question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
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<p>I wonder, what is content of output of zeolite-based pressure swing adsorption oxygen concentrators (both oxygen output, and exhaust output)? </p>
<p>Yes, they can produce 95% oxygen. </p>
<p>But what's the remaining 5%? Is it just argon and other noble gases, or some air contaminants could also be concentrated (like CO2, NO2, CO)? </p>
<p>Any references to quantitative gas analysis results would be extremely useful (wasn't able to find any, probably bad google skills). </p> | g7127 | [
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<p>I have always taken for granted that 'the aperture of a loss-less isotropic antenna is $\dfrac {\lambda^2} {4\pi}$'. </p>
<p>On a whim, I tried to look up how this expression was derived, but so far I have not been able to find out a reference that works it out. Can someone outline the proof, or help me with any pointers to some on-line source? Hopefully this can be done using 3D vector calculus? </p>
<p>Thanks... </p> | g7128 | [
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<p>Extrapolation of the expansion of the Universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past.</p>
<p>If the matter contained within our galaxy were concentrated within a small radius wouldn't that lead to the entire universe being a black hole? If so how is it that all the matter of our observable universe could have originated from a region of infinite density?</p> | g15 | [
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<p>I am working on a concept for something and i want to make sure i understand something clearly before i start on everything else. Note, my project is more about the interactions of elements of complex systems rather than physics. Im just using this paragraph as an example, not doing a project on quantum mechanics. Is this paragraph accurate:</p>
<p>The universe is built on probabilities. In the whole scope of the universe, absolute mathematics and absolute certainty do not exist. Its incorrect to say 1 + 1 = 2, the more accurate way to say it is 1 + 1 probably equals 2, but not always. It is all based on the probability that what you expect to happen, will. Its quantum probabilities that dictate that a group of sub atomic particles, at this exact moment in time, line up precisely in a certain way that allow an atom to exist. That atom lives in an environment (dictated by other probabilities) that has a calculable probability to grab onto another atom and form an object with mass. That object was hammered into a shape by a craftsman trusting that the probabilities dictating the actions of the subatomic particles allow it to not crack, or disintegrate, or break the tool. That object is now sitting on your desk holding your soft drink in the form of a can. The subatomic particles that are almost insignificantly small form a thread of interaction that leads up to that can sitting on your desk. If that thread breaks at any point, that can ceases to exist as you know it and your soda is running all over your desk. </p>
<p>Thanks everyone, im not sure if this falls in the scope of this site, but i can't think of any other place to ask this question.</p> | g7129 | [
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<p>When I first learned about the <a href="http://en.wikipedia.org/wiki/Depletion_force">depletion interaction</a>, my initial reaction was that it looks very similar to the Casimir effect. On making this remark to the professor, he replied somewhat mystically: "It <strong>is</strong> the Casimir effect." No further detail was supplied, however. </p>
<p>Nevertheless, it really looks like both problems can be understood in terms of degrees of freedom maximising their positional entropy by reducing the volume of some "forbidden region" between two objects. For the depletion interaction, the fluctuating degrees of freedom are small particles, while in the Casimir effect, these degrees of freedom are long-wavelength modes of the free radiation field. However, a key difference is that in the first case the fluctuations arise thermally, while in the second case they are unavoidable quantum fluctuations of the vacuum.</p>
<blockquote>
<p>Is it possible to derive the Casimir force between two conducting plates from entropic considerations alone?</p>
</blockquote> | g7130 | [
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<p>If light is travelling vertically upwards and I am travelling horizontally and perpendicular to light, the velocity of light in the vertical direction will get reduced. How does this happen? How does motion in x-direction cause a reduction in speed of light in y-direction ?</p>
<p>Also, in Lorentz Transformation, suppose two observers measure a rod, can one of the observers see that the other person who is moving w.r.t. him, measure the rod to be less than his own measurement ? In other words, can the metre sticks of a moving observer get bigger than the observer who views the moving observer and sees himself to be at rest ?</p> | g7131 | [
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<p>i was wondering if anyone could give an explicit calculation or show a link that shows the proof to Furry's theorem. showing how the vacuum expectation value of any odd number of electromagnetic currents vanishes. in particular the case for n=3.</p> | g7132 | [
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<p>Inspired by <a href="http://physics.stackexchange.com/questions/79089/intuitive-explanation-of-why-orbits-are-closed">this recent question</a>, I would like to understand from a more general and mathematical perspective why closed orbits are only found for the Kepler ($V(r) \sim 1/r$) or harmonic ($V(r) \sim r^2$) potential problems, as follows from <a href="http://en.wikipedia.org/wiki/Bertrand%27s_theorem" rel="nofollow">Bertrand's theorem</a>. </p>
<p>There are two aspects that make these problems special, which I suspect may be related to the closed-orbit property. First, both problems are <a href="http://en.wikipedia.org/wiki/Superintegrable_Hamiltonian_system" rel="nofollow">superintegrable</a>. This property sits intuitively well with the idea that phase-space orbits should close "as quickly as possible", thus implying that real-space orbits close after a single revolution. Second, each problem possesses an additional "unexpected" conserved quantity, due to a larger symmetry of the problem than the obvious $O(3)$. For the Kepler problem, this is the <a href="http://en.wikipedia.org/wiki/Laplace%E2%80%93Runge%E2%80%93Lenz_vector" rel="nofollow">Runge-Lenz vector</a>, related to the $O(4)$ symmetry of the Hamiltonian. Meanwhile, the harmonic oscillator Hamiltonian conserves the Fradkin tensor:
$$ F_{ij} = \frac{p_i p_j}{m\omega^2} + m\omega^2 q_i q_j, $$
which is related to an $SU(3)$ symmetry. In fact these symmetries and corresponding conserved quantities exist for <em>any</em> central field problem (<a href="http://ptp.oxfordjournals.org/content/37/5/798.short" rel="nofollow">D. M. Fradkin, Prog. Theor. Phys. <strong>37</strong> (1967), p.798</a>). However the conserved quantities only take a "nice" form for the Kepler and harmonic problems, which also allows the corresponding quantum problems to be diagonalised exactly by symmetry arguments alone. </p>
<p>These considerations motivate the following question:</p>
<blockquote>
<p>What specific physical/mathematical feature(s) do these two problems share that gives them the property of closed orbits? Does this feature bear relevance to the quantum counterpart?</p>
</blockquote> | g7133 | [
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<p>I recently came across a comment that when we push a rubber ball into water filled in a bucket, the water level rises because of the force applied by our hand (i.e. the more force we apply, the more water rises). But I do believe it's absurd, water rise occurs as a function of volume (of our hand).</p>
<p>If water level rose with force applied, that would mean that if I moved my fingers in water, giving force to the body, without changing the immersed hand volume, then a water rise would occur. Isn't that creation of water from water?</p> | g7134 | [
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<p>The NOVA show on the string theory have mention once that the proton and neutron will be disappear in finite amount of time, then reappearing on somewhere else. Is there any experiment have shown that this is true?</p> | g7135 | [
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<p>Could someone explain how, or at least show me a link that explicitly shows the calculation of a two-loop corrections to scalar’s two-point function
in $\varphi^4$ theory in the massless limit. </p> | g7136 | [
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<p>We are able to see this beautiful world because of light. When light gets reflected from the object, the reflected light enters our eye retina and thus we are able see that particular object from which light was reflected from. In our daily life, we see certain things which are transparent, they appear transparent because most of the light is refracted instead of getting reflected. So, there will be only very less reflected rays which enters our eye and thus enables see up to certain extent. Suppose we have mirror or any other matter which is perfectly transparent, i.e it reflects no light incident on it. If this happens, we will not be able to see that particular object! So, if this is a possibility we can create invisible things like invisible robot, etc from those perfectly reflecting matter (like ideal transparent glass). </p>
<p>Is this really possible? If yes what kind of things would be better to create in invisible form, like one may show their idea by displaying their model (ex. spy robot). Every one can give their idea, so that there will be value of saying why this site is for scientists. </p>
<p>I don't know whether I have misunderstood anywhere, if so pardon me and explain. </p> | g7137 | [
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<p>The formula for <a href="http://en.wikipedia.org/wiki/Magnetic_levitation" rel="nofollow">magnetic levitation</a> is</p>
<p>$$ B \frac{dB}{dz} = \frac{ \rho g }{\chi} $$</p>
<p>but as always, I have a hard time figuring the units in SI. The left hand side is $\mathrm{T^2 /m}$, while $\chi$ has units of $\mathrm{m^3\,mol^{-1}}$, which makes the right hand side with units of..</p>
<p>$$\mathrm{kg\,m^{-5}\,s^{-2}\,(mol)}$$</p>
<p>Obviously there must be some constant, but I don't know what is it, as all texts use this natural unit system. Help?</p>
<p><strong>Update:</strong></p>
<p>using the <a href="http://en.wikipedia.org/wiki/Permeability_of_free_space" rel="nofollow">permeability of free space as reported by Wikipedia</a>, which seems to be Tesla-meter per Ampere, leaves the right hand side as</p>
<p>$$\mathrm{kg\,T\,m^{-4}\,s^{-2}\,Ampere\,mol}$$</p>
<p>still far from being recognizable to the left side</p> | g7138 | [
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<p>I recall vaguely that energy is absorbed/radiated in packets called quanta. Quanta were what are now known as photons. </p>
<p>What I'm curious about - Is absorption/radiation vis-a-vis photon lossy? Do the total number of photons exactly match the energy acquired/released?</p> | g7139 | [
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<p>I understand the definitions "theorem" and "conjecture" in mathematics, but I wasn't sure for physics. I mean, if it's <em>proved</em> mathematically, it's a theorem, otherwise it's a conjecture. But for physics (i.e. when the idea is meant to correspond to a physical reality - and - can only said to 'true' if tested experimentally), how does one make a distinction?</p> | g7140 | [
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<p>As you know the equation of capillary action id given by:</p>
<blockquote>
<p>$h=\dfrac{2\gamma\cos\theta}{\rho gr}$</p>
<p>Where:</p>
<p>$h$ is the height the liquid is lifted,</p>
<p>$\gamma$ is the liquid-air surface tension,</p>
<p>$\rho$ is the density of the liquid,</p>
<p>$r$ is the radius of the capillary,</p>
<p>$g$ is the acceleration due to gravity,</p>
<p>$\theta$ is the angle of contact described above.</p>
<p><a href="http://en.wikipedia.org/wiki/Surface_tension" rel="nofollow">Capillary action equation</a></p>
</blockquote>
<p>So my problem is I don't know what is the meant by $h$ the height the liquid is lifted?
