, but we still have discrete translations. This allows us to define "crystal momentum" that is conserved modulo a reciprocal lattice vector.</p>
<p>In a crystal, we don't have full rotational symmetry, but we still have discrete 2, 3, 4, and/or 6-fold rotational symmetry. Can we define a "crystal angular momentum"?</p>
<p>Also, unrelated question: if we have a semiconductor impurity state that resembles a hydrogen 1s state, 2p state, etc... what is its angular momentum?</p>
| 9,699 |
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<p>If a star is 1 billion light years away, it means that the light we see from the star is emmitted billions of years ago.</p>
<p>How does this light not undergo a frequency change or get damped inspite of the collosal distance of travel? I am asking this as doppler effect is used to know star-distances and is one of the basis for big-bang theory</p>
<p>Also it travels in vacuum. According to Maxwell/Gauss, a charged particle is responsible for electric field whose change creates magnetic filed. Inturn, its change causes Electric field, a process that occurs infinitely. Even if we assume that the energy travel in vacuum as the energy produced from a charged particle elsewhere is used for propagation in vacuum, does the waves not damp significantly?</p>
<p>In the radio waves emitted/transmitted for earthly communications, power of source is directly proportional to the distance travelled by the wave. Is this not contradicting the fact that stars light reach us from the humongous distances?</p>
| 9,700 |
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<p>I recently came across a question, for which I saw two possible methods of finding the solution. I was required to calculate the "current flowing" $I$ when given the voltage $V$, frequency $f$, total resistance $R$ and impedance of the circuit $Z$. In the book that these questions were written, there were two methods (Note - AC Current):</p>
<p>First Method:</p>
<p>$$V=|I\cdot Z|\ \Longrightarrow\ \frac{V}{|Z|}=|I|$$</p>
<p>Second Method:</p>
<p>$$V=I\cdot R\ \Longrightarrow\ \frac{V}{R}=I$$</p>
<p>(I use all the time for DC Currents)</p>
<p>As I found out, through trial and error, both of these give different solutions. Personally, I tended towards the first solution, but I couldn't help noticing the second method, as it gave a nice round answer, as opposed to the fractional answer the first gave. Which of these two methods is the correct one to use?</p>
| 9,701 |
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<p>If a small black hole (say about .1 mm radius or 1% of Earth's mass) came flying along at the speed of a comet or higher and impacted the earth, what would happen? Would it pass through the earth (and atmosphere) with minimal damage? Would it leave a crater (entry or exit?) Would it create a big enough shock wave to significantly damage the earth? Would it be captured and wander around inside the earth?</p>
<p>I read a book a few years ago with this as the primary part of the plot, and I have wondered about the physics ever since.</p>
| 885 |
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<p>Hello everybody I am kind of struggling with an assignment question related to general relativity. I am just going to type what the question is and explain what I am having trouble with: </p>
<p>Consider an electromagnetic plane wave in Minkowski space. We assume that in stationary coordinates $(t,x,y,z)$ the wave propagates in the positive $x$-direction, and that the components of the electric field $E$ and the magnetic field B are only a function of $u = t-x\ ($here $c = 1)$:</p>
<p>$E = E_{y}(t-x)\frac{\partial}{\partial{y}}+E_{z}(t-x)\frac{\partial}{\partial{z}}$</p>
<p>$B = B_{y}(t-x)\frac{\partial}{\partial{y}}+B_{z}(t-x)\frac{\partial}{\partial{z}}.$</p>
<p>Moreover, we assume E and B are compactly supported in $u$.</p>
<p>(1) Use Maxwell's equations to show that:</p>
<p>$B_{y}=-E_{z},$ $\space$ $B_{z}=E_{y}$.</p>
<p>First of all sorry if the formatting isn't that great. Now I am having trouble with this because I am not exactly sure what $E$ and $B$ are... by that I mean I know $E$ and $B$ are supposed to be vector fields but in that format they look like scalar fields. Is there another way to represent those two equations, I feel that if I understand the notation it would make doing this question pretty easy. Any help would be greatly appreciated. I just want to understand the notation properly and how to work with it so that I can actually apply Maxwell's equations on them and figure out those identities. Thank you and have a good day!</p>
| 9,702 |
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<p>Can anyone explain to me what is actually "curved" when we speak of a Berry Curvature?</p>
| 9,703 |
