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<p>If a spring is cut up into n pieces, does the spring constant also change for these cut pieces?
I know spring constant is inversely proportional to deformation but is the same true for even the true length of the spring?</p> | 194 | [
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<p>Suppose we have a finite , discrete set of orthonormal states $|k\rangle $</p>
<p>We can construct raising and lowering operators intuitively, for example $$a_+ =\sum_{k=1}^nC_{k+1}|k+1\rangle \langle k|$$</p>
<p>However most textbooks begin by defining ladders in terms of the linear combinations of hermitian operators. </p>
<p>How do we get from the above construction to showing that such ladder operators have the form $$a_\pm = \frac{\alpha\pm i\beta}{\sqrt{2}}$$ where $\alpha,\beta$ are hermitian?</p> | 5,466 | [
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<p>What equation would give me the answer to the question, "If i have a cup of water at a tempature of say boiling, how long would that cup of water take to cool off compared to say half that size of a cup of water." So the volume is in half. Its a general question I am just looking for where to start.</p> | 5,467 | [
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<p>I've read the definition of the electromagnetic field tensor to be
\begin{equation}F^{\mu\nu}\equiv\begin{pmatrix}0&E_x&E_y&E_z\\-E_x&0&B_z&-B_y\\-E_y&-B_z&0&B_x\\-E_z&B_y&-B_x&0\end{pmatrix}\hspace{0.5in}(\dagger)\end{equation}
in <em>Introduction to Electrodynamics</em> by David Griffiths, or as
$$F_{\mu\nu}\equiv\begin{pmatrix}0&-E_x&-E_y&-E_z\\E_x&0&B_z&-B_y\\E_y&-B_z&0&B_x\\E_z&B_y&-B_x&0\end{pmatrix}$$
on the <em><a href="http://arxiv.org/abs/gr-qc/9712019" rel="nofollow">Lecture Notes on GR</a></em> by Sean Carroll, which I know to be consistent via ${F_{\mu\nu}=\eta_{\mu\alpha}F^{\alpha\beta}\eta_{\beta\nu}}$ where the metric $\eta_{\rho\sigma}$ has a (-+++) signature.</p>
<p>However <a href="http://en.wikipedia.org/wiki/Electromagnetic_tensor" rel="nofollow">on Wikipedia</a> and other sources (sorry I can't remember) they use a (+---) signature and they define the EM tensor to be the negative of ${(\dagger)}$.</p>
<p>These are my thoughts about it:
The antisymmetry $F^{\mu\nu}=-F^{\nu\mu}$ may point out that it's just an unfortunate mix of index letters and that for the sources notation to be consistent, either the first two or Wikipedia should change $\mu\nu$ to $\nu\mu$. If not the case, the properties seem to be the same; at first I thought the inner product would pop out a minus sign of difference, but it of course didn't happen, and as for other entities I've worked with, e. g. the 4-velocity, though the metric signature can change, the contravariant vector is the same in either case. However again, I've read the stress-energy tensor does change sign depending on the signature.</p>
<p>So is the signature of the metric involved in the definition of ${F^{\mu\nu}}$ or any tensor whatsoever? If so, how can I know what signature is involved? or if not, what's the matter with the minus sign difference on the definitions?</p> | 5,468 | [
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<p>The expression $\int | \Psi\left(x\right)|^2dx$ gives the probability of finding a particle at a given position. </p>
<p>If wave function gives the probabilities of positions, why do we calculate "expectation value of position"?</p>
<p>I don't understand the conceptual difference, we already have a wave function of a position. Expectation value is related to probabilities. </p>
<p>So what is the differences between them? And why do we calculate expectation value for position, although we have a function for probability of finding a particle at a given position?</p> | 5,469 | [
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<p>I've understood that the Cosmic Background Radiation(CBR) is an electromagnetic wave that originated from the big bang. However, we now live on a planet which that is also originating from the big bang.</p>
<p>Why does that Cosmic Background Radiation reaches us now? Why does CBR reaches us now, and not a couple of billion years earlier?</p> | 5,470 | [
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<p>It's well known that the planets don't orbit the sun in perfect circles and the characteristics of the elliptical orbits which serve as better approximations to their motion have been calculated fairly accurately.</p>
<p>How accurately do elliptical orbits model their actual paths?</p> | 5,471 | [
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<p>What is meant with the fact that Super Yang-Mills flows to a conformal field theory in the infrared? Also, is this a general fact or does this depend on the fact of considering a certain class of theories (such as $N=4$, $d=3$ for example)?</p>
<p>I have seen this statement numerous times in various articles such as</p>
<p><a href="http://arxiv.org/abs/hep-th/0207074">http://arxiv.org/abs/hep-th/0207074</a></p>
<p><a href="http://arxiv.org/abs/hep-th/0206054">http://arxiv.org/abs/hep-th/0206054</a></p>
<p>Every time this fact is stated by some author it is given as a known thing, and it is not explained.
With an online research I could not make sense of this.</p>
<p>Could someone please explain?</p> | 5,472 | [
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] |
<p>How would I calculate the uncertainty for the average of this set?</p>
<p>$32.5 \pm 0.1$</p>
<p>$32.0 \pm 0.1$</p>
<p>$32.3 \pm 0.1$</p> | 5,473 | [
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] |
<p>Is there a real difference between <a href="http://en.wikipedia.org/wiki/Eternal_inflation" rel="nofollow">eternal inflation</a> and "chaotic inflation" theories? </p> | 5,474 | [
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<p>I'm trying to come up with an expression for the partition function of a system of spin-1/2 ideal gas particles on a line of length $L$. The total number of particles $N$ is fixed, with $N = N_\uparrow + N_\downarrow$. Here, $N_\uparrow$ is the number of spin-up particles and $N_\downarrow$ is the number of spin-down particles in a particular microstate.</p>
<p>I have the following Hamiltonian for the particles of mass $m$.</p>
<p>$$H = \sum_{i=1}^{N}{\frac{(p_i + \beta s_i)^2}{2m} -b s_i} $$</p>
<p>Here, $s_i = 1$ for the spin-up $N_\uparrow$ particles and $s_i = -1$ for the spin-down $N_\uparrow$ particles. $\beta$ and $b$ are constants.</p>
<p>I'm trying to use the Hamiltonian to write down the energy for the spin-up and spin-down particles so I can write down the partition function. If I expand the Hamiltonian, I get:</p>
<p>$$H = \sum_{i=1}^{N}{\frac{p_i^2}{2m} + \frac{p_i \beta s_i}{m} - b s_i + \beta^2} $$</p>
<p>How do I find the energy of the two sets of spin particles from this and use it to come up with the partition function? Is the energy of the particles just?</p>
<p>$$E_\uparrow = \frac{p_i^2}{2m} + \frac{p_i \beta}{m} - b + \beta^2$$
$$E_\downarrow = \frac{p_i^2}{2m} + \frac{-p_i \beta}{m} + b + \beta^2$$</p>
<p>How would one evaluate this in the canonical partition function:</p>
<p>$$Z = \sum_{\mu_s}e^{-\beta H}$$</p>
<p>where $\mu_s$ is the summing over all microstates. I'm not sure how to evaluate this.</p> | 5,475 | [
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<p>According to the Newtons gravity we can write,
$$\vec F = \frac{\hat r_{12} G m_1 m_2 }{r_{12}^2}$$ and we are well known that this law satisfies the planetary motions. What changes will we see if we rewrite the law in this way,
$$\vec F = \frac{\hat r_{12} G m_1 m_2 }{r_{12}^{2+p}}$$ where p is a positive number. I mean shape of the arbit, angular and linear momentum etc. </p> | 5,476 | [
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<p>According to Einstein's theory of relativity, the more speed something has the slower that time passes for it; and presumably when traveling at the speed of light, time stops entirely. So this means that when a photon is created, the rest of existence virtually pauses until the photon ceases to exist, and then the rest of existence begins again. If time is stopped while the photon exists, then what are we measuring when we measure light? In order to measure the actual photon, we would need to take the measurement while time was standing still. Speed requires time, so why do we say that light travels at a speed?</p> | 195 | [
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<p>We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's principle) and even General Relativity (we get Einstein's equation from the Einstein-Hilbert action). However, how do we explain this very principle, i.e., more mathematically, I want to ask the following: <br/></p>
<blockquote>
<p><em>If I am given a set of generalized positions and velocities, say, $\{q_{i}, \dot{q}_{i}\}$, which describes a classical system with known dynamics (equations of motion), then, how do I rigorously show that there always <em><strong>exists</strong></em> an action functional $A$, where</em>
$$A ~=~ \int L(q_{i}, \dot{q}_{i})dt,$$
<em>such that $\delta A = 0$ gives the correct equations of motion and trajectory of the system?</em> <br/></p>
</blockquote>
<p>I presume historically, the motivation came from Optics: i.e., light rays travel along a path where $S = \int_{A}^{B} n ds$ is minimized (or at least stationary). (Here, $ds$ is the differential element along the path). I don't mind some symplectic geometry talk if that is needed at all.</p> | 5,477 | [
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<p>A bucket is filled with water and a handful of sand. The water is then spun. Why and what forces are in play which cause the sand particles to congregate in the centre of the bucket?</p> | 196 | [
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<p>When walking, if I apply a force of 2N on the earth, the earth applies a force of 2N back on my feet due to Newtons 3rd Law of Motion. These 2 forces are equal in magnitude but opposite in direction, so they negate each other and add up to zero. So how can we move then if the net force adds up to zero? </p> | 197 | [