Picture 1 or picture 2?</p>
<p>Picture 1:</p>
<p><img src="http://i.stack.imgur.com/46fCl.jpg" alt="Picture 1"></p>
<p>Picture 2:</p>
<p><img src="http://i.stack.imgur.com/7kdqU.jpg" alt="Picture 2"></p> | g7141 | [
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<p>Consider a cement block of the same density as sea-water resting on the (perfectly polished) seafloor. I also assume the side-faces of the cement block are highly polished, so that no vertical hydrostatic forces can attack on them. A cable is attached to the top of the block.</p>
<p>My question ist: How much force must one apply to the cable before the cement block begins to lift off the seafloor?</p>
<p>The normal response would be to say that only a negligible force is needed - as the block is practically suspended in the water.</p>
<p>However, as the bottom surface of the cement block is not in contact with the water, it is NOT experiencing the hydrostatic pressure from below - only from above.</p>
<p>Before the crane starts lifting, the (zero-sum) forces on the cement block are:</p>
<p>$$F_{Seawater Pressure} +F_{Gravity on Cement Block} - F_{Seafloor Resistance} = 0$$</p>
<p>as the crane starts applying Force, the Seafloor will reduce its Resistance in the same measure, leaving the forces on the cement block zero:</p>
<p>$$F_{Seawater Pressure} +F_{Gravity on Cement Block} - (F_{Seafloor Resistance}+F_{Crane}) = 0$$</p>
<p>Just before the Cement block lifts, the Seafloor will stop applying Force and the Crane will be applying the only upward Force:</p>
<p>$$F_{Crane} = F_{Seawater Pressure} +F_{Gravity on Cement Block}$$</p>
<p>Once the Cement block lifts off the sea-floor, hydrostatic pressure kicks in on the lower cement surface, suspending the block, but before that - boy does it take a lot of force to lift it!</p>
<p>What is wrong with this reasoning? </p>
<p><img src="http://i.stack.imgur.com/Ny5U8.jpg" alt="Hauling up a Cement block from the sea-floor"></p> | g7142 | [
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<p>I've seen the <a href="http://en.wikipedia.org/wiki/Kerr_metric" rel="nofollow">Kerr metric</a> usually presented in the Boyer-Lindquist coordinates where there is a cross term in the $d\phi$ and $dt$ term. I've done a good bit of searching and cannot find any coordinates which express the Kerr metric in an orthogonal fashion. Is there ANY choice of coordinates that eliminates all cross terms/off-diagonal terms for the Kerr metric? </p>
<p>If not, is it just a fact that you can never find such a coordinate transformation because of the inherent geometry of the Kerr space-time? </p> | g7143 | [
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<p><img src="http://i.stack.imgur.com/qay6o.jpg" alt="Universe"></p>
<p>I would be interested in what people think of Fulvio Melia's <a href="http://arxiv.org/abs/1205.2713" rel="nofollow">argument</a> for a linearly expanding Universe.</p>
<p>I realize that the experimental evidence seems to be pointing to an accelerating Universe but does Melia's argument have any merit?</p>
<p>This is my version of his argument.</p>
<p>Imagine that we are at point $P$ in a homogeneous, isotropic Universe. Point $P$ is on the surface of sphere $S_1$. Therefore, in Newtonian terms, there is an acceleration $g_1$ at point $P$ directed towards the center of sphere $S_1$ with magnitude:</p>
<p>$$g_1 = \frac{G\ M_1}{R_1^2}.$$</p>
<p>But point $P$ is also on the surface of sphere $S_2$. Therefore one can construct another argument, independently of the previous one, that there is an acceleration $g_2$ at point $P$ directed towards the center of sphere $S_2$ with magnitude:</p>
<p>$$g_2 = \frac{G\ M_2}{R_2^2}.$$</p>
<p>However since the Universe is homogeneous and isotropic then, again in Newtonian terms, there should not be any net acceleration vector at any point.</p>
<p>How do we resolve this paradox?</p>
<p>Either the Universe is empty so that $g_1 = g_2 = M_1 = M_2 = 0$ or General Relativity gives us another solution.</p>
<p>In GR pressure also has "weight" so that the gravitational acceleration $g$ at the surface of a uniform density sphere of mass $M$ and radius $R$ with density $\rho$ and internal pressure $p$ is given not by:</p>
<p>$$g = \frac{G\ M}{R^2} = \frac{4\ \pi}{3}G \rho R$$</p>
<p>but rather by:</p>
<p>$$g = \frac{4\ \pi}{3}G (\rho + 3 p/c^2)R.$$</p>
<p>Thus if for symmetry reasons we require $g$ to be zero for all spheres touching point $P$ then we must have the equation of state:</p>
<p>$$p = -\frac{\rho c^2}{3}.$$</p>
<p>When substituted into the Friedmann equations (without cosmological constant) this equation of state implies that $\ddot{a}=0$, where $a$ is the scale factor, so that the Universe can only be expanding linearly with time.</p> | g7144 | [
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<p>I was looking up X-Ray crystallography using Bragg's Law:</p>
<p>$2d\sin\theta = n\lambda$</p>
<p>and I can understand the values of everything except this integer value $n$.</p>
<p>As far as my research got $n$ is used to describe the atom spacing in the crystal lattice, but I don't understand how you'd express $n$ or how it would describe it.</p>
<p>Could someone please explain this to me please?</p>
<p>Note: diagrams tend to be very useful in developing my understanding and if anyone has any reference to a video that might help as well. Thanks.</p> | g7145 | [
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<p><img src="http://i.stack.imgur.com/xtzJm.png" alt="Physics doubt"></p>
<p>In which of the following situation will the bullet of the pistol penetrate deeper in the wall? Why? Alternatively will the penetration in both cases be the same? Can you explain the concepts behind this?</p> | g7146 | [
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<p>According to equation 5.2.5 in Polchinski :-</p>
<p>$$\int d^2 \sigma~ \delta^{'}g_{ab} \times [-2(P_1 \delta \sigma)_{ab} +(2\delta w - \Delta \cdot \delta \sigma)g^{ab}]=0$$</p>
<p>The assumption here is that " Moduli correspond to variation $\delta^{'}g_{ab}$ of the metric that are orthogonal to all variations of DiffxWeyl type given by the quantity in []"</p>
<p>My question is that why are we imposing that orthogonality ? How can variation in the metric due to moduli be orthogonal to variation due to other Diff x Weyl ?</p> | g7147 | [
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<p>I pulled apart a flashlight and found a similar lens as the one shown below.</p>
<p><img src="http://i.stack.imgur.com/k4Vhh.jpg" alt="enter image description here"></p>
<p>I assume that the light starts off as a “point source” somewhere inside and the curvature and/or shape of the “lens” makes parallel wavefronts (or rays) exit the flashlight in a somewhat collimated beam. Is this approximating correct? Almost all of the websites really didn’t give any detailed information or was unclear that I found. I would love for someone to explain this in more detail if possible.</p> | g7148 | [
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<p>Given formula:</p>
<p><img src="http://i.stack.imgur.com/JsywY.png" alt="enter image description here"></p>
<p>How I can use to calculate distribution of points in space, so if i choose path which contains most of the points I get path that close to "free-fall path".
As far as I know i should use square root of Determinant of given formula to do this, but i am not sure. </p>
<p>Please, be gentle, I am computer scientist student that in process writing black hole simulation for academic purposes.
NOTE: Simulation is in 2D. so some parameters may be irrelevant.</p> | g7149 | [
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<p><a href="http://www.youtube.com/watch?feature=player_detailpage&v=jfySIeS1XZE#t=118s" rel="nofollow">http://www.youtube.com/watch?feature=player_detailpage&v=jfySIeS1XZE#t=118s</a></p>
<p>If so, how are they created (roughly speaking). Earlier in the video he says that a laser scanned the surface of the object, which suggests that no physical object needs to be present at the time of viewing the hologram, like what is required for a Mirage toy (seen here: <a href="http://www.youtube.com/watch?v=lFqlQiTTHRs" rel="nofollow">http://www.youtube.com/watch?v=lFqlQiTTHRs</a>). Is this right? </p>
<p>I am aware that this is a fictional show, so what they are saying should not be taken too seriously and the hologram effect could be added by CG effects, but I am interested in the actual workings of this type of hologram (as opposed to a "flat" <a href="http://en.wikipedia.org/wiki/Holography" rel="nofollow">hologram</a>).</p> | g7150 | [
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<p>I am interested to know how the (non)existence theorems of <a href="http://en.wikipedia.org/wiki/Constructive_quantum_field_theory">constructive QFT</a> and <a href="http://ncatlab.org/nlab/show/AQFT">algebraic QFT</a> are related (or not). I have only a weak grasp of either, so I'm looking for something like a quick overview. Here's how I understand things:</p>
<p>Constructive QFT has shown that quantum fields can be well-defined in $d$ < 4, by showing that the distributions and interactions exist in that case. Apparently there are specific examples, but this is an existence result for 1) techniques coming from analysis, 2) $d$ < 4, and 3) interactions are included.</p>
<p>Algebraic QFT comes from looking at the canonical commutation relations on spacetime, and has shown that a single Hilbert space cannot represent both the interacting and non-interaction picture (I think this is one statement of Haag's theorem). So this is a non-existence result 1) based on the algebra of CCR and 2) includes interactions (apparently a way out is to assume periodic boundary conditions - I'm not overly interested in that part).</p>
<p>So several specific questions - can I think of these as a Lagrangian vs Hamiltonian picture? What do these two results mean to each other - are they even related at all since they are essentially QFT in different dimensions? </p>
<p>References with reviews of these theories would be nice - I've checked out Haag's book enough to know that if I spent time I could probably understand it, but I'd rather good review articles if anyone knows of any.</p> | g7151 | [
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<p>When we write equations in QM, in certain places, the wave function is represented as $\psi(x,t)$, which is the wave function in position space, and in some other places, it is written as $\Psi(t)$. What is the difference between the two?</p> | g7152 | [
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<p>I was watching one of Neil Degrasse Tyson talks and there was a scientist (can't recall his name sorry) who was talking about a recent discovery: </p>
<blockquote>
<p><em>"Doubly-even self-dual linear binary error-correcting block code" has been discovered embedded within the equations of superstring theory.</em></p>
</blockquote>
<p>Is this for real? Does it imply that our universe just a sophisticated emulation running on some supercomputer?</p>
<p>EDIT:</p>
<p>Would it be possible to set up an experiment that would be able to test this hypothesis?</p>
<p>I am thinking about World of Warcraft, for example, how would an elf in WoW test if his world is an emulation or not? Is it even possible?</p> | g7153 | [
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<p>Weinberg on p. 287 of his QFT vol. 1 introduces the extended interaction operator:
$$
\tag 1 \hat{V}(t) \to \hat{V}(t) + \sum_{a}\int d^{3}\mathbf x \hat{o}_{a}(\mathbf x ,t)\varepsilon_{a}(x).
