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<p>The generalized 2-qubit state is given as:
$$ \rho = \frac{1}{4}[ I\otimes I + (m_x\sigma_x + m_y\sigma_y + m_z\sigma_z)\otimes I + I \otimes (n_x\sigma_x + n_y\sigma_y + n_z\sigma_z) + \sum_{ij}t_{ij}\sigma_i\otimes\sigma_j] $$</p>
<p>Then, is there a method to map a given density matrix:
$$ \rho_g = \pmatrix{a & b & c & d \\ e &f &g &h \\ i & j & k & l \\ m &n &o &p } $$
to the generalized state in terms of relations between the coefficients, without having to expand and compare terms?</p>
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<p>Recently, some experiments show that the supersymmetry is not realised by Nature according to the simple models that we currently have. Nevertheless, it is far from saying that the "game is over" as SUSY might be realised at an unknown energy. I would like to ask what are the experiments that could give us a clue whether SUSY assumption is wrong. Will the LHC / VLHC be able to rule it out in the future?</p>
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<p>I need two formulas in dealing with ice and water. </p>
<p>First:<br>
If I have 2 x 2 x 2 (cm) ice cube, after it melts, how much water will there be ?</p>
<p>Second:<br>
If I have 2 x 2 x 2 (cm) ice cube, after how much time will it melt ?</p>
<p>I know that there are many variables: temperature, density and so on.<br>
So you can give and more complicated formulas.</p>
<p>Also, for second question I suspect that outer area of ice is also effecting speed of melting.</p>
<p>Thanks in advance </p>
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<p>I would like to pick the correct doping of silicon to get 1 Mohm cm resistivity at liquid helium temperature of 4.2 K. The metal insulator transition implies that I need a very accurate doping. Are there any other effects and is there a way to calculate the correct doping?</p>
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<p>My question is even though photons have no (rest) mass, do they emit a external force due to EM radiation causing electrons to be excited and jump to higher energy shells which electrons have mass thus photons can emit a kinetic force? I am new so I would like to get the record straight on this issue. </p>
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<p>Understanding on <a href="http://en.wikipedia.org/wiki/Quantum_entanglement" rel="nofollow">quantum entanglement</a>? I am very vague on this topic and would appreciate a detailed explanation on this phenomenon.
Also what are the possible applied uses for quantum entanglement? What are the problems of putting this phenomenon in practice?</p>
| 250 |
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<p>I just tried to calculate the magnetic moment of a proton. I took the </p>
<p>proton <a href="http://en.wikipedia.org/wiki/G-factor_%28physics%29" rel="nofollow">g-Factor</a> of $g=5.585694$ <br>
<a href="http://en.wikipedia.org/wiki/Nuclear_magneton" rel="nofollow">nuclear magneton</a> of $\mu_k = 5.050783 * 10^{−27}$ J/T <br>
proton spin of $I=1/2$ <br></p>
<p>At first I calculated the norm of the proton spin $|\vec{I}|=\hbar \sqrt{I*(I+1)}=\hbar \frac{1}{2}\sqrt{3}$ </p>
<p>And then I put everything together in $\mu=g\mu_k\frac{|\vec{I}|}{\hbar}$ and obtain 2,44134228 × 10^-26 instead of <a href="http://en.wikipedia.org/wiki/Proton" rel="nofollow">1.410606 × 10^-26</a> ...</p>
<p>Interesting enough, I obtain the correct value if I devide by $\sqrt{3}$. But I see no reason to do this... </p>
<p>It would be great if you could help me.</p>
<p>Thanks in advance</p>
<p>ftiaronsem</p>
| 7,505 |
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<p>Given two identical microphones arranged in an ideal XY pattern, recording a single sound source at equal distance from both capsules, the two signals obtained are equal in amplitude, perfectly in phase with each other, and distorted identically by microphone frequency response. Therefore, other than small differences that result from noise, what exactly causes the difference between the left and right channel, such that when heard, a stereo field is perceived?</p>
<p>I ask because I am developing an audio synthesis application, and need a way to simulate real stereophonic sound given a single input signal.</p>
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<p>I know <a href="http://en.wikipedia.org/wiki/Quantum_computer" rel="nofollow">quantum computers</a> are very complicated and my question is is there any way in "Principle" to create one? Are there already quantum computers being created?</p>
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] |
<p>Google has no results found for "energy not proportional to frequency" and many results for E=hf. Is there an example of an energy that is not proportional to frequency?</p>
| 7,508 |
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<p>It was established by Dennis, Kitaev et al. that the 2D Toric Code
can be mapped to a 2D Random Bond Ising Model. The original derivation
was given in the paper "Topological quantum memory" which can be found in
J. Math. Phys. 43, 4452 (2002); doi: 10.1063/1.1499754 or online at <a href="http://dx.doi.org/10.1063/1.1499754" rel="nofollow">http://dx.doi.org/10.1063/1.1499754</a> . A free arXiv preprint version is available online <a href="http://arxiv.org/abs/quant-ph/0110143" rel="nofollow">here</a>.</p>
<p>The derivation that shows that the 2D Toric Code can actually mapped to
a 2D Random Bond Ising Model is given in section IV - D "Derivation of the model" (Starting page 4469). </p>
<p>The point where I'm getting lost is when he is trying to set
up a function that for a fixed chain E outputs the probability of a
"homotopically equivalent" chain $E'$ (which he calls $p(E'|E)$). </p>
<p>To obtain this function he first calculates the probability of a link
being occupied that lies on $E'$ but not on $E$.
He obtains (Eq. 13) that the probability is equal to</p>
<p>\begin{equation}
\left(\frac{p}{1-p}\right)^{n_{C}(\ell)}
\end{equation}</p>
<p>up to an overall normalization and with $C$ being the cycle corresponding to $E'$. </p>
<p>I don't really see how he arrives at that results or what the overall normalization factor actually is (after all "normalization" is crucial when talking about probabilities - what is the meaning of probability 35 if I don't know the normalization?)
Then he obtains in Eq. (15) an explicit exponential-like form for
$p(E'|E)$ which isn't clear to me neither.
He also seems to omit a lot of explanations at least at this stage. </p>
<p>Could anyone explain to me in a bit more details how the derivation is
carried out in more detail? This would really help me a lot. </p>
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] |
<p>What would the calculation look like when computing the wind pressure of a moving vehilce versus compressed air pressure pushing against the the moving vehicle, how much compressed air pressure would be needed to combat the wind of the moving vehicle.?</p>
| 7,510 |
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<p>I've read a classbook on the field theory (including EM): it perfectly describes quantitive patterns in EM-theory, but I have no luck understanding how and why it works.</p>
<p>I mean, magnetic substances are described mainly by magnetic moments of electrons, but all explanations of the phenomenon I've found are rather of deep high-level focus on fields exclusively, than on explanation why it works and what underlying mechanisms bring all those ideas to life (including explanation of what field is, except that it is an abstraction).</p>
<p>So, the question is: may anyone try to give (or point to) a popular and thorough explanation of magnets and on low-level mechanisms, which unifies and explains how this long-distance interaction really works (i.e., not only modelled and described mathematically)?</p>
<p>p.s.: also, I'd like to see some papers on computing magnetic properties of bodies (iron ball, for example, finite plane, NeoCube's ball chains, etc).</p>
<p>Thanks in advance!</p>
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<p>I've been working through the derivation of quantities like Gibb's free energy and internal energy, and I realised that I couldn't easily justify one of the final steps in the derivation. </p>
<p>For instance, in deriving the formula for Gibb's Free Energy, we first found the differential equation:</p>
<p>$$dG = dH - TdS$$</p>
<p>which has the property that, for spontaneous processes, $dG \leq 0$. We then went from there to defining the state function:</p>
<p>$$G = H - TS$$</p>
<p>and claimed that this had the analagous property that $\Delta G\leq0$ for all spontaneous processes. Apparently we can reason this way because the second equation can be obtained from the first by integration. But I'm not entirely sure of this. For instance, temperature is not necessarily independent of entropy, so I'm not convinced that $TS$ must be the integral of $TdS$. Physically I'm not convinced because the derivative refers to small changes at constant temperature, while the state function applies at all temperatures.</p>
<p><a href="http://en.wikipedia.org/wiki/Gibbs_free_energy" rel="nofollow">Wikipedia's Gibbs free energy page</a> said that this part of the derivation is justified by 'Euler's Homogenous Function Theorem'. Now, I've done some work with ODE's before, but I've never seen this theorem, and I've been having trouble seeing how it applies to the derivation at hand.</p>
<p>If anyone can shed any light on the matter or recommend some further reading I'd appreciate it. Thanks</p>
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<p><a href="http://en.wikipedia.org/wiki/Fermi_energy" rel="nofollow">Wikipedia</a> states the definition of Fermi energy as for "a system of non-interacting fermions". If we have to assume free electrons in a solid behave this way before we are able to calculate Fermi energy, how can Pauli exclusion be justified (because electrons are non-interacting)? Can Fermi energy be similarly defined for electrons confined to a single atom?</p>
| 7,513 |
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<p>Is Helmholtz's 1870 paper "<a href="https://www.degruyter.com/view/j/crll.1870.issue-72/crll.1870.72.57/crll.1870.72.57.xml" rel="nofollow">Ueber die Bewegungsgleichungen der Elektricität für ruhende leitende Körper</a>," <em>Journal für die reine und angewandte Mathematik</em> <strong>72</strong>:57-129 translated into English anywhere?