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] |
<p><em>For topological insulators</em>
<strong>Is there any way to define <a href="http://www.google.com/search?as_q=order+parameter+topological+phase+transition" rel="nofollow">order parameter for topological phase transitions</a>?</strong></p> | 5,478 | [
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<p>In an arbitrary number of dimensions, one can naturally define two tensors, Kronecker delta and Levi-Civita epsilon tensor. However, why isn't it advantageous to define some totally symmetric tensor as well? Is there an intuitive reason for that or is it basically related to differential forms?</p> | 5,479 | [
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<p>I read that Wu's experiment illustrates that parity violation is possible for weak processes. In that experiment, when Co-60 undergoes beta decay, the emitted electrons come out opposite to the direction of nuclear spin. The mirror image process does not occur.</p>
<p>I also read that parity is conserved for EM and strong processes. But consider the following from EM. Say I have a positively-charged particle moving to the right, and the magnetic field is into the page. Then force on the particle is up (i.e. the particle is accelerated upwards initially). And here, the mirror image also does not occur! The mirror image (the mirror I am thinking of lies in the plane that cuts your head between the eyes) would be moving left, magnetic field into page, acceleration still pwards - but EM would predict that the acceleration is supposed to be downwards!!</p>
<p>Why isn't this an example of parity violation?</p> | 5,480 | [
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<p>I'm interested in designing and building a Stirling engine which uses air that has been heated, which expands and then acts upon a piston producing power. </p>
<p>There is a fixed amount of air inside the sealed 2" cylinder, and a relatively stable heat supply. The piston compresses cool air and is powered by the expanding, heated air.</p>
<p>Two questions here:</p>
<ol>
<li><p>How to find the power needed to compress air inside the 2" diameter cylinder to different depths?</p></li>
<li><p>Depending on the amount of compression produced by the piston, how does that affect the rate of expansion of the heated air?</p></li>
</ol>
<p>If the power needed to compress the air to a certain pressure exceeds the net power output of the expanding air, then the engine won't function. So, I need to calculate the stroke of the piston inside the cylinder to a depth that the engine can use efficiently. </p>
<p>Thanks.</p> | 5,481 | [
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<p><img src="http://i.stack.imgur.com/h8s8B.png" alt="enter image description here">
Consider a cell containing Rubidium and enlight it with a laser. Connect the system with an oscilloscope and give a triangular wave as input (so you can know when the Rubidium is resonant). This is the signal that you see downward. You can see the output in the upper signal. It is given by the difference between input signal and the signal received by the photodiode... Looking at the spectral line relative to D2 rubidium transition, the oscilloscope gives me this picture. </p>
<p>I need a pragmatic hint. I have to measure the Doppler broadening so I need to convert time scale to frequency scale. </p>
<p>How can I do that?
Thanks a lot!</p> | 5,482 | [
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<p>Suppose I would like to have maximally physical image format. Which quantities should I store in the pixel? Obviously, it should be frequency spectrum, i.e. table with frequency vs. WHAT?</p>
<p>How to convert RGB values to any sort of physical quantities and vise versa?</p> | 5,483 | [
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<p>A charge is at rest in an inertial reference frame. </p>
<p>Consider this situation from the point of view of an observer who is accelerating relative to the charge. Would the observer observe electromagnetic waves generated by the charge?</p> | 5,484 | [
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<p>I found this explanation somewhere:
Since wavelength=c/freq so in a AC power line of 50 Hz, wavelength=(3*10^8)/50 = 6000 Km, so voltage phase reverses after 6000 Km in a ac Power line.</p>
<p>Now this would have been correct if it was a 50 Hz E.M. Transmission line, but does the same occur in metal wire with A.C. ? Clearly the power transmission through the wire would not be through E.M. waves. I am also confused if a wave phenomenon does occur in a AC wire or not. If it occurs then how (in terms of flow of electrons) and at what speed/wavelength ?</p> | 5,485 | [
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<p>Suppose we have a capacitor of capacitance $C$ and a cell of emf $E$, why is the maximum energy stored in a capacitor equal to $\tfrac{1}{2}CE^2$? I feel confused because, the potential difference against the capacitor will be less than the emf of the cell because of the potential drop across the resistor. What is the flaw in my thinking?</p> | 5,486 | [
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] |
<p>How to prove the identity
$$
\tilde {\sigma}_{\alpha}\sigma_{\beta}\tilde {\sigma}_{\gamma} = g_{\alpha \beta}\tilde {\sigma}_{\gamma} + g_{\alpha \gamma}\tilde {\sigma}_{\beta} - g_{\beta \gamma} \tilde {\sigma}_{\alpha} + i\varepsilon_{\alpha \beta \gamma \delta}\tilde {\sigma}^{\delta}, \qquad (1)
$$
where
$$
\sigma_{\alpha} = (\hat {\mathbf E}, \sigma ), \quad \tilde {\sigma}_{\beta} = (\hat {\mathbf E}, -\sigma ), \quad \varepsilon_{\alpha \beta \gamma \delta } = -\varepsilon_{\beta \alpha \gamma \delta} = ..., \quad \varepsilon_{0123} = 1, \quad g_{\alpha \beta} = diag(1, -1, -1, -1)?
$$
I tried to do this by constructing the relation
$$
\sigma_{\alpha}\tilde {\sigma}_{\beta} = g_{\alpha \beta}\sigma_{0} + i\varepsilon_{0\alpha \beta \gamma}\sigma^{\gamma} - \delta^{0}_{\alpha}(\delta^{0}_{\beta}\sigma_{0} - \tilde {\sigma}_{\beta}) - \delta^{0}_{\beta}(\delta^{0}_{\alpha}\sigma_{0} - \sigma_{\alpha}),
$$
where first summand corresponds to $\alpha = \beta$, the second - to $\alpha , \beta \neq 0$, the third - to $\alpha = 0, \beta \neq 0$, the last - to $\beta = 0, \alpha \neq 0$, and $\sigma^{\mu} = g^{\mu \nu}\sigma_{\nu}$.</p>
<p>But I can't get the answer in a compact form of $(1)$ by using my construction. In particular, I don't understand how $\varepsilon_{\alpha \beta \gamma \delta}$ is appeared in the final answer. </p>
<p>An edit.</p>
<p>I proved it, but the proof is terrible.</p> | 5,487 | [
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<p>I am solving a Hamiltonian including a term $(x\cdot S)^2$.
The Hamiltonian is like this form:
\begin{equation}
H=L\cdot S+(x\cdot S)^2
\end{equation}
where $L$ is angular momentum operator and $S$ is spin operator. The eigenvalue for $L^2$ and $S^2$ are $l(l+1)$ and $s(s+1)$. </p>
<p>If the Hamiltonian only has the first term, it is just spin orbital coupling and it is easy to solve. The total $J=L+S$, $L^2$ and $S^2$ are quantum number. However, when we consider the second term position and spin coupling $(x\cdot S)^2$, it becomes much harder. The total $J$ is still a quantum number. We have $[(x\cdot S)^2, J]=0$. However, $[(x\cdot S)^2,L^2]≠0$, $L$ is not a quantum number anymore.</p>
<p>Anybody have ideas on how to solve this Hamiltonian?</p> | 5,488 | [
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<p>Whenever I have seen Venus described, its high surface temperature is attributed to an intense greenhouse effect. This seems to make sense, as its atmosphere is roughly 96% CO<sub>2</sub>. But on Earth, the greenhouse effect works because the atmosphere is (mostly) transparent to sunlight, but (somewhat) opaque to longer wavelength light radiated back from the surface.</p>
<p>The atmosphere of Venus would be very opaque to longer wavelength light from the surface, just like Earth (at least around the CO<sub>2</sub> absorption bands). But isn't Venus also very cloudy and largely opaque to visible light? If the solar radiation that reaches the surface is limited, wouldn't this also limit the ability of the CO<sub>2</sub> to "trap" heat?</p>
<p>The atmospheric pressure at the surface of Venus is much higher than it is at the surface of Earth. Isn't this a more straight-forward explanation for much of the high temperature?</p> | 5,489 | [
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] |
<p>I'm having a hard time understanding the deal with <a href="http://en.wikipedia.org/wiki/Self-adjoint_operator" rel="nofollow">self-adjoint differential opertors </a> used to solve a set of two coupled 2nd order PDEs.</p>
<p>The thing is, that the solution of the PDEs becomes numerically unstable and I've heared that this is due to the fact, that the used operators were not self-adjoint and the energy is not preserved in this case.</p>
<p>The two coupled 2nd order PDEs are:</p>
<p>$$\frac{\partial ^2p}{\partial t^2}=V_{px}^2 {H_2} p + \alpha V_{pz}^2 {H_1} q + V_{sz}^2{H_1}(p - \alpha q) + S\tag{1}$$</p>
<p>$$\frac{\partial ^2q}{\partial t^2}=\frac{V_{pn}^2}{\alpha}{H_2} p + V_{pz}^2 {H_1} q - V_{sz}^2{H_2} \left(\frac{1}{\alpha}p - q \right) + S\tag{2}$$</p>
<p>where p is the pressure wave field and q is an auxiliary wave field, $S$ is the Source term $V_{px}$ and $V_{sz}$ are seismic velocities into the x - or z-direction respectively, $\alpha = 1$ and $H_1$ and $H_2$ are the rotated differential operators:
\begin{eqnarray}
{H_1}& =& \sin ^2 \theta \cos ^2 \phi \frac{\partial ^2}{\partial x ^2}+\sin ^2 \theta \sin ^2 \phi \frac{\partial ^2}{\partial y ^2} + \cos ^2 \theta \frac{\partial ^2}{\partial z ^2}+\\ &&\sin ^2 \theta \sin 2 \phi \frac{\partial ^2}{\partial x \partial z} + \sin 2 \theta \sin \phi \frac{\partial ^2}{\partial x \partial y}+ \sin 2 \theta \cos \phi \frac{\partial ^2}{\partial x \partial y}\end{eqnarray}</p>
<p>$$
{H_2} = \frac{\partial ^2}{\partial x ^2}+\frac{\partial ^2}{\partial y ^2}+\frac{\partial ^2}{\partial z ^2} - {H_1}.
