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<p>How can we show that the weak interaction violates the charge conjugation symmetry?</p>
| 8,150 |
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<p>In the common configuration of the <a href="http://en.wikipedia.org/wiki/Hall_effect" rel="nofollow">Hall Effect</a>, why wouldn't the conductor move?
It follows the same principle of the Lorentz force or basic electric motor doesn't it?</p>
<p>I can't seem to find the difference between them...</p>
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<p>The density matrix (or state matrix) is a generalization of a wave function that is able to describe incoherent superpositions of an N-state system. It is often written as a matrix and observables are calculated by taking the trace of the product of itself with the operator in question.</p>
<p>Hestenes' spinors are a geometric algebra description of things like a wave function and Dirac 4-component spinor, but if one applies the matrix representation of the algebraic elements directly, it resembles a density matrix-like entity much more closely than a wave function, especially when looking at the mathematical expressions for observables. I know and understand the map from "normal" spinors to Hestenes' spinors, which kind of contradicts my proposition.</p>
<p>Nevertheless, a Hestenes spinor can be written as more general entities (a rotor and a scalar). Is this, in light of the above, a further "generalization" so to say? Or how do these objects relate?</p>
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] |
<p>How do I find the orbit of a moving point object given 3 past passing positions and the tangents at these passing positions, and given that the orbit is known to be an ellipse?</p>
| 8,153 |
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<p>What are the circumstances in which neutrinos can harm humans or even kill them.?</p>
| 8,154 |
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<blockquote>
<p>2 particles are constrained to move in a ring. Both particles begin moving at $t=0$ from $p=0$, each particle moving in the opposite direction of the other. It is known that they are moving at different constant velocities. Both particles pass each other (without interaction) 4 times before simultaneously returning to $p=0$.</p>
</blockquote>
<p>With this information, how can I find out the ratio between the particles' respective velocities?</p>
<p>It seems to me that this would hold true in any case where $x:y$ is the ratio of the particles' velocities and $|x - y| = 5$. In that case, all the following would qualify: $${-2:3},\ {-3:2},\ {1:6},\ {2:7}$$</p>
<p>If furthermore, I know that the order of the positions where they pass is (in radians):
$$\frac{4π}{5},\frac{8π}{5},\frac{2π}{5},\frac{6π}{5}$$
then can I definitively extrapolate the ratio?</p>
<hr>
<p><em>Bonus points to anyone who can figure out what gave me the idea for this question in the first place.</em></p>
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<p>Imagine I have a long rod of metal. Let's say it's 1m long, 1cm wide and 1mm high. Now suppose I pass DC through it. But instead of running the current through lengthwise, I want to run it sidewise. That is, in ascii art:</p>
<pre><code> \/ - attach "+" here
+-----------------------------------------+
| The rod |
+-----------------------------------------+
/\ - attach "-" here
</code></pre>
<p>So, according to the right-hand rule, the magnetic field lines should encircle the rod length-wise. If I placed a small static magnet on top of it, it would theoretically start sliding towards one end of the rod (well, if it didn't flip over, that is). (This is what I'd like to achieve, in truth).</p>
<p>Somehow I don't think that would be the case. It seems more intuitive that the magnetic field should be the strongest in the middle, between the two points of attachment, and rapidly get weaker towards either end.</p>
<p>Is that so? I do not know where to start looking for formulas that would describe this, so I'm afraid I haven't done any prior research. Also - what could make the magnetic field equally strong at the entire length? If, instead of one point, I attached the electrical wire at 10 points on both sides, would that make it better? 100 points? How can I make that small static magnet slide from one end to the other when I flip the switch?</p>
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<p>I am currently designing a lighting solution for Phillips as part of my university degree. However I am stuck on a small problem, as stated above. If I was to have a strip of perspex, with the sides matt and the bottom polished, would I achieve more light through the polished surface or the matt surface. And why?? </p>
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<p>I have a college-level understanding of Physics. A <a href="http://phys.org/news/2014-05-team-accurately-teleported-quantum-ten.html" rel="nofollow">recent study</a> from the University of Delft in the Netherlands that seems to suggest that quantum teleportation of information (as in "<em>communication of information</em>") is possible left me confused.</p>
<p>I read:</p>
<ul>
<li><a href="http://physics.stackexchange.com/q/14276/">Why can't quantum teleportation be used to transport information?</a></li>
<li><a href="http://physics.stackexchange.com/q/78118/">Quantum entanglement as practical method of superluminal communication</a></li>
</ul>
<p>and the answers in both threads suggest that one cannot use quantum teleportation for superluminal communication in the traditional/practical sense of the word. </p>
<p>The publications in Nature & Science are <a href="http://www.nature.com/nature/journal/v497/n7447/full/nature12016.html" rel="nofollow">here</a> and <a href="http://www.sciencemag.org/content/early/2014/05/28/science.1253512" rel="nofollow">here</a>.</p>
<p>Perhaps more interestingly, the university site (in dutch): <a href="http://www.tudelft.nl/nl/actueel/laatste-nieuws/artikel/detail/tu-delft-legt-fundament-voor-quantum-internet/" rel="nofollow">http://www.tudelft.nl/nl/actueel/laatste-nieuws/artikel/detail/tu-delft-legt-fundament-voor-quantum-internet/</a> the statement ends with a quote from the authors saying:</p>
<blockquote>
<p>"Ten tweede biedt teleportatie de mogelijkheid om informatie volledig
veilig te versturen. Bij teleportatie reist de informatie niet door de
tussenliggende ruimte en kan daarom niet worden afgeluisterd".</p>
</blockquote>
<p>which can be translated as: "<em>Secondly, teleportation offers the possibility to transmit information in a completely safe way. With teleportation the information does not travel through the space in between thus precluding eaves dropping.</em>"</p>
<p>Can these results be understood as a claim that superluminal communication (again, in the traditional/practical sense) is more feasible that previously believed?</p>
| 8,158 |
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<p>I'm confused about an exercise of a book. I understand that the units for angular velocity is $\text{rad/s}$; but I don't understand, how can I get it from the relation $\omega=\sqrt{k/m}$.</p>
<p>Solving this equation: $\omega^2=(10^4\text{ N/m})/50\text{ kg}$. From this, I get these units:</p>
<ul>
<li><p>For $\mathrm{N}$: $\mathrm{kg\ s^2/m}$,</p></li>
<li><p>$1/\mathrm{m}$, and</p></li>
<li><p>$1/\mathrm{kg}$</p></li>
</ul>
<p>So, I get, $\mathrm{s^2/m^2}$.</p>
<p>Can you help me to realize what can I do?</p>
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<p>I want to know the rate at which air will ascend above a stove element.</p>
<p>Is there some relationship between ambient air temperature, element temperature, and speed of the resulting updraft?</p>
<p>If nothing definite, is there anything approximate that I could use?</p>
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<p>An electron is trapped in a one-dimensional well of width $0.132\,$nm. The electron is in the ninth excited state ($n=10$) state. What is the uncertainty in its momentum? The problem gives a hint to use the equation $\Delta{p_x}=\sqrt{(p_x^2)_{avg}}$ (the root mean square of the momentum of the particle). I know the wavefunction of the electron is this:</p>
<p>$$\psi(x)=\sqrt{\frac{2}{L}}\sin\left(\frac{10\pi}{L}x\right)$$</p>
<p>But since the probability density function is a function of position, and not momentum, how do I calculate the RMS of the momentum from this?</p>
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<p>Unlike most <a href="http://en.wikipedia.org/wiki/Planck_units" rel="nofollow">Planck units</a> named after "Planck" such as Planck length, Planck temperature, etc, the <a href="http://en.wikipedia.org/wiki/Planck_mass" rel="nofollow">Planck mass</a> seems more closed to daily life. It is about $10^{-5}$g, same order of magnitude of one eyebrow hair or a flea egg.</p>
<p>I am just wondering is there any interesting explanation about the relation between Planck mass and the mass of small lives such as flea.</p>
| 8,162 |
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<p>I have a tank of oil at 55 degrees c. I plan to run a copper pipe 8mm in diameter (1mm thickness) into a coil 15m long inside the tank. For all purposes of assumption, the copper pipe is perfectly transferring heat across to the oil and vice-versa.</p>
<p>I have a pump of 10l/min that circulates this oil around the tank, so we will just assume that the 55degree oil is always well distributed.</p>
<p>Question:</p>
<p>I want to cool this down as much as possible, and was wondering if I was running tap water (28degrees), cold water (10degrees), how much would the coil be able to bring the temperature down by. We will assume that water is running through the coil at 5l/min.</p>
<p>Specifically I'm looking to convert the heat removal capacity into temperature in degrees. So that I can decide whether I want to </p>
<p>i) Use cold or room temperature water
ii) Whether this concept works at all</p>
<p>Thanks</p>
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<p>Re-reading <a href="http://physics.stackexchange.com/a/33156/5265">http://physics.stackexchange.com/a/33156/5265</a>; I find myself thinking if light, being EM in the humanly visible spectrum, may possess gravity - does a magnetic field also possess gravity?</p>
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<p>On page 54 of Weinberg's QFT I, he says that an element $T(\theta)$ of a connected Lie group can be represented by a unitary operator $U(T(\theta))$ acting on the physical Hilbert space. Near the identity, he says that</p>
<p>$U(T(\theta)) = 1 + i\theta^a t_a + \frac{1}{2}\theta^a\theta^bt_{ab} + ...$</p>
<p>Weinberg then states that $t_a$, $t_{ab}$, ... are Hermitian. I can see why $t_a$ must be by expanding to order $\mathcal{O}(\theta)$ and invoking unitarity. However, expanding to $\mathcal{O}(\theta^2)$ gives</p>
<p>$t_at_b = \frac{1}{2}(t_{ab} + t^\dagger_{ab})$,</p>
<p>so it seems the same reasoning cannot be used to show that $t_{ab}$ is Hermitian. Why, then, is it?</p>
<p>Thanks!</p>
| 8,165 |
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<p>This question is dedicated to Martin Fleischmann (1927-2012).</p>
<p>When a molecule is adsorbed on a metal surface, the Raman scattering amplitude from the molecule is enhanced. According to <a href="http://en.wikipedia.org/wiki/Surface_enhanced_Raman_spectroscopy" rel="nofollow">Wikipedia</a>, the downconversion rate is sometime enhanced by a factor of $10^{10}-10^{11}$). Also accoding to Wikipedia, the effect has been attributed to electric field enhancement near the metal, but it has also been attributed to chemical sharing of electrons in the molecule and in the metal. The sharing idea means that many delocalized electrons in the metal can downconvert the photon through the adsorbed molecule, leading to enhancement.</p>
<p>There seems to be controversy. So which is it? What causes the Raman enhancement?</p>
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<p>It seems a positive cosmology constant behaves like a negative pressure. However, the positive cosmology constant cause a expanding universe. So I am puzzling about this: </p>
<p>A negative pressure cause a expanding universe?</p>
<p>To me, it is easy to imagine the positive pressure cause expanding just like gas.