thanks</p>
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<p>Related to <a href="http://physics.stackexchange.com/questions/83633/how-trustworthy-are-numerically-obtained-periodic-solutions-to-the-three-body-pr?rq=1">this post</a></p>
<p>Just out of curiosity, I have a question about the current status of classical (Newtonian) three-body gravitional numerical simulation. I found wikipedia is relatively limited on this topic.</p>
<p>Given three stellas, how accurate can we predict their trajectories using numerical methods based on current compuational techniques and computer capacity? Is there any comparison with astrophysics observation? (Presumably we can update our observed initial conditions during calculation)</p>
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] |
<p>For industrial furnaces, in order to improve radiation heat transfer and save energy, some people say applying a high emissivity coating on to the interior surface of a furnace will do, while some people say applying a high reflectivity coating will do. we all know that at given wavelength and for an opaque object surface, emissivity + reflectivity =1, anyone can explain to me please?</p>
<p>With best regards</p>
<p>Sean </p>
| 7,516 |
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<p>I'm puzzled about what should be the normal ordering of the identity operator (or any proportional operator):</p>
<ul>
<li>looking at it from the "Fock space operators POV",the prescription is to move all the creation operators to the left and the annihilators to the right, but the identity by definition as non of those, so should be left invariant.</li>
</ul>
<p>But I run into several contractions:</p>
<ul>
<li><p>normal ordering of any operator should have a vanishing vev, so $$<\, : \mathbb{I} :\, > = 0 \ne\, < \mathbb{I}>$$</p></li>
<li><p>using the commutator between the $a$ and $a^{\dagger}$:
$$:aa^{\dagger}: \, = \,a^{\dagger}a =\, :a^{\dagger}a + \mathbb{I}: = \,a^{\dagger}a + :\mathbb{I}:$$
where I used the commuator to get from the first to the third and the normal ordering otherwise. Identification of the second and fourth gives me again $\,:\mathbb{I}:\,\, = 0$.</p></li>
<li><p>last the vev of the exponential of any operator should be zero ($<:e^{A}:>\, = 0$), expanding the exponential gives me again $<\,:\mathbb{I}:\,>\, = 0$.</p></li>
</ul>
<p>Is this the final result or are there more subtleties?</p>
| 7,517 |
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<p>On page 237 in PS we have (the unnumbered equation after eq. 7.58)</p>
<p>$$\mathcal{P} \sim \frac{iZ}{p^2-m^2-iZ\,\mathrm{Im}M^2(p^2)}$$</p>
<p>but after deriving it myself I obtained</p>
<p>$$\mathcal{P} \sim \frac{iZ}{p^2-m^2-iZ\,\mathrm{Im}M^2(p^2)-iZ\frac{\mathrm{d}\,\mathrm{Im}\, M^2}{\mathrm{d}\,p^2}\cdot(p^2-m^2)+\dots}$$</p>
<p>why do they omit the derivative term? Why is it considered small?</p>
<p><strong>Note: My mistake was that I also expanded the imaginary part of $M^2$...please see answer below for solution.</strong> </p>
| 7,518 |
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<p>We have electric charge density $\rho(r) = kr$ in a cylinder of infinite height and radius $a$.</p>
<p>I'm asked to find the electric field.</p>
<p>I'm doing it using two methods and I don't undesrtand why then don't yield the same result</p>
<p><strong>Method 1</strong></p>
<p>Gauss' theorem applied to a cylindrical surface;</p>
<p>$$E(r) 2\pi rh = \frac{Q}{\epsilon_0}$$</p>
<p>$Q = h\int_A \rho = h\int_A kr$, where A is the unit circle $\Rightarrow Q = h\pi k r^2$</p>
<p>So I find $$E(r) = \frac{kr}{2\epsilon_0}$$</p>
<p><strong>Method 2</strong>
Divergence in polar coordinates:</p>
<p>$$\nabla \cdot E (r) = \frac{\rho}{\epsilon_0}$$
$$\nabla \cdot E(r) = \frac{1}{r} \frac{\partial rE(r)}{\partial r} = \frac{1}{r} (\frac{\partial E(r)}{\partial r} + r\frac{\partial E(r)}{\partial r}) = \frac{\partial E(r)}{\partial r} \frac{r+1}{r} = \frac{\rho}{\epsilon_0}$$</p>
<p>$$\frac{\partial E(r)}{\partial r} = \frac{k}{\epsilon_0} \frac{r^2}{1+r}$$
$$\Rightarrow E(r) = \frac{k}{\epsilon_0} (\frac{r^2}{2} + r + \ln{(1+r)})$$</p>
<p>What's wrong with that?</p>
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<p>What is the cause of <a href="http://en.wikipedia.org/wiki/Centripetal_force">centripetal</a>/<a href="http://en.wikipedia.org/wiki/Centrifugal_force">centrifugal</a> force? When an object of mass $m$ is moved in a circular orbit, it experiences a centrifugal force radially away from the center. What is the cause of this centrifugal force? Is these related to the four fundamental forces (gravity,electromagnetic,weak and strong forces)?</p>
<p>This force is equivalent to a force experienced while stopping a mass in motion (Inertia). But is this inertia caused by some force? or what causes inertia? A photon particle does not have inertia of rest.</p>
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<p>I learned $F = iLB$ recently. However, I don't understand why $L$ is marked as a vector but $i$ is not.<br>
For a normal rod, how should I define the direction of length vector $L$? And if I reverse the current in it, the force exerted on it by the magnetic field would reverse direction, correct?<br>
So I think in this formula, $i$ should be the vector but not $L$. Am I right?</p>
<p>I'm using the Physics II by <em>Halliday Resnick and Krane</em></p>
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<p>A guy <a href="http://stackoverflow.com/a/4888033/56541">suggested to me</a> that getting speed from an accelerometer required the use of this equation:</p>
<p>$\text{speed} = \sqrt{x^2 + y^2 + z^2}$</p>
<p>This does not make any sense to me, all that you would get from this equation would be the magnitude in $m/s^2$ of the acceleration in the $x, y$ and $z$ axes. Am I correct? Or is my reasoning flawed?</p>
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<p>I have a question regarding the $E$ vs $k$ curve in the first Brillouin zone. Why does the curve have an inflection point at some value of $k$ in the curve?