$$<br>
Here
$$
\hat{S} = \hat{T}e^{i\int \hat{V}(t)dt}, \quad \hat{o}_{a}(\mathbf x, t) = e^{i\hat{H}_{0}t}\hat{o}_{a}(\mathbf x , 0)e^{-i\hat{H}_{0}t}.
$$</p>
<p>Then he says that S-matrix arbitrary element $S_{\beta \alpha} = \langle \beta | \hat{S}| \alpha \rangle$ after extension $(1)$ becomes the $\varepsilon $-functional, and after that he introduces generalized Feynman rules by adding new vertexes corresponding to $\hat{o}_{a}$ with $n_{a}$ lines (the number $n_{a}$ coincides with the number of fields in $\hat{o}_{a}$) and c-factor $\varepsilon_{a}$.</p>
<p>After that he introduces variational derivative
$$
\tag 2 \left( \frac{\delta^{r}S_{\beta \alpha}}{\delta \varepsilon_{a_{1}}(x_{1})...\delta \varepsilon_{a_{r}}(x_{r})}\right)_{\varepsilon = 0} = (i)^{r}\langle \beta | \hat{T}\left(e^{i\int \hat{V}(t)dt} \hat{o}_{a_{1}}(x_{1})...\hat{o}_{a_{r}}(x_{r})\right)|\alpha\rangle
$$
and notices that all $n_{a_{1}}, ..., n_{a_{r}}$ lines correspond to $\hat{o}_{a_{1}},...,\hat{o}_{a_{r}}$ respectively are internal, i.e. in case when $n_{a_{1}} = ... = n_{a_{r}} = 1$ they are compared to the propagators.</p>
<p>Finally, he says, that if we want to get Feynman diagram with $r$ external lines with types $a_{1},...,a_{r}$ in momentum representation we need to do following with $(2)$: </p>
<p>1) to throw out of propagators $D_{a_{1}a_{r}}(x_{1} - x_{r})$,</p>
<p>2) to apply the Fourier transformation, </p>
<p>3) to add corresponding coefficient functions $u_{a_{1}},...$. </p>
<p>Here is the question: сould you make the sense of introduction of mechanism 1)-3) clearer for me? Why do we need additional $r$ external lines which with corresponding vertexes which aren't connected to other vertexes (so the diagram is non-connected), as I think?</p>
<p>I need to rephrase the question. I know that n-point Green functions $\langle \beta | \hat{T}\left(\hat{o}^{H}_{a_{1}}(x_{1})...\right)|\alpha \rangle$ where the operators are in Heisenberg picture are equal to $(2)$. Also these functions are widely used for derivation of some non-perturbative results for scattering processes. But I don't understand how to apply these non-perturbative results for S-matrix, because we need to set $r$ to zero for obtaining the exact sets of Feynman amplitudes $S_{\beta \alpha}$, but I'm not sure that it is possible without loss of nonperturbative results. Here is some incorrect understanding of Weinberg method, so it will be very good if someone help me.</p> | g7154 | [
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<p>Specifically, I am trying to roughly determine the sound produced by a ball when it hits the floor and bounces. If the ball exerts a pressure onto the floor, then certainly this pressure will go on to create a sound wave in the floor (infinite block) and the air. I was just wondering if there is any way to find the sound wave (or the energy of the sound wave) released by the ball, thus finding the energy lost and the ball's approximate rebound height. Is the velocity of the sound wave given as follows?: </p>
<p><img src="http://i.stack.imgur.com/r3bgq.gif" alt=""></p>
<p>or is it more complicated than the basic equations provided in most physics textbooks?</p> | g7155 | [
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<p>Suppose we have action $S[q]$ and its stationary path $q_s$, I want to find the orthonormal paths $\psi_n$ that can diagonalize the second variation of the action $S[q]$. How to do that? Thanks</p> | g7156 | [
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<p>I drive a Volvo v40 with a 110hp diesel engine. It usually use 4.6L/100km.</p>
<p>If I plug my laptop which is 85W, will this change the fuel need? If so, by how much?</p> | g7157 | [
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<p>I've heard that scientist proof that viruses of the Tobacco mosaic virus could interfere with themselves. I'm referring to quantum interference-- the same as photons. Unfortunately, I couldn't find any material on this problem on the Internet , so I don't know if it's true. Viruses have a width between 20nm and 1000nm, so they should be applied to mesoscopic physics, where that phenomenon is possible. </p>
<p>Is there proof that some species of virus can interfere with themselves?</p>
<p>If not, which is the biggest object where we may observe that interference? </p> | g7158 | [
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<p>The question pretty much sums up what I need to know. Why is it that light only gets dispersed into a spectrum when travelling through two non-parallel sides(like a prism) and not through something like a glass slide with parallel slides.</p>
<p>And how does this experiment(an experiment conducted by Newton) explain this? Because this is what is in my school textbook.</p>
<p><a href="http://i.imgur.com/A28RZ.png" rel="nofollow">Newton's Two Prism Experiment</a></p> | g7159 | [
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<p>shouldn't be the quantization formula (in one dimension) equal to</p>
<p>$ N_{smooth}(E)+N_{osc}(E) = \oint_{C}p.dq $ ??</p>
<p>where the Oscillating term is just the correction from Gutzwiller trace formula or a sum over Orbits</p>
<p>why is just the oscillating term ignored ..</p> | g7160 | [
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<p>I have a question about the $ \hat{n} $ in this formula $\sigma = P \dot{}\hat{n}$.</p>
<p>Why do sometime in my book they get $\sigma = P \cos{\theta}$ for a sphere. Isn't $\hat{n} = r$ ? </p>
<p>And then in another problem, where $P = \cfrac{k}{r}\hat{r}$ and r = a (inner) and r = b (outer) they get $\sigma =\cfrac{k}{a}$ and $\sigma =\cfrac{k}{b}$.</p>
<p>$\sigma$ = surface charge density</p>
<p>$P$ = polarization</p> | g7161 | [
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<p>Is the holographic principle applicable everywhere, e.g. is it possible to learn everything about any whatsoever volume of space everywhere in the universe from the boundary of it or does it have to be bounded by some special feature like an event horison? And do the same thing always apply in the reverse direction too, from the perspective of investigating from inside the same volume? Do these questions depend on the nature of space(time), it for example being de sitter one place or the other.
The question is intented as a generalization of
<a href="http://physics.stackexchange.com/questions/76766/holographic-principle-inside-out-view">Holographic principle "inside-out view"</a></p> | g7162 | [
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<p>A particle is projected from a point on level ground with a speed of $u$ meters per second and an angle of elevation $\theta$. The maximum height reached by the particle is $42$ meters above the ground and the particle hits the ground $196$ meters from its point of projection. Find the values of $\theta$ and $u$.</p> | g7163 | [
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<p>I've been reading about Cosmic Background Radiation (CMBR) lately. My understanding so far is that this is the "Noise"/"Flash" from the big bang. Assuming that information is correct, how far away is it traveling in order to reach us? The way it was described to me makes it sound as if it should be coming from the "end" of the universe. Or is it omnipresent? </p> | g10 | [
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<p>When i apply high voltage (through a capacitor bank) across an aluminium foil, it gets converted into plasma. I want to simulate this process and study the properties of the plasma produced henceforth. I would then like to change my experimental parameter and see if my simulation predicts the correct output. </p>
<p>How do i proceed to do so?