Could you give me a explanation about this?</p>
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<p>Suppose there is a material with heavy nuclei attached on its surface, presumably binded by the outer shell electrons. Now, the surface is exposed to a cold positron gas, which annihilates against some of these outer shell electrons.</p>
<p>What might happen with the heavy nuclei? do they have to become free from the material surface? can they become binded by inner shell electrons?</p>
<p>Also, i presume that as the positron gas annihilates the outer shell electrons, and further assuming that the heavy nuclei remain attached somehow to the surface, these heavy nuclei will increase their effective charge, so there might be an equilibrium condition where the repulsion of the heavy nuclei wards off the positron gas from further annihilating against the inner core electrons. Can this be validated heuristically? Is it just a plain wrong assumption? </p>
| 8,168 |
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<p><img src="http://i.stack.imgur.com/YH1BH.png" alt="enter image description here"></p>
<p>What happens? we have 2 Generators and 2 intensities, when I2 and I3 come together (they have opposite sides ) what happens?</p>
<p>I tried writing down the voltage relations but I'm stuck because I don't know what intensity should i work with (to determine positive sides) I2 or I3 </p>
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<p>I'm taking a graduate physics class.
I usually sit at the front and madly scribble down everything the teacher writes....
But the professor also publishes his notes on the internet.
I find it sometimes difficult to understand what is going on in class . Often the problem is that I am spending most of my time scribbling what the prof. writes and trying to stay up to speed, but he is obviously working at a bit faster rate than me since he knows this stuff alot better than I do. I usually learn best by doing reading on my own and then asking questions.</p>
<p>Is there a recommended path for someone with my learning style, how to effectively use my class time?</p>
<p>for instance, it might be more useful to sleep through class so that I am well rested but then I might miss some stuff. thoughts?</p>
<p>thanks</p>
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<p>I always thought that the microcanonical partition function would measure the number of states that correspond to some fixed energy. Despite, I found in this paper (equation 3.4) that we integrate over all configurations that have an equal or lower energy than some fixed number $E$. Does this make sense to you?</p>
<p>See eq. 3.4 in <a href="http://www.ueltschi.org/teaching/2007-StatMech.pdf" rel="nofollow">this reference.</a></p>
<p>or somewhat faster see at eq 3.1 here <a href="http://www.ueltschi.org/teaching/chapensembles.pdf" rel="nofollow">in this paper.</a></p>
| 8,171 |
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] |
<p>What is the difference between these laws?
Which law is more useful?
When to use <a href="http://en.wikipedia.org/wiki/Ampere%27s_Law" rel="nofollow">Ampere's law</a> and when to use <a href="http://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law" rel="nofollow">Biot-Savart law</a>?</p>
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<p>Whilst observing a lighthouse, I noticed that I could only see the cone of light reflected in the water when the lighthouse light was directly pointed at me. At all other points, I could just about see the cone of light in the air, but no light was visible on the water. Why is this the case?</p>
<p><strong>NB:</strong> I would appreciate any answers to include a "laymans" explanation (being more or less a physics layman myself)</p>
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<p>Can someone explain me the purpose of auxiliary lens in microscope. </p>
<p>The specification says:</p>
<pre><code>Eyepiece: Extra wide field 10x Eyepiece w Spectacle Correction 30mm Ocular
Objective 0.7-45x , Auxiliary 2x
</code></pre>
<p>And the manufacturer claims that it is having magnification of 90X. Is it true ?</p>
<p>Perhaps they are multiplying the power of Objective, Eyepiece and Auxiliary to get 90X. But is correct to say the magnification is 90 X</p>
<p>BTW this is the <a href="http://www.ebay.in/itm/7-90x-Zoom-Stereo-Industrial-Biology-Digital-Microscope-w-1-3Mp-USB-Camera-/161265313969?pt=LH_DefaultDomain_203&hash=item258c2968b1" rel="nofollow">microscope</a> I am talking about and the specification is given at the end. </p>
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<p>I've come across the <a href="http://en.wikipedia.org/wiki/Onsager_reciprocal_relations#Abstract_formulation" rel="nofollow">Onsager reciprocal principle</a>. It's almost clear, except for <strong>thermodynamic conjugate quantities</strong> - what's that, physical meaning (except the formal definitions: $X_i = -\frac{1}{k}\frac{\partial S}{\partial x_i}$, which isn't clear) and why:</p>
<p>\begin{equation}
\langle X_i\cdot x_k\rangle = \delta_{ik}
\end{equation}</p>
<p>The Wikipedia is lack for references in this article.</p>
| 8,175 |
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<p>Scott Aaronson asked a very deep question at <a href="http://physics.stackexchange.com/q/39383">Hawking radiation and reversibility</a> about what happens if black hole evolution is reversed thermodynamically. Most of the commenters missed his point entirely. Of course it's overwhelmingly improbable statistically to set up the initial conditions needed to get a thermodynamically reversed black hole evolution. But that's not the point of the question at all. It is theoretically possible to have a thermodynamically reversed black hole evolution as a valid evolving state by CPT symmetry, even if it's improbable for all practical purposes. As it exists as a possible solution, we can ask questions about the properties of such a solution.</p>
<p>In a thermodynamically probable evolution, we can have a massive object with a significant fraction of the black hole's mass fall into a black hole, and the blak hole automatically increases in mass by a huge fraction over a timescale of order of the Schwarzschild radius R. Then, it slowly evaporates away Hawking radiation with a remaining lifetime of order $R^3$. In the thermodynamically reversed version of this event, over a time period of order $R^3$, thermal radiation is fed into a black hole which increases in size very gradually as a result. There is an incredible fine-tuning of the ingoing radiation fed in with fine-tuned higher order multipartite entanglement (this is a theoretical state, not a practical engineering one) so that as a result, over the time period of order $R^3$, no Hawking radiation is <em>emitted</em> from the black hole because of fine-tuned quantum cancellations between the contributions from the black hole, and the contribution from frequency mixing of the radiation fed into the hole. Then, after a time period of order $R^3$, suddenly over a time period of order $R$, the black hole emits as "Hawking radiation" a massive body a huge fraction of its mass, and the black hole's mass decreases accordingly. The area of its event horizon goes down by a huge fraction over a time period of order R. According to Raychaudhuri's optical equation, this requires a significant negative null energy. This is too large to come from Casimir effects, as that would require a time period of order $R^3$ to lose that much black hole mass. So, what is the origin of this huge negative null energy?</p>
<p>Let's look at what happens just outside the black hole before the massive body is ejected. In the semiclassical approximation, the massive body must have come from a firewall ( <a href="http://physics.stackexchange.com/q/38005">What are cosmological "firewalls"?</a>) at an exponentially small distance above the event horizon. This exponential factor comes from the very high boost factor and Lorentz contraction. Semiclassically, this firewall couldn't have originated from entangled Hawking pair production just outside the horizon. So, it must have originated from the fine-tuned radiation fed into the hole.</p>
<p>What if a probe is sent during an earlier time to measure this firewall? Unfortunately, this probably can't be done. See, we are conditioning a significant part of the future state by stipulating that a huge massive body is ejected as Hawking radiation. To further specify a probe hovering just above the horizon requires in addition a significant condition on the past. Ordinarily, with no thermodynamic conspiracies, we only have past conditions and no future conditions, and so, there's no problem. However, such fine-tuned conditioning of both the past and future might actually be impossible?</p>
| 8,176 |
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<p>Is it possible for two spheres (a & b) to have an inelastic collision with BOTH the total linear and angular momentum preserved? I'm doing some physics simulation of some spheres attracting each other like gravity and and a initial net angular momentum making them spin around a center. I want to have inelastic collisions while keeping the same total linear and angular momentum. </p>
<p>The simulation is in 3 dimensions. Therefore, all velocities are 3d vectors. I can calculate the velocity the particles after an completely inelastic collision by solving the following equations for $v$:</p>
<p>$$
m_a \vec v_{a_0} + m_b \vec v_{b_0} = \vec v (m_a + m_b)
$$
This gives velocity (v) zero degrees of freedom, yet I have not taken into account the formula for preservation of angular momentum (around origin):</p>
<p>$$
m_a (\vec p_a \times \vec v_{a_0})+m_b (\vec p_b \times \vec v_{b_0}) = m_a (\vec p_a \times \vec v_{a_1})+m_b (\vec p_b \times \vec v_{b_1})
$$
And for an inelastic collision $\vec v_{a_1} = \vec v_{b_1} = \vec v$
$$
m_a (\vec p_a \times \vec v_{a_0})+m_b (\vec p_b \times \vec v_{b_0}) = \vec v \times (m_a \vec p_a+m_b \vec p_b)
$$
Where $\vec p_a$ and $\vec p_b$ is the position vector of the spheres.