How does it physically support it?</p>
<p><img src="http://i.stack.imgur.com/Y4DGl.jpg" alt="E vs k"></p>
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<p>I understand the first law-elliptical orbits, and the second-equal area in same time, but I need help with the third one. Note that I am not in an AP course or taking calculus at the moment so simple quadratics/cubics/CP level explanations would suffice.</p>
| 7,524 |
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<p>I'm not asking about how we worked backward from an expanding universe to the age of the big bang, but rather what is the meaning of time in a near infinitely dense point in the context of general relativity? Wouldn't time flow infinitely slowly for a theoretical (though physically impossible) observer?</p>
| 7,525 |
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<p>What latitude is needed before you can reliably see the globular cluster <a href="http://en.wikipedia.org/wiki/Omega_Centauri" rel="nofollow">Omega Centauri</a>, say it reaches 20 degrees above the horizon? What about if you are up on a hill looking down, what's the theoretical highest latitude where you could have any chance of seeing it?</p>
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<p>After reading up on irregular moons in the solar system - moons that are thought to be captured, most seem to be in retrograde orbit around their parent body. That led me to wonder if retrograde orbits are easier to capture objects than prograde orbits - say prograde orbits are more likely to gravitationally slingshot the object away from the parent body before capture, whereas retrograde orbits would be more likely to capture before flinging the object away.</p>
<p>When viewing the capture from the perspective of the parent body, an object that is moving retrograde past the body appears to slow down as it interacts with the gravity well of the body, whereas an object moving prograde past the body appears to accelerate in the same frame of reference.</p>
<p>Is there any validity to this, or is that just a flaw in reasoning?</p>
| 7,527 |
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<p>Millisecond pulsars are supposed to be old neutron stars. However, they are spinning even more rapidly than newly formed pulsars. Since pulsars slow down as they age, something must have caused these older pulsars to "spin up" and be rotating as fast as they are. What is the mechanism for doing so?</p>
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<p>Where can I find <a href="http://en.wikipedia.org/wiki/Public_domain" rel="nofollow">public domain</a> astronomical pictures of <a href="http://en.wikipedia.org/wiki/Nebula" rel="nofollow">nebulae</a>, <a href="http://en.wikipedia.org/wiki/Star" rel="nofollow">stars</a>, etc. that can be freely used?</p>
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] |
<p>If I wanted to explore a <a href="http://en.wikipedia.org/wiki/Discrete_mathematics" rel="nofollow">discrete mathematics</a> approach to <a href="http://en.wikipedia.org/wiki/Continuum_mechanics" rel="nofollow">continuum mechanics</a>, what textbooks should I look into? </p>
<p>I suppose a ready answer to the question might be: "computational continuum mechanics", but usually textbooks that discuss such a subject are usually focused upon applying numerical analysis to continuous theories (i.e. the base is continuous), whereas I would like to know if there is a treatment of the subject that builds up from a base that is discrete. </p>
| 38 |
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<p><strong>tl;dr</strong></p>
<p>Is there any meaningful (physical) way to compare the energy expended in the exercise of doing $x$ pushups in $t_1$ seconds, vs the exercise of doing the plank for $t_2$ seconds?</p>
<hr/>
<p>I'm confused about the concepts of energy, work, and power, in the case where no distance is traversed.</p>
<p>For instance, take a push-up. I can approximate the work I've done by using the change in potential energy $\Delta U = mgh$, ie. $$W = mg \Delta h$$ $$= m [kg] * 9.8 [m/s^2] * h[m]$$ where $m$ is some proportion of my body mass, and $h$ is a bit less that the length of my arm.</p>
<p>The result has the units of $Newton-meters$, or $kg m^2/s^2$, aka $Joules$. I can also measure the average <em>power</em> of my push-up using $\Delta W/\Delta t$, which has the units of $J / s$, or $kg m^2/s^3$, aka $Watts$.</p>
<p>Fine so far -- but now take a plank (holding the push-up position for some time). Obviously when you do a plank, you are expending some energy, even though you are not doing any work (since there is no change in potential energy). What are you doing then? You are counteracting the force of gravity on your body mass (that is, $9.8 [m/s^2] * mass [kg]$) for a fixed time. This would produce units of $kg m/s^3$ -- these units are not named, that I can recall.</p>
<p>So my question is twofold:</p>
<ol>
<li>Is there an actual unit that describes the energy I've expended in doing a plank, beyond $(mass * g * time) kg m/s^3$</li>
<li>Is there any meaningful way to <em>compare</em> the energy I've expended by doing a plank, with the energy I would expend in doing $x$ pushups? (Beyond <em>work</em> or <em>power</em>, since those values are always <em>zero</em> for the plank, which is not helpful.)</li>
</ol>
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<p>For example, could the numbers / letters on a postage stamp in a randomly specified location be clearly visible from space.</p>
<p>This is to settle a discussion with a friend that piqued my curiosity. </p>
| 7,531 |
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<p>I was thinking about my answer to <a href="http://physics.stackexchange.com/questions/25431/are-the-inner-planets-on-planar-orbits-because-there-was-more-dust-in-the-inner">Are the inner planets on planar orbits because there was more dust in the inner solar system (early on in planetary accretion)?</a>
- when it occurred to me that maybe I was reversing cause and effect. Specifically, that perhaps spiral galaxies simply arise from high-angular-momentum progenitors, while elliptical arise from low angular-momentum progenitors. In this scenario, the spiral wave-pattern would merely be how that excess angular momentum organizes itself, and the matter can't help but stir itself.</p>
<p>For a warm-up question and consistency checker, do spiral galaxies in fact have substantially greater total angular momentum than elliptical?</p>
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<p>As far as I know, astronomy is generally an observational science. We see something and then try to explain why it is happening. The one exception that I know of is black holes: first it was thought of, then it was found.</p>
<p>Einstein's relativity is middle ground to me, he thought of light beams at the speed of light but obviously could observe gravity's effects.</p>
<p>Anyway, I guess my question is, what are the biggest discoveries that were thought of before they were seen in the sky? </p>
| 7,533 |
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<p>As I understand it, Stars emit visible light, OBAFGKMRNS, in the range of $10^3 - 10^4 K$.
Yet materials such as steel emit similar frequencies at much lower temps; red is around 800K.
Why the difference? I thought black body radiation applies to all materials and environments.
I am an interested amateur. </p>
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] |
<p><img src="http://i.stack.imgur.com/uCrT3.jpg" alt="enter image description here"></p>
<p>The current I is flowing upward in the wire in this figure. The direction of the magnetic filed due to the current can be determined by the right hand rule.</p>
<p>Can we determine the north and the south of the magnetic field produced by the current I by using a hand rule?</p>
| 7,535 |
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<p>Quantum phase arises when a spin-j state is sent through a sequence of transitions that return it to its original position. For example with spin-1/2, a state picks up a complex phase of $\pi/4$ when it goes through three perpendicular (not orthogonal!) transitions:</p>
<p>$\frac{<+z|+y><+y|+x><+x|+z>}{|<+z|+y><+y|+x><+x|+z>|} = e^{2i\pi/8}$</p>
<p>where $|+y>$ means the state with spin-1/2 in the +y direction. Since the above path covers an octant, or one eighth of the surface of a sphere, the total quantum phase for the whole sphere in the spin-1/2 case is $2i\pi$.</p>
<p>More generally, for a spin state $|j,m,+z>$, we will have</p>
<p>$\frac{<j,m,+z|j,m,+y><j,m,+y|j,m,+x><j,m,+x|j,m,+z>}{|<j,m,+z|j,m,+y><j,m,+y|j,m,+x><j,m,+x|j,m,+z>|} = e^{2i n_{jm} \pi/8}$</p>
<p>where $n_{jm}$ is an integer. The same phase is picked up for a spin-1 state with m=1, but a spin-1 state with m=0 picks up no phase at all. (In fact the m=0 states do not depend on the orientation.) At the moment, I believe that the j=1,m=-1 state will pick up n=-1 (in analogy with the spin-1/2 case), but I haven't bothered to actually run the computation.</p>
<hr>
<p>Yes, Dr. Motl found it. For a journal reference see "Geometric Phases" by Péter Lévay. The appropriate equation is (36) on page 19. Note that our $m$ is his $r-J$.</p>
<p><a href="http://arxiv.org/abs/math-ph/0509064v1" rel="nofollow">http://arxiv.org/abs/math-ph/0509064v1</a></p>
<p>Also, the method of looking at an infinitesimal rotation works because Berry-Pancharatnam phase doesn't depend on stuff like the arbitrary complex phases of spinors and of course there's no preferred region on the sphere of possible orientations for the spin axis.</p>
<p>As an aside, I was convinced that the j=1, m=+-1 case had the same coefficient as the j=1/2,m=+-1/2 case. This was because the geometric phase for light is the same as that for spin-1/2. But now it's clear that this is mixing apples and oranges.</p>
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<p>If the universe didn't have the relativity principle, would it be able to support life?</p>
<p>Life consists of very complicated organisms. The operation of these organisms depends on the laws of physics.</p>
<p>If the laws of physics depended on absolute velocity, then it seems that life would have a more difficult task; organisms would have to adapt their biochemistry to the different absolute speeds of the planet as it moves with or against the motion of the sun around the galaxy.</p>
<p>If the laws of physics depended on the absolute gravitational potential, or on acceleration, then the biochemistry of life would have to adapt to the different accelerations / gravitational potential as life colonized higher altitudes. In addition, there would be a seasonal effect as the earth moves closer and farther away from the sun.</p>
<hr>
<p>I think there's a way this question could be answered quantitatively. Begin with a modification of general relativity such as the post Newtonian parameters. See wikipedia article:<br>
<a href="http://en.wikipedia.org/wiki/Parameterized_post-Newtonian_formalism" rel="nofollow">http://en.wikipedia.org/wiki/Parameterized_post-Newtonian_formalism</a><br>
Now analyze an important biological molecule whose shape is extremely important to life such as <a href="http://en.wikipedia.org/wiki/Hemoglobin" rel="nofollow">hemoglobin</a>. Find out what range of post-Newtonian parameters are compatible with the operation of that molecule.</p>
<p>Unfortunately, I suspect that this is a research problem. If someone solves it, I presume they will publish it.</p>
| 7,537 |
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<p>I just finished reading <a href="http://arxiv.org/abs/physics/0507125" rel="nofollow"> this research</a> about antimatter induced fusion and thermonuclear reactions.
And one conclusion I could make is that very little mass of antimatter (in range of micrograms) is needed to initiate a fusion reaction in lithium-deuteride fuel.</p>
<p>Also, in page 14 in this PDF file, there is a theoretical design of a 1-kiloton antimatter induced fusion bomb.</p>
<p>Now, I actually have 2 questions.