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<p>Is a quantum system necessary if we want to generate true random sequence? The mathematical framework used for classical mechanics doesn't involve any random value. But the mathematical framework of quantum mechanics involves randomness by definition. Can we argue based on these information that a true random number generator must use quantum mechanics? If anyone claims that s/he has a true random number generator and fails to prove that s/he is exploiting quantum mechanics can I discard the claim on the basis that s/he is not using quantum mechanics?</p>
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<p>I am reading this very interesting paper:
<a href="http://m.iopscience.iop.org/1751-8121/41/40/402002/pdf/1751-8121_41_40_402002.pdf" rel="nofollow">http://m.iopscience.iop.org/1751-8121/41/40/402002/pdf/1751-8121_41_40_402002.pdf</a> about thermodynamics of channels in information theory.</p>
<p>More generally, establishing a dictionary between information theory and thermodynamics is an old idea, but it seems to me that we only transpose state parameters (entropy, energy, temperature) and not transformations (adiabatic, isothermic).</p>
<p>For instance, mutual information between input and output is related in this paper to internal energy. Suppose we are trying to simulate the BSC using other channels. We would quantify the efficiency of this simulation by looking at the mutual information. The channels having exactly the same mutual information as BSC are indistinguishable from BSC. The dictionary with thermodynamics would lead us to think that we are performing an adiabatic transform in the space of channels. However I can find no rigorous formulation for this intuition, nor any paper on the possible interpretations of thermodynamic transforms for information theory channels.</p>
| 9,705 |
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<p>I have a simple question, can you spin a <a href="http://en.wikipedia.org/wiki/Conical_pendulum" rel="nofollow">conical pendulum</a> fast enough so that it rotates at 90 degrees?</p>
<p>The equation is $\tan(\theta)=v^2/rg$ , but at 90 degrees, $\tan(\theta)=\infty$ ... so what does this mean? Please provide supporting data.</p>
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<p>One of the great unsolved problems in physics is <a href="http://en.wikipedia.org/wiki/Turbulence">turbulence</a> but I'm not too clear what the mystery is. Does it mean that the Navier-Stokes equations don't have any turbulent phenomena even if we solve it computationally? Or does it mean we simply don't have a closed-form solution to turbulent phenomena?</p>
| 9,707 |
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<p>There's a mechanism by which the southern ocean sequesters carbon from the atmosphere. It happens when strong winds displace a large slab of surface water, accumulating in a specific region where the localised excess water in the surface layer gets injected downward into the ocean's interior. This makes the ocean's absorb about 25% of annual man-made $CO_2$ emissions.</p>
<p>Are any geophysicists and engineers working on developing a man-made mechanism by which we can make the ocean's absorb more carbon and therefore reduce climate change? Is it humanly possible?</p>
<p>NOTE: I read an article on the phenomenon in Physics World magazine, and it didn't mention anything about scientists looking to make it happen more.</p>
| 9,708 |
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<p>A vector in one dimension has only one component. Can we consider it as a scalar at the same time?</p>
<p>Why time is not a vector, although it can be negative and positive (when solving for time the kinematics equation for example)?</p>
| 9,709 |
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<p>please i want to ask when induced current produced by changing magnetic field according to faraday's law is this current DC or AC current ?</p>
| 9,710 |
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<p>I'm currently working on an underwater robot and was hoping to use the gas bubbles for buoyancy control .</p>
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] |
<p>Assume a central body of mass $M$, and call $a$ the acceleration of a test
body at a distance $r$ due to any interaction whatsoever with the central
body. Is is correct to say that the ratio $a r^2/ M$, for any interaction, is always larger than or equal to the gravitational constant $G$?</p>
| 9,712 |
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<p>Can the fact that energy is distributed homogeneously in the universe be explained through heat flow and not the Cosmic Microwave Background(or in other words, can we say CMB is a result of heat flow and not the universe expanding from a singularity)?</p>
| 9,713 |
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<p>Is it possible to "extract" energy from a magnet, making it lose its magnetism? Or, to put in another way, is magnetism a form of energy? (I am not talking about potential energy in a magnetic field). Since matter is equivalent to energy, is the property of magnetism equivalent as well?</p>