$$</p>
<p>where $\phi$ is an azimuth angle and $\theta$ is a tilt angle.</p>
<p>In this case I am solving for the solution of a pressure wavefield.</p>
<p><strong>EDIT</strong>
Is there a physical explanation for self-adjoint operators?
The paper I am referring to can be found <a href="http://www.cgg.com/technicalDocuments/cggv_0000009953.pdf" rel="nofollow">here</a> were equation 14 and 15 resemble my postet equations.</p> | 5,490 | [
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<p>So, I have a couple questions about transfer orbits.</p>
<p>As I understand it, an object's, say a satellite, orbit is basically tied to it velocity relative to the object, the planet, that it is orbiting.</p>
<p>The basic premise is that you have the satellite in a circular orbit of X radius, going speed v. Now, if the satellite decelerates, it reduces its velocity.</p>
<p>Since the new velocity is not enough to maintain its original orbit, the satellite will "fall" towards the planet. Now, even though the satellite was (say) originally at the proper velocity for the new lower orbit due to the deceleration, by the time it actually arrives at the new orbit, its velocity likely changed, due to the different acceleration vector of the planet, the vector causing the actual fall. Even if it was at the proper velocity, it's actual vector would like be wrong, it would no longer be tangential to the planet, it would likely be steeper. This would effectively cause the satellite to fall right through the lower orbit and keep accelerating toward the planet. Minimally it would not be in the stable orbit desired.</p>
<p>So, this is why there is a second acceleration/deceleration necessary to correct the satellites velocity and perhaps it vector once it reaches the new orbit.</p>
<p>Of course, the opposite all applies if trying to get to a higher orbit.</p>
<p>My question is during the initial deceleration, is that simply applied opposite the current orbital velocity vector? And when the satellite arrives at the new orbit, what direction is the correctional acceleration/deceleration made? Is it the difference of the desired tangential direction that it wants to go and the current direction it is going? or simply opposite its current vector?</p>
<p>I understand that the point of the Hohmann transfer orbits is to use as little velocity change (and thus fuel) as possible, but can an orbital transfer be faster or slower if you're willing to burn more fuel to affect the velocity change? Will a slower satellite "fall faster" than a faster one? Intuitively that makes sense to me, but at the same time there's the concept that no matter how fast the bullet, it hits the ground at the same time, it just travels farther. So I'm not sure.</p>
<p>On the other hand, if you apply more thrust and you're trying to lift to a higher orbit, that seems directly related to the amount of thrust you're willing to use.</p>
<p>Is this how the transfer orbits work? There's the math and formulas to calculate the delta v necessary on both ends of the transfer, but I'm just trying to visualize the process.</p>
<p>Finally, if you had unlimited fuel, and time was more a consideration, would you even bother with this process versus something more "point and shoot, turn and burn"?</p> | 5,491 | [
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<p>Does the axis of Time point into a black hole or away from?</p>
<p>Can you give a reference paper?</p> | 5,492 | [
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<blockquote>
<p>The wheel of a car has a radius of 20 cm. It initially rotates at 120
rpm. In the next minute it makes 90 revolutions. What is the angular
acceleration?</p>
</blockquote>
<p>So the answer is solved by using one of the angular kinematic equations. More specifically delta theta. The problem I am having trouble understanding is the answer which probably stems from my poor fundamentals. </p>
<p>The answer is: (90x2pi) = 4pi(60) + 1/2 (alpha) (60)^2</p>
<p>So where does 90x2pi come from?</p> | 5,493 | [
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<p><em>I have encountered this claim while searching for sources answering " <a href="http://skeptics.stackexchange.com/questions/5310/can-we-see-the-curvature-of-earth-from-the-top-of-worlds-tallest-building">Can we see the curvature of earth from the top of world's tallest building?</a> ".</em></p>
<p>Wikipedia <a href="http://en.wikipedia.org/wiki/Horizon#Curvature_of_the_horizon" rel="nofollow">article on horizon</a> claims (with no references), that compared to a geometrical model, the the apparent curvature of Earth is less than expected due to refraction of light in the atmosphere.</p>
<p>Thinking about the problem, I fail to see why this could be so. It is easy to see the refraction affects a distance of the apparent horizont, but I fail to see how it could affect its curvature, as the refraction seems to have the same effect in all directions, because your distance to horizon is the same in all directions. </p>
<p>Is that claim just bogus and there is no such effect, or is the effect real?</p> | 980 | [
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<p>I want to create a soap blaster using:</p>
<ol>
<li>a 1" hose with 8 bar compressed air</li>
<li>a non pressured container of soap and water mix</li>
<li><strong>without</strong> the use a pressurized tank</li>
</ol>
<p>I.e. something like this <a href="http://www.biltema.no/no/Verktoy/Trykkluft/Verktoy/Sandblasing/Sandblasepistol-17355/" rel="nofollow">sand blaster</a>:
<img src="http://i.stack.imgur.com/khJu3.jpg" alt="enter image description here"></p>
<p>where the sand is picked up from the vacuum of the air flow.
The question is really which laws of physics apply in this creation and how can I calculate the dimensions for my soap blaster with the maximum allowed pickup of soap mixture at the lowest noise level?</p> | 5,494 | [
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<p>Noether's Theorem is used to related the invariance under certain continuous transformations to conserved currents. A common example is that translations in spacetime correspond to the conservation of four-momentum.</p>
<p>In the case of angular momentum, the tensor (in special relativity) has 3 independent components for the classical angular momentum, but 3 more independent components that, as far as I know, represent Lorentz boosts. So, what conservation law corresponds to invariance under Lorentz boosts?</p> | 252 | [
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<p>I'm not a current student at any school, but I am learning a new profession, and some of it is a basic understanding of elecrticity. I have some knowledge, but definitely not enough, and I have had to self teach most of what I know using old textbooks that I have found added to some military experience in ths subject. anyways I'm trying to teach myself how to calculate current through resistors, but I'm having trouble setting up and working through word problems. I know this may seem simple to most people on here, and I apologize for that, but sucking at something is the first step at being sorta good at something.</p>
<p>Examples</p>
<p>A 242Ω resistor is in parallel with a 180Ω resistor, and a 240Ω resistor is in series with the combination. A current of 22mA flows through the 242Ω resistor. The current through the 180Ω resistor is <em>_</em>_mA.</p>
<p>Two 24Ω resistors are in parallel, and a 43Ω resistor is in series with the combination. When 78V is applied to the three resistors, the voltage drop across the 24Ω resistor is___volts.</p> | 5,495 | [
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<p>I learned that neutrinos have a much lower energy than electrons. Pair production of electrons occurs when the photon energy is above 2 times the energy of an electron. So I am wondering if pair production of neutrinos wouldn't be even more common and occur at much lower energy levels?</p> | 5,496 | [
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<p>Given d(slit separation)= $0.158\:\rm{mm}$, $\lambda _{red}= 665\:\rm{nm}$, $\lambda _{g/y}= 565nm$, L(distance from screen)= $2.24\:\rm{m}$</p>
<p>What is the distance between the third order red and green/yellow fringes? </p>
<p>I am using the equation $X _{3}= \frac{m \lambda L}{d}$ (just to find the distance to the third red fringe). My teacher told me this equation is approximate, but I think this is beyond simple approximation error... I keep getting the answer $2.8284 \times 10^{7}\:\rm{m}$. This seems unreasonable; what am I doing wrong? </p>
<p>$\:\rm{m} = \:\rm{mm}\times10^{-13}, \:\rm{m}= \:\rm{nm}\times10^{-9}$, right? </p> | 5,497 | [
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<p>I know that in quantum mechanics there is no "time operator", so such a question is ill-posed. Anyway if the tunneling is instantaneous, this would imply an information transmission faster than $c$. On the other hand, how could someone define such a "time"?</p> | 5,498 | [
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<p>One of the weirdest things about quantum mechanics (QM) is the exponential growth of the dimensions of Hilbert space with increasing number of particles.