Firstly, 100 grams of lithium-deuteride is used in this theoretical 1 kt design. But according to <a href="http://physics.info/weapons/" rel="nofollow">this</a>, 100 grams of lithium-deuteride should yield 6.4 kilotons not only 1 kiloton, so is there any explanation of this ?</p>
<p>Secondly, since I seem to find only low yield designs of antimatter induced/catalyzed fusion bombs, a doubt about the feasibility of larger yield came to my mind. So, if a single kiloton fusion reaction is feasible with a certain amount of antimatter, then should we consider fusing more fuel with even more antimatter feasible too ?</p>
<p>Note : I completely understand the difficulty of making, handling and storing antimatter, and I am not saying this thing is going to be made any time soon. I am just curious about the physics part behind it.</p>
| 7,538 |
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<p>Several posts and my classes in thermodynamics equate increase in entropy with loss of information. Shannon clearly showed that the information content of a message is zero when its entropy is zero and that its information content increases with increasing entropy. So entropy increase leads to more information, which is consistent with the evolution of the universe from a disordered plasma to one that contains lots of order. Why does physics continue to get the relationship between entropy and information backwards?</p>
| 7,539 |
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<p>In my textbook there are 2 formulas for <a href="http://en.wikipedia.org/wiki/Electric_power" rel="nofollow">electric power</a>:</p>
<p>$$\begin{array}{cccr}
P &=& E/t &\hspace{10pt} (1) \\
P &=& VI. &\hspace{10pt} (2)
\end{array}$$</p>
<p>What is the difference between the 2 formulas? Do they both calculate electrical power? If so, how do you know which formula to use in a given situation?</p>
| 7,540 |
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<p><img src="http://i.stack.imgur.com/kUyg1.png" alt="enter image description here"></p>
<p>A wheel rolling down a hill has two axis of rotation. One is where the center or mass is and the other is the point of contact with the surface which acts as a fulcrum. I was trying to understand how this happens, how it rotates down the hill. What causes friction and torque? Please mind me over this simple issue, but I just want to further understand how things work. My ideas are as follow:</p>
<ul>
<li>
<strong>F1</strong>, the component of gravity, pulls the wheel from the center of mass (<strong>CM</strong>). This pull will create friction <strong>f</strong>. Friction then creates a torque about its center of mass. The object is at the same time rotating around the point where it touches the surface, like a fulcrum, the torque is created with lever-arm <strong>L</strong> and force <strong>W</strong>. </li>
</ul>
<p>I don't know if this is right or not. Maybe one should not consider the component of gravity at all acting on the wheel. If so, what is rotation originated? Is it because the position of the <strong>CM</strong>? Maybe someone can explain better. Thanks you.</p>
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<p>Say I do an an experiment 5 times, each of which gives you a list of data points. Do I fit a curve to each one separately and then average the parameters and their uncertainties? Or do I take the average of all the experiments and then do fit a single curve to that?</p>
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<p>Let's say I have a triangular light source. From that light source I want to calculate a pyramidal frustum (tetrahedron with no apex). How would I calculate the maximum bottom area where light would be visible to the naked eye? And how would I calculate the apparent brightness?</p>
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<p>In the newly released movie "Gravity" the main character is left alone floating in space in spacesuit, in a fast spin. Assuming there are no external forces (no tether, jet-pack etc) the system is closed and the initial angular momentum has to be preserved. However, can the astronaut change the axis of rotation? Say, initially the rotation is around the principal axis going perpendicular to the body in the plane of the shoulders (Fig. A). Can the astronaut, using only his/her body, transition to rotation around the principal axis going along the body (Fig. B)? The body shape is the same in the initial and final position, only the orientation is different.<img src="http://i.stack.imgur.com/iG1UZ.jpg" alt="enter image description here"><a href="http://i.stack.imgur.com/iG1UZ.jpg" rel="nofollow">1</a></p>
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] |
<p>In other words, how strong does gravity have to be to cause Hawking radiation to occur?</p>
| 7,545 |
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<p>I would like to know if mirrors have a quality of "resolution" to them like a regular photograph might, or like a JPEG does.</p>
<p>For example, if you looked to closely, or magnified a photograph, you would soon come to a point where the image blurs, or that which was too far away when photographed is not discernible.</p>
<p>If a high quality microscope was applied to a mirror, would it be possible to observe far-away objects reflected by the mirror, taking only the quality and scope of the microscope into account?</p>
<p>Are there different quality mirrors, all other things (<em>e.g.</em> shape) being the same? </p>
<p>Could you also talk about any loss of luminescence if possible?</p>
<p>Also, do all plane mirror have the same converging/diverging power i.e, the image size will be same on all plane mirrors ? </p>
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<p>Let's look at the measurement problem in the orthodox interpretation of quantum mechanics as an inconsistency between inner and outer treatment of the measurement apparatus. You can always push your boundaries of treating the evolution of your system as unitary further and further. You can say OK, the universe as a whole is evolving unitarily (let's not worry about information loss in a blackhole). So it's up to me to consider the boundary to see the evolution of my system and apparatus together or just my system. And I should be able to work out the reduced density matrix of my system equally in every treatment unambiguously! However, If you treat the apparatus externally, the evolution of the system would be:</p>
<p>$$a|\uparrow\rangle + b|\downarrow\rangle \to |\uparrow\rangle$$
</p>
<p>with probability $|a|^2$ or</p>
<p>$$a|\uparrow\rangle + b|\downarrow\rangle \to |\downarrow\rangle$$
</p>
<p>with probability $|b|^2$.</p>
<p>Whereas, an internal treatment of the apparatus would give</p>
<p>$$|\uparrow\rangle\otimes|\text{ready}\rangle\to U\bigl(|\uparrow\rangle\otimes|\text{ready}\rangle\bigr) = |\uparrow\rangle\otimes|\text{up}\rangle$$
</p>
<p>and</p>
<p>$$|\downarrow\rangle\otimes|\text{ready}\rangle\to U\bigl(|\downarrow\rangle\otimes|\text{ready}\rangle\bigr) = |\uparrow\rangle\otimes|\text{down}\rangle$$
</p>
<p>with $U$ a linear operator, $U(a|\psi\rangle + b|\phi\rangle) = aU|\psi\rangle + bU|\phi\rangle$, which evolves</p>
<p>$$\bigl(a|\uparrow\rangle + b|\downarrow\rangle\bigr)\otimes|\text{ready}\rangle$$
</p>
<p>to</p>
<p>$$U\bigl[a|\uparrow\rangle\otimes|\text{ready}\rangle + b|\downarrow\rangle\otimes|\text{ready}\rangle\bigr] =a|\uparrow\rangle\otimes|\text{up}\rangle + b|\downarrow\rangle\otimes|\text{down}\rangle$$
</p>
<p>However, pushing the boundary after the measuring apparatus gives a difference physics. This could be viewed as a problem with measurement in orthodox quantum mechanics (as opposed to realist or operational strategies to solve the measurement problem)
But I was thinking it's not really an inconsistency within a theory. It's just an inconsistency between two different choices of the internal-external boundaries! I'm not asking about the role of decoherence theory. It sounds to me like the measurement problem wasn't really a problem in the first place! Am I right about that?</p>
<p><strong>update:</strong> It has been pointed out that the question is not clear enough yet. Here is my last attempt: It's believed that for an adequate postulates for quantum mechanics, the inner and outer treatment of measuring apparatus shouldn't affect the physics of the system. Which for the orthodox interpretation of quantum mechanics does. For instance in the Bohm's model this has been resolved by denial of representational completeness. And in Operational interpretation it's bypassed by avoiding talking about physical state of the system. Here the question is <strong>Are we really allowed to change the boundaries?</strong> Because if you don't believe you can, the problem will never appear in the first place.
I hope that explains what I'm asking. Because I don't think I can make it more clear :-)</p>
| 7,547 |
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] |
<p>Anyone have good mnemonics for remembering standard packets of data in physics?