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<p>I had a college student build an overclocked PC using phase-change technology. (This is essentially an air-conditioning unit with the evaporator attached directly to the motherboard.) He said that cold temperature made the CPU more stable at higher clock speeds (5.5 GHz) by affecting how the atoms and electrons behave. My question is, is this true? If so, in what way does cold temperature affect semiconductors?</p>
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<p>So I wanted to find out how to (simply, if that's possible) derive the formula for a period of spring pendulum: $T=2\pi \sqrt{\frac{m}{k}}$. However, Google doesn't help me here as all I see is the ready-to-bake formula. Could you please point me some directions?</p>
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<p>Consider a pendulum of length $h$ with a bob of mass $m$ it is held horizontally at and angle of $90^{\circ}$ with the vertical. A rod of mass $M$ and length $h$ is pivoted at its upper end and this pivot coincides with the point of suspension of the pendulum. The rod hangs downwards along the vertical. The pendulum is released. It collides with the rod and sticks there. Find the angle rotated by the rod.</p>
<p><img src="http://i.stack.imgur.com/kx49m.png" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/wmAuX.png" alt="enter image description here"></p>
<p>This can be easily accomplished using conservation of mechanical energy. Clearly, the initial energy of the system is purely potential energy:</p>
<p>$$E_i = U_{bob} = mgh \tag1$$</p>
<p>The final potential energy, when the rod has rotated through $\theta$ is also purely potential energy:</p>
<p>$$E_f = U_{bob} + U_{rod}$$</p>
<p>$$U_{bob} = mg(h - h\cos\theta) = mgh(1 - \cos\theta)$$</p>
<p>$$U_{rod} = \int dU = \int dmdhg$$</p>
<p>Consider a small length $dx$ on the rod at a distance $x$ from the top. The potential energy of this length is $dm(h - x\cos\theta)g$. The mass per unit length of the rod is $\frac{M}{h}$, so $dm = \frac{Mdx}{h}$. Putting these into the integral and integrating over all segments on the length of the rod, we get:</p>
<p>$$U_{rod} = \int_0^h \left(\frac{Mdx}{h}\right)(h - x\cos\theta)g = \frac{Mg}{h}\int_0^h (h - x\cos\theta)dx$$ </p>
<p>$$= \left[Mgx - \frac{Mgx^2\cos\theta}{2h}\right]_0^h = Mgh - \frac{Mgh\cos\theta}{2}$$</p>
<p>$$\therefore E_f = mgh - mgh\cos\theta + Mgh - \frac{Mgh\cos\theta}{2}$$</p>
<p>Equating the above with $(1)$:</p>
<p>$$mgh = mgh - mgh\cos\theta + Mgh - \frac{Mgh\cos\theta}{2}$$</p>
<p>$$\implies Mgh = \cos\theta gh\left(m + \frac{M}{2}\right)$$</p>
<p>$$\implies \boxed{\cos\theta = \frac{2M}{2m + M}}$$</p>
<p>But consider the case where the bob has a mass of $100 \ \rm{grams}$ and the rod a mass of $240 \ \rm{grams}$. </p>
<p>$$\cos\theta = \frac{2\cdot 0.24}{2\cdot0.1 + 0.24} = \frac{0.48}{0.44} > 1$$</p>
<p>which is clearly not possible. But, from experience, we know that the rod <em>will</em> rotate through some valid angle. Where did I go wrong?</p>
| 9,717 |
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<p>The Heisenberg Uncertainty Principle suggests that the more precisely the position of a particle is measured, the less precisely its momentum can be known, and vice versa. </p>
<p>$$\sigma_x \sigma_p \geq \frac{\hbar}{2}$$</p>
<p>What I've read is that in order to measure the position of a particle accurately, we need a very energetic quantum of light to measure it but the more energetic the photon is, the greater it will disturbe the velocity of the particle, thus letting us unable to obtain its momentum accurately.</p>
<p>This sounds just like an observer effect to me. However, I'm told that it shouldn't be thought of as an observer effect and instead, measurement only gives the the particle's momentum and location corresponding to one of its possible states (and so before the measurement it exists in all the possible states, in others words, it is in a superposition). </p>
<p>And this confuses me. Why can't it be interpreted as an observer effect and why do we have to think of the measurement as just obtaining one of the particle's possible states? And why it exists in all its possible state before measurement? Because it exhibits both particle properties and wave properties simultaneously? If that is the reason, how does its wave-particle duality imply that it exists in all states?</p>
| 471 |
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<p>I have this problem: I have a capacitor formed by two parallel square-shaped plates, of side $a$, and with distance $d$ between them. They're asking me out of other things, the magnetic force as a function of some things. I calculate de magnetic force by calculating the gradient of the magnetic energy, given by:</p>
<p>$$E=\frac{1}{2}\iiint_VB\cdot H\;dV$$</p>