I am an absolute beginner in plasma physics.</p> | g7164 | [
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<p>First of all, I know that light does indeed travel slower in a medium like air or water, but that's because the photons are bouncing off of the medium's particles and in different directions so the light beam as a whole is slowed down (or at least that's the classical explanation I've read somewhere).</p>
<p>But my question is about light traveling freely in the vacuum.<br>
What if an astronaut during a spacewalk switches on a flashlight towards the opposite direction he is moving. Will that light travel slower than normal?</p>
<p>If not, is there another way to make light move slower?<br>
For example, can you make a beam of light move so slow that you can visually perceive it being affected by gravity?</p> | g7165 | [
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<p>I have started doing <em>Relativistic Quantum Mechanics</em> from <em>Greiner</em>.</p>
<p>I'm having difficulty understanding the following derivation for commutation relations (page 4):</p>
<p>$$[\hat{p}^\mu, x^\nu] = i\hbar[\frac{\partial}{\partial{x_\mu}},g^{\nu \sigma}x_\sigma]=$$
$$= i\hbar g^{\nu \sigma}\frac{\partial x_\sigma}{\partial x_\mu}=$$</p>
<p>now this is the part I don't understand, how did we got from last equation to next one:</p>
<p>$$=i\hbar g^{\nu \sigma}\delta^{\mu}_\sigma$$</p>
<p>Why is:
$$ \frac{\partial x_\sigma}{\partial x_\mu}= \delta^{\mu}_\sigma$$</p>
<p>where $$\delta^{\mu}_\nu = g^{\mu \sigma}g_{\sigma \nu}$$</p> | g7166 | [
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<p>As an electrical/computer engineer, I already have a relatively thorough understanding of classical electromagnetism. </p>
<p>From what I understand though, classical EM is only an approximation to quantum electrodynamics. I'm very curious about how it all <em>really</em> works though.</p>
<p>So as an ECE engineer, what would be the best way to approach quantum electrodynamics? (assuming taking a course at a community college is not an option)</p> | g7167 | [
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<p>In Sakurai's <em>Modern Quantum Mechanics</em> (2nd ed) p.99, he says</p>
<blockquote>
<p>We know from the theory of partial differential equations that
(<em>time-independent Schrodinger equation</em>) subject to boundary
condition ($\psi(\mathbf{x}')\rightarrow 0$ as
$|\mathbf{x}'|\rightarrow\infty$) allows nontrivial solutions only for
a discrete set of values of $E$. It is in this sense that the
time-independent Schrodinger equation yields the quantization of
energy levels. Once the partial differential equation
(<em>time-independent Schrodinger equation</em>) is written, the problem of
finding the energy levels of microscopic physical systems is as
straightforward as that of finding the characteristic frequencies of
vibrating <strong>strings or membranes</strong>.</p>
</blockquote>
<p>Although I've found a paper (<a href="http://www.scientificexploration.org/journal/jse_21_1_hocking.pdf" rel="nofollow">http://www.scientificexploration.org/journal/jse_21_1_hocking.pdf</a>) about this, the relationship is still not very explicit. So would you please explain briefly about the relationship between the Schrodinger equation and string/membranes? Many thanks.</p> | g7168 | [
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<p>I have a bottle of vodka that has a load of gold flakes suspended in it. It has been sat still for over 24 hours and the flakes are all still suspended within the liquid: they have not risen to the surface or sunk to the bottom. Any ideas as to the physics behind this? </p> | g7169 | [
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<p>I know that the electric field is zero inside a perfect conductor. However, I am here discussing non-perfect conductors. So let's suppose we have a conducting medium with conductivity $\sigma_1$ and electric permittivity $\epsilon_1$. Another conducting medium is enclosed by the first medium and this one has conductivity $\sigma_2$ and electric permittivity $\epsilon_2$. Now both media are subjected to an external uniform electric field. The question is what is the electric field inside the first medium and what is the electric field inside the second medium. My understanding is that a steady-current is induced that flows in both media but I'm little confused and would appreciate some help.</p> | g7170 | [
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<p>In scattering theory, what is a good intuitive picture to think of s-wave, p-wave or d-wave collisions ? What is their importance and what are the examples where a particular one is assumed to be the only important one and rest are taken as negligible ?</p> | g7171 | [
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<p>As a planet moves through the solar system, a <a href="http://en.wikipedia.org/wiki/Bow_shock">bow shock</a> is formed as the solar wind is decelerated by the magnetic field of the planet. Presumably the creation of this shock wave would cause drag on the planet, certainly in the direction of orbit but possibly rotation as well.</p>
<p>Is there an estimate for the amount of drag on the Earth as it orbits the Sun? Based on the drag, how long would it take before the orbital velocity slows to the point that we spiral slowly into the Sun? Would any planets fall into the Sun prior to the Sun expanding into a Red Giant, gobbling them up?</p> | g7172 | [
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<p>I'm doing a project (dissertation) on the mathematics of Aerofoil Theory. I wonder if I could get some advice on a possible structure. I'm new to fluid dynamics, so it's quite hard to know where to start. </p>
<p>So far I've looked at different types of flows; streamlines and velocity potentials. I've also covered a fair amount of complex variable theory - and can (loosely) see how conformal mappings are used to map for instance a cylinder to an aerofoil shape using Joukowski's transform. I would guess from here, I would want to look at Bernoulli's equation for lift and start looking at modelling an example. </p>
<p>It would be useful to know if this is the right kind of structure to follow or if I'm approaching this the wrong way! So any help would be appreciated. Thanks! </p> | g7173 | [
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<p>I have a question about the most general (diff$\times$Weyl)-invariant and Poincare-invariant form of action. In Polchinski's string theory p15, there is an action for manifold without boundary
$$S_{\mathrm{p}}'= - \int_M d \tau d \sigma (-\gamma)^{1/2} \left( \frac{1}{4\pi \alpha'} \gamma^{ab} \partial_a X^{\mu} \partial_b X_{\mu} + \frac{ \lambda}{4\pi} R \right) \tag{1.2.33}$$</p>
<p>It is said </p>
<blockquote>
<p>This is the most general (diff$\times$Weyl)-invariant and Poincare-invariant action with these fields and symmetries. </p>
</blockquote>
<p>My question is, how to prove Eq. (1.2.33) is the most general one (without boundary)? Not saying what else could it be...</p> | g7174 | [
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<p>I have three questions about the BRST symmetry in Polchinski's string theory vol I p. 126-127, which happen together </p>
<p>Given a path integral
$$ \int [ d\phi_i dB_A db_A d c^{\alpha}] \exp(-S_1-S_2-S_3) \tag{4.2.3}$$
with $$ S_2 =-iB_A F^A (\phi) \tag{4.2.4}$$
$$ S_3 = b_A c^{\alpha} \delta_{\alpha} F^A(\phi) \tag{4.2.5} $$</p>
<p>the BRST transformation
$$ \delta_B \phi_i = -i \epsilon c^{\alpha} \delta_{\alpha} \phi_i \tag{4.2.6a} $$
$$ \delta_B B_A=0 \tag{4.2.6b} $$
$$ \delta_B b_A = \epsilon B_A \tag{4.2.6c} $$
$$ \delta_B c^{\alpha} = \frac{i}{2} \epsilon f^{\alpha}_{\beta \gamma} c^{\beta} c^{\gamma} \tag{4.2.6d} $$</p>
<p>It is said </p>
<blockquote>
<p>There is a conserved ghost number which is $+1$ for $c^{\alpha}$, $-1$ for $b_A$ and $\epsilon$, and 0 for all other fields.</p>
</blockquote>
<p>How to see that?</p>
<blockquote>
<p>The variation of $S_2$ cancels the variation of $b_A$ in $S_3$</p>
</blockquote>
<p>I could get $i B_A \delta F^A$ in $\delta S_2$ and $(\delta_B b_A) c^{\alpha} \delta_{\alpha} F^A= \epsilon B_A c^{\alpha} \delta_{\alpha} F^A $ in $\delta S_3$. But there is a $c^{\alpha}$ in $\delta S_3$</p>
<blockquote>
<p>the variations of $\delta_{\alpha} F^A$ and $c^{\alpha}$ in $S_3$ cancel. </p>
</blockquote>
<p>How to see that?</p> | g7175 | [
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<p>In a semi conductor, for an electron in valence band to transfer to conduction band, it needs energy which can be provided by applying an electric field such that a force is applied on it until it breaks free from its parent atom. Now till the time it is at rest no change in kinetic energy is there. Hence, the energy that it gained and transfered to conduction band is electric potential energy. But this electric potential energy is stored in the field configuration i.e. The number at every point in space. And when u change that number you have to give off energy. N when the number is reverted back. It gives back to you the same energy. </p>
<p>Now my question is that this case of the electron breaking free requires that the electric potential energy be localised at the electron like the electron's kinetic energy and not be stored in the field configuration. How is this happening? Is electric potential energy stored in electron or the electric field configuration at each point in space? And if in the field then how does the electron jump the energy gap and enter the conduction band, where does it get the energy from? Is kinetic energy locally stored in the particle or it is also a field configuration kind of thing?
Is there a field associated with kinetic energy ?</p>
<p>Or my understanding is wrong in which case please explain what is meant by electric potential energy is stored in electric field? And what is electric field energy density?</p>
<p>edit: leaving the semiconductor example aside. Suppose i have an atom and i apply external electric field and that causes the atom to ionise. Where did the electron that flew away got the energy from?</p> | g7176 | [
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<p>How can I determine the focal length and position of a lens mounted in an inaccessible position inside a tube by a laboratory experiment?