Any field within physics would be welcomed. Examples of such "packets":</p>
<ul>
<li><p>data in the standard model of particle physics</p></li>
<li><p>charges/masses of common subatomic particles and light atoms</p></li>
<li><p>cosmological data -- numbers, masses, luminosities
(I recall "Oh Be A Fine Girl/Guy Kiss Me Right Now Smack" for star types)</p></li>
<li><p>thermodynamics</p></li>
<li><p>material properties
(I note also <a href="http://physics.stackexchange.com/questions/75/mnemonics-to-remember-various-properties-of-materials">Mnemonics to remember various properties of materials</a>)</p></li>
</ul>
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] |
<p>Would an object like a wooden bed interfere or block the signal coming from a 802.11 wireless router?</p>
| 7,549 |
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<p>We found that water with salt, sugar, or baking soda dissolved in it cools faster than pure water.<br>
Water has a very high specific heat; how do these solutes lower it?</p>
<p>We heated a beaker (300ml) of water to 90° C and let it cool, checking the temperature every 5 minutes. We repeated the experiment adding a tablespoon of salt. At each 5 minute interval, the temperature was higher for pure water than for salt water. Same result with baking soda and sugar.</p>
| 266 |
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<p>I've just come across Krasinsky and Brumberg's <a href="http://iau-comm4.jpl.nasa.gov/GAKVAB.pdf" rel="nofollow">paper</a> that claims, from an analysis of radiometric measurements, that the astronomical unit (earth-sun distance) is increasing at the rate:</p>
<p>$$\frac{d}{dt}AU = 15 \pm 4 \ m/yr.$$</p>
<p>If one assumes that the Solar system is expanding with the Universe then the Earth-Sun distance is given by:</p>
<p>$$R = R_0 \ a(t),$$</p>
<p>where $R_0$ is the present Earth-Sun distance and $a(t)$ is the scale factor.</p>
<p>From the definition of the Hubble parameter we have:</p>
<p>$$\frac{da/dt}{a} = H.$$</p>
<p>Therefore</p>
<p>$$dR = R_0 da$$</p>
<p>$$dR = R_0 \ a \ H \ dt$$</p>
<p>At the present time $H=H_0$ and $a=1$ so that:</p>
<p>$$dR/dt = R_0 H_0.$$</p>
<p>If I use $R_0=1.49\times10^{11}m$, $H_0=1/13.77\times10^9 yr^{-1}$ and $dt=1yr$ I find:</p>
<p>$$dR/dt = 1.49\times10^{11} \cdot (1/13.77\times10^9)$$</p>
<p>$$dR/dt = 10.8 \ m/yr.$$</p>
<p>Thus the rate of increase of the AU unit might well be explained if the Solar system is expanding like the Universe.</p>
<p>PS Krasinsky seems to dismiss the possibility that his results are explained by cosmic expansion because he somehow derives the rate $dR/dt = 1 \ km/yr$ under such an hypothesis. I can't see how he got that result.</p>
| 251 |
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<p>I can find the energy of a spring using $F = -kx$, or by using the formula $e = 1/2mv^2 + 1/2I\omega^2 + mgh + 1/2kx^2$. The first way, I get $mg/k = x$, but the second way, I get $2mg/k = x$. Which one is correct to use and why?</p>
<p>This is assuming that there is no angular velocity or linear velocity. </p>
| 7,550 |
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<p>Let $\hat{x} = x$ and $\hat{p} = -i \hbar \frac {\partial} {\partial x}$ be the position and momentum operators, respectively, and $|\psi_p\rangle$ be the eigenfunction of $\hat{p}$ and therefore $$\hat{p} |\psi_p\rangle = p |\psi_p\rangle,$$ where $p$ is the eigenvalue of $\hat{p}$. Then, we have $$ [\hat{x},\hat{p}] = \hat{x} \hat{p} - \hat{p} \hat{x} = i \hbar.$$ From the above equation, denoting by $\langle\cdot\rangle$ an expectation value, we get, on the one hand $$\langle i\hbar\rangle = \langle\psi_p| i \hbar | \psi_p\rangle = i \hbar \langle \psi_p | \psi_p \rangle = i \hbar$$ and, on the other $$\langle [\hat{x},\hat{p}] \rangle = \langle\psi_p| (\hat{x}\hat{p} - \hat{p}\hat{x}) |\psi_p\rangle =
\langle\psi_p|\hat{x} |\psi_p\rangle p - p\langle\psi_p|\hat{x} |\psi_p\rangle = 0$$
This suggests that $i \hbar = 0$. What went wrong?</p>
<p><strong>EDIT:</strong> This seemingly little curiosity, as I perceived it initially, evolved into a major problem, as can be seen from the discussion below. Quantum mechanics indeed leads to non-physical results in my opinion and not just to resolvable paradoxes, at that regarding one of its basic claims, the one involving commutators. It seems most of what could be said on this issue has already been addressed below and probably there is no need to continue the exchange here. I would suggest that we discuss it further in the chat.</p>
| 7,551 |
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] |
<blockquote>
<p>Is there any case of potential $V$, such that the continuity of the operator
$H=c\ \Delta+V$
is not spoiled? </p>
</blockquote>
<p>And I don't know any non-differnetial operator examples for continous spectra. I guess I don't know the full spectrum of operators (ba dum tss!).</p>
<p>My question comes about as I wonder about the justification of the term "bounded state", especially in relatoion to the fairly straight forward classical concept.</p>
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<p>There is the idea that there is no time in a completely closed (thus unobservable) system. Within such a system, a subsystem may be imagined to be split off by some virtual boundary. However, one wants to continue to consider the remaining system as if it was the complete system (which of course is not correct). In that case the description of the effects of the subsystem on the remaining system requires "time".</p>
<p>Does anyone know more about this idea?</p>
| 7,553 |
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<p>For a pure species, the equlibrium between liquid phase and vapour phase is given by the equality of molar Gibbs energy in both phase:</p>
<p>$$\underline{G}^l=\underline{G}^v$$</p>
<p>Where $\underline{G}$ with an underline represents molar Gibbs energy.</p>
<p>In a multicomponent system, the equilibrium criterion is the equality of the <strong>partial</strong> molar Gibbs energy (aka chemical potential) for each component between each phases:</p>
<p>$$\overline{G}^l_i=\overline{G}^v_i$$</p>
<p>Now, because of the relation between molar quantities and partial molar quantities, $\underline{G}=\Sigma x_i\overline{G}_i$, the second criterion contains the first by setting $x_i=1$.</p>
<p>My question is : is the first criterion still valid between phases? If yes this would seem to imply that $x_i^l=x_i^v$, which is clearly wrong.</p>
| 7,554 |
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<p>Noether's Theorem states that if a Lagrangian is symmetric for a certain transformation, this leads to an invariant: Symmetry of translation gives momentum conservation, Symmetry of time gives Energy conservation etc.</p>
<p>The Galilean principle stating that all reference frames that move with constant speed relative to each other are equivalent is also a symmetry principle: Setting up a physical system that is identical to the original except for a constant velocity (boost) added will have the same behaviour.</p>
<p>Shouldn't there be an invariant associated with this symmetry? If yes, what is that invariant?</p>
| 252 |
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<p>I have a volume which is deforming (using explicit time-integration scheme) uniformly with velocity gradient $L$ and stress tensor $\sigma$. I would like to determine work done by the volume deformation during one timestep $\Delta t$, knowing both current and previous values of $L$, $\sigma$ and volume $V$.</p>
<p>I've seen somewhere the formula $\Delta W={\mathrm tr}(L\sigma)V\Delta t$, but I don't know if it is correct and how to derive it. $L\sigma$ should be energy density, but why are its non-diagonal terms discarded?</p>
<p><em>Remark:</em> the integration scheme actually is leap-frog, but I ignored mid-step/on-step business for now and supposed everything are on-step values. The formula above would correctly compute the increment mid-step, reading $\Delta W(t-\Delta t/2)={\mathrm tr}\left(L(t-\Delta t/2)\frac{\sigma(t-\Delta t)+\sigma(t)}{2}\right)\frac{V(t-\Delta t)+V(t)}{2}\Delta t$</p>
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<p>I listen to the radio via my iPad with wifi. When I switch the microwave oven on, the radio cuts out. When the microwave oven is finished, the radio comes back on. (This is 100% reproducible!)</p>
<p>So - is it (as I suspect) the microwave oven affecting the wifi? If so, how can that happen (I thought microwaves could not escape the oven)? And (most importantly for me), is it harmful?</p>
<p><strong>Update:</strong> when I stand between the microwave and the iPad, the radio comes back on! :S</p>
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] |
<p>Since low-energy, non-relativistic thermal field theories are defined in Euclidean spacetime, while high-energy relativistic theories are define in Minkowski spacetime, I was wondering if there are renormalization methods that can show such a change in metric signature.</p>
| 7,557 |
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] |
<p>I am interested in the pratical method and I like to discover
if it is cheap enough to be done as an experiment in a high school.