<p>I have calculated $B$ and $H$, that form, during the charge of the capacitor, loops around the center proportional to $r$, being $r$ the distance from the central axis. The problem is that I have to integrate that to a cubic volume: $a^2d$, one of those variables is independent, but the other two are not, and this problems never involve complicated integrals, such that one: $$\int_0^a\int_0^a rdxdy$$
If the plates were circles it would be trivial, but being squares, I'm sure I'm missing something.</p>
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<p>What is the nature of <strong>nuclear energy</strong>? This is closely related to the correct explanation of mass defect.</p>
<p>I did some research of that topic and cannot come to a single comprehensive and consistent description.</p>
<p>Below are related statements I gathered or can think of, describing the problem area. To me, each of them seems to make sense, but some of them are contradictory, so obviously - wrong. Please kindly point out and explain these errors.</p>
<p>A) The more nucleons in a nucleus, the bigger the nucleus is, so the average distance of a nucleon to each another is higher, hence the long-distance electromagnetic repulsion tends to overcome short-distance strong nuclear force, up to the point of occasional alpha decay in elements of transuranic end of the spectrum.</p>
<p>B) The less nucleons in a nucleus, the closer in average they are, so the strong force per each is higher and easily overcomes electromagnetic repulsion.</p>
<p>C) Given A and B, the smaller the nucleus, the stronger it is bound</p>
<p>D) The stronger the nucleus is bound, the higher its <strong>binding energy</strong></p>
<p>E) The higher the binding energy of nucleus, the more energy is stored per nucleon in the system</p>
<p>F) The higher the binding energy per nucleon, the more difficult it is to split the atom</p>
<p>G) The more difficult it is to split the atom, the more <strong>stable</strong> the atom is</p>
<p>H) The more energetic a binding, the more difficult it is to break the binding, the more stable the atom made out of such bindings</p>
<p>I) Natural systems tend to evolve to lower, not higher energy states.</p>
<p>J) The literature presents the binding energy chart per element, with its peak at iron (~56 nucleons). Both the lighter and heavier elements tend to have smaller binding energy.</p>
<p>K) Iron is the most stable element. It is abundant in the universe, as natural atomic evolution tends to get close to it from both ends of atomic number spectrum.</p>
<p>L) The surplus energy in the nuclear reaction is achieved when heavy elements are split (fission), or light element are fused (fusion). </p>
<p>M) The surplus energy is the energy taken out of the system, i.e. average energy per nucleus is higher before the reaction and lower after the reaction.</p>
<p>N) After the reaction - the resulting elements are closer to the iron atomic number</p>
<p>O) <strong>Mass defect</strong> is directly proportional to the binding energy. The stronger the binding energy per nucleon, the less mass per nucleon.</p>
<p>Example for neutron, proton and them bound together in deuterium:<br>
$$m_n=1.008665 u\ ,\ m_p=1.007276u$$
$$m_{n+p}=2.015941 u\ ,\ m_d=2.013553 u$$
$$\Delta_m=0.002388 u = 2.224\ \frac{MeV}{c^2}$$</p>
<p>The explanation of below (seemingly) contradictions somehow eludes me. Hope it is apparent to you:</p>
<ul>
<li><p>why the lightest elements are not the ones which are most strongly bound? Possibly the peak at iron might be caused the geometry factor - i.e. when accounting for nucleons 3D positions, the average forces between them are no longer proportional to just the number of nucleons.</p></li>
<li><p><strong>why does iron seem to</strong> need in its properties: <em>the highest energy per nucleon</em> as the most strongly bound, most stable element; and on the other hand: <em>the lowest energy per nucleon</em>, for the surplus energy be given off when approaching iron in fission/fusion reactions from either side of atomic number spectrum?</p></li>
</ul>
<p>Also - what is the definition and explanation of the mass defect:</p>
<ul>
<li><p>mass defect is the surplus energy given off from fusion/fission and hence is the difference between total mass-energy of the system before and after reaction</p></li>
<li><p>mass defect comes from different proportion of mass vs energy in an atom depending on its binding energy. When the binding energy is higher in an atom, the more of the total mass-energy of the system is stored in the binding of the nucleons and less in their mass - and the total stays the same. If so then why does the total mass-energy change after the split/fuse reaction?</p></li>
</ul>
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<p>As I understand it, the twin paradox was integral to Einstein's conclusion that nothing can travel faster than the speed of light. </p>
<p>Why wasn't there a similar conclusion for a hypothetical scenario where 2 blind musicians play the trumpet whilst moving away from each other at a speed close to the speed of sound. They would obviously hear a slower/lower tone (doppler shift) but at no point did someone suggest that time was slowing down. </p>