Please help.</p> | g7177 | [
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<p>I'm working through some problems for a QM exam and I've realised I don't really understand the concept of parity of solutions. I'm looking at a simple finite potential well problem: $$V(x)=0, \quad |x|>d$$
$$V(x) = V_0 \quad |x|<d$$
where $V_0$ is positive. I'm looking at bound states, so that $0<E<V_0$. I divide the x-axis into three regions, from left to right, in the standard way, so that my wavefunction is as follows:</p>
<p>$$ \psi(x) =
\begin{cases}
Ce^{ax}, & x\in I\\
A \sin kx + B\cos kx, & x\in II \\
De^{-ax}, &x \in III
\end{cases}$$</p>
<p>Where $a^2\equiv \frac{2m(V_0-E)}{\hbar^2}$ and $k^2\equiv \frac{2mE}{\hbar^2}$. Now this is the general wavefunction, but to make any progress I know I need to consider even and odd solutions (because the potential is symmetric). These I can find by imposing symmetry/antisymmetry on the wavefunction, so I get</p>
<p>$$ \psi_S(x) =
\begin{cases}
Ce^{ax}, & x\in I\\
B\cos kx, & x\in II \\
Ce^{-ax}, &x \in III
\end{cases}$$</p>
<p>$$ \psi_{AS}(x) =
\begin{cases}
Ce^{ax}, & x\in I\\
A\sin kx, & x\in II \\
-Ce^{-ax}, &x \in III
\end{cases}$$</p>
<p>But what ARE those functions? Am I right in thinking that "half" the eigenvalues of energy correspond to eigenfunctions which are symmetric (and the other half - antisymmetric)? So that the entire energy spectrum looks like this: $$\{ E^S_n , E^{AS}_n \}_{n \in \mathbb{N}}$$</p>
<p>Is my understanding correct?</p> | g7178 | [
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<p>Does anybody know how to implement the WKB approximation for the two-dimensional Schrodinger equation with a harmonic oscillator potential:</p>
<p>$\frac{1}{2}\Biggl[-\biggl(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}\biggr)+x^2 + y^2 + 2xy\Biggr]\Psi(x,y) = E\Psi(x,y)$</p> | g7179 | [
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<p>I still don't really understand what contextuality means in reference to quantum mechanics. If someone could give a clear definition that would be great. It sounds like it means you can't always relate the state of a system to its wavefunction or something? That confuses me since it seems to violate quantum mechanics. So a clear explanation would be great.</p>
<p>The question is then, does any interpretation of quantum mechanics require us to accept contextuality? This paper seems to claim yes, but I don't know enough to evaluate it, so would appreciate a professional's eye: <a href="http://arxiv.com/abs/1006.0500" rel="nofollow">http://arxiv.com/abs/1006.0500</a></p>
<p>(This is a follow up on a previous question: <a href="http://physics.stackexchange.com/questions/7276/what-combinations-of-realism-non-locality-and-contextuality-are-ruled-out-in-qu">What combinations of realism, non-locality, and contextuality are ruled out in quantum theory?</a> )</p> | g7180 | [
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<p>I'm confused with the Gauss' Law to calculate the electric field for two coaxial cylindrical conductors of finite length.</p>
<p>I know that we can use the Gauss' Law to calculate the electric field for two coaxial cylindrical conductors of INFINITE length, but I don't see why we can use the Gauss' Law for the one of finite length.</p>
<p>Ok here is the problem.</p>
<blockquote>
<p><img src="http://i.stack.imgur.com/GsLwh.gif" alt="enter image description here">
Two coaxial cylindrical conductors are shown in perspective and cross-section above. The inner cylinder has radius a = 2 cm, length L = 10 m and carries a total charge of Qinner = + 8 nC (1 nC = 10-9 C). The outer cylinder has an inner radius b = 6 cm, outer radius c = 7 cm, length L = 10 m and carries a total charge of Qouter = - 16 nC (1 nC = 10-9 C). What is Ex, the x-component of the electric field at point P which is located at the midpoint of the length of the cylinders at a distance r = 4 cm from the origin and makes an angle of 30o with the x-axis? </p>
</blockquote>
<p>The problem I have is that, I thought, in order to use the Gauss' law, the electric field has to be constant through out a gaussian surface, but I don't see why we can use a cylindrical shell of radius $4cm$ and length $10m$ to calculate the electric field at $P$ since I think the elctric field is not the same if I move from $0m$ to $10m$ on z-axis. Help me.</p> | g7181 | [
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<p>Classically, we obtain the equations of motion by finding a path which has an action that is stationary with respect to small changes in the path. That is the path for which:</p>
<p>$\delta S =0$</p>
<p>Scaling the action by a constant should therefore do nothing. However, some books seem to consider the overall sign of the action important (since if we changed the sign we could find a path with arbitrarily negative action). Does a scaling factor or change in sign actually matter?</p>
<p>For quantum mechanics we have:</p>
<p>$K(x,y;T) = \langle x;T|y;0 \rangle = \int_{x(0)=x}^{x(T)=y} e^{i S /\hbar } Dx $</p>
<p>Now it looks like scaling the action $S$ will cause changes in how paths will interfere, but the overall sign of the action looks like it still won't matter. So now we can somehow measure the absolute scale of the action?</p> | g7182 | [
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<p>If water is introduced in a container maintained at 20 °C in vacuum conditions, a gaseous phase will appear and the pressure will stabilize at the vapour pressure for the given temperature inside the container. So far so good.</p>
<p>Now imagine the experiment is repeated but instead of vacuum conditions, the water is presurized with nitrogen at 1 atm. According to the phase diagram of water, liquid is the stable form of water in these conditions. Yet it is commonly observed that the water molecules with the highest kinetic energy will escape and form a gaseous phase. The partial pressure of gaseous water will be equal to the saturation pressure at this temperature.</p>
<p>Why do we say that this is a liquid/vapour equilibrium in this case, since the liquid phase is not at pressure required for this equilibrium to appear?</p>
<p>Edit: I just realized that my question seems to be answered by Raoult's law.</p>
<p><a href="http://makethiseditlonger.com" rel="nofollow"></a></p> | g7183 | [
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<p>Using Fujikawa's path integral treatment of the triangle diagram, one can show that</p>
<p>$$\mathrm{Tr} \gamma^5 = \int d^4 x\ \partial_{\mu}j^{\mu} $$</p>
<p>Where $j^{\mu}$ is the Noether current of $U(1)_A$. Thus, the $U(1)_A$ anomaly can be traced to to fact that the trace of $\mathrm{Tr} \gamma^5 \neq 0$ at loop order. My question is, why isn't $SU(2)_A$ anomalous too? I fail to understand why this applies only to $U(1)_A$.</p> | g7184 | [
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<p>Hi guys I'm currently trying to solve a mock exam for an exam in a few days and am a bit confused by the solutions they gave us for this exercise:</p>
<p>Exercise:</p>
<blockquote>
<p><em>A solid is composed of N atoms which are each localized at points in a lattice. Excursions about the equilibrium position of each results in each atom behaving as a 1-dimensional harmonic oscillator. Write down the partition function for an individual atomic harmonic oscillator, and for the collection, assuming that they have arrived in thermal equilibrium with each other at temperature T.</em></p>
</blockquote>
<p>$ Z_{SP} = \sum\nolimits_{n=1}^\infty e^{(-E_n \beta)}$ where $\beta$ is $1/(k_B T)$ and the Energy levels of the quantum harmonic oscillators are $E_n = \hbar \omega (n + 1/2)$. I now tried to use geometric series to evaluate the sum:</p>
<p>$ Z_{SP} = e^{(-\beta \hbar \omega / 2)}\sum\nolimits_{n=1}^\infty e^{(-\beta \hbar \omega)n} = e^{(-\beta \hbar \omega / 2)} \frac{1}{(1 - e^{(-\beta \hbar \omega)})}$
With the substitution $\theta = \hbar \omega \beta $ it says the solution for $Z_{SP}$ should be $e^{(-\theta /2)} \frac{1}{e^{\theta} - 1)}$ which isn't quite the expression I got. </p>
<p>Can anybody tell me where I went wrong or is the solution just false?</p> | g7185 | [
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<p><code>Question</code>: Show that the radial wave function for the hydrogen atom are orthogonal with no exceptions.</p>
<p><code>Attempt</code>:
We know that the wave function for the hydrogen atom is orthonormal; that is,</p>
<p>$$\langle\psi_{nml}\mid \psi_{n'm'l'}\rangle=\delta_{nn'}\delta_{mm'}\delta_{ll'}$$</p>
<p>Splitting up $\psi$ into a radial component $R_{nl}$ and a angular component $Y_{lm}$, we have</p>
<p>$$\langle R_{nl}Y_{lm}\mid R_{n'l'}Y_{l'm'}\rangle=\delta_{nn'}\delta_{mm'}\delta_{ll'}$$</p>
<p>We know that the angular component $Y_{lm}$ is orthonormal, and thus </p>
<p>$$\langle Y_{lm}\mid Y_{m'l'}\rangle=\delta_{ll'}\delta_{mm'} $$</p>
<p>I believe that, if we do not have orthogonality in the radial component, we will not have orthogonality in the wave function. For example, if we do not have radial orthogonality, then at $n=n'$, we might have the radial component be zero. Thus, the radial wavefunction must be orthonormal. Is this correct reasoning? i' worried I' missing something.</p> | g7186 | [
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<p>I understand how the mechanism of spontaneous symmetry breaking works, and why it produces Goldstone bosons (for global symmetries) and massive gauge bosons (for local ones).</p>
<p>However, I'm confused as to why we identify Goldstone bosons as we do. Take the linear sigma model for example. Why do we say that the fields $\phi^n$ are unphysical, whereas the fields $\phi^n - v^n$ are? </p>
<p>I get the feeling that it's a sort of definition that a physical field must have zero vacuum expectation value. At least in order to be interpreted as a particle, that is. But why is this the case? It's not a Wightman axiom, as far as I know!</p>
<p>There's a related question <a href="http://physics.stackexchange.com/questions/43714/what-is-the-role-of-the-vacuum-expectation-value-in-symmetry-breaking-and-the-ge">here</a> but the answers aren't really rigorous enough for my liking. In particular they both rely on "hand-waving" claims that "particles are small oscillations around a vacuum".</p>
<p>I'd rather know that zero VEV is a physical principle, or see a proof that somehow zero VEV follows from a physical requirement. The other question seems to deal with the converse.</p>
<p>Many thanks in advance for your help!</p> | g7187 | [
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<p>Specifically, my question is:
Should one expect energy quantization for a particle in the following potential well?