The problem here is that the spheres also have a radius, so in the instant of a collision $p_a$ and $p_b$ is not equal. The only way I could see both angular and linear momentum being preserved is if the radius changes. Is this at all possible?</p>
| 8,177 |
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<p>I have a series of waves that I would like to compare to one another. The measurements are two-dimensional with time on the x-axis and an intensity measurement on the y-axis. </p>
<p>I'd like some way of quantifying how different each wave is to the other. Is there a technique to do what I am looking for? </p>
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<p>Why can the hyperon $\Omega^{-}$ not decay by strong interaction? It seems that strangeness must be violated, but why is it the only way?</p>
| 8,179 |
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<p>Asume we have a particle sitting at the point A(0,0) in a gravitational field.
(g=9.81) It is going to move along some path to the point B(a,b) Where a>0 and b<0.
What is the curve the particle needs to be moving at to arrive at B in the
least time possible?</p>
<p>(Fastest curve between two points. )</p>
<p><img src="http://i.stack.imgur.com/D9fRA.png" alt="Example image,, various possible paths."></p>
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<p>I have read the paper "Steady state entanglement between hybrid light-matter qubits", <a href="http://arxiv.org/abs/0711.1830" rel="nofollow">arXiv:0711.1830v2</a>.
There, writers obtained density operator in matrix form after solving steady state equation (13). I want to know how one can trace out polaritonic degree of freedom of one of two cavities. </p>
| 8,180 |
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<p><img src="http://upload.wikimedia.org/wikipedia/commons/b/ba/Feynman_EP_Annihilation.svg" alt=""></p>
<p>I am having some trouble understanding this fenyman diagram, it seems to indicate that the electron produces the positron, as the arrow of the positron is pointing from the electron.</p>
<p>Additionally the arrow is in directed downwards, implying that the particle is going backwards in time? Is this diagram wrong, or does the arrow mean something else, or does the positron go back in time?!?</p>
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<p>It's pretty straight-forward to visualise <em>second-order non-linear optical mixing processes</em> in which two waves of frequencies $\omega_{1}$ and $\omega_{2}$ mix up to generate new waves of different frequencies.</p>
<p>For example the sum-frequency generation:
<img src="http://i.stack.imgur.com/hnoco.jpg" alt="enter image description here"></p>
<p>Or the difference-frequency generation:
<img src="http://i.stack.imgur.com/yXpWi.jpg" alt="enter image description here"></p>
<p>But my question is, what new waves could the two ($\omega_{1}$ and $\omega_{2}$) waves generate by <em>third-order non-linear optical mixing processes</em>?</p>
<p>Would it be possible to have a two-wave input and a two-wave output?
For example, $\omega_{1}$ and $\omega_{2}$ input; $\omega_{1}+\omega_{2}$ and $\omega_{1}+2\omega_{2}$ output?</p>
<p>The only examples of third order processes that I found on my references involve an input of three waves, as in:
<img src="http://i.stack.imgur.com/RHYIl.jpg" alt="enter image description here"></p>
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<p>This question is the continuation of the <a href="http://physics.stackexchange.com/questions/90200/einstein-action-and-the-second-derivatives">following one</a>. I still don't understand why $(1)$ may be set to zero. This refers to the zero value variations of metric and its derivatives on the infinitely far surface. But why we can assume that? To which principle does it refer?</p>
| 8,183 |
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<p>I'm looking to improve my understanding of quantum superposition. Consider the two-slit setup, where $|A\rangle$ is the state of the electron at the source, $|z\rangle$ is the state at some point on the detector, and $|S_{1}\rangle$ and $|S_{2}\rangle$ are the states at the two slits. As I understand it, the probability of finding the electron in $|z\rangle$ is:</p>
<p>$\langle z|A\rangle= \langle S_{1}|A\rangle\langle z|S_{1}\rangle + \langle S_{2}|A\rangle\langle z|S_{2}\rangle$</p>
<p>which yields</p>
<p>$|A\rangle= \langle S_{1}|A\rangle|S_{1}\rangle + \langle S_{2}|A\rangle|S_{2}\rangle$</p>
<p>Does this imply that $|A\rangle$ is a superposition of states $|S_{1}\rangle$ and $|S_{2}\rangle$? I'm confused as to what this would mean -- given the electron is in $|A\rangle$, there is a chance upon measuring it to find it in $|S_{1}\rangle$ or $|S_{2}\rangle$?</p>
<p>[I found this at: <a href="http://physics.mq.edu.au/~jcresser/Phys301/Chapters/Chapter7.pdf" rel="nofollow">http://physics.mq.edu.au/~jcresser/Phys301/Chapters/Chapter7.pdf</a> ]</p>
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<p>At one point, I decided to make friends with the low-lying spectrum of QCD. By this I do not mean the symmetry numbers (the "quark content"), but the actual dynamics, some insight.</p>
<p>The pions are the sloshing of the up-down condensate, and the other pseudoscalars by extending to strangeness. Their couplings are by soft-particle theorems. The eta-prime is their frustrated friend, weighed down by the instanton fluid. The rho and omega are the gauge fields for flavor SU(2), and A1(1260) gauges the axial SU(2), and they have KaluzaKlein-like echoes at higher energies, these can decay into the appropriate "charged" hadrons with couplings that depend on the flavor symmetry multiplet. The proton and the neutron are the topological defects. That accounts for everything up to 1300 but a few scalars and the b1.</p>
<p>There are scalars starting at around 1300 MeV which are probably some combination of glue-condensate sloshing around and quark-condensate sloshing around, some kind of sound in the vacuum glue. Their mass is large, their lifetime is not that big, they have sharp decay properties.</p>
<p>On the other hand, there is nothing in AdS/QCD which should correspond to the sigma/f0(600), or (what seems to be) its strange counterpart f0(980). While looking around, I found this discussion: <a href="http://www.physicsforums.com/showthread.php?t=241073">http://www.physicsforums.com/showthread.php?t=241073</a>. The literature that it pointed to suggests that the sigma is a very unstable bound state of pions (or, if you like, tetraquarks).</p>
<p>This paper gives strong evidence for an actual pole: <a href="http://arxiv.org/PS_cache/hep-ph/pdf/0512/0512364v2.pdf">http://arxiv.org/PS_cache/hep-ph/pdf/0512/0512364v2.pdf</a>. A more cursory review is <a href="http://arxiv.org/PS_cache/hep-ph/pdf/0608/0608218v1.pdf">http://arxiv.org/PS_cache/hep-ph/pdf/0608/0608218v1.pdf</a>. The location of the pole is far away from the real axis, the width is larger than the mass by 20% or so, and the mass is about 400MeV. The authors though are confident that it is real because they tell me that the interpolation the interactions of pions is safe in this region because their goldstone properties dominate the interactions. I want to believe it, but how can you be sure?</p>
<p>I know this particle was controversial. I want to understand what kind of picture this is giving. The dispersion subtraction process is hard for me to visualize in terms of effective fields, and the result is saying that there is an unstable bound state.</p>
<p>Is there a physical picture of the sigma which is more field theoretical, perhaps even just an effective potential for pions? Did anyone who convinced himself of the reality of the sigma have a way of understanding the bound state properties? Is there an analog unstable bound state for other goldstone bosons? Any insight would be welcome.</p>
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<p>If I'm sitting in the den with my door slightly cracked, I can hear my wife washing dishes in the kitchen down the hall. But why can't I also 'see' images of her washing dishes if, say, I looked up on my wall? </p>
<p>Broken down:</p>
<ol>
<li>Sound waves bounce off things. </li>
<li>Light waves bounce off things. </li>
<li>You can hear sound of someone washing dishes in the next room. </li>
<li>Why don't you can't see the light (visuals) from them?</li>
</ol>
| 186 |
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] |
<p>What is the difference between <a href="http://en.wikipedia.org/wiki/Work_%28thermodynamics%29" rel="nofollow">work</a> in thermodynamics and <a href="http://en.wikipedia.org/wiki/Work_%28physics%29" rel="nofollow">work</a> in mechanics?</p>
| 8,186 |
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<p>QFT says that all particles are indistinguishable from one-another [1]. That is, take a proton from cosmic ray from a supernova a billion light-yeas away, and compare it to a proton that just got smashed out in the LHC, and they are indistinguishable from one-another. Replace either with the other, and nothing will change. (As I understand) this applies to all particles that arise from the standard model fields- fermions and bosons. So if I have an atom, all the electrons in the atom are indistinguishable from all the other electrons in the atom. Theoretically I then take that atom and interchange it with any other "indistinguishable" atom. Or can I?</p>