This was already discussed by Born and Schrodinger but here's a recent reference:</p>
<p><a href="http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.4770v2.pdf" rel="nofollow">http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.4770v2.pdf</a></p>
<p>and another one:</p>
<p><a href="http://www.scottaaronson.com/papers/are.pdf" rel="nofollow">http://www.scottaaronson.com/papers/are.pdf</a></p>
<p>Another difference between quantum mechanics and classical physics is that QM is discrete.<br>
A good example is the line spectrum of hydrogen.</p>
<p>Is there any good observational example which demonstrates the exponential growth of Hilbert space dimensions?<br>
Even for low numbers?<br>
(Does it perhaps show up in the line spectrum of a three or four valent atom?)</p> | 5,499 | [
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<p>Does increasing the amount of electric charge on a conductor cause an increase in its <em>electric potential</em> to a point at which it becomes maximum; where it can hold no more extra charge?</p>
<p>Is it true? How?</p>
<p>I read it from a book while studying <em>capacitance</em>.</p>
<p>Does this idea sound <em>foolish</em>?</p> | 5,500 | [
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<p>One would say that $AdS_n$ satisfies the equations for the scalar curvature (R) and Ricci tensor ($R_{\mu \nu}$), $R = - \frac{n(n-1)}{L^2}$ and $R_{ab} = - \frac{n-1}{L^2}g_{ab}$. </p>
<ul>
<li>But do the signs in the above depend on the sign of the metric convention? </li>
</ul>
<hr>
<p>I am confused when I look at these two metrics,</p>
<ul>
<li><p>$ds_1^2 = \frac{r^2}{Q^2}dt^2 - \frac{Q^2}{r^2}dr^2$</p></li>
<li><p>$ds_2^2 = \left ( 1 - \frac{\Lambda r^2}{3} \right ) dt^2 - \frac{ dr^2 } { \left ( 1 - \frac{\Lambda r^2}{3} \right ) }$</p></li>
</ul>
<p>Are both the above valid metrics of $AdS_2$? (with what sign of $\Lambda$?)</p>
<p>For the first one has, $R = 2/Q^2$ and $R_{ab} = \frac{1}{Q^2}g_{ab}$ </p>
<p>For the second one has $R = - \frac{2\Lambda}{3}$ and $R_{ab} = -\frac{\Lambda}{3}g_{ab}$</p>
<p>Now I am not sure how to consistently define $L>0$ for these two metrics using the same formula for both!</p> | 5,501 | [
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<p>What's the conserved quantity corresponding to the generator of conformal transformations? </p> | 5,502 | [
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<p><strong>Problem</strong>: For a $P,V,T$ system with constant mass,entropy can be considered a function of $U,V$, i.e. $S=S(U,V)$. The goal is to derive the rest of the thermodynamic functions via Legendre transformations.</p>
<p><strong>Attempted answer</strong>:</p>
<p>I start with the 1st law of thermodynamics $dU = TdS - PdV$, which I solve for $dS$: \begin{equation}dS=(1/T)dU+(P/T)dV\end{equation}</p>
<p>Let, $Y\equiv S,C_1\equiv 1/T,X_1\equiv U, C_2\equiv P/T, X_2\equiv V$.</p>
<p>The first Legendre transformation and the associated differential are:</p>
<p>\begin{equation}\widetilde{T1} = Y - C_1 X_1 = S - (1/T)U\end{equation}</p>
<p>\begin{equation}d\widetilde{T1} = dS - (1/T)dU + (1/T^2)UdT = (P/T)dV +(U/T^2)dT\end{equation}</p>
<p>Therefore $\widetilde{T1} = \widetilde{T1}(V,T)$.</p>
<p>Does this seem correct to you ?</p>
<ol>
<li>Do I stop here for $\widetilde{T_1}$ or is there more to do?</li>
<li>What are the natural variables for $\widetilde{T_1}$? I am a little concerned due to the fact that $T$ is intensive variable and if I recollect correctly, the natural variables are always extensive.</li>
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<p>On a <a href="https://en.wikipedia.org/wiki/Porkchop_plot" rel="nofollow">porkchop plot</a> for a given departure date (X axis), why are there two local energy minimums along the arrival date (Y-axis) for a transfer between Earth and Mars? The Hohmann transfer orbit seems to have one optimal solution, but the plot's two minimums seem fairly distinct in time but similar in energy; 15.0 to 15.5 and 15.5 to 16.0 in terms of C3L (something I only vaguely understand; KSP mostly deals in delta-V)</p>
<p><a href="https://en.wikipedia.org/wiki/File%3aPorkchop_plot.gif" rel="nofollow"><img src="http://i.stack.imgur.com/rer1W.png" alt="Earth to Mars porkchop plot"></a></p>
<p>A <a href="http://mars.jpl.nasa.gov/spotlight/porkchopAll.html" rel="nofollow">NASA page</a> about sending spacecraft to Mars refers to "Type 1" and "Type 2" transfer orbits, which clashes with a perhaps simple view that there should be a singular optimal Hohmann transfer orbit; the smallest ellipse tangent to two orbits. Granted, the planets' orbits are not perfectly circular, but the different transit times (red contours) for local minimums differ by almost a factor of two! (about 200 days and about 400 days) I'm not sure if I'm reading the plot correctly though, as there is a disconnect between the given Earth-Mars plot, and the prose on the page as well, which talks about 7 month (~200 day) or 10 month (~300 day) transfers.</p> | 5,504 | [
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<p>I think I remember a talk where a professor said that <a href="http://en.wikipedia.org/wiki/4_Vesta" rel="nofollow">Vesta</a> is a particularly important asteroid because its gravity is strong enough to perturb other asteroids.</p>
<p>In spite of Vesta's size, this effect might be so strong that some smaller asteroids might be kicked out of their orbits - making their way to Jupiter, or to the inner solar system.</p>
<p>Can Vesta dominate the orbits of other asteroids?</p>
<p>All related to the one question, there are particular points I'm interested in:</p>
<ul>
<li>if so, how often, presumably?</li>
<li>is there a preferred direction (inwards / outwards)? </li>
<li>has the perturbation rate been constant over geologic timescales?</li>
<li>do the "victims" stay in the plane of the ecliptic? </li>
<li>did someone model such processes?</li>
</ul>
<p>I currently think the whole process is chaotic - essentially unpredictable. </p> | 5,505 | [
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<p>When trying to find the Fourier transform of the Coulomb potential</p>
<p>$$V(\mathbf{r})=-\frac{e^2}{r}$$</p>
<p>one is faced with the problem that the resulting integral is divergent. Usually, it is then argued to introduce a screening factor $e^{-\mu r}$ and take the limit $\lim_{\mu \to 0}$ at the end of the calculation.</p>
<p>This always seemed somewhat ad hoc to me, and I would like to know what the mathematical justification for this procedure is. I could imagine the answer to be along the lines of: well, the Coulomb potential doesn't have a <em>proper</em> FT, but it has a <em>weak</em> FT defined like this …</p>
<p>Edit: Let me try another formulation:</p>
<p>What would a mathematician (being unaware of any physical meanings) do when asked to find the Fourier transform of the Coulomb potential?</p> | 5,506 | [
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<p>I am studying a perturbed Toric Code model that is not analytically solvable.
On a torus the ground state degeneracy of the unperturbed model is 4.
Once we turn on the perturbation there is a change in the ground state degeneracy.
I would like to detect this change in ground state degeneracy numerically using exact diagonalization techniques. </p>
<p>On my computer I have stored the action of the Hamiltonian on a set of basis states. So if you give me some state $\left|\psi\right\rangle$ I can give you
$\hat{H}\left|\psi\right\rangle$ in terms of the basis states. Now I used this information to compute the spectrum using the Lanczos algorithm and the Jacobi-Davidson algorithm. While the spectrum itself is correctly reproduced neither of these algorithms reproduces the degeneracy of the ground state correctly - not even in the unperturbed case. </p>
<p>Hence the following question: What are common exact diagonalization algorithms for this type of many-body system that correctly resolve the degeneracy of the ground state? </p>
<p>I am looking forward to your responses!</p> | 5,507 | [
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<p>I'm looking for the contactless methods to collect the information of the body construction especially skeletal structure to calculate in the computer model .