<img src="http://i.stack.imgur.com/qhXAW.png" alt="potential"></p>
<p>More generally, how can one tell whether or not energy should be discrete/quantized just by looking at the potential function?</p> | g7188 | [
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<p>A simple question about wormholes: What happens if a large object is pushed through a much smaller wormhole? For example, what happens if I push an elephant through a palm-sized wormhole? My intuition is that depending on the magnitude of the force applied, either a part of the elephant is ripped out, or the elephant sort of gets stuck in the wormhole, as if hitting a wall. Is this correct?</p> | g7189 | [
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<p>I have the following problem on my homework. The actual problem has numbers, but I figure using symbolic notation will help me understand the concept in the long run.</p>
<p>A block of mass $M$ is launched by a spring of negligible mass and constant $K$ along a frictionless surface. Prior to launch the spring is compressed a distance of $D_1$. Some time after launch mass then travels up an incline (the angle doesn't matter) that is also frictionless. However, at some point between leaving contact with the spring and entering the incline, the block passes over a rough patch of of distance $D_2$ where the coefficient of Kinetic friction is $C$. Find the max height the mass will travel up the incline. </p>
<p>I've managed to work through the following:</p>
<p>Looking at this I believe it is a conservation of energy problem. We have the Initial energy is equal to energy final - energy lost through friction.</p>
<p>So, Initial Energy is </p>
<p>$$E_i = \frac 1 2 kx^2 $$</p>
<p>Then our final Energy is simple $MGH$ since at it's max height it stops and all energy is potential again. </p>
<p>So $MGH = \frac 1 2 kx^2 - \text{Friction}$</p>
<p>and this is where I get confused. I'm not to sure how I calculate the energy loss of friction.</p>
<p>I believe it is the work friction does is equal to energy loss.</p>
<p>So that would $W=FD$ distance is $D_2$ and the force would be $CMG$ since the normal force is equal to gravity on the flat surface. Am I correct in this?</p>
<p>This would lead me to</p>
<p>$$H = \frac{(1/2kx^2)-(CMGD_2)}{MG}$$</p>
<p>Which simplifies down to:</p>
<p>$$H=\frac{1/2kx^2}{MG} - (CD_2)$$</p>
<p>This also confuses me, if my above calculations are correct, then the amound of energy loss due to friction does not depend on the mass of the object?</p> | g7190 | [
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<p>I have read so many forums on this and I still do not understand and it's affecting my ability to move forward with learning physics right now.</p>
<p>Imagine the following scenario: a person on a frictionless surface pushes on a stationary object. Both the person and the object have the same mass. I understand that if the person pushes with 100N both the person and the object will feel that force (though in opposite directions) due to Newton's third law (though I'm not sure WHY the reaction occurs, but that is a question for another day).</p>
<p>Now imagine the same scenario but instead of an object with the same mass it is another person with the same mass. Both people push off each other with 100N. I have been told that this will look the same; both people will feel 100N. However in my mind I am imagining that each person will feel the 100N push from the other person as well as the 100N reaction force from their own push. Should this not total to 200N? And if not, WHY NOT? I do not understand this and I can't stop ignoring it anymore.</p>
<p>Thank you for your help, I'm sorry that this is probably a really obvious concept that I'm just not grasping but I cannot wrap my mind around it at all. Thank you. </p> | g7191 | [
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<p>Kirchhoff's loop/current rule is just law of conservation of energy and Kirchhoff's junction rule is just law of conservation of charge.So, I think that these can be applied to any circuits unlike Ohm's law. Is there any exceptions? </p> | g7192 | [
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<p>I'm studying the Simple Harmonic Motion, and I am hesitant about, how to get mass values for infinite period?</p>
<ul>
<li>When mass is 0.</li>
<li>When mass is infinite.</li>
</ul>
<p>With $\tau=2\pi/\sqrt{k/m}$. </p> | g7193 | [
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<p><a href="http://en.wikipedia.org/wiki/Eratosthenes">Eratosthenes</a> famously observed that the suns rays were perpendicular to the ground in one location, yet non-perpendicular to the ground at a location some miles to the north. On the assumption that the sun's rays are all parallel, this means the earth is round (or at least not flat).</p>
<p>But how do we know the sun's rays are parallel? The rays of light from my desk lamp aren't parallel by the time they reach my desk. The spot directly below the lamp is hit perpendicularly, but the edge of the desk is hit obliquely. The issue is clearly determining whether or not the sun is far enough away that its rays can be assumed to be parallel. But how can we know that?</p> | g7194 | [
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<blockquote>
<p>A sailboat is moving at a constant velocity. Is work being done by a net external force acting on the boat?</p>
</blockquote>
<p>The answer key is "No" according to the work energy theorem about work is done when there is a change in final and initial velocity. But if I use Work = Force x displacement, even though the velocity is constant there is still some displacement done by the (constant) force acting on it. So I figured that the answer is "Yes". Which one is true?</p> | g7195 | [
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<p>Problem: A bungee-cord jumper is on a bridge that is $y_1$ above water level $y_2$.
The bungee cord obeys Hooke's law with spring constant $k$ and has a relaxed length $L$
The jumper stops before reaching the water, what height is her feet above the water at this point $d$?</p>
<blockquote>
<p>I define the positive y direction as up and $y_2=0$.</p>
</blockquote>
<p>From this definition and given that the initial energy is </p>
<p>$$E_i=mgy_1\tag{1}$$</p>
<p>I reason $\Delta h$ should be $y_1$ by a separate isolated case where a mass has $E_g =mgh$, when it is distance $h$ above a given 0 reference point.</p>
<p>The final energy is a combination of $U_s=\frac{1}{2}kx^2$ and remaining $U_g=mgd$.</p>
<p>Remembering the defined positive y direction, $d$ is positive by the same reasoning as for $y_1$. $x$ would be negative but can be ignored due to the even power.</p>
<p>$g$ would be negative.</p>
<p>The total initial energy in the system will be equivalent to the total final energy in the system given no non conservative forces apply. However, setting $E_i = E_f$ and solving for x to calculate the required $d$,</p>
<p>$$\frac{1}{2}kx^2 - mgx - mgL=0\tag{2}$$</p>
<p>Yields a quadratic equation with no real solutions (as $g$ is negative). It is clear that my <b>interpretation</b> of my defined axes is incorrect.</p>
<p>The problem is provided for situational awareness only, my question is given the convention I have used, why should $E_i=mg\Delta h$ be $mg(y_2-y_1)$ (a negative value as opposed to $y_1$).</p>
<p>If this is the case wouldn't that also mean that $d$ should be negative and so the quadratic would still have no real solutions?</p> | g7196 | [
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<p>In MTW, p. 398, "Box 16.4 (continued)", there's an interesting sketch (which can also be seen on<br>
<a href="http://www.pma.caltech.edu/~ph236/yr2008/readings/MTW_Chapter16.pdf" rel="nofollow">p. 15 of this excerpt (www.pma.caltech.edu/~ph236/yr2008/readings/MTW_Chapter16.pdf)</a>.<br>
(It's not the only sketch of this kind in MTW; but it happens to be the only sketch on p. 398.)<br>
Shown are (cmp. text of p. 397) </p>
<ul>
<li><p>two open-ended lines representing two "<i>particles</i>" (They are supposed to satisfy additional relations which are not of immediate interest here, however.), </p></li>
<li><p>several line segments criss-crossing between the two open-ended lines, representing "<i>light rays bouncing back and forth between [the two particles]</i>", and</p></li>
<li><p>two of the criss-crossing segments being extended such that they meet, with the coincidence point of these two segments denoted as $\mathscr Q$.</p></li>
</ul>
<p>In order to describe what's represented by that third feature (which, unfortunately, MTW don't seem to spell out explicitly) it is convenient to refer to the two explicitly shown particles by explicit distinct names; say "Paul" for one and "Eric" for the other (i.e. by names which have been suggested through <a href="http://en.wikipedia.org/wiki/User:Marc_Goossens/EPS_Spacetime#mediaviewer/File:Establishing_spacetime_radar_coordinates.jpg" rel="nofollow">this sketch by M. Goossens</a>).</p>
<p>Accordingly, it may be said that the sketch of MTW p. 398 shows that </p>
<p><code>(a)</code>: Paul observed $1$ <i>light ray bounce to, and back from</i> event $\mathscr Q$ (or: $1$ "ping wrt." event $\mathscr Q$), and</p>
<p><code>(b)</code>: for his same initial/signal indication, and his same final/reception indication, Paul counted $3$ consecutive <i>back and fourth bounces</i> (or: "pings") with respect to Eric.</p>
<p>And likewise:</p>
<p><code>(c)</code>: Eric observed $1$ <i>light ray bounce to, and back from</i> event $\mathscr Q$ (or: $1$ "ping wrt." event $\mathscr Q$), and </p>
<p><code>(d)</code>: for his same initial/signal indication, and his same final/reception indication, Eric counted $2$ consecutive <i>back and fourth bounces</i> (or: "pings") with respect to Paul.</p>
<p>Now, rather than considering only one such event $\mathscr Q$, we may ask about, and Paul and Eric may under certain conditions even actually find, a set $\cal L$ with several <b>additional events</b> (and including event $\mathscr Q$) such that the conditions <code>(a)</code> - <code>(d)</code> had been satisfied by <b>all events of</b> $\cal L$.</p>
<p>Taking again the suggestion from the already mentioned <a href="http://en.wikipedia.org/wiki/User:Marc_Goossens/EPS_Spacetime#mediaviewer/File:Establishing_spacetime_radar_coordinates.jpg" rel="nofollow">sketch by M. Goossens</a> it may be found that there can be (at least) one particle identified who participated in all events of such a set $\cal L$; let's refer to it by the name "Lutz". </p>
<p>If "Paul", "Eric" and "Lutz" have been identified accordingly, as having satisfied conditions <code>(a)</code> - <code>(d)</code> throughout some sufficiently extended trial, then obviously</p>
<p><code>(1)</code>: Paul found any $3$ consecutive pings wrt. Eric same as the corresponding $1$ ping wrt. Lutz; symbolically: " $\overset{\leftarrow ~ \rightarrow}{{}^EP{~}^L} = 3$ ",</p>
<p><code>(2)</code>: Eric found any $2$ consecutive pings wrt. Paul same as the corresponding $1$ ping wrt. Lutz; symbolically: " $\overset{\leftarrow ~ \rightarrow}{{}^PE{~}^L} = 2$ ",</p>
<p>and apparently (without further conditions or reservations) it follows that</p>
<p><code>(3)</code>: Lutz found any $3$ consecutive pings wrt. Eric same as the corresponding $2$ consecutive pings wrt. Paul; symbolically: " $\overset{\leftarrow ~ \rightarrow}{{}^EL{~}^P} = \frac{3}{2}$".</p>
<p>This relation between such three participants together may be recognized as a general kind of "<i>rigidity</i>"; which I'd call in default of any other terminology: "(triplewise) ping rigidity"; in the above example symbolically: " $\underset{\{P, E, L\}}{\shortmid \leftrightarrows \shortmid} = \{2, 3, 1\}$ ".</p>
<p><b> My question:</b></p>
<p>Have such relations, of three (or more) participants "<i>bouncing light rays back and forth between</i>" each other and counting <b> constant integer or rational ratios </b> for the numbers of (consecutive, or individual) "corresponding pings" been recognized and already named elsewhere?</p> | g7197 | [
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<p>Dirac equation is $i \hbar \gamma^\mu \partial_\mu \psi - m c \psi = 0 $</p>
<p>To show its Lorentz invariance, we convert spacetime into $x'$ and $t'$ from $x$ and $t$ and then</p>
<p>$( iU^\dagger \gamma^\mu U\partial_\mu^\prime - m)\psi(x^\prime,t^\prime) = 0$</p>
<p>The question is, how does one show from the above equation the following equation follows?:</p>
<p>$U^\dagger(i\gamma^\mu\partial_\mu^\prime - m)U \psi(x^\prime,t^\prime) = 0$</p>
<p>where $U$ is some unitary matrix for lorentz transformation for $\psi$. </p> | g7198 | [
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<p>I'm doing an exercise on vertex operators in the CFT book by Di Francesco & al.; exercise 9.2 p.329 :</p>
<p>Using mode expansion show that: $$\langle\tilde{\phi(z)}\tilde{\phi(w)}\rangle= - \text{ln} \;(1-\frac{w}{z})$$</p>
<p>I managed to complete the calculation but I'm bothered by the fact that the right hand side is not apparently translation invariant.</p>
<p>It seems that we have no charges (at infinity or wherever) and this should be a function of $(z-w)$. Am I missing out on something?</p>
<p>The same way one line below we have:</p>
<p>$$\langle V'_{\alpha_1}(z_1)\ldots V'_{\alpha_n}(z_n)\rangle = \Pi_{i<j} (z_i-z_j)^{2\alpha_i \alpha_j}z_i^{-2 \alpha_i \alpha_j}$$</p>
<p>which again doesn't seem translation invariant because of the last term.</p> | g7199 | [
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<p>I have person weighing spring scale. I live in Japan where the house has wood floors which deflect significantly under weight. I weighed my self in the bathroom and in the tiled bath area. The difference was 2.5 kilograms greater in the bath area but it could still be affected by possibly an angled floor or deflection. So how you get as true a result as possible with that spring scale? </p> | g7200 | [
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<p>Suppose that two matrices $A$ and $B$, representing real($\mathbb{R}$) physical quantity, can be multiplied commutatively with each other; i.e. $AB =BA$. However, each matrix cannot be multiplied commutatively with other matrices all the time (obviously). If two matrices represent physical quantity, can they be stated to have definite values togeether still? Or as two matrices cannot be multiplied commutatively with other matrices, is it not possible for two matrices to have definite values together?</p>
<p>Also, suppose $C=A+B$. If A and B can be multiplied commutatively with each other, does $C$ have definite values? If $A$ and $B$ cannot be multiplied commutatively with each other, is there any way $C$ can have definite values?</p> | g7201 | [
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<p>In my textbook, it says that when $L$ is a matrix that represents real($\mathbb{R}$) physical quantity, $L^2$ represents non-negative real physical quantity. What would be the proof of this?</p> | g7202 | [
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<p>I have been reading Hawking's 'A Brief History of Time' and it has gotten me thinking about Einstein's theory of relativity, in that it assumes that an object must have infinite mass if it is to be traveling at the speed of light (please correct if I'm wrong in my beginner's knowledge of physics).</p>
<p>But, do light waves have any sort of measurable mass? Or in that same vein, do sound waves?