<p>Obviously I can't replace hydrogen-1 with deuterium (their masses are different), so atoms are at least distinguishable to their isotopes. What about within isotopes? The volume of an orbital in an electron cloud is larger than the Compton length of the electron by a factor of about 10^7, giving a tremendous volume that is vacuum, and the probability of getting the election clouds just right to have negligible effects on the quantum field seems unlikely. So, are two ${}^2\text{H}$ atoms indistinguishable from one another?</p>
<p>Let's say that does work, and we can say isotopes are indistinguishable. Now, I pose the same question for molecules. What do I need to know about two water molecules? In QFT and GR, there are the 4 spacetime dimensions. I clearly can't just take a water and replace it with another water by swapping their $(\vec{x}, t) properties, because they might be "upside -down" and then all the hydrogen bonds will get messed up and their dipole moments will be wacky (and let's not even think about ionic or superionic water) and there will be some change in the system while the molecule "rights" itself. So, it seems I have at least answered my question at that scale - molecules are not indistinguishable from one another on their physical properties alone. For polar molecules in a "normal" form, we have at least 6 dimensions that must be swapped (assuming we can get away with calling the atoms themselves indistinguishable).</p>
<p>The final question, then, is what is the limit that systems are no longer indistinguishable based on just their physical properties?</p>
<p>[1] <a href="http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf" rel="nofollow">http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf</a> page 3.</p>
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<p>In Special Relativity, the spacetime interval between two events is $s^2 = -(c{\Delta}t)^2+({\Delta}x)^2+({\Delta}y)^2+({\Delta}z)^2$ giving the Minkowski metric $\eta_{\mu\nu}=\text{diag}(-1, 1, 1, 1)$. What is the justification for making time have a negative coefficient, and how closely is that related to the 2nd law of thermodynamics? Sure, by letting $\eta = \text{diag}(1, 1, 1, 1)$, we get a pretty boring spacetime, and the boosts in the Poincaré group become trig instead of hyperbolic functions, but what's the physical reasoning behind this?</p>
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<p>Suppose we have an atom with several energy levels (e.g. an hydrogen), and it is hit by photons. </p>
<p>I know that in order to have the atom change energy levels, the photon must have an energy level precisely equal to the energy difference of the two levels.</p>
<p>What happens if the photon has more energy than the ionization energy for the ground state (i.e., the sum of the series of differences between consecutive levels)?</p>
<p>It is not clear to me. Thanks!</p>
| 8,189 |
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] |
<p>If two light rays start simultaneously in the space from exactly opposite ends in opposite direction that is separated by a distance of 600000 km in a way they meet at the mid point (300000 km from source), then:</p>
<ol>
<li><p>How much time it will take to meet the front most photon of one ray to meet the front most photon of opposite ray and </p></li>
<li><p>What will be the speed of photon of the first ray relative to photon of other ray?</p></li>
</ol>
| 8,190 |
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<p><img src="http://i.stack.imgur.com/k0rQo.png" alt="enter image description here"></p>
<p>M1 slides down a frictionless ramp and collides with M2 They both compress the spring. How far is the spring compressed? What is the final velocity of M1 on the rebound up the ramp?</p>
<p>I was thinking if its possible to look at the entire system in the center of mass reference frame in order to find the final velocity of m1? </p>
<p>This isn't a homework question.. I have an upcoming physics test and I was trying to figure out different scenarios. </p>
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<p>I know this is probably some basic math once you have the figures, but my Google-fu is failing me.</p>
<p>Say I have <strong>5 pounds of air</strong>. Air meaning, the typical composition of the atmosphere of Earth. And by 5 pounds I mean the weight of the mass of the air, not it's pressure or anything like that.</p>
<p>I want to know approximately how much <strong>volume</strong> that amount of air would take up at a given pressure -- specifically, sea level pressure. I know that can vary -- lets just say its a typical warm summer day, or just an average. I'm not looking for exact numbers.</p>
<p>Actually, I'd rather a subjective interpretation of the exact figure if you can offer one. Something like 'about the volume of the air in a 12x12 room', or what have you. I have no idea how big 5 pounds of air is.</p>
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<p>Visible light diapason is 400 - 700 nm which is 1.43 - 2.5 Mhz.</p>
<p>If using an antenna I would broadcast steady sinusoidal wave in this range, why the EM emitted by the antenna are not visible?</p>
<p>Suppose the power source for antenna in a range of Kilo or Mega watts</p>
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<p>I'm given this commutator:
$$\left[PXP,P\right]$$
Being $P\psi=-i\hbar\partial_x\psi$, and $X\psi=x\psi$</p>
<p>I've solved it in two ways, the first one is just aplying the commutator to some function $\psi$ and see what I get. My final result is:
$$\left[PXP,P\right]=-i\hbar^3\partial_{xx}$$
The second one is using some commutator properties:
$$\left[PXP,P\right]=-\left[P,PXP\right]=-(P\left[P,XP\right]+\left[P,P\right]XP)$$
$\left[P,P\right]=0$, so the second term goes away. I again expand the first term:
$$-P\left[P,XP\right]=-P(X[P,P]+[P,X]P)=-P[P,X]P=i\hbar P^2=\boxed{-i\hbar^3\partial_{xx}}$$</p>
<p>I again get the same result. When the teacher solved it in class, the final result was:
$$\left[PXP,P\right]=2i\hbar P^2$$
I have no idea where that $2$ comes from. Am I missing something? Am I doing something wrong?</p>
| 8,194 |
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<p>If you were to build an upright machine that had a rod fitted into a ball bearing at the base and was secured to another rod at the top of the initial rod extending perpendicularly. To which you attached a magnet, and around this machine you also placed several upright rods containing magnets that would push/pull the magnet attached to the rod, would this cause the initial magnet to spin the machine for some period of time?</p>
<p>(Assuming I'm giving the machine a push to start the motion initially)</p>
<p>Inevitably, provided the above would work, friction would lead to an eventual slowing. With that said is there anyway to postpone that slowing for a reasonable period of time? Can magnetic shielding be used in any fashion to maintain the motion for longer?</p>
| 8,195 |
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<p>If you consider the damping force is friction like in:
<img src="http://i.stack.imgur.com/4JAFJ.jpg" alt="enter image description here"></p>
<p>then the force should be $$F=\mu N$$ where $\mu$ is the coefficient of kinetic friction. Why then is the damping force assumed to be linearly dependent on velocity?</p>
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<p>I've seen force defined in special relativity as the rate of change of 4-momentum</p>
<p>$$ {\bf{F}} = \frac{d {\bf{p}}}{dt} $$</p>
<p>Can anyone comment on the following derivation of that relation? </p>
<p>Take one dimension of space. If I'm moving with 4-velocity ${\bf U}(t) = \frac{d{\bf x}}{d \tau}$, then I'd experience an acceleration of $\frac{d{\bf U}}{d \tau}$. (Quick clarification: since ${\bf U}$ has constant norm, it will be orthogonal to its derivative, so ${\bf U} \cdot \frac{d{\bf U}}{d \tau} = 0$. And since in my momentarily co-moving reference frame (MCRF), ${\bf U}$ is entirely in the time direction, my acceleration, $\frac{d{\bf U}}{d \tau}$, will be entirely in the space direction.) So, in my MCRF,</p>
<p>$$ \frac{d{\bf U}}{d \tau} = a \left(\begin{array}{c}0\\1\\\end{array}\right) = a \cdot \vec{{\bf e}}_x
$$</p>
<p>Here's the step I'm unsure about: would it be correct to equate the acceleration I feel, $a$, with the force my rocket engine applies on me, divided by my mass, $F/m$? That would give us</p>
<p>$$ F \vec{{\bf e}}_x = m \frac{d{\bf U}}{d \tau}
$$</p>
<p>Generalizing to three spacial dimensions, you'd get</p>
<p>$$ {\bf F} := F_x \vec{{\bf e}}_x + F_y \vec{{\bf e}}_y + F_z \vec{{\bf e}}_z = m \frac{d{\bf U}}{d \tau}
$$</p>
<p>Finally, in my MCRF, $d \tau = dt$, so you'd get the original force law. Is this a correct way to derive the force law in special relativity?</p>