Are there physical methods to inspect internal side of the body other than X-ray and no any exposure of radiation ? For example, echo , MRI and so on . </p> | 5,508 | [
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<p>A photons energy is given by $E=h *f$ and momentum $p=E/c$ (spin?) but the photon has no (rest) mass! Therefore it is the ultimate probing tool for looking at any mass position and velocity because mass transfer is not involved only momentum.But to calculate/ measure the particles exact position by scattering a photon from the mass into a detector
dictates some of the photons momentum has been transferred to the mass i.e. the mass has to move (is disturbed from it initial position by some delta). This is intuitively obvious ;I would like to see how Heisenberg quantified(proved) this uncertainty hopefully without referring to an ansatz wave function. </p> | 5,509 | [
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<p>I'm quite stuck with this problem. </p>
<p>I know that I have an object in orbit. I know the eccentricity of that orbit, as well as the semi-major axis of the orbit. </p>
<p>Giving a <a href="http://en.wikipedia.org/wiki/True_anomaly" rel="nofollow">true anomaly</a>, how do I find the speed and altitude of that object? The true anomaly is the angle between the line made with the focus of the ellipse and the position of the object.</p>
<p>Thank you!</p>
<p>P.S. I'm more looking for a general help, more than a specific answer. That's why I didn't give any numbers.</p> | 5,510 | [
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<p>My question is regarding T-Duality between the 2 Type H string theories.</p>
<p>I know that the Type II String theories are T-dual to each other because T-Duality changes the sign of the Gamma Matrix so
$$\operatorname{T}:{{\cal P}}_{{\mathop{\rm GSO}\nolimits} }^ - \leftrightarrow {{\cal P}}_{{\mathop{\rm GSO}\nolimits} }^ + $$</p>
<p>Since the Type IIB String theory employs the same GSO Projections on the left and right movers while Since the Type IIA String theory employs the different GSO Projections on the left and right movers, the 2 theories are T-Dual to each other.</p>
<p>However, when one considers T-Dualities on the Type HE string theory and the Type HO String theories, why are they T-Dual to each other?</p>
<p>I presume that maybe T-Duality switches $\operatorname{Spin}(32)/\mathbb Z^2$ and $E(8)\times E(8)$, so therefore, the theories to T-Dual to each other. But if so, then why? Why does T-Duality switch $\operatorname{Spin}(32)/\mathbb Z^2$ and $E(8)\times E(8)$?</p>
<p>Thanks in advance.</p> | 5,511 | [
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<p>Is it correct to define Quantum Physics as the study of Physics in sub-atomic scale? Does Quantum Physics studies something else other than sub-atomic phenomena?</p>
<p>This may be a very stupid question but realize that I am <strong>!!!VERY NOOB!!!</strong> at Physics.</p> | 5,512 | [
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<p>In more detail:
If i have two soda cans, both are cooled to exactly 4 degrees celsius,
And i put one in a 25 degrees room, and the other next to an AC vent set to 16 degrees.
After three minutes, which one should be colder than the other and why?</p>
<p>Edit: To clarify - if I have a cold soda can, should I place it near the AC vent or not (if I like my drink cold)? Which location will cause faster heating?</p> | 5,513 | [
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<p>I was reading this page:</p>
<p><a href="http://www.guardian.co.uk/science/2011/oct/23/brian-cox-jeff-forshaw-answers" rel="nofollow">http://www.guardian.co.uk/science/2011/oct/23/brian-cox-jeff-forshaw-answers</a></p>
<p>and I found this sentence by Brian Cox:</p>
<blockquote>
<p>That seems to imply that everything is flying away from us and we're therefore somehow in a privileged position; that isn't true. The way it's often described is if you imagine some bread with raisins in it that you're baking in the oven and as you heat it, it expands. On any particular raisin, if you look, you can see all the other raisins receding from it. So it's space that stretching, it's not that everything's flying away.</p>
</blockquote>
<p>I already heard this raisins analogy, but it never persuaded me:</p>
<p>I understand that the "big bang" is more like a "big stretch", and I see how every 2 observers in the universe are being distanced farther and farther away (regardless of their position)</p>
<p>Yet one of the Big Bang ideas is that the universe isn't anymore considered infinite and completely homogeneous</p>
<p>But the fact that the universe is finite, while inflating to me implicates that it should have some kind of bounds (not that we can reach these "bounds", since our distance to them is getting bigger, but they should still exist)</p>
<p>(And the fact that it's spreading inhomogeneous mass and energy over big distances, is thus making it more homogeneous, but this doesn't probably matter)</p>
<p>So: the very idea of a big bang seems to me in contradiction to the assertion that there's no such thing as a "center of the universe":</p>
<p>If it has a finite mass and some kind of bounds, then it should also have a barycenter.</p>
<p>And if we consider the bread with raisins analogy: the bread has a center from which it's expanding</p>
<p>Surely, the universe isn't homogeneous (like the distribution of the raisins), and so, in its hypothetical center, there may not be actually anything... but I think (even if it's really unlikely) it should still be theoretically possible to have a raisin in the exact centre of the bread</p> | 5,514 | [
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<p>In <a href="http://arxiv.org/abs/1004.0726" rel="nofollow">this paper</a> on co-orbital dynamics the authors discover, numerically, "Anti-Lagrangian" solutions to the restricted 3 body problem. These Anti-Lagrange $L_4$ and $L_5$ points are 120 degrees ahead and behind the planet (if I understand correctly).</p>
<p>It is possible, as Lagrange demonstrated, to prove that the usual $L_4$ and $L_5$ <a href="http://en.wikipedia.org/wiki/Lagrangian_point" rel="nofollow">points</a> are stable solutions to the restricted circular 3 body problem. But how can you prove that these new-fangled Anti-Lagrangian $L_4$ and $L_5$ points are stable solutions? The method used by Lagrange will not result in such a proof.</p> | 5,515 | [
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<p>Let's say I have a cylindrical piston containing saturated liquid ammonia that is fitted with an electrical heater and a paddle wheel for stirring at an initial pressure and an initial temperature. When the gas expands, some of it evaporates to form a two phase, liquid-vapor solution inside the system. By the way, this process occurs at a constant pressure.</p>
<p>My real question is, what happens to the temperature as the pressure is constant and the volume increases, also causing the specific volume to increase. I would assume the temperature increases, but when I look at the steam table, there is only one temperature corresponding to the pressure. For example, if the initial temperature is 20C, the initial pressure is 8.57bar. If that pressure is constant so the final pressure is 8.57bar, the steam table still says the temperature is 20C.</p>
<p>Why is this? Because I was just looking at the ideal gas equation and it essentially says temperature increases as volume increases. But can I use this intuition with the ideal gas law when the system is 2 phase?</p> | 5,516 | [
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<p>Srednicki writes the Lagrangian density of an interacting scalar field theory as
$$ \mathcal{L} = -\frac{1}{2} Z_\phi \partial^\mu \phi \partial_\mu \phi -\frac{1}{2} Z_m m^2 \phi^2 + \frac{1}{6} Z_g g \phi^3 + Y\phi $$</p>
<p>He claims that $Y=O(g)$ and $Z_i=1+O(g^2)$. What is the basis of this claim?
Why do we ignore the $Y_0$ in the expansion of $Y(g)$:
$$Y(g) = Y_0 + Y_1 g + Y_2 g^2 + \cdots \cdots $$
and again why do we take the $Z_0 = 1$ in the expansion of $Z_i(g)$:
$$Z(g) = Z_0 + Z_1 g + Z_2 g^2 + \cdots \cdots $$</p>
<p>Why $Z_1 = 0$ ?</p>
<p>Are there any references where $\phi^3$ diagrammatics is explained clearly?</p> | 5,517 | [
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<p>In general relativity, time-like geodesics are the trajectories of free-falling test particles, parametrized by proper time. Thus, they are easy to interpret in physical terms and are easy to measure (at least in principle).</p>
<p>Is there a similar interpretation/measurement for space-like geodesics? For example, how do I measure the shortest path between two space-like separated points? What is the interpretation of such a path (apart from it being a geodesic)?</p>
<p>My first guess is that the answer will involve a static picture (with no change in time), e.g. how elastic springs stretch between two fixed points. The problem with this picture is that the curves the springs bend along depend on the stiffness of the spring. (I believe one gets a geodesic when the stiffness is infinite, but this is no effect one would be able to measure for everyday gravitational fields.) </p>
<p><strong>Addition:</strong></p>
<p>As VM9 pointed out below, I should fix something like a space (a space-like hypersurface) before talking about the geodesic distance.</p>
<p>So, let me define space-like geodesic for my purpose as follows, which will be a local notion: Take an observer, which simply shall be a time-like vector $u$ at an event $P$ of space-time $M$. Let $V$ be the orthogonal complement of $u$ (a three-dimensional space of space-like directions at $P$). Let $\Sigma$ be the image of a small neighborhood of $0$ in $V$ under the exponential mapping (that is the set of events that are connected to $P$ by small geodesics that are orthogonal to $u$ at $P$).</p>
<p>It is that space-like submanifold my observer is interested in. How can one physically measure lengthes in $\Sigma$? While every measurement process takes time as VM9 pointed out as well, let's assume that time flies rather slowly ($c \to \infty$) so that one could work, for example, in Gaussian coordinates (synchronous coordinates) with respect to $\Sigma$.</p> | 5,518 | [
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<p>Here's a homework problem I'm working on. I am not asking for the answer, but any guidance or comments on the approach are appreciated.</p>
<blockquote>
<p>Given that a measurement of $L^2$ for a free particle has resulted in the value $6\hbar^2$, what are the possible results for a measurement of $L_x$?</p>