Is it somehow possible?</p> | g7203 | [
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<p>Taking off from the Rutherford-Bohr model,</p>
<p><img src="http://i.stack.imgur.com/R8c0f.png" alt="Rutherford-Bohr model"><br>
<strong>Figure 1.</strong> <em>Rutherford-Bohr model.</em></p>
<p>when an electron absorbs energy (from light, heat, or otherwise) it jumps to a higher energy level, or shell. Then when the electron loses that energy, it reverts back to a lower-numbered shell.</p>
<p>Now that the atomic orbital model is now more widely accepted, how does the above concept relate to it?</p>
<p><img src="http://i.stack.imgur.com/88Kwj.jpg" alt="atomic orbitals"><br>
<strong>Figure 2.</strong> <em>Atomic orbitals 1s, 2s, 2px, 2py, and 2pz.</em></p>
<p>I understand that the orbital model is based on the premise that we can never pinpoint the exact location of an electron at any time, hence the <em>electron cloud</em>, or <em>probability density</em> representation. Let's take a hydrogen atom for example. Its lone electron will be likely to be found in the volume defined by 1s. If that is excited to a higher energy level, will it be more likely to be found in the volume defined by 2s?</p>
<p>What about for other elements with more electrons? When excited, will they follow the electron placement rules as shown below? (I wonder why I couldn't find 2px, 2py, 2pz in the illustration below, but that's probably for another question)</p>
<p><img src="http://i.stack.imgur.com/qPYcN.png" alt="Electron placement"><br>
<strong>Figure 3.</strong> <em>Electron placement.</em></p>
<p>I may have some terms and concepts mixed up, so corrections will be much appreciated. Also, please keep the jargon to a minimum, if possible.</p>
<p><em>All pictures are from Wikipedia.</em></p> | g7204 | [
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<p>Why is the amount of energy transferred to a driven mechanical oscillator largest when the drive frequency is the same as the natural frequency of the oscillator? Why are they exactly out of phase by π/2?</p>
<p>Clarifying example experimental setup: <a href="http://av.ph.tum.de/Experiment/1000/Grafik/b1605.gif" rel="nofollow">http://av.ph.tum.de/Experiment/1000/Grafik/b1605.gif</a></p> | g7205 | [
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<p>I am coding in c++ and am computing the position of an orbiting body as a function of time.</p>
<p>Everything is almost working. I have a nice elliptical orbit. Except, my orbiting body speeds up as it moves away from the "sun" and slows down as it approaches it.</p>
<p>The best way I can describe it is that it's like the sun is at the wrong focus of the ellipse.</p>
<p>I'm hoping someone can point me to what could cause this to happen? I've gone through all my code and I don't see any mistakes.</p>
<p>My steps are:</p>
<ol>
<li>Compute the Mean Motion of a satellite.</li>
<li>Use this to compute the Mean Anomaly</li>
<li>Calculate the Eccentric Anomaly from this (that was a doozy)</li>
<li>Calculate the True Anomaly from the Eccentric Anomaly</li>
<li>Calculate the Heliocentric Distance</li>
<li>Finally I take the Polar Coordinates and convert to Cartesian Coordinates which I then position over the top of my "sun"</li>
</ol>
<p>Somewhere in here I'm screwing up. I don't believe it's the final step as the calculated coordinates are derived from the angle and radius, which should be based on the correct focus.</p>
<p>EDIT for the equations I'm using:</p>
<p><strong>Mean Motion</strong></p>
<p>$$
n = \sqrt{\frac{G(M+m)}{4\pi^2a^3}}
$$</p>
<p>This is from <a href="http://en.wikipedia.org/wiki/Mean_motion" rel="nofollow">Wikipedia</a>.</p>
<p><strong>Mean Anomaly</strong></p>
<p>This is just $n \times t$ elapsed.</p>
<p><strong>Eccentric Anomaly</strong></p>
<p>I'm not really sure how to write this up for a non programmer. Basically the way I did this was based very much on some code that I found on the internet that I can no longer find. There's some recursion involved to gradually refine the answer. I'm convinced the issue isn't in here because I can enter my values into something like <a href="http://www.jgiesen.de/kepler/kepler.html" rel="nofollow">http://www.jgiesen.de/kepler/kepler.html</a> and I have similar results.</p>
<p><strong>True Anomaly</strong></p>
<p>$$
\nu = 2\ \arg\left(\sqrt{1-e} \ \cos \left(\frac{E}{2}\right), \sqrt{1+e} \ \sin \left(\frac{E}{2} \right)\right)
$$</p>
<p>$e$ is Eccentricity
$E$ is Eccentric Anomaly from above</p>
<p>Taken from here <a href="http://en.wikipedia.org/wiki/True_anomaly#From_the_eccentric_anomaly" rel="nofollow">Wikipedia</a>.</p>
<p><strong>Heliocentric Distance</strong></p>
<p>$$
r = a \frac{1-e^2}{1+e \ \cos(\nu)}
$$</p>
<p>$a$ is my semi-major axis
$\nu$ is the True Anomaly from above</p>
<p>Taken from <a href="http://en.wikipedia.org/wiki/True_anomaly#Radius_from_true_anomaly" rel="nofollow">Wikipedia</a>.</p> | g7206 | [
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] |
<p>I've found several articles discussing experimental evidence of a deuterium state of densities over $140 \textrm{ kg}/\textrm{cm}^3$:</p>
<ul>
<li><p>F. Winterberg. Ultradense Deuterium. <a href="http://arxiv.org/abs/0912.5414" rel="nofollow">arXiv</a>.</p></li>
<li><p>Shahriar Badiei, Patrik U. Andersson, Leif Holmlid. High-energy Coulomb explosions in ultra-dense deuterium: Time-of-flight-mass spectrometry with variable energy and flight length. <em>International Journal of Mass Spectrometry, Volume 282, Issues 1–2, 15 April 2009, Pages 70-76.</em> <a href="http://dx.doi.org/10.1016/j.ijms.2009.02.014" rel="nofollow">DOI</a>.</p></li>
<li><p>Patrik U. Andersson, Leif Holmlid. Superfluid ultra-dense deuterium D(−1) at room temperature. <em>Physics Letters A, Volume 375, Issue 10, 7 March 2011, Pages 1344-1347.</em> <a href="http://dx.doi.org/10.1016/j.physleta.2011.01.035" rel="nofollow">DOI</a>.</p></li>
</ul>
<p>Have these super-dense states been replicated by third parties?</p>
<p>Have these super-dense states yet to be replicated by third-parties? </p> | g7207 | [
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<p>Which is the model that best shows the relationship between velocity and distance: </p>
<ul>
<li>$v \propto d$</li>
<li>$v \propto d^2$</li>
<li>$v^2 \propto d$</li>
<li>$v^2 \propto d^2$</li>
</ul>
<hr>
<p>What I think is from: </p>
<p>$$v=at \Rightarrow t=\frac{t}{a}$$</p>
<p>Then substitute into: </p>
<p>$$\begin{aligned}
d &= \frac{1}{2} at^2 \\
&= \frac{1}{2} \frac{v^2}{a^2} \\
&= \frac{1}{2} \frac{v^2}{a} \\
\end{aligned}$$</p>
<p>So can I say closest model should be $d \propto v^2$? But my experimental data shows that $d^2 \propto v$. That is by plotting a least linear squares fit with excel and using the $r^2$ value. Could use <code>LINEST()</code> too. </p>
<p><a href="http://i.stack.imgur.com/rbr2o.png" rel="nofollow"><img src="http://i.stack.imgur.com/rbr2o.png" alt="enter image description here"></a></p>
<p>Is my data wrong then? </p> | g7208 | [
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<p>In the The Emperor's New Mind book. While author explains why classical physics fails to explain our universe, says:</p>
<blockquote>
<p>The root cause of these is that two kinds of physical object must
coexist: particles, each described by a small finite number (six) of
parameters (three positions and three momenta); and fields, requiring
an infinite number of parameters. This dichotomy is not really
physically consistent. For a system with both particles and fields to
be in equilibrium (i.e. 'fully settled down'), all energy gets taken
from the particles and put into the fields. This is a result of the
phenomenon called 'equipartition of energy': at equilibrium, the
energy is spread evenly among all the degrees of freedom of the
system. Since the fields have infinitely many degrees of freedom, the
poor particles get left with none at all. <a href="http://rads.stackoverflow.com/amzn/click/0192861980" rel="nofollow">http://www.amazon.com/The-Emperors-New-Mind-Concerning/dp/0192861980</a></p>
</blockquote>
<p>My questions:
What does "energy gets taken from the particles and put into the fields" mean?