Thank you.</p>
| 7,558 |
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<p>Perhaps someone can suggest the right terms for the following mathematical objects related to moment of inertia?</p>
<ol>
<li>A <em>inertia tensor</em> $I$. $$I \equiv \begin{bmatrix} I_{1,1} & I_{1,2} & I_{1,3} \\ I_{2,1} & I_{2,2} & I_{2,3} \\ I_{3,1} & I_{3,2} & I_{3,3} \\\end{bmatrix}$$</li>
<li>A <em>product of inertia</em> is an off-diagonal entry in the tensor: $I_{1,2} = I_{2,1}$, $I_{1,3} = I_{3,1}$, or $I_{2,3} = I_{3,2}$.</li>
<li>A <em>principal moment of inertia</em> is a diagonal entry in the tensor: $I_{1,1}$, $I_{2,2}$, or $I_{3,3}$. This is the semantic of moment of inertia discussed in elementary treatment of Physics.</li>
<li>What is the term for $I_2$ and $I_3$ in the last line below? $$\begin{align*}
I_{1,1}
&= \sum_{j} m_j\;\left(r^2_{j,2} + r^2_{j,3}\right) \\
&= \sum_{j} m_j\,r^2_{j,2} + \sum_{j} m_j\,r^2_{j,3} \\
I_{1,1} &= I_2 + I_3
\end{align*}$$</li>
</ol>
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<p>I am an undergraduate physics student. I have a question in approximation methods for time-dependent problems in quantum mechanics. I read the proof of the <a href="http://en.wikipedia.org/wiki/Adiabatic_theorem" rel="nofollow">adiabatic theorem</a> but I didn't understand it. This theorem states:</p>
<blockquote>
<p><em>If the Hamiltonian $H(t)$ changes very slowly with time, a system which is initially in a discrete non-degenerate state $u(0)$ with energy $E(0)$ is very likely to go over to the corresponding state $u(t)$ with energy $E(t)$ at time $t$, without making any transition.</em></p>
</blockquote>
<p>Could you present a comprehensive and simple proof for it?</p>
| 7,560 |
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] |
<p><img src="http://i.stack.imgur.com/Z1Sko.jpg" alt="enter image description here"></p>
<p>How do you from 2.8 to 2.10 ? I'm confused :/</p>
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<p>We often find bathroom mirrors get fogged while hot water is used. Looking this up on the internet, we find several easy solutions:</p>
<ul>
<li>use a hot air blower</li>
<li>use a heater behind the mirror</li>
<li>vinegar + water mixture</li>
<li>thin film shaving cream/foam lather</li>
<li>thin film of regular(any) bath soap lather</li>
</ul>
<p>I would like to know:</p>
<p><strong>How does a thin film of soap lather prevent condensation on the mirror surface during a hot shower?</strong></p>
<p>A thread on DIY(StackExchange): <a href="http://diy.stackexchange.com/questions/7933/is-there-a-technique-to-make-a-shower-mirror-fog-free">technique to make a shower mirror fog-free</a>.</p>
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<p>If we accept $E=\hbar \omega$, $p=\hbar k$, and $E^2-(pc)^2=(m_0 c^2)^2$, then we find $$(m_0 c^2)^2 = (\hbar \omega)^2-(\hbar kc)^2 = \hbar (\omega^2 - (kc)^2)=0$$i.e. the rest mass of any particle is $0$. Therefore every particle is a photon. What is wrong with this?</p>
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<p>why is SUSY QM important ? i mean for each one DImensional Hamiltonian , can we write 'H' as</p>
<p>$ H= A.A^{+}+C$ (or similar constant)</p>
<p>here $ A= \frac{d}{dt}+A(x)$ and $ A^{+}= -\frac{d}{dt}+A(x)$</p>
<p>1) can we always express 'x' and 'p' as a combination of A and its adjoint?</p>
<p>2) does SUSY QM makes easier to solve the Hamiltonian</p>
<p>3) can we apply second quantizatio formalism with operators $ A,A^{+}$ in the same way we did for the Harmonic oscillator</p>
<p>4) let be $ Ay(x)=\lambda _{n} y(x) $ an eigenfunction of the anhinilation operator, then is it true that $ E_{n} =C+ |\lambda _{n}|^{2} $ ¿what happens for the eigenfunctions ??</p>
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<p>Gravity is the weakest of the fundamental forces, so what is so special about gravity that it can form an inescapably strong field while a force like the EM force cannot? It seems to me that if there were some extremely strong electric field, that it would only have an influence on particles that carry a charge, and so it would make sense that a black hole could not from from the EM force because it could not affect particles like neutrons. However, the same logic cannot be applied to black holes caused by gravity, because things like photons, which have no mass, still cannot escape the intense gravitational field. Why does gravity influence things that have no "gravitational charge" while the EM force cannot influence things that have no "electric charge." Because otherwise it would follow that a strong enough EM field should be fundamentally inescapable in the same way a black hole is inescapable. I know E=mc^2, so obviously a strong enough EM field would eventually act like a gravitational black hole, but why wouldn't it be easier for an EM black hole to form than a gravitational one since the EM force is so much stronger? </p>
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<p>It follows from special relativity that nothing can travel faster than light. Einstein believed this would have to hold so generally that he assumed the <a href="http://en.wikipedia.org/wiki/EPR_paradox" rel="nofollow">Einstein-Podolsky-Rosen paradox</a> to indicate a contradiction in quantum physics. Nowadays we know we have to be a bit more specific, and maybe it would be safe to say that nothing that can carry information can travel faster than the speed of light.</p>
<p>If information can be transferred faster than light, it would be possible to change the past. If I understand correctly it is the contradictions arising from the hypothetical possibility to influence the past that lead to the assertion that nothing can travel faster than light. </p>
<p>My questions: </p>
<ol>
<li>Is this indeed the reason why it is said to follow from special relativity that nothing can travel faster than the speed of light?</li>
<li>Aren't the contradictions associated to influencing the past more of a philosophical nature than of a purely logical (or at least physical) nature?</li>
</ol>
<p><strong>EDIT</strong></p>
<p>I realize now that instantaneous transfer (action at a distance) is actually physically in contradiction with special relativity: what is instantaneous/simultaneous in one inertial frame is not in the other, so the laws of physics would not be the same. I suspect that for finite velocities faster than that of light there must be a similar argument, I would appreciate if anyone could elaborate on that.</p>
| 7,566 |
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] |
<p>It seems that the entropy for AdS$_2$ black hole is independent of the temperature $s=s_0$. While for near extremal AdS RN black brane, $s=s_0+ s(T/\mu)$. Should not these two entropies be the same since the AdS$_2$ black hole can be thought of a near horizon geometry of near extremal AdS RN black brane? </p>
| 7,567 |
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<p>What is the approximate mass density of dark matter in our solar system at the radius of the Earth's orbit?</p>
<p>I would like some idea of the mass of dark matter going through each cubic meter of material on earth. </p>
| 7,568 |
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<p>I am trying to solve a time dependent perturbation theory problem, and it involves the Hamiltonian
$$H=-\mu B\sigma_z$$
And a perturbation
$$V=-\mu B_1\sigma\cdot(\cos(\omega t)\hat x-\sin(\omega t)\hat y)$$
I want to find the probability that the spin will go from the Ground state of $H_0$ at t=0 to the excited state at time t.</p>
<p>I understand the perturbation theory, I just need to figure out the initial and final states. I thought there were two ground states (either up or down). So what are the excited state and the final state?</p>
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<p>You can use a vacuum cleaner to vacuum the floor but if you tried to vacuum the the air in a small room would this work or will the laws of physics stop this from working in any way?