</blockquote>
<p>I've been following the approach given on pp. 378-380 in Liboff (4th ed.). I've made it as far as expressing the eigenfunctions of $L_x$ as sums of the eigenfunctions of $L^2$... Here's what I've got: </p>
<p>$$\begin{align*}
X_1 &= \frac{1}{2}\left(|2,2\rangle - |2,1\rangle + |2,-1\rangle - |2,-2\rangle\right)\\
X_2 = -X1 &= -\frac{1}{2}\left(|2,2\rangle - |2,1\rangle + |2,-1\rangle - |2,-2\rangle\right)\\
X_3 &= \frac{1}{2}\left(\sqrt{\frac{3}{2}}|2,2\rangle - |2,0\rangle + \sqrt{\frac{3}{2}}|2,-2\rangle\right)\\
X_4 = -X3 &= -\frac{1}{2}\left(\sqrt{\frac{3}{2}}|2,2\rangle - |2,0\rangle + \sqrt{\frac{3}{2}}|2,-2\rangle\right)\\
X_5 &= \frac{1}{2}(|2,2\rangle + |2,1\rangle - |2,-1\rangle - |2,-2\rangle)\\
X_6 = -X_5 &= -\frac{1}{2}\left(|2,2\rangle + |2,1\rangle - |2,-1\rangle - |2,-2\rangle\right)
\end{align*}$$</p>
<p>The next step appears to be to express $L^2$ as sums of the eigenfunctions of $L_x$, which does not seem possible.</p>
<p>It was a lot of algebra, matrices, determinants, etc. to get to this point so it is certainly possible that I've miscalculated something accidentally, but does anyone see anything fundamentally wrong here with this approach? And/or is there a simpler way?</p> | 5,519 | [
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<p>now, I have read a lot of explanations on that but still can't really understand why it would happen so if you can give some examples for a such a thing happening. I mean lets say gravity attracts the air and due to air viscosity all of the air gets carried with the Earth but why will the speed be same ? </p> | 162 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/2178/how-efficient-is-a-desktop-computer">How efficient is a desktop computer?</a> </p>
</blockquote>
<p>I believe the energy conversion efficiency of a modern CPU is extremely low, because it dissipates pretty much all of it as heat, which is not a desired product. But what's the order of magnitude of the fraction that gets spent on the actual computation?</p>
<p>Are there absolute maximums imposed on this efficiency by the known laws of physics, or can information processing occur without any waste heat generation as a by-product?</p>
<p>I'm a bit out of my depth here, having no idea quite how information processing relates to heat and energy (other than suspecting that there is a very deep connection), so apologies if this is nonsensical or vague.</p> | 198 | [
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<p>This diagram from <a href="http://en.wikipedia.org/wiki/Lagrangian_point">wikipedia</a> shows the gravitational potential energy of the sun-earth two body system, and demonstrates clearly the semi-stability of the L1, L2, and L3 lagrangian points. The blue arrows indicate lower potential energy, red higher - so any movement in the plane perpendicular to the masses would require energy and without it, an object there would settle.</p>
<p><img src="http://i.stack.imgur.com/ehngn.png" alt="Lagrange Points"></p>
<p>However, the L4 and L5 are claimed to be stable, even though the direction arrows indicate it's at the top of a gravity well, and would fall into lower potential energy in any direction. What is it that makes these points stable if not gravity? What am I missing?</p> | 103 | [
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<p>I am taking a short introduction course on lasers. I never knew that the frequency of a laser is so high for a given wavelength (e.g. 780nm). I am wondering how people can measure the frequency of the laser. Do they downconvert the frequency of the light so that we could measure it with scope?</p> | 5,520 | [
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<p>A good buddy of mine and I have had a friendly debate about the origins of the current state of our universe (namely; Earth and life on Earth) and have fundamentally disagreed in our stances with respect to probabability, infinity in time and space and possible/probable event outcomes. He maintains the position that given a set of possibilities and enough trials, each outcome <em>must</em> have occured; which is his reasoning for why life must exist. I do not necessarily take issue with this particular concept, as given an infinite amount of time and states of matter life is bound to come from one of those states. In our discussions, however, we have been using a specific example in which I disagree vehemently with his stance. The example:</p>
<blockquote>
<p>If you throw a handfull of sand in the air an infinite number of
times, and that sand lands on a flat surface, every
configuration <em>will</em> happen (according to his position). For instance,
the sand landing in a pattern which spells your name out is a
mathematically possible outcome, and will therefore happen given
enough trials.</p>
</blockquote>
<p>To counter his stance on this example, I took the position that there is a mathematical (but not physical) possibility that every grain of sand lands in the same one inch square of the surface; but I maintain that even though it is a mathematically possible outcome it will never happen because of the way the physical world works - that sand will be roughly evenly distributed for each throw, even if over an infinite number of trials, assuming consistent and fair trials (ie, no God or other being moving grains of sand). I submit that even though it is a mathematical possibility, you'll never see your name spelled out in block letter English anywhere in the universe without the influence of intelligence, even if you were able to attempt a verification for this - he disagrees. I held him liable for mathematical/physical proof of reasoning for his stance and he has taken to dismissing me as ignorant of probability and infinity. Can anyone provide some good reasoning for either side of this argument? I realize that either is an impossible stance to prove, since we can't verify our positions, but any well-reasoned insight will be appreciated. A similar question, with an answer I found to be relatively useful:</p>
<p><a href="http://physics.stackexchange.com/questions/22187/infinite-universe-jumping-to-pointless-conclusions">Infinite universe - Jumping to pointless conclusions</a></p>
<p><strong>EDIT:</strong></p>
<p>After reading some of the comments and answers here it has become apparent that I may have misrepresented my ultimate question. I realize that given a non-zero probability and an infinite number of trials, the mathematical probability of encountering the event described by said probability converges to 1. Some have taken the position that there is no disconnect between a mathematical probability and the likelihood (read: possibility) of a physical event happening.</p>
<p>To simplify the argument, the surface can be thought of as a grid - in which case every single configuration has some mathematical probability associated with it. My stance regards certain configurations as physically impossible, however, which is the reasoning behind my one-inch-square analogy. Can anyone show clear reasoning (and sources!) for their belief that it is possible to toss a handful of sand into a one inch square?</p> | 5,521 | [
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<p>So I came across a question while studying laws of motion. Roughly, this is how it goes:
There are two astronauts in a space shuttle, who together have mass 200 kg. If by doing exercise, they manage to lose 80 kg, what will be the percentage increase in speed of the shuttle. The question is pretty straight forward, if thought about directly. However, my instant reaction was that by conservation of mass, the mass that the astronauts lose will still be contained within the space ship in the form of water, CO2, etc. So technically there won't be any change in mass, thus no change in speed. </p>
<p>I would like to know if this assumption is correct and in what forms is the mass we lose released.</p> | 5,522 | [
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<p>Intuitively, if energy can be stored in rotational motion, it has to obey $E=mc^2$.
Does rotation of typical stellar-sized objects - BHs, pulsars, binaries - have measurable effect on their overall gravity? </p>
<p>(I'm not talking about nearby effects, like frame dragging described by Kerr metric, the effect on measurements from the Earth is of interest)</p> | 5,523 | [
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<p>suppose that, there is a plano convex lens and its thickness is 5.00cm. If you watch it straight from the convex side, it seems that its of 4.4 cm. What is the refractive index of this lens?</p> | 5,524 | [
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<p>We have studied so far that electric field inside a conductor if no charge is placed inside is zero. But we know that every conductor has only a limited number of electrons. What happens when ALL the electrons have aligned to cancel the field inside conductor under application of external field and then we increase the field a little bit more certainly there are no more electrons to cancel the field and this additiknal field must be present inside the conductor now.</p>
<p>I know that practically under electric fields of magnitude that can drag out all electrons from the conductor's body to surface field emission and/or electrical breakdown would be taking place, But is this phenomenon theoretically possible ?</p> | 474 | [
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<p>Including air resistance, what is the escape velocity from the surface of the earth for a free-flying trajectile?</p> | 5,525 | [
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<p>I'm taking an optics lab in which I'm required to construct an interferometer, and measure the wavelength of a laser, and the coherence length of the light emitted from a candle fire.</p>
<p>Now, I've been hinted by my instructor that when working with mirrors (which are present in an interferometer), it is best to make sure that the laser is polarized to either "P" or "S" polarization - otherwise, the mirrors might give an elliptic component to the polarization, which in turn will spoil the measurment, due to interference effects.</p>
<p><strong>So now comes the question: should the light from the candle be polarized as well??</strong></p>
<p>I have a reason to suspect that polarizing it will improve the coherence length, and on the other hand, I'm pretty sure that elliptical polarization will take effect if the light remains untouched.</p>
<p>What is your opinion on this dilemma??