<p>If a spacecraft left earth accelerating up to 80% of the speed of light and views earth through a telescope and notices both a red shift and an appearance of time slowing down (as you would expect), then on the return journey there is a blue shift and time appears to speed up (as you would expect) why does time actually HAVE to be tied to the blue/red shift effect? Why is it different than the hypothetical scenario with the sound waves? Furthermore the time's apparent slowing down on earth on the journey to the star is "made up" by the time speeding up on the return journey isn't it?</p>
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<p>Is there a systematic procedure for obtaining a deconfined theory from an s-confining theory (as defined in hep-th/9610139 for example)?</p>
| 9,720 |
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<p>The question I'm about to pose is from a physics book I had recently bought. Since I am very interested in physics I am quite keen in understanding how this question can be solved. Before I present this question, I would like to explain the context in which this question was posed. It is a question related to the chapter entitled - Measurement, dealing with the understanding of the basic quantities like mass, time, length etc. Now let me pose the question:<br><br>Suppose that while laying down on a beach near the equator of the Earth, you watch the sun setting below the horizon. You start a stopwatch the moment the top of the sun disappears below the horizon. You then stand to a height of 1.70 metres, and stop the watch when the top of the sun disappears again. The time interval is exactly 11.1 seconds. What is the radius of the Earth?<br><br>I must inform you that this is not a homework question or any such related assignment, I am simply asking a question whose solution I have been unable to find myself or online. I hope you'll be able to answer this question.</p>
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<p>If we have an <strong>isolated</strong> system $Sb$ with thermodynamic entropy $Eb=X$
(and growing by the 2nd law of thermodynamics),</p>
<p>we could define an abstract system $Sa$ (containing the system $Sb$) but define the possible microstates as a single bit, being 1 (one) when $Eb>=X$, and 0 (zero) when $Eb < X$.</p>
<p>The microstate will tend to be $1$, so the entropy of the system $Sa$ tends to zero.</p>
<blockquote>
<p>po-->0 </p>
<p>p1-->1</p>
<p>Eb = - k [p0 * log (p0) + p1 * log (p1)] --> 0 </p>
</blockquote>
<p>How could it be possible that an isolated system have a decreasing entropy?</p>
<p>Does the growth (or lack of growth) of the entropy depend on the microstates choosen?</p>
<p>Finally, if there is a restriction on how to choose the definition of the microstates, then what is that restriction?</p>
<p>Thanks.</p>
| 9,722 |
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<ol>
<li><p>If Ricci scalar describes the full spacetime curvature, then what do we mean by $k=0,+1,-1$ being flat, positive and negative curved space? </p></li>
<li><p>Is $k$ special version of a constant "3d-Ricci" scalar? </p></li>
<li><p>What is the difference between the local and global spacetime curvature?</p></li>
</ol>
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] |
<p>An observer stands 3 m from speaker A and 5 m from speaker B. Both speakers, oscillating in phase, produce waves with a frequency of 250 Hz. The speed of sound in air is 340 m/s. What is the phase difference between the waves from A and B at the observer's location?</p>
<p>$$v=fλ\\ λ=1.36m\\ \\ Δr=|{ r }_{ 2 }-{ r }_{ 1 }|\\ =2$$</p>
<p>I have nothing that relates any of this to phase angle. :(</p>
| 9,724 |
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] |
<p>The <a href="http://en.wikipedia.org/wiki/Hydrogen_spectral_series" rel="nofollow">hydrogen spectral series</a> is given by the Rydberg formula: </p>
<blockquote>
<p>The energy differences between levels in the Bohr model, and hence the
wavelengths of emitted/absorbed photons, is given by the Rydberg
formula:</p>
<p>$${1 \over \lambda} = R \left( {1 \over (n^\prime)^2} - {1 \over n^2}
\right) \qquad \left( R = 1.097373 \times 10^7 \ \mathrm{m}^{-1}
\right)$$ where $n$ is the upper energy level, $n'$ is the lower
energy level, and $R$ is the Rydberg constant. </p>
</blockquote>
<p>There is a similar formula for every <a href="http://en.wikipedia.org/wiki/Hydrogen-like_atom" rel="nofollow">hydrogen-like atom</a>. </p>
<p><strong>Question</strong>: Is there a theoretic formula for the spectral series of a given atom (other than hydrogen-like)? Else, why, what are the difficulties?</p>
| 9,725 |
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<p>When the wavefunction of a particle is not an eigenfunction of an operator, the property to which the operator corresponds does not have a definite value, Why?