| 8,197 |
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<p>Obviously this is impossible in relativity; however, if we ignore relativity and use only Newtonian mechanics, is this possible? How (or why not)?</p>
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<p>I know that $0 \,\mathrm{K}$ cannot be reached, this is discussed <a href="http://physics.stackexchange.com/q/32830/">here</a> and <a href="http://physics.stackexchange.com/q/81589/">here</a>.</p>
<p>But, why is it such an important statement? </p>
<p>I mean, there are many properties which will never be zero, like: acceleration, torque, force, etc. But these facts are almost never discussed. Is it because the absolute temperature has stronger implications?</p>
| 8,199 |
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<p>For flat FLRW cosmology, we can write down two Friedman equations and one matter equation:</p>
<p>(1) $H^2=\frac{8 \pi G}{3} \rho$</p>
<p>(2) $\frac{\ddot{a}}{a} = -\frac{4 \pi G}{3} (\rho +3p)$</p>
<p>(3) $\dot{\rho} = -3 H (\rho +p)$</p>
<p>It is well known that, given an equation of state, (1)+(3) implies (2) [also (1)+(2) implies (3)]. My question is: Why are (2) and (3) (plus equation of state) not a complete set of equations? </p>
<p>I'm sure it's probably completely obvious to some of you, but not to me.</p>
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<p>The initial velocity is 14 m/s the final velocity is 0. The distance is 9.0 m and the time is 1.5 s. When solving for the acceleration, why do I get different values when using different kinematic equations?</p>
<p>$x = v_i t + \frac{1}{2} a t^2 \rightarrow a = -11.2 \frac{m}{s^2}$</p>
<p>$v_f = v_i + a t \rightarrow a = -9.6 \frac{m}{s^2}$</p>
<p>$v_f^2 = v_i^2 + 2 a x \rightarrow a = -11.52\frac{m}{s^2}$</p>
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<p>I am trying to read up some review articles about Majorana physics in topological material, but I am not really familiar with the condensed matter terminology (with condensed matter in general I should say) since I come from a high-energy background, so I come across quite a lot of vocabulary and visualization issues. </p>
<p>From the little that I know from semi-conductor physics, a gap is an energy difference between two bands such that a particle cannot go from one band to the other without being given at least that amount of energy. With that picture of band structure in mind, I don't really know what a gap potential is, nor how it can have vortices in it. For instance, in a $p_x + i p_y$ superconductor in 2D, it is said that Majorana fermions appear in vortices in the superconducting pairing potential, or when the gap is closed by variations in the chemical potential. I am wondering if there is an intuitive picture of what a "pairing potential vortex" is, without getting into solving the BdG equations for the superconductor, and on how Majorana fermions actually appear in them? </p>
<p>Moreover, another question that pops into mind is related to the use of chemical potential in the Hamiltonians describing superconductors. Statistical mechanics tells us that the chemical potential is the energy necessary to add one particle to a system from a reservoir, and also conveniently describes the energy costs related to diffusion processes in solutions. How does one interpret the chemical potential in a superconductor then? I have read somewhere that a non-homogeneous chemical potential $\mu(x)$ is a sign of an electric field $E(x) \sim \mu'(x)$, so it seems there would be a relation between $\mu$ and the electrostatic potential, but I don't find anything information that explains the relations between all these quantities in superconductors.</p>
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<p>I am working on solving the equation of motion for a particular system. It has been a long time since I've worked with matrix equations and need help in simplifying the following:</p>
<p>$\frac{d}{dt}$$(I_G\omega)$ + $\omega \times(I_G\omega)$ + $My\times [(−\dot\omega\times y)$−$\omega \times (\omega \times y)]$ = 0</p>
<p>This equation came from substituting:</p>
<p>$a_G$ = $−\dot\omega \times y$ - $\omega \times (\omega \times y)$
into:</p>
<p>$\frac{d}{dt}(I_G\omega)$ + $\omega \times (I_G\omega)$ + $My \times a_G$ = 0</p>
<p>Any suggestions or references that would help me simplify this equation would be greatly appreciated! :)</p>
<p>$I_G$ is the inertia tensor at the center of gravity of the mean model. $M$ is the mass matrix. There are no external forces or moments. $\omega$ is the angular velocity vector and y is the distance vector $r_{GG}$ (an arbitrary point $P$ is coincident with $O$ and both are defined as $G$ bar from the mean model, but I have to call it $G$ since I can't find the over bar command). $a_G$ is the acceleration vector at the center of gravity of the mean model, therefore it can not be zero. The system is a block that is rotating and translating. The frame is body fixed. </p>
| 8,203 |
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<p>There is a system of N particles. They interact and are bound together with a binding energy Eb (or potential energy). To characterize the system there are multiple terms</p>
<ul>
<li>Energy per particle Eb(N)/N</li>
<li>Energy of a particle leaving the cluster Eb(N) - Eb(N-1)
Can I call this evaporation energy?</li>
</ul>
<p>How is this connected with the chemical potential, if there are no other observables changing in the system, besides the number of particles in the cluster? If $\mu=\delta E_b / \delta N$ is a good approximation than the evaporation energy is the chemical potential? </p>
<p>Is there a good reference around for the explicit definitions of macroscopic thermodynamic properties in a N<1000 body system?</p>
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<p>I have a one BHP water pump, the water pressure of a coiled hose connected to the water pump output side was not that great. Would an unwound water hose produce greater water pressure? [Friction Losses?]</p>
<p>Thanks,
Alan</p>
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<p>I need to know if I understand this point.</p>
<p>The factor of HZZ vertex in the SM Lagrangian is half the value of the Feynman rule which appears in Diagrammatica.</p>
<p>When I calculate the decay of Higgs into 2 Z, I have to integrate over only half the phase space, because the two Z's are identical.</p>
<p>So, at the end, I get the same result as if I took the exact Lagrangian factor and integrated over the entire phase space, i.e. $2\cdot0.5=1$. </p>
<p>But, in the second way, I would in fact do two mistakes which cancel each other and accidentally get the correct answer.
Is this correct?</p>
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<p>Can you recommend books or papers that highlight or discuss extensively, or at least more than average, the similarites/differences between phase space and Hilbert space? I am primarily interested in physics, not mathematics, but am willing to look at good math books also.<br>
For all I know, this might be one of the standard intro to QM books that I am unaware of. Or a more advanced text. Or a survey paper.</p>
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<p>Let's say we have two identical spinning flywheels, that have arbitrary geometry, and are made of copper. </p>
<p>Now we apply some heat energy at the center point of flywheel A, causing it to slow down a bit, because some mass was added into it. </p>
<p>And we apply a force, but no torque, at the center of flywheel B, causing it to slow down a bit, because some kinetic mass-energy was added into it. (the flywheel starts to move linearly)</p>
<p>If the energies added are the same, are the new spinning rates the same?</p>
<p>Have we explained the mechanism behind time dilation of moving flywheels? </p>
| 8,208 |
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<p>I can model this interaction as Zee does in "Quantum field theory in a nutshell". In chapter I.4 section "from particle to force" he uses two delta functions for the source. The integral gives $E=-\frac{1}{4\pi r}e^{-mr}$</p>
<p>I consider $J=\delta^{(3)}(x-x_1)-\delta^{(3)}(x-x_2)$.
Im assuming that this represents a particle and an antiparticle. I have done the calculations quantum and classically and I obtain $E=\frac{1}{4\pi r}e^{-mr}$ </p>
<p>So as this simple model is used to describe the long range nucleon interactions I think I could conclude that this is the potential interaction between a neutron and an antineutron, a repulsive Yukawa potential. </p>
<p>I want to know If Im right. Textbooks dont talk about this and Zee seems to say that the force is always attractive.</p>
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] |
<p>Is it only necessary a human consciousness? A measurement device?
Can it be said that any of them cause the wave function collapse?</p>
| 75 |
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<p>As the title says, what would be non-ergodic processes that occur in statistical physics?