Thanks!!</p> | 5,526 | [
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<p>How do I go about finding the pressure exerted on a rectangular surface in a free flowing air stream?</p>
<p>I wouldn't imagine that this is directly related to the airspeed / surface area, but have no idea where to start. Is there even an equation, or does one need to do some kind of FEA?</p>
<p>For instance a 1.2m x 2.4m metal sheet suspended some distance above ground level, if I have a gust of wind at 8m/s (directly perpendicular to the sheet), what is the average pressure across the face of sheet?</p> | 5,527 | [
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<p>According to the first law of thermodynamics, sourced from wikipedia
"In any process in an isolated system, the total energy remains the same."</p>
<p>So when lasers are used for cooling in traps, similar to the description here: <a href="http://optics.colorado.edu/~kelvin/classes/opticslab/LaserCooling3.doc.pdf">http://optics.colorado.edu/~kelvin/classes/opticslab/LaserCooling3.doc.pdf</a> where is the heat transferred? </p>
<p>From what I gather of a cursory reading on traps, whether laser, magnetic, etc the general idea is to isolate the target, then transfer heat from it, thereby cooling it.</p>
<p>I don't understand how sending photons at a(n) atom(s) can cause that structure to shed energy, and this mechanism seems to be the key to these systems. </p> | 608 | [
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<p>I have a question with regard to probabilistic quantum cloning - see for example <a href="http://prl.aps.org/abstract/PRL/v80/i22/p4999_1">http://prl.aps.org/abstract/PRL/v80/i22/p4999_1</a>.</p>
<p>It does seems like I can use the proof for no-cloning theorem to disproof the existence of equation (7) in the paper quant-ph/9704020. Do you think this is true?</p>
<p>Suppose probabilistic quantum cloning is actually possible, now according to the current papers, if the cloning process fails, the state that we intend to clone would be destroyed. Looking at the equation in the original paper, however, it does seem that a repair or a reverse operation might be possible in the event of a failure. More specifically, in the paper quant-ph/9704020, if I replace the $\left|\phi\right>$ state in Equation (7) with say, $\left|\psi_T\right>\left|0\right>$ where $\left|\psi_T\right>$ is a state orthogonal to the input state $\left|\psi\right>$, the proof would work just as fine. Do you think this is true? If this is true, a repair would be possible in case of cloning failure. The process would still be probabilistic, but I can repeat till it is successful.</p>
<p>I do hope for some feedback from experts out there. Thanks!</p> | 5,528 | [
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<p>Within my master's thesis, I try to model a machine elements and have to model the exact slipping and exact sticking between the bodies. So I noticed that such problems can be formulated as a LCP. </p>
<p>However I have difficulties at finding any literature where the usage is described well with examples..</p>
<p>I would like to have something like a 1-DOF model such a box on a plane pulled with a spring and friction modeled with coulomb or so. </p>
<p>I would be very grateful of mentioning any literature/sites which can bring me further. </p>
<p>I am really desperate at implementing the coulomb friction..</p> | 5,529 | [
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<p>I have been reviewing the basics of mechanics in preparation of studying Spivak's text book on mechanics (I am from a more mathematical background and I am taking an advanced analytical mechanics course next quarter which is using this text). I recently came across a problem in a text different from the one that I am using (University Physics), and I was having difficulty understanding how to approach it, and indeed even understanding the details of the situation (the problem is stated with little detail). Unfortunately, my text does not seem to cover anything like it, in the exercises or otherwise.</p>
<blockquote>
<p><em>Imagine a flat surface inclined at 45 degrees. A 1500 kg block is placed on the incline, and it is (according to the figure) attached directly to a pulley of radius $r$. The pulley itself has a cable rolling over it which extends along the incline with one end connected to the surface and the other end connected to a larger pulley of radius $3r$, but at a point of contact which is only $r$ from the center. Another block of unknown mass $m$ is attached to the larger pulley at the edge ($3r$ from the center) and is allowed to hang. We are asked to compute the mass $m$ of the hanging block required to counteract the motion of the block of mass 1500 kg. (The physical situation [I will try to update this with a picture as soon as I can] is basically just like the traditional one pulley/two-block system on an incline first encountered with problems involving Newton's laws; except here there are two pulleys involved as described above).</em></p>
</blockquote>
<p>To be perfectly honest, I am really not at all sure what is going on in this problem. If we take the axis of rotation to be the center of the larger pulley, then it is clear the second block imparts a torque of $3rmg\sin\left(\frac{\pi}{4}\right)$ and a tension on the cable is just $mg$. It seems to be the block on the incline imparts no torque since its action is directed parallel to the radial coordinate of the axis (if we are taking the natural coordinate system with axes perpendicular and parallel to the axis of rotation). What is the significance of the smaller pulley to which the mass is attached?</p> | 5,530 | [
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<p>I have seen a few Dalitz plots so far and tried to understand how they are useful.
So one of the advantages of these plot is that the non-uniformity in the plots can tell something about the intermediate states that we cannot detect. My question is how do you extract the mass of these resonant particles from such plots? What additional information would you need?</p> | 5,531 | [
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<p>Since a week or so a constant high pitch sound (~4khz) emanates from my active monitor speakers. After eliminating any ground or power source issues I noticed, that the sound rises in volume whenever I open my window - which is exactly between my speakers and an array of cellular antennas on the opposite building. I recall there were new antennas added a few weeks ago. Our public database shows that there are over 20 transmitters on there, with 3 pointing exactly in my direction.</p>
<p><strong>Question</strong>: Can HF-EMWs produce such a sound in an audio amplifier or through it's connectors (it's not the cables or whatever comes through them)?</p> | 5,532 | [
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<p>There are a lot papers explaining why Laughlin's wavefunction are energetically favorable, but seldom explain why a lower energy state could explain the plateau at $\nu=1/3$. I met at several places claims like: a lower energy state at $\nu=1/3$ will pin the electron density at $\nu=1/3$. But why is that? And what actually it means? when we move $\nu$ from $1/3$ what happens? electrons adjust there distance or new particle been added? And is this a phase transition?
Hope someone familiar this field could give me some help, thanks! </p> | 5,533 | [
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<p>At lower altitude an aeroplane usually has more lift. However an aeroplane flying at low altitudes (with gear/flaps up) at low velocity burns the same amount of fuel it would flying much faster at a higher altitude. Why?</p> | 5,534 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/18527/does-the-pauli-exclusion-principle-instantaneously-affect-distant-electrons">Does the Pauli exclusion principle instantaneously affect distant electrons?</a> </p>
</blockquote>
<p>If this rule works, could you not set up an experiment to test the theory (as described by Brian Cox in his <em>A Night with the Stars</em> lecture$^1$) and monitor another piece of diamond to see if the electrons change levels in time with the changes in energy of the electrons in the heated piece? If you used a pin point heating element that could change temperature at different frequencies, would you detect the frequency change in the monitored piece?</p>
<p>--</p>
<p>$^1$ The Youtube link keeps breaking, so here is a <a href="http://www.youtube.com/results?search_query=brian+cox+night+with+the+stars" rel="nofollow">search</a> on Youtube for Brian Cox' <em>A Night with the Stars</em> lecture.</p> | 199 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/18950/how-to-debunk-the-electric-universe">How to debunk ‘The Electric Universe’?</a> </p>
</blockquote>
<p>I am just wondering why there exists such a strong feeling within the physics community against theories such as Plasma Physics and <a href="http://www.holoscience.com/wp/" rel="nofollow">The Electric Universe</a>. </p>
<p>Every single atom is governed by electromagnetic forces, molecules are formed through chemical (electromagnetic) bonds, the universe is 99% plasma which is an great conductor of electricity, the sun is made of plasma and bombards the solar system with electromagnetic energy, centers of galaxies radiate enormous amount of electromagnetic energy, etc.</p>
<p>It is such a simple and elegant solution that truly explains everything in a rational way which, most importantly, can be <strong><em>experimentally verified</em></strong>. It can explain the true nature of mass and matter, gravity, how our sun works, how the universe works, weather systems, earthquakes, and many other phenomena that are mysteries to modern science.</p>
<p>So my question is: can someone explain to me why mainstream scientists are <strong>SO</strong> against these theories that they won't even consider them? I'm not saying they are 100% correct, but why not at least look at the theories and consider their implications?</p>
<p>Here are some articles I have found that explain many of the things I am talking about (no affiliation with me, I just think they well-written):</p>
<ul>
<li><a href="http://www.holoscience.com/wp/sciences-looming-tipping-point" rel="nofollow">http://www.holoscience.com/wp/sciences-looming-tipping-point</a></li>
<li><a href="http://www.holoscience.com/wp/a-real-theory-of-everything" rel="nofollow">http://www.holoscience.com/wp/a-real-theory-of-everything</a></li>
</ul>
<p>Can any real physicist explain to me why these theories could not be at least plausible? I am not trying to create controversy, but merely trying to understand why they seem so outrageous.</p> | 200 | [
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<p>Although the electromagnetic wave is made op of both electric and magnetic fields the electric field contributes much in vision and is thus, called the light vector. But, why is it that the electric field has a major role? </p> | 5,535 | [
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] |
<p>The bar with length l, density r, diametr d, Young's modulus E, Poisson's ratio mu, is spinning around the cross-section, what is the change in the width of this bar?</p> | 5,536 | [