Also consider a linear combination of basis functions:
$$\psi=c_1\psi_1+c_2\psi_2+...=\sum_kc_k\psi_k$$
When the momentum is measured, in a single observation one of the eigenvalues corresponding to the $\psi_k$ that contribute to the superposition will be found, why?</p>
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<p>Photons are packets of electromagnetic radiation (wave), what about other particles? Are other particles, say electrons, really just packets of waves?</p>
| 304 |
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<p>One can hear some sounds when boiling water, and usually the sound is loud initially, then it becomes quieter. When the water is about to boil, the sound starts to be louder again. Also, one may notice the pitch of the sound varies. Can anyone explain this phenomenon? Thank you!</p>
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<p><strong>Assumption:</strong> Cell-phones generate some degree of electro-magnetic radiation. Whether it's harmful or not is not the question here.</p>
<p><strong>Claim:</strong> Certain devices may "neutralize" this radiation. (Ex: <a href="http://www.giawellness.com/2/products/terra-gia/cell-guard/" rel="nofollow">http://www.giawellness.com/2/products/terra-gia/cell-guard/</a>)</p>
<p><strong>Questions:</strong> </p>
<ul>
<li>Is such a claim even physically possible with what is known today (in stick-on form, as advertized)? </li>
<li>Presumably a full case made out of special material could limit it.. What effect would a suitable case have on the call quality and/or wifi connectivity?</li>
</ul>
<p>(Related Question: <a href="http://physics.stackexchange.com/questions/12069/could-cell-phone-radiation-cause-cancer?newreg=c6fecd11e8e1497bb89c9ab474e8f2f2">Could cell-phone radiation cause cancer?</a>)</p>
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<p>I'm wondering if there's any simple way to define and solve for a null cone for a general spacetime geometry in $n+1$ dimensions, given its vertex $p^\mu$. I can't seem to find a simple way to do it that doesn't involve solving for null geodesics. It seems like it's something that should be in a lot of GR textbooks, but I can't seem to find a simple alternative (perhaps I'm not looking hard enough, but that's why I'm asking).</p>
<p>So far, the best I can do is to define it as the $n$-surface formed by the family of null geodesics $y_{\bf\Omega}^\mu$ passing through some spacetime point $p^\mu$, where $\bf\Omega$ is a combination of $n-1$ angles that distinguishes the curves (at $p^\mu$, it's the collection of angles specifying the direction of the null curve).</p>
<p>The problem is, I'm interested in doing a foliation of spacetime using future or past null cones with respect to some timelike curve $\gamma$, and would like to define the null cones in the form of a constraint:</p>
<p>$C_{\gamma}(x^\mu)=\tau$</p>
<p>Where $\tau$ is the proper time along the timelike curve $\gamma$. This constraint satisfies:</p>
<p>$U(C_{\gamma})=0$</p>
<p>Where $U$ is the vector field defined using the tangent vectors to $y_{\bf\Omega}^\mu$ (this can be defined for all spacetime, if you take the union of all the null cones along $\gamma$). In any case, I still have to solve for the null geodesics, given what I have so far.</p>
<p>I'm not a fan of solving for all the null geodesics at every point along the curve, so I'm looking for a simpler way to do it.</p>
<p>I have the feeling that there should be a simpler way of defining and solving for null cones--it seems like they've been extensively studied in GR. Is there any way to do this without resorting to solving for the null geodesics? In particular, has anyone written down a general constraint form for the null cone?</p>
| 9,728 |
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