Many textbooks do not really cover <a href="http://en.wikipedia.org/wiki/Ergodicity" rel="nofollow">ergodicity</a> really well so I ask this question. I can't suddenly remember any non-ergodic process in physics..</p>
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<p>We know that this strange behavior is there but I am not to able grasp, how do we know it exists? Have we ever tried any experiments confirming this? Do we make use of this?</p>
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<p>If you have a board, say a standard 2x4 of finite length, where one end is fixed in a cement wall and the other end is free, and you begin adding weight to the free end until it breaks, where will the board break? Assume the board is made of typical wood and it is perpendicular to the wall in which it's affixed.</p>
<p>I was asked this question over 20 years ago in a job interview and I never knew if I answered correctly.</p>
<p>I answered that I thought the board would break in the middle. I figured the force bending the free end would be countered by an opposite force from the other end and they'd meet in the middle. I also noted that I'd never seen a tree branch break at the trunk. They always seem to break near the middle.</p>
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<p>When playing woodwind instruments, e.g., flute, if one blows harder, the sound will be one octave higher. Even harder gives even higher overtones. Does anyone know why?</p>
| 270 |
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<p>I'm attempting to follow a proof that the commutator of two Killing vectors is itself a Killing vector. The source that I've posted is from my course notes.</p>
<p><img src="http://i.stack.imgur.com/F5R5p.png" alt="Question"></p>
<p>I've highlighted the part I'm stuck on. I've been working on this question for quite a while, and I've understood everything else in the solution. I'm struggling to see how the 4 terms in the first row inside the red box cancel out.</p>
<p>Thanks for any help!</p>
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<p>In the movie Gravity, two characters are dangling from the international space station by a long tether. I've previously wondered exactly how you could calculate the tidal forces that act on an object connected to another object in orbit. </p>
<p>I think I've got most of a solution... the <a href="http://en.wikipedia.org/wiki/Orbital_speed" rel="nofollow">orbital speed</a> of an very small object orbiting a very large one is defined as
$$
v=\sqrt{\frac{\mu}{a}}
$$
where $\mu$ is <a href="http://en.wikipedia.org/wiki/Standard_gravitational_parameter" rel="nofollow">standard gravitational parameter</a> for the large object and $a$ is the semi-major axis. $\mu$ for the Earth is 398,600.4418, and the semi-major axis for the ISS is 6775 km. This gives us an orbital velocity of 7.670333 km/s. We can substitute in the new semi-major axis by subtracting in the length of the tether (be very generous and say 500 meters) and get 7.670616 km/s, which would be the orbital velocity of something that is floating free at that distance from the ISS... but that doesn't really help me. </p>
<p>What I need to be able to do is calculate, given an apogee of 6774.5 km, and an orbital speed of 7.670333, what is the perigee height. If I have that I have both a distance (apogee - perigee) and a time (one half the orbital period of about 90 minutes). This will tell me how many meters per second the tethered object wants to move, but I'm not sure how to turn that into an effective acceleration, or how to calculate the orbital heights. </p>
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<p>How did they take photos of Jupiter - I mean Jupiter is illuminated and that's a lot of light to produce. Am I missing something, and there was some sort of dark photo technology used, or was there simply enough light from Sun to begin with? Or is this photo a fake? </p>
<p><img src="http://i.stack.imgur.com/wwJOv.jpg" alt="enter image description here"></p>
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<p>Say we have a hollow conducting sphere (with some finite thickness).
If this object has an excess charge amounting to +Q coulomb, and there is no extra electric field in the surroundings (due to other charges), how will the charge be distributed?</p>
<p>Intuitively it seems that the charge will be symmetrically distributed..(all other cases seem too ugly), but in this case how is charge inside the conducting surface zero?
Does this have something to do with solid angle and the fact that two cones with vertex at a point in the conductor will have a special relation of the (charge/distance^2) factors? (more charge is distance is more...)</p>
<p>If this is the case can someone please prove that the effect of the two corresponding cones will cancel each other out? </p>
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<p>Given the distance among stars (the most massive objective in the space) is so huge, the difference of order of magnitude is about 7.
And also, since gravity is such a weak force, how is it likely for gravity to shape <a href="http://en.wikipedia.org/wiki/Galaxy" rel="nofollow">galaxy</a> the way it is?
Would it make more sense to say galaxy is collapsing? </p>
<p>I would like to know if my reasoning is improper, where goes wrong,</p>
<p>and how to test my reasoning or your reasoning with experiment? </p>
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<p>In <a href="http://books.google.com/books/about/Modern_Supersymmetry_Dynamics_and_Dualit.html?id=799ss7qTGlQC" rel="nofollow">Modern Supersymmetry</a>, John Terning, on pgs 151, and 153 performs a so called 'reliable' instanton calculation when dealing with the ADS superpotential 'since the gauge group is completely broken'. Alternatively, see his slides #16, and 19 <a href="http://particle.physics.ucdavis.edu/modernsusy/slides/Slides9ADSSuppot.pdf" rel="nofollow">here</a>.</p>
<p>My question has 2 parts, depending on the answer to the first part:</p>
<p>(1) What does he mean by 'reliable'? Is it a question of rigor?</p>
<p>Depending on the answer to (1):</p>
<p>(2) What is an example of an 'unreliable' instanton calculation? Is it back-of-the-envelope?</p>
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/20752/electrodynamics-textbook-that-emphasizes-applications">Electrodynamics textbook that emphasizes applications</a> </p>
</blockquote>
<p>I am a graduate student in applied mathematics and I am looking for a concise introduction to <a href="http://en.wikipedia.org/wiki/Maxwell%27s_equations" rel="nofollow">Maxwell's equations</a> / basic principles of <a href="http://en.wikipedia.org/wiki/Electromagnetism" rel="nofollow">electromagnetism</a>. (I have enjoyed the book by Purcell, <em>Electricity and Magnetism,</em> as an undergrad but I have forgotten most of it). I would like something that covers the conceptual details in a quick way and not necessarily a big textbook. You may assume that I have the necessary mathematics background. I am looking for something that will explain the physics, i.e not a huge textbook with intricate calculations but a short book to get a feel for what is going on. </p>
| 271 |
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<p>Moreover, how can you make your voice productive? for example, using it to light an LED, charge a battery, purificating water, growing plants in a more efficient way. I want to do a project that involves using my singing voice to achieve something. </p>
| 8,219 |
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<p>From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix}
0 & \sigma^i \\
-\sigma^i & 0
\end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix}
I & 0 \\
0 & -I
\end{pmatrix}$$
Now what do we understand by this operation $\gamma^0 \gamma^{\mu \star}\gamma^0 =\gamma^{\mu T}$</p>
<p>Do we have to verify the above equation by doing matrix operation details? or anything short important idea can do this quickly.</p>
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<p>I am very interested in Thermodynamics, but though it is easy to find good books and information about classical thermo, it seems that is not the same for non-equilibrium thermodynamics. I would like to know what important discoveries (theoretical or practical) has the non-equilibrium thermo has made, and what things of this discipline are really worth knowing. </p>
| 8,221 |
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<p>Let's imagine that we have a tridimensional metal object of infinite size, and decide to calculate the resistance between two arbitrary points. How would we go about doing this?</p>
<p>I have thought of two possibilities for calculating this, the first one being an adaptation of the conductivity (S/m) using the Pythagorean theorem to find a distance and isolating the resistance from there, treating it like we would treat an electrolytic liquid.</p>
<p>The second possibility I have been thinking about would be a 3-dimentional adaptation of the infinite-resistors problem (which I have only seen in 2d).</p>
<p>Would one of these methods result in giving a decent approximation, or would another method give better results?</p>
| 8,222 |
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<p>I googled in vain and found nothing. I am surprised. Maybe somebody knows about videos of Julian Schwinger available on Internet?</p>
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<p>I'm currently reading about complex geometry in order to get a feeling of how to determine the Hodge numbers, e.g. of certain orbifold constructions. Since I'm a physicist with no deeper mathematical knowledge in algebraic geometry and complex geometry, I apologize for the following possibly trivial questions. </p>