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<p>I watched this <a href="http://www.youtube.com/watch?v=_hmXrHvmwOM" rel="nofollow">video</a> featuring Michio Kaku explaining parallel universes. In the last two minutes he said that experiments in the LHC could reveal that there might be parallel universes and then he stops. What experiment was he talking about? And how would that be possible? </p> | 5,537 | [
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<p>In one derivation of the corrected period of a pendulum, we started off like so: </p>
<p>The mass has a height $y$ given by $l(1-\cos \theta )$. $E = K + E \rightarrow \frac{1}{2}ml^2 \dot{\theta}^2 + mgl(1-\cos \theta)$</p>
<p>The next step introduces $\theta _0$, and I've got no idea where this came from. </p>
<p>$$\frac{1}{2}ml^2 \dot{\theta}^2 + mgl(1-\cos \theta)= mgl(1-\cos \theta _0)$$</p>
<p>Now we just solve for $\dot{\theta}$ and solve the DE.W I'm interested in the theta side of the equation. </p>
<p>$$\int \frac{d\theta}{\sqrt{\cos \theta - \cos \theta _0 }}$$</p>
<p>We go through a bunch of subs and changes of vairble to arrive at </p>
<p>$$\int ^{2\pi} _0 \frac{du}{\sqrt{1-K^2 \sin ^2 u }}$$</p>
<p>So my two questions are </p>
<ul>
<li>Why are we involving two $\theta$ values? The text didn't make it clear why we needed an extra $\theta _0$. It appears that $mgl(1-\cos \theta _0)$ is the total energy of the system. Our total energy cannot surpass the initial gravitational potential energy, this is clear. My only thought as to what $\theta$ means is the instantaneous position of the angle. </li>
<li>My text mentioned that this is an elliptical integral. Mathematically speaking, what <em>is</em> an elliptical integral? Can this integral be solved exactly, or does it always require approximations from the expansion? </li>
</ul> | 5,538 | [
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<p>The game <a href="http://gamelab.mit.edu/games/a-slower-speed-of-light/">"A slower speed of light"</a> from MIT claims to simulate effects of special relativity:</p>
<blockquote>
<p>Visual effects of special relativity gradually become apparent to the
player, increasing the challenge of gameplay. These effects, rendered
in realtime to vertex accuracy, include the Doppler effect (red- and
blue-shifting of visible light, and the shifting of infrared and
ultraviolet light into the visible spectrum); the searchlight effect
(increased brightness in the direction of travel); time dilation
(differences in the perceived passage of time from the player and the
outside world); Lorentz transformation (warping of space at near-light
speeds); and the runtime effect (the ability to see objects as they
were in the past, due to the travel time of light).</p>
</blockquote>
<p>But does restricting the render engine to special relativity not miss out several effects that might happen close to the speed of light? Especially I'm thinking about effects related to inertia and acceleration/rotation of the observer. So are there any important effects missing which would make the game a even more realistic simulation of the movement close to the speed of light?</p> | 5,539 | [
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<p>I have read that plasma is a state of matter that resembles gas but it consists of ions and electrons coexisting. So my question is : If plasma is just ionized gas, will ideal gas law apply for it ?</p> | 5,540 | [
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] |
<p><img src="http://i.stack.imgur.com/GkwGl.jpg" alt="enter image description here"></p>
<p>How eq(4.4) is a solution of eq(4.3) </p> | 5,541 | [
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<p><a href="http://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment" rel="nofollow">The Stern Gerlach experiment</a> was meant to prove the orbital quantization of electrons where there should be +ml,0,-ml states. So for l=2, there should be 5 beams.</p>
<p>But they saw 2 beams, which was shown to be due to the 2 states of spin.</p>
<p>Now, because of the addition of the spin magnetic moment, shouldn't there be now 10 beams?(2 additional states for each the 5 orbital states).</p>
<p>What happened to the orbital magnetic contribution?</p> | 5,542 | [
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<p>For a static electric field $E$ the conservation of energy gives rise to $$\oint E\cdot ds =0$$ Is there an analogous mathematical expression the conservation of momentum gives rise to?</p> | 5,543 | [
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<p>....is an oblate spheroid because centrifugal force stretches the tropical regions to a point farther from the center than they would be if the planet did not rotate. So we all learned in childhood, and it seems perfectly obvious. However...</p>
<p>I am at $45^\circ$ north latitude. Does that mean</p>
<ul>
<li>An angle with vertex at the center of the earth and one ray pointing toward the equator at the same longitude as mine, and one ray pointing toward me, is $45^\circ$ (that would mean I'm closer to the north pole than to the equator, measured along the surface, as becomes obvious if you think about really extreme oblateness); or</li>
<li>The normal to the ground where I stand makes a $45^\circ$ angle with the normal to the ground at the equator at the same latitude (this puts me closer to the equator than to the north pole); or</li>
<li>something else?</li>
</ul>
<p>If for the sake of simplicity we assume the earth is a fluid of uniform density, it seems one's potential energy relative to the center of the earth would be the same at all points on the surface.</p>
<ul>
<li>Would the force of gravity at my location, assuming no rotation, be directly toward the center? Would it be just as strong as if the whole mass of the earth were at the center and my location is just as far from the center as it is now?</li>
<li>Would the sum of the force of gravity (toward the center or in whichever direction it is) and the centrifugal force (away from the axis) be normal to the surface at my location?</li>
<li>Given all this, how does one find the exact shape?</li>
<li>How well does that shape in this idealized problem match that of the actual earth?</li>
</ul> | 5,544 | [
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<p>The argument for <a href="http://en.wikipedia.org/wiki/Eternal_inflation" rel="nofollow">eternal inflation</a> is we have some patch of metastable vacuum with positive cosmological constant, and so it expands exponentially a la de Sitter. Most of the patch decays to something which expands more slowly, but only a tiny fraction continues to expand at that fast exponential rate. The magic of exponentiality is despite only being a tiny fraction, it still dominates, and this process continues forever.</p>
<p>OK, but add in causal patch complementarity, and well, only the causal patch counts, right? The fraction counting is no longer admissible because we can only measure the fraction within the causal patch, and any observer will always exit the inflationary phase with probability 1. What gives? </p>
<p>The spatial multiverse presupposes there is such a thing as outside the patch. Is that a no no? The multiverse of different string compactifications, well, how many of them are there inside a causal patch simultaneously? As for many worlds multiverses, is many worlds even true?</p> | 5,545 | [
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<p>Schrodinger believed that the phisical interpretation of the wavefunction $\Psi$ was the vibration amplitude and $ |\Psi|^2 $ was the electric charge density. While no-one disagrees with his interpretation of $\Psi$, many physicists believed Schrodinger was wrong about about $|\Psi|^2$ and argued that $|\Psi|^2$ is a probability. Schrodinger never accepted this view, but registered his "concern an disappointment" that this "transcendental, almost psychical interpretation" had become "universally accepted dogma." Why did Schrodinger forever think that $|\Psi|^2$ was the electric charge density and not a probability?</p> | 5,546 | [
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<p>I have tough problem I am not sure how to solve:</p>
<p>For this question, we are confined to a plane. Consider a gravitational field that is proportional to $\frac{1}{r^3}$ instead of $\frac{1}{r^2}$, and consider its potential which is then proportional to $\frac{1}{r^2}$. Suppose that I put $n$ identical point masses in this plane, all at different locations and let $U(x,y)$ be the potential function. </p>
<blockquote>
<p>What can we say about the critical points of $U(x,y)$? Specifically, can we show that the number of critical points is always $\leq n$?</p>
</blockquote>
<p>Thank you for your help!</p>
<p><strong>Remark:</strong> By critical point, I mean the usual definition in vector calculus, that is a place where both partial derivatives are zero.</p> | 5,547 | [
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<p>I was wondering, why in Newtonian physics <a href="http://en.wikipedia.org/wiki/Torque" rel="nofollow">torque</a> is called "torque" while in static mechanics they call it "moment"? </p>
<p>I prefer by far the term "torque", for not only it sounds strong, but also instead of moment, the correct synonym of torque is moment of force.</p> | 5,548 | [
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<p>There is a recent paper on arxiv receiving lot of acclaim <a href="http://arxiv.org/abs/1105.4714">http://arxiv.org/abs/1105.4714</a></p>
<p>The authors experimentally show that moving a mirror of a cavity at high speeds produces light from high vacuum. The usual doubts about the experimental techniques seem to be very clearly addressed and reviewed (as per Fred Capasso's comments) <a href="http://www.nature.com/news/2011/110603/full/news.2011.346.html">http://www.nature.com/news/2011/110603/full/news.2011.346.html</a>)</p>
<p>My question is :
Can someone explain how correlated/squeezed photons are generated in this process ? I can get a feel for how a moving mirror can generate real photons by imparting energy to the vacuum (correct me if this is not consistent with the detailed theory). But, I don't see how photons are generated in pairs. Could someone describe the parametric process happening here ? </p> | 5,549 | [
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<p>Landau writes "It is found, however, that a frame of reference can always be chosen in
which space is homogeneous and isotropic and time is homogeneous."</p>
<p>Does he mean that we can prove the existence of an inertial frame or does he want to say that it is assumed by doing enough number of experiments?</p>
<p>Can we start with some axioms and definitions of properties of space and time and then deduce the existence of such a frame in which space is homogeneous and isotropic and time is homogeneous?</p> | 5,550 | [
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<p>Supposing there is an iron nail that is left to rust, if we compare the time it takes to rust with that of a magnetized iron nail, will there be any difference in the time of corrosion (assuming other environmental factors are constant)?</p> | 5,551 | [
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<p>Well I have a couple of questions regarding Black holes so here they are,</p>
<p>1.Shouldn't they be called black spheres?(holes are in 2D right?)</p>
<p>2.What will happen if black holes collide?(If they can)</p>
<p>3.Will they have the "information" of what they have eaten?</p>
<p>4.What's a white hole?
(i'm only 16, so sorry if these seem stupid)</p> | 5,552 | [
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