In what way would attempting to vacuum clean the air be different from using an air scrubber(in terms of physics). </p>
<p>Thanks</p>
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<p>Would not speed of the light emitted from the front of the fast moving object be the speed of light + the speed of the fast moving object? </p>
| 109 |
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<p><img src="http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/imgmag/sol.gif" alt="solenoid"></p>
<p>To calculate the magnetic field, a rectangle amperian loop was drawn, and since the sides of the rectangle are perpendicular to the magnetic field, and the top is too far away to have any field lines cross it, only BL makes a contribution. </p>
<p><img src="http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/imgmag/sol2.gif" alt="equation"></p>
<p>I don't understand why this magnetic field is only contained within the solenoid. Shouldn't the magnetic field at any point on the amperian loop equal μnI, according to Ampere's law?</p>
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<p>I was considering <a href="http://xkcd.com/1366/" rel="nofollow">this</a> xkcd comic from 5/10/14, with the alt-text "Trains rotate the Earth around various axes while elevators shift its position in space." I'm wondering about its accuracy.</p>
<p><img src="http://i.stack.imgur.com/EvUsH.png" alt="http://xkcd.com/1366/"></p>
<p>I first considered the elevator scenario. As the elevator accelerates (to start or stop its motion), the occupants feel a fictitious force, demonstrating conclusively that it is the elevator and not the planet which is in motion. By this argument, an elevator is fundamentally different from a device which physically displaces the planet. Similarly, I suspect that a train doesn't "rotate the Earth," since such a rotation would be felt by occupants on Earth as an angular or centripetal acceleration. Any observer can conclude definitively that it is the train which is in motion around the Earth, not the Earth rotating under the train.</p>
<p>For this reason, is the comic is not strictly correct?</p>
<p>(Note that there is a minimal motion of the Earth resulting from the action-reaction force pair between the train and the planet, but it's safe to say that this motion is negligible relative to the distance traveled by the train, since $I_{earth} \gg I_{train}$.)</p>
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<p>Alright, so David Griffiths in his "Introduction to Electrodynamics" states that the Twin Paradox is not a paradox at all since the traveling twin returns to Earth. By returning to Earth, the twin had to reverse direction, thus undergoes acceleration, and therefore cannot claim to be a stationary observer. </p>
<p>However, what if the traveling twin simply Skypes the twin that is on Earth. The twin on earth will still appear older, which would make no sense since in that case the rocket can be seen as the stationary frame of reference while the Earth "travels" at a speed close to the speed of light. No acceleration is undergone, yet the paradox remains. </p>
<p>Is Griffiths just completely glossing over important nuance again?</p>
| 7,573 |
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<p>From this <a href="http://physics.stackexchange.com/questions/11940/if-you-view-the-earth-from-far-enough-away-can-you-observe-its-past?rq=1">Stack Exchange Physics Post</a>, I am certain that it is possible to view the past. </p>
<p>But then this interesting question came to me.</p>
<p>Is it possible to hear the past?</p>
<p>Ok, you might say, "Well, we are hearing the past, aren't we?" and go onto immense details about the speed of sound against the difference and stuff.</p>
<p>But what if I wanted to hear the sound of a place extremely close by days, weeks, months or even years back?</p>
<p>Would that be possible?</p>
| 7,574 |
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<p>I want to know why different colours appear when viewed with a different angle. Can anyone tell me why?</p>
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] |
<p>What is the origin of electromagnetic interaction between molecules? Anyway, it should have some relation with atoms. Also, These electromagnetic interactions are playing a major role in different properties of matter including the transition between solid-liquid-gas. Hence, what would be the <strong>source</strong> of these interactions..?</p>
<p>If these interactions originate from atoms, then some other questions come into <strong>focus</strong>:</p>
<ul>
<li><p>Are they related to the transition of electrons between various energy levels and emission of photons from an atom..?</p></li>
<li><p>Are they related to <a href="http://en.wikipedia.org/wiki/Cohesion_%28chemistry%29" rel="nofollow">cohesive</a> forces between molecules in solids & liquids?</p></li>
</ul>
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<p>How does quantum electrodynamics actually explain HOW reflection occurs on a microscopic scale? </p>
<p>Note that Feynman's QED lecture series/book is not sufficient, as he only assumes that light DOES reflect ('turn around and go back') in order to expound his path integral theory. My question is why does light have the propensity to turn around in the first place.</p>
<p>Is it just the absorption and re-emission of photons, and if so, why does it happen so uniformly (i.e. on a shiny thing, entire scenes are reflected near-perfectly). In essence, why are flat things shiny? Are all the molecules arranged at exactly the same angle?</p>
| 92 |
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<p>I've on many occasions that there are various numbers of 'extra' dimensions above the 4th. However, I've heard that they are 'compacted' or 'folded' tightly and unimaginably small. Now, as I understand, we live in 3 dimensional space coupled with time. So, by extension, those four dimensions should be present all around us and in our universe. Now, if these hypothetical extra dimensions are folded and compacted, obviously smaller than our universe, doesn't that mean that the extra dimensions are 'somewhere' in the universe and contained within it rather than enveloping it? </p>
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<p>Recently I was made aware of the following arXiv preprint by Maxim Raykin: <a href="http://arxiv.org/abs/1204.1540">Analytical Quantum Dynamics in Infinite Phase Space</a>. As far as I understand it, Raykin's idea is to reinterpret quantum mechanics as a theory of ordinary classical particles moving around in R<sup>3</sup> -- except with the twist that now the differential equation governing the particles takes as input not only their positions and the first derivatives of the positions, but all the higher derivatives as well. Once you decide to look for this sort of "evolution rule," Raykin says that you can find a not-even-very-complicated one that perfectly reproduces all the predictions of QM, at least in the (special?) case that the wavefunctions are analytic. Indeed, the differential equation that you get, describing the particle trajectories, ends up being identical to the guiding equation in Bohmian mechanics. However, the key difference from Bohmian mechanics is that here one makes no explicit reference to any "wavefunction" or "guiding field" -- only to all the higher derivatives of the "actual" particle positions.</p>
<p>On this account, Raykin wants to explain "quantum nonlocality" as arising from the fact that an analytic function is determined by its collection of higher derivatives at any point. The idea, I suppose, is that you can't specify all the higher derivatives of the positions of the particles in Alice's lab, without also knowing what's going on in Bob's lab. While Raykin <i>doesn't</i> discuss this, I imagine one could also explain the exponentiality inherent in (say) quantum computing, in terms of the fact that given n particle positions x<sub>1</sub>,...,x<sub>n</sub>, the number of tuples (k<sub>1</sub>,...,k<sub>n</sub>) for which one can form the combined derivative</p>
<p>$\frac{d^{k_1}}{dx_1^{k_1}} ... \frac{d^{k_n}}{dx_n^{k_n}}$</p>
<p>increases exponentially with n, even after a finite cutoff is imposed on max{k<sub>1</sub>,...,k<sub>n</sub>}. In any case, there has to be <i>some</i> explanation, since (just like in Bohmian mechanics) this account is specifically constructed to give exactly the same predictions as standard QM.</p>
<p>Look: if you follow the quant-ph arXiv, you see another revolutionary solution to the conceptual problems of QM trumpeted every week. Most of those solutions can safely be rejected on the ground that they contain no new idea, <i>not even a terrible idea.</i> But I was unable to reject the present idea on that ground: this way of thinking about QM seems bizarre to me, but it's not one that I've seen before, nor would it ever have occurred to me.</p>
<p>I can envision at least five possible reactions to Raykin's idea:</p>
<p>(0) There's some error that prevents it from working.</p>
<p>(1) There's no error, but it's a completely uninteresting triviality. <i>Because</i> an analytic function is completely determined by its higher derivatives at any point, Raykin's "differential equation" is really just an elaborate way of stating the tautology that a particle's future trajectory is completely determined by its future trajectory. Obviously, that would be true <i>regardless</i> of what the trajectories were (provided only that they're analytic): nothing specific about QM is being used here. Differential equations that depend on infinitely many derivatives simply lack predictive power. And as for the use of analytic functions' global nature to "explain quantum nonlocality" --- it's no better an explanation than Gerard 't Hooft's "superdeterminism." In both cases, the cosmic conspiracy one needs to posit, with every particle's trajectory mysteriously constrained by every other's since the beginning of the universe, is astronomically worse than the relatively-benign nonlocality (e.g., Bell inequality violations) that one was trying to explain in the first place.</p>
<p>(2) Sure, the fact that QM can be formulated in this way is a tautology, but it's a kind of <i>cute</i> tautology, one that could conceivably provide useful insights.</p>
<p>(3) This is a genuinely new reformulation of quantum mechanics, in the same sense that (say) Bohmian mechanics was -- so it's important in a similar way, regardless of whether you like it philosophically.</p>
<p>(4) [Raykin's own view, apparently] This is the true, unique solution to the measurement problem, which resolves all known conceptual problems with QM, is a necessary stepping-stone to quantum gravity, etc. etc.</p>
<p>Of the five views above, the only one that I feel extremely confident in rejecting is (4). Since Raykin's paper appears to have gotten zero (public) reaction so far, my question is the following:</p>
<p><b>Does anyone else have thoughts or observations that would support or rule out reactions (0), (1), (2), or (3)?</b></p>
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<p>We could use either the current configuration $x$ or the displacement $u$ as unknown while solving for the deformation, for example, of a solid object. I want to know what's the difference between them? Is it that there is no difference, or one is numerically better than the other?</p>