How does this relate with classical physics failure? </p> | g7209 | [
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<p>How can compactifying IIA (non-Chiral) and IIB (Chiral) Superstring on $T^2$ (2-torus) gives rise to ($2$ dual descriptions of) the same $\mathcal N = 2$ supergravity in $8$ dimensions? I don't see it. Could you please explain it to me or recommend me some literature to read about it? </p>
<p>Thank you! </p> | g7210 | [
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<p>While standing on a planet its gravitation force is noticeable and manifests only through the normal force, e.g. if jupiter had rocky surface, standing on the surface will apply about 2.5 times more force than when standing on earth. However sky diving on earth and on jupiter (without atmosphere) would apply the same amount of "destructive" force, that is 0. Thus gravitation force cannot really destruct matter without something for the matter to interact with.<br>
If a black hole with no matter falling into it exists, will a person with space suite die if he would "jump" into it? he will have nothing applying "destructive" force on it, just kinetic energy that cannot manifest without something to hit.</p> | g7211 | [
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<p>Why are white holes the same thing as black holes in quantum gravity? Their Penrose diagrams in semiclassical gravity are utterly different.</p> | g7212 | [
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<p>Can vortices be self-sustaining?</p>
<p>I suppose vortices in water are not self sustaining, since they need constant supply of water at speed i.e. kinetic energy. But is the same case applicable to space time vortices? like wormholes?? or do they need some energy source for sustenance?</p>
<p>Please try to give a intuitive explanation.</p> | g7213 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/10933/why-do-we-say-that-the-earth-moves-around-the-sun">Why do we say that the earth moves around the sun?</a> </p>
</blockquote>
<p>I should preface by stating that I'm not a physicist and my knowledge of the theory of relativity is limited to what Encarta told me in the 90's (does everyone know what Encarta was?) and I don't even understand the Wikipedia entry!</p>
<p>Encarta had a video on the theory of relativity that basically explained in part that (i suppose in vacuum) there's no way to tell which body is in motion relative to another (without observing from outside the space in which they are moving i suppose).</p>
<p>so my question is whether this warrants a reassessment of our reliance on a heliocentristic model. is it possible the planets do not revolve the way we've modeled them? i'm not necessarily talking geocentric, just different from our current model. should we be exploring this?</p>
<p>ps -- while researching this question i came across geocentricity.com, the first sentence of which starts "Of all the sciences, the Holy Bible..." I'm really not interested in starting a religious debate so please keep answers strictly physics related (though i hope i don't have to even say that on <strong><em>physics</em></strong>.stackexchange.com!)</p> | g205 | [
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<p>Since a <a href="http://en.wikipedia.org/wiki/Pulse_tube_refrigerator" rel="nofollow">pulse tube cooler</a> is basically a Stirling engine without moving parts running "in reverse", does that imply that when I keep the cold end at ambient temperature and apply heat to the hot end, I get pressure oscillations? Or do I need the pistons and crankshaft of a standard Stirling engine for that?</p>
<p>I think the question can be boiled down to how the working fluid gets back to the hot end after cooling, and the reason I don't seem to understand this might be that I have not yet fully understood how the buffer volume and orifice work in the pulse tube cooler.</p> | g7214 | [
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<p>I understand that a particle approaching a finite potential barrier with $E < V_0$, there still is a probability of finding the particle on the other side of the barrier due to quantum tunneling.</p>
<p>My question is, since the wavefunction is nonzero inside the barrier region, is it possible to actually make a position measurement and locate a particle inside the barrier?</p>
<p>I mean, if we can say that "there is a nonzero probability that the particle is inside the barrier", surely this would suggest we can do so?</p>
<p>If not, why not? Am I understanding the whole wavefunction / probability distribution thing right?</p> | g855 | [
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] |
<p>This is a followup to a <a href="http://physics.stackexchange.com/questions/67525/gaseous-fission-has-it-even-been-demonstrated-experimentally"><strong>prior question</strong></a> I asked about gaseous nuclear fission. What is the lowest nuclear fuel density required to initiate fission? This is critical for a gas core reactor with a solenoid magnetic bottle containment system in terms of how strong the magnetic field should be keep the fuel at a high enough density to trigger fission. Of course, the reactor vessel would be a cylinder with an inner jacket made of beryllium to reflect neutrons back into the core.</p> | g7215 | [
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<p>Assume we have a "somewhat" ideal voltage source like a DC power supply powered by mains. Take just one terminal and form a conductive path between it and earth ground. Assuming that no conductive path exists going back to the power plant ground spike, and a fuse isn't blown, wouldn't a huge amount of current flow into the earth due to the massive capacitance of the earth?</p>
<p>Once again, I am assuming that this voltage source can maintain its voltage indefinitely.</p> | g7216 | [
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<p>Is there any physical matter which won't appear on x-ray i.e. invisible matter?
I think I learnt at university that all phsyical matter appears on x-ray and there is no matter that can be invisible. Is this true? For instance, does dark matter and antimatter appear on x-ray or what technology is used to prove that there is something instead of nothing?</p> | g960 | [
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<p>How can one calculate the mass of air inside a tyre, given a particular tyre size; a pressure, in $kPa = \frac{1000kg}{m\cdot s^2}$; and assuming room temperature, and normal air composition? I can't quite work out what part of the equations I'm missing to remove the $s^2$ component.</p>
<p>I realise that surface/volume ratio is important, but for the purposes and approximation to a torus would be fine. For example, assuming a 700cx25 bicycle tyre, we might assume a torus where the diameter between centre of the two cross-section circles is about 630mm, and the diameter of the circles themselves is about 30mm. Let's assume a tyre pressure of 500kPa (~73psi).</p>
<p>Rough volume would be $630$mm$\times\pi \times \pi (15$mm$)^2 = 1.4\times10^6$mm$^3 = 0.0014$m$^3$</p>
<p>Rough surface area: $630$mm$\times\pi \times 30$mm$\times\pi = 1.87\times10^5$mm$^2 = 0.187$m$^2$</p> | g7217 | [
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<p>Is travel through stable macroscopic wormholes between remote points of spacetime going to be possible in a definitive theory of gravity, be it string theory or something beyond it?</p>
<p>Physicists level of understanding about the holographic principle and AdS/CFT correspondence has improved significantly and continues to evolve, as it is suggested by the current ongoing debate regarding black hole firewalls. </p>
<p>I understand that the semiclassical picture of wormholes cannot survive because string theory demands that the required positive energy conditions are satisfied, so nontrivial classical topologies are censored from geodesically-complete world lines, just like naked singularities. But i cannot help but wonder (and hence my reason to do this question) if all the thorny subject about information being conserved by unitarity, while at the same time, holography implying there is a connection between all the boundaries of the bulk spacetime (understanding as such the union of the cosmological horizon and all the black holes in its interior), <em>could allow room for solutions where the infalling information in black holes survives by coming out, scrambled or otherwise, out of some other distant event horizon</em> (behaving at times as a white hole, at others like a black hole)</p> | g7218 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/39616/what-is-the-physical-interpretation-of-force-times-area">What is the physical interpretation of force times area?</a> </p>
</blockquote>
<p>If force times area has any physical meaning, what would it be? Where would it be used?</p>
<p>I know that force equals to the change of momentum divided by time, but never heard of the quantity force times area.</p> | g244 | [
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<p>I'm working on a classical mechanics problem in which the problem states that a particle of mass $m$ moves in a central field of attractive force of magnitude:</p>
<p>$$F(r, t) = \frac{k}{r^2}e^{-at}$$</p>
<ul>
<li>$r$ is the distance from the force center,</li>
<li>$t$ is time,</li>
<li>and $k$, $a$ are constants.</li>
</ul>
<p>I am concerned about the $t$ in the exponent. I did more than half of the question already (which involves finding lagrangian/hamiltonian equations) using a potential I'm not even sure is correct.</p>
<p>I calculated it by taking the integral of $F(r, t)$ with respect to $r$. It is just that there is a $t$ in the magnitude so I know I shouldn't be able to do that.</p> | g7219 | [
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<p>Consider a system of N quantum mechanical particles described on Hilbert spaces $\mathcal{H}_1,...,\mathcal{H}_N$ and with Hamiltonians $H_1,...,H_N$. The Hamiltonian operator $H_1$ acts on the Hilbert space $\mathcal{H}_1$ etc. These particles are non-interacting if the Hamiltonian of the system can be written as the sum of the Hamiltonians of each particle:
$$H=H_1+...+H_N$$</p>
<p>Why the Hilbert space of the combined system of these non-interacting particles is considered to be a tensor product of the Hilbert spaces of each particle? </p>
<p>$$\mathcal{H}=\mathcal{H}_1\otimes...\otimes \mathcal{H}_N$$</p>
<p>For interacting particles is it a tensor product too?</p> | g7220 | [
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