<p>In the following I'm referring to two examples of the string theory book by Becker², Schwarz. </p>
<p>Example 1 (p. 368): </p>
<p>$T^4/\mathbb{Z}_2$, i.e. $z_1 \sim z_1+1$ and $z_2 \sim z_2 + i$, where the $\mathbb{Z}_2$ isometry is generated by $\mathcal{I}:(z_1,z_2) \to (-z_1,-z_2)$. First of all, it is easy to see that there is no invariant $(1,2)-$form, hence $h^{1,2}=0$ and that $dz_1 \wedge dz_2$ is the only $(2,0)-$form, i.e. $h^{2,0}=1$. Moreover, there are four invariant $(1,1)-$forms (they're obvious, so I'm not gonna write them down) which contribute to $h^{1,1}$. But there are in total also $16$ fixed points of the orbifold which can be blown up à la Eguchi-Hanson. It is claimed that $h^{1,1}=4+1 \times 16 =20$ because there is one $(1,1)-$cycle for every blown up singularity. </p>
<p>Sorry for this questions: How do I see that there is just one $(1,1)-$form for every singularity? And why aren't there cycles from the EH-Space that contribute to $h^{2,2}$ and the other Hodge-numbers?</p>
<p>Example 2 (pp. 372): </p>
<p>Now we consider $T^2 \times T^2/ \mathbb{Z}_3$ with the action $(z_1,z_2) \to (\omega z_1, \omega^{-1}z_2)$ with $\omega =\exp(2\pi i/3)$. One has then $9$ singularities.<br>
In this case there are $2$ invariant $(1,1)-$forms. It is claimed that there are now $2$ $(1,1)-$cycles for every blow-up, i.e. $h^{1,1}=2+ 2 \times 9 =20$. </p>
<p>Why are there now two $(1,1)-$cycles for each singularity? And why aren't there other cycles contributing to the remaining Hodge-numbers?</p>
<p>I would be happy if someone could explain me the intuition and the maths behind this counting. </p>
<p>psm</p>
| 8,224 |
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<p>If a cable used to power something is exposed to a radioactive source will it over time make the entire cable radioactive? </p>
| 8,225 |
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<p>I came across the term <em>generalized free field</em> in a paper recently but I don't know its definition. Google leads to other papers which take it for granted and use it without defining it. It appears that O.W. Greenberg introduced the term in the paper <em>Generalized free fields and models of local field theory</em>, Ann. Physics 16. Unfortunately I can't access this paper. Can someone please explain it to me or give me a link to that paper? Thank you.</p>
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<p>$^{17}_8 O$ <a href="http://ie.lbl.gov/toi/nuclide.asp?iZA=80017" rel="nofollow">quoted here</a> has a spin of 5/2 and parity of +1 for the ground state, I agree with this, the unpaired neutron is in the $1d_{1/2}$ state so l = 2, spin = 5/2.</p>
<p>Now I want to figure out the spin an parity of the first two excited states, but how do I know which proton and which neutron move up.</p>
<p>I am thinking that the first excited state is where the unpaired neutron moves to the $2s_{1/2}$ state, so that l = 2, and spin = 1/2, thus the parity remains 1.</p>
<p>But how do I figure out the configuration for the second excited state.</p>
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<p>I want to prove that $^{38}Ar$ is stable with respect to $\beta$ decay, that $^{38}Cl$ decays by $\beta^-$ and that $^{38}K$ decays by $\beta^+$.</p>
<p>I know from Googling that this is true, and I also know that $^{38}Ar$ has the highest binding energy for mass number 38, thus its definitely stable with respect to $\beta$ decay. </p>
<p>However I would like to prove this from a method other than calculating out all the binding energies from the semi empirical mass formula, is there and easier way?</p>
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<p>Suppose there are only two hydrogen atoms in the entire universe. Suppose further that they are both situated at the very limits of the cosmos, equally distant. Would they exert an attractive force on one another? </p>
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<p>One of the unsolved problems I still have is measuring temperature in furnace at 700-1100C range (I need some +-0.1% repeatability and +-1% precision).</p>
<p><strike>Obviously, contact thermometers are quite rare & expensive for this range, everything I was able to find is rated at 450-500C max (especially as this should work in aggressive oxygen/ozone/chlorine atmosphere).</strike></p>
<p>Consumer grade pyrometers does not work above ~400C.</p>
<p>I've checked blackbody emission for 700-1100C objects, and it seems that even at 500C objects start to emit at 1um range (not much though), which is easily measurable by cheap silicon photo-diodes (ones I have on the desk have maximum at 880nm, with 70% sensitivity at 1um and 10% at 1.1um, visible light filtered).</p>
<p>As my target is always the same with fixed emissivity, there should be no vital need for 2-band measurement.</p>
<p>Are there any issues with this single-band temperature measurement approach? Alternatively, I might add PbS photoresistor (2.1um maximum), but they are not that precise, quite expensive and scarce. What are your thoughts or suggestions?</p>
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<p>Consider an Einstein solid with quantized energy values $U=q\epsilon$ and $N$ oscillators. I calculated some values of an Einstein solid numerically through a function in R (at the bottom of the post). In an exercise I'm supposed to estimate $\epsilon$. </p>
<p>Apparently the answer is that I can estimate it by showing that $kT/\epsilon$ is approximately $1/3$ when the heat capacity reaches half of its maximum value (this value is called the equipartition value). I find this conclusion really confusing, since the energy quanta don't have anything to do with the heat capacity (or do they?). The <strong>exact</strong> wording in the solution of the exercise is </p>
<blockquote>
<p>Note that in the high-temperature limit the heat capacity approaches the result predicted by the equipartition theorem, $C=Nk$ (since there are two degrees of freedom per oscillator). Below $kT=\epsilon$. however, the heat capacity falls off dramatically. (...) The value of $\epsilon$ can be estimated by noting that the heat capacity reaches half of its equipartition value at $kT\approx\epsilon/3$.</p>
</blockquote>
<p>Could anyone please explain how does conclusion works? I can't get a grasp on understanding the relation between the energy quanta and the equipartition value of heat capacity.</p>
<p>The function I wrote to produce a table uses column names such as <code>C_Nk</code> where I in fact mean $C/Nk$, R just doesn't handle slashes in function names so well:</p>
<pre><code>install.packages('gmp');install.packages('Rmpfr');library('gmp');library('Rmpfr')
EinsteinProperties <- function(N){
q_total=100
q=0:q_total
Omega=formatMpfr(chooseMpfr(N+q-1,q),digits=2)
S_k=formatMpfr(log(chooseMpfr(N+q-1,q)),digits=4)
kT_eps=rep(0,length(q))
C_Nk=rep(0,length(q))
for(i in 0:q_total){
if(i>0&&i<q_total){
kT_eps[i+1]=formatMpfr(2/(log(chooseMpfr(N+(i+1)-1,i+1))-log(chooseMpfr(N+(i-1)-1,i-1))),digits=2)
}else if(i==0||i==q_total){
kT_eps[i+1]=0
}
}
for(i in (0:q_total)){
if(i==1){
C_Nk[i+1]=formatMpfr(2/(2/(log(chooseMpfr(N+(i+2)-1,i+2))-log(chooseMpfr(N+(i)-1,i))))/N,digits=2)
} else if(i>1&&i<q_total){
C_Nk[i+1]=formatMpfr(2/(2/(log(chooseMpfr(N+(i+2)-1,i+2))-log(chooseMpfr(N+(i)-1,i)))-2/(log(chooseMpfr(N+(i)-1,i))-log(chooseMpfr(N+(i-2)-1,i-2))))/N,digits=2)
} else {
C_Nk[i+1]=0
}
}
table <- cbind(q,Omega,S_k,kT_eps,C_Nk)
layout(matrix(1:2,1,2))
graph_S_k <- plot(q,S_k,type="l",xlab="U/eps",ylab="S/k",main="Entropy",xlim=c(0,100))
graph_C_Nk <- plot(kT_eps[2:q_total],C_Nk[2:q_total],type="l",xlab="kT/eps",ylab="C/Nk",main="Heat capacity",xlim=c(0,2),ylim=c(0,1))
return(table)
}
EinsteinProperties(50)
</code></pre>
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] |
<p>Related post : <a href="http://physics.stackexchange.com/questions/62858/derricks-theorem">Derrick’s theorem</a></p>
<p>Consider a theory in D spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form $$L= \frac{1}{2} G_{ab}(\phi) \partial_\mu \phi_a \partial^\mu \phi_b- V(\phi)$$
where the eigenvalues of G are all positive definite for any value of $\phi$, and V = 0
at its minima.
Any finite energy static solution of the field equations is a stationary point of
the potential energy
$$E = I_K + I_V ,$$
where
$$I_K[\phi]= \frac{1}{2} \int d^Dx G_{ab}(\phi) \partial_j \phi_a \partial_j\phi_b$$
and $$I_V = \int d^Dx V(\phi)$$
are both positive. Since the solution is a stationary point among all configura-
tions, it must, a fortiori, also be a stationary point among any subset of these
̄
configurations to which it belongs. Therefore, given a solution $\phi(x)$, consider the one-parameter family of configurations,
$$f_\lambda(x)= \bar{\phi}(\lambda x)$$
that are obtained from the solution by rescaling lengths. The potential energy of these configurations is given by</p>
<blockquote>
<p>\begin{align} E_\lambda &= I_K(f_\lambda) + I_V(f_\lambda)\\
> &=\lambda^{2-D} I_K[\bar\phi]+\lambda^{-D} I_V[\bar\phi]\tag{1}
> \end{align}</p>
</blockquote>
<p><strong>My query from the above statement:</strong></p>
<ol>
<li><p>Can you explain The $G_{ab}$</p></li>
<li><p>how equation (1) came from the previous equation.</p></li>
</ol>
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<p>I have an issue with 2D acoustic wave field modelling.</p>
<p>In order to estimate the energy propagation direction of an acoustic wave I use Poynting vectors $S$ which can be described by</p>
<p>$$
\vec{S} = - \dot{p} \nabla p
$$</p>
<p>where $p$ is the pressure field, $\dot{p}$ represents the time derivative of the pressure field and $\nabla p$ represents the spatial gradient of the pressure field.