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] |
<p>I need a full explantation for this concept.</p>
<p>Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid.</p>
| 7,580 |
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<p>Consider a scalar field $\phi$ described by the Klein-Gordon Lagrangian density
$L = \frac{1}{2}\partial_\mu \phi^\ast\partial^\mu \phi - \frac{1}{2} m^2 \phi^\ast\phi$.</p>
<p>As written in every graduate QM textbook, the corresponding conserved 4-current $j^\mu = \phi^\ast i \overset{\leftrightarrow}{\partial^\mu} \phi$ gives non-positive-definite $\rho=j^0$. If we are to interpret $\phi$ as a wave function of a relativistic particle, this is a big problem because we would want to interpret $\rho$ as a probability density to find the particle.</p>
<p>The standard argument to save KG equation is that KG equation describes both particle and its antiparticle: $j^\mu$ is actually the charge current rather than the particle current, and negative value of $\rho$ just expresses the presence of antiparticle.</p>
<p>However, it seems that this negative probability density problem appears in QFT as well. After quantization, we get a (free) quantum field theory describing charged spin 0 particles. We normalize one particle states $\left|k\right>=a_k^\dagger\left|0\right>$ relativistically:</p>
<p>$$ \langle k\left|p\right>=(2\pi)^3 2E_k \delta^3(\vec{p}-\vec{k}), E_k=\sqrt{m^2+\vec{k}^2} $$</p>
<p>Antiparticle states $\left|\bar{k}\right>=b_k^\dagger \left|0\right>$ are similarly normalized.</p>
<p>Consider a localized wave packet of one <strong>particle</strong> $\left| \psi \right>=\int{\frac{d^3 k}{(2\pi)^3 2E_k} f(k) \left| k \right>}$, which is assumed to be normalized. The associated wave function is given by</p>
<p>$$ \psi(x) = \langle 0|\phi(x)\left|\psi\right> = \int{\frac{d^3 k}{(2\pi)^3 2E_k} f(k) e^{-ik\cdot x}} $$</p>
<p>$$ 1 = \langle\psi\left|\psi\right> = \int{\frac{d^3 k}{(2\pi)^3 2E_k} |f(k)|^2 } = \int{d^3x \psi^\ast (x) i \overset{\leftrightarrow}{\partial^0} \psi (x)}$$.</p>
<p>I want to get the probability distribution over space. The two possible choices are:</p>
<p>1) $\rho(x) = |\psi(x)|^2$ : this does not have desired Lorentz-covariant properties and is not compatible with the normalization condition above either.</p>
<p>2) $\rho(x) = \psi^\ast (x) i \overset{\leftrightarrow}{\partial^0} \psi(x)$ : In non-relativistic limit, This reduces to 1) apart from the normalization factor. However, in general, <strong>this might be negative at some point x, even if we have only a particle from the outset, excluding antiparticles.</strong></p>
<p>How should I interpret this result? Is it related to the fact that we cannot localize a particle with the length scale smaller than Compton wavelength ~ $1/m$ ? (Even so, I believe that, to reduce QFT into QM in some suitable limit, there should be something that reduces to the probability distribution over space when we average it over the length $1/m$ ... )</p>
| 7,581 |
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] |
<p>The common argument for vanishing Goldstone boson is like, if there is some massless particle generated from the spontaneous symmetry breaking, it should be detected. Since we never saw that, it is not possible.</p>
<p>However, if there is some particle which has not been found, it could be (a) very heavy; (b) very weakly interacting. The Goldstone particle was rejected based on reason (a). Could (b) somehow be true? e.g. as a candidate of dark matter? Or since the Higgs mechanism was confirmed, this possibility (very weakly interacting) is already ruled out?</p>
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<p>Assume that we got a Lagrangian of a classical wave $\phi(x,t)$ and a classical particle $q(t)$. The interaction term in the lagrangian is </p>
<p>$$ L_{int}=\frac g 2 \dot{\phi}(x=q(t),t)$$</p>
<p>It is very likely that this interaction has already been investigated, but I find it hard to search for such a lagrangian on the web. Does someone know an efficient method to search the web for a lagrangian? Or maybe does someone recognize it? </p>
<p>This interaction might be similar to a setup where one catches an atom in a dipole field. Then the field would correspond to the electric/magnetic field. Another similar setup might be catching a dielectric sphere in a standing wave.</p>
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<p>It is well known fundamental behaviour that, <em>oppositely charged bodies attract each other</em> (I don't know whether it applies also for charges of equal magnitude or not), and identical charges repel each other. </p>
<p>It is also well known that, a system of oppositely charged bodies with equal charge in magnitude, has zero net charge. </p>
<p>If a system has oppositely charged bodies, with equal charge in magnitude, it would imply that, there will be zero net charge, and the vector field's had got cancelled each other, like around a current carrying conductor, there is no electric field because, charge on current carrying conductor is zero, as one electron enters the conductor, the other will be leaving the conductor. Now, if there is no field, how could the oppositely charged bodies (of equal charge in magnitude) attract each other, they should not feel any force, isn't? </p>
<p>Taking into account all the above statements, would it imply that, two oppositely charged bodies (of equal charge in magnitude) attract each other?</p>
<p><em>[All statements made, are up to my view. Any correction advisory is welcome]</em> </p>
<p><em>LINKS</em> </p>
<ul>
<li><a href="http://physics.stackexchange.com/questions/81612/what-are-the-fields-produced-around-a-current-carrying-conductor">What are the fields produced around a current carrying conductor?</a> (Provides an idea of whether, there exists a electric field around a neutral body or not, like the current carrying conductor) </li>
</ul>
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<p>Let's say a clothespin is modeled as a simple torsion spring as follows.</p>
<p><strong>Given:</strong></p>
<ul>
<li>$p_1,\ p_2,\ p_3$: point-like objects of equal mass in 2-D space.</li>
<li>All objects float in space, i.e. the center of mass will not change.</li>
<li>At time $t_0$ a torsion spring is inserted at $p_1$, such that it exerts torque on $p_2$ and $p_3$, with:
<ul>
<li>$\theta$: the angle of twist from its equilibrium position in radians</li>
<li>$\kappa$: the spring's torsion coefficient</li>
<li>$\tau = -\kappa \theta$ is the torque exerted by the spring</li>
</ul></li>
</ul>
<p><strong>Question:</strong> what are the resulting forces on $p_1$, $p_2$ and $p_3$?</p>
<p><strong>My answer:</strong>
Because all objects have equal mass, we can leave mass out of the equation.
F2 is a force perpendicular to $p_1,\ p_2$ of magnitude $\dfrac{\tau }{ |p_1-p_2|}$ .</p>
<p>By Newton’s 3rd law, F2’ is a force of equal magnitude and opposite direction as F2
Similar for F3 and F3’</p>
<p><img src="http://i.stack.imgur.com/seUSe.png" alt="Torsion spring at p1 exerting torque on p2 and p3"></p>
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<p>Imagine two parallel conductive plates. Charge up both to have the same amount of positive charge. Then put positive test particle between the two.</p>
<p>The Coulomb's law is an inverse square law, so one might think the positive test particle is repelled from the nearby plane and accelerated towards the middle between the plates making it do an oscillating motion (until it radiates away it's energy due to the acceleration and stops in the middle).</p>
<p>On the other hand, since the two plates have the same charge, there is no voltage between the plates that would do work on the electric charge. So it won't move at all.</p>
<p>I'm a confused here. Is Coulomb's law just a special case for 2 point charges? </p>
| 7,586 |
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<p>If I have a drum floating in water, how do I find the equivalent spring constant?</p>
<p>I know that the water has density $\rho$, the drum has diameter $d$ and height $\ell$, and the positive direction is in the downward direction. Therefore, the buoyancy pushing up on the barrel is my spring.</p>
<p>I have been reading the section of this topic in Mechanical Vibrations by Rao but there isn't any information that helps me figure this out.</p>
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<blockquote>
<p>Quantum mechanics (QM; also known as quantum physics, or quantum theory) is a branch of physics which deals with physical phenomena at nanoscopic scales where the action is on the order of the Planck constant.</p>
</blockquote>
<p>-wiki</p>
<p>Time is much less finite than matter. Matter can be split to the point where it is so small that it gains the classification of nanoscopic and subatomic. However the Planck constant is a measurement of mass and time so I find it difficult to separate the measurements. What measurement of time is so small that it qualifies as quantum? Could someone clear up the misconception? </p>
| 7,588 |
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-0.01659398525953293,
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-0.05930838733911514,
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-0.037400368601083755,
0.028305020183324814,
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-0.006489197723567486
] |
<p>Normal <a href="http://en.wikipedia.org/wiki/Surface_wave">surface water waves</a>, as generated by <a href="http://en.wikipedia.org/wiki/Ocean_surface_wave">wind</a>, do not have sine form but wave peak is higher and shorter than wave trough with different wave steepness. What parameters characterize such a surface water wave and how can one predict amplitude of water for given waves as function of time?</p>
| 7,589 |
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<p>I know that the <a href="http://en.wikipedia.org/wiki/Generalized_coordinates" rel="nofollow">generalized coordinates</a> obtained after taking into account the constraint forces are independent. How can I prove this?</p>
| 7,590 |
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<p>Given that a worldline, worldsheet, worldvolume, are representation in a 4D-spacetime of a point particle, a string or a <a href="http://en.wikipedia.org/wiki/Membrane_%28M-theory%29" rel="nofollow">brane</a>, respectively, I was wondering if those objects necessarily have to be static in spacetime, or if they are allowed to move.</p>
<p>If they can move, what dimension is being used to measure their changes in position?</p>
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<p>I'm tutoring senior high school students. So far I've explained them the concepts of atomic structure (Bohr's model & Quantum mechanical model) very clearly. Now the next topic to be taught is semiconductors.</p>
<p>I myself am not conviced with the concept of electron holes. If there is no electron then there is no electron. How can it be a hole. We define a hole when there is some thing every where except at a place. But inside an atom how can we define a HOLE.</p>
<p>Kindly explain it with the help of Bohr's model.
What was the need of introducing such abstract concept in semi conductors? </p>
| 834 |
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