Taking the absolute value of $\vec{S}$ it is possible to estimate the energy of the wave field at a certain grid point at a certain time step.</p>
<p>Since $\nabla p$ can become very small, the Poynting vector field may become quite noisy for complicated wave fields. As a result, I want to reject Poynting vectors, that are too small by comparing the actual energy of the wave field with $|\vec{S}|$.</p>
<p>Unfortunately, I have no idea how to determine the energy of an accoustic wave field other than by using Poynting vectors.</p>
<p>Do you have any suggestions for me?</p>
<p>I appreciate any help - thanks! </p>
<p><strong>EDIT:</strong>
Is there a counterpart to the elastic energy density foracoustic media which does not involve the medium density $\rho$ ?</p>
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<p>Using a tennis ball as an example object, if one ball weighs 1 ounce and the other is 2 ounces, and both are struck at 100 mph on the same trajectory, would there be any difference in the deceleration rate between the 2 different mass balls? (All other things about the two balls being equal). For instance, would the elapsed time for the ball to travel let's say 100 feet be different or the same?</p>
<p>FOLLOW UP QUESTION (based on answer #1):
If it's true that the lighter ball would decelerate faster (and consequently take longer to travel a given distance), then what would be the difference in the initial velocity of the two balls (one 1 ounce, the other 2 ounces) if both are struck with the same implement with the same force (let's say a tennis racket travelling 100 mph). </p>
<p>I'm assuming the lighter ball would have a higher initial speed. If so, would the higher initial speed of the lighter ball offset the increased deceleration rate for the lighter ball. In practical terms: with the initial speed being different, which ball would arrive first in the above example of 100 feet, the lighter ball or the heavier ball? </p>
<p>If not too difficult, could you explain how this relationship (first the initial speed difference and then the total travel time difference for 100 feet) would be calculated? </p>
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<p>This question concerns the Dirac equation and the $4\times4$ $\gamma$-<a href="http://en.wikipedia.org/wiki/Gamma_matrices" rel="nofollow">matrices</a>. The task is to prove that a similarity transformation of the standard $\gamma$-matrix conserves the commutation relation</p>
<p>$$
\{\gamma^\mu,\gamma^\nu\} ~=~ 2g^{\mu\nu},
$$</p>
<p>where $2g^{\mu\nu}$ is the metric tensor $\text{diag}(1,-1,-1,-1)$, and the similarity transformation is defined as</p>
<p>$$
\tilde{\gamma}^\mu = S \gamma^\mu S^\dagger,
$$</p>
<p>and $S$ is a unitary matrix. I will write down the start of my proof to show where I stop. First of all, we can use that $S$ is unitary and show that $\gamma^\mu = S^\dagger\tilde{\gamma}^\mu S$, and insert this into the commutator. This leaves us, again using that $SS^\dagger = I$, with</p>
<p>$$
S^\dagger\{\tilde{\gamma}^\mu,\tilde{\gamma}^\nu\}S = 2g^{\mu\nu}
$$</p>
<p>which again gives us</p>
<p>$$
\{\tilde{\gamma}^\mu,\tilde{\gamma}^\nu\} = 2Sg^{\mu\nu}S^\dagger.
$$</p>
<p>In order for the proof to hold, it requires that $g^{\mu\nu}$ and $S$ commute so that</p>
<p>$$
2Sg^{\mu\nu}S^\dagger = 2g^{\mu\nu}SS^\dagger = 2g^{\mu\nu}.
$$</p>
<p>So my question is: Do all unitary matrices commute with the metric tensor $g^{\mu\nu}$? If yes, how can I show this easily?</p>
| 8,235 |
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<p>I have numerically integrated the (reduced) homogeneous equation of a damped harmonic oscillator in order to see how the error propagates.</p>
<p>$$\frac{d^2 X}{d\phi^2} + \frac{1}{Q}\frac{dX}{d\phi}+X(\phi) = 0$$
where $\phi = 2 \pi \tau$ and $\tau$ is the reduced time</p>
<p>In the process I have also extracted the logarithm of the energy and plotted it against time, for different values of the quality factor, Q. One can expect the energy to decay slower for larger Q.</p>
<p>$$ E = P^2 + X^2$$ where $P = \dot{X}$</p>
<p>What I found is that for very large values of Q, the energy of the oscillator begins to <strong>increase</strong>. I checked my code several times and I couldn't see anything wrong with it so I suspected that it purely something to do with numbers so I began playing around with them, but first here is the graph.</p>
<p><img src="http://i.stack.imgur.com/9LTVF.png" alt="enter image description here"></p>
<p>What I found is odd; say I'm using a step size of $1 \times 10^{-n}$ . If Q's magnitude matches or exceeds $10^{n}$ the energy begins to increase!
What is causing this? <strong>What is the connection between Q and the step size?</strong> </p>
<p><strong>Also, should the energy be oscillating?</strong> (If you zoom in on the red and green lines on the graph you will see that it is oscillating much slower there.)</p>
<hr>
<p>Here is how I am integrating the equation for those interested: </p>
<ol>
<li>Let $\dot{X} = P$ </li>
<li>Thus original equation becomes $\dot{P} + \frac{1}{Q} P + X = 0$ </li>
<li>Now we have two 1st order DEs. </li>
<li>Using discrete steps we can roughly find the next point of $X$ and $P$ by considering that $\dot{X} = \frac{dX}{d\phi} = \frac{X_{n+1} - X_n}{\Delta \phi}$ and approaching the other eqution in the same manner. </li>
<li>We can then rearrange for $X_{n+1}$ and $P_{n+1}$ and create a code that calculates those points, given some basic initial conditions. </li>
</ol>
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<p>I took an empty bottle and placed it on the floor, then tilted the bottle to one side such that the the displacement caused a disturbance in its balance but not enough to completely tilt it over. The bottle started oscillating back and forth. But as the time passed and the amplitude of oscillation decreased (as expected for damped oscillation) but its time period also decreased with time, that is it started oscillating more vigorously and the finally the oscillation stopped. Why?</p>
<p>(I'm sorry if I am missing something obvious here)</p>
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<p>I have the flat FLRW metric,</p>
<p>$$ ds^2=-dt^2+a(t)^2(dx^2+dy^2+dz^2) $$
and a geodesic $\gamma(s)=(t(s),x(s),y(s),z(s))$ with parameter $s$. Two of the Killing vectors of the metric are $ \partial_x$ and $\partial_y$ which give rise to the constants of motion $ a^2\dot x$ and $ a^2 \dot y $ respectively. This is how far I am. Now I need to show that from this follows that I can assume that the geodesic has $y(s)=0=x(s)$. This is not obvious for me from the above constants of motions, because they also permit $\dot x=\frac{const.}{a^2}$</p>
<p>If I can rule this out, I get $\dot x =0$ and therefore $x=const.$ and because I can set $x$ to zero locally, it is zero on the whole spacetime.</p>
<p>So my question is: Why is $\dot x =0$</p>
<p>Edit: Or am I completely on the wrong track?</p>
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<p>I am referring to this very famous paper. <a href="http://arxiv.org/abs/hep-th/9806087" rel="nofollow">http://arxiv.org/abs/hep-th/9806087</a></p>
<ul>
<li>I am referring to equations 20 and 27 and 28. Anyone can help derive them? </li>
</ul>
<hr>
<p>I vaguely think that they substituted equation 9 in the bulk part of equation 10 and power series expanded in $\rho$ and isolated the "log" term in the integral to get 20 and 27. But (1) I am not seeing how this calculation is done and (2) how does $g_2$ and $g_4$ and $g_0$ (all of which look like arbitrary functions!) get repackaged in terms of curvature tensors (as in 28)!? </p>
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<p>At this point in this documentary about the history of electricity: <a href="https://www.youtube.com/watch?v=oPnS2WO2_0k&t=4m40s" rel="nofollow">https://www.youtube.com/watch?v=oPnS2WO2_0k&t=4m40s</a> the guy says the Maxwell calculations predicted the generation of certain types of waves, when there is a change in the direction of the current.
<p>I did not have time to study the derivation of the Maxwell equations, so I don't know exactly how they work, but could somebody show me what calculations predicts this phonomena?
<p> Further, in this video, the guy shows a wireles telegraph, simply made with this theory. What is the minimum knowledge I need to build one? (i'm gonna build it inside my mind)
<p>I need to know if there's a paper or book that talks about this subject: how to generate this waves with an experiment, and how to construct a simple wireless telegraph. </p>
| 8,240 |
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<p>Does the current acceleration of universe imply that our universe is open?
If the universe is closed, from the <a href="http://en.wikipedia.org/wiki/Friedmann_equations" rel="nofollow">Friedmann's equation</a>, the acceleration of universe wouldn't be possible, would it be? (Of course, except for the very earlier time of inflation era.)</p>
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] |
<p>A book on Quantum Mechanics by Schwinger states, "A unitary operator can be considered to be a complex valued function of a Hermitian operator."</p>
<p>Please give a hint on how to prove this assertion.</p>
| 8,242 |
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<p>Is there any equation that calculates the $C_d$ value in the formula of air drag ?
$$F_d = \rho C_d v^2 A$$
I have found that there are tables for this constant but I am looking for the equation that evalutes it.</p>
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<p>In a table fan, the blades move around in circular way and we feel air/wind when sitting on front of it. How does this happen?</p>
| 8,244 |
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