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<p>Let's consider the following situation. We put a body of mass $m$ at a distance $A$ from the center of Earth. We let the Earth attract the body and analyze the situation at a point $B$, closer to the Earth.</p>
<p>Now, the work done by the gravitational force (a conservative force, which seems to be important) is given by:</p>
<p>$$W = GMm\left(\frac{1}{r_B} - \frac{1}{r_A}\right)$$</p>
<p>This work equals the change of the kinetic energy of the system (approx., the Earth didn't budge too much) and the negative change of the potential energy of the system. The mechanical energy hasn't changed, the system is isolated.</p>
<p>What bothers me is this: why doesn't the work done by the gravitational force change the overall energy? It seems inconsistent to say "the work done equals the energy change, BUT not when the work is done by a conservative/internal force". Why does one work differ from another?</p> | 2,997 | [
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<p>An electron is ejected from the surface of a long thick straight conductor carying a current, initially in direction perpendicular to the conductor. The electron will:
a) ultimately return to the conductor
b) move in a circular path around the conductor
c) gradually move away from the conductor along a spiral
d) move in helical path with the conductor as the axis</p>
<p>According to me, $$mv^2/r=qvB\implies r=mv/qB$$ since B is the magnetic field due to the conductor, $B=\mu i/2\pi R$ where R is the distance from a conductor. So$$r=2\pi mvR/\mu qi$$
Since the force will always be perpendicular to the velocity, the electron moves in a circle. As the electron moves, $R$ increases since the electron has to move outwards first to complete the circular motion. As $R$ increases, $r$ also increases. So I think the electron should move away from the conductor along a spiral.</p>
<p>What is the correct answer?</p> | 2,998 | [
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<p><strong>Chern bands or Chern insulators</strong> in 2 spatial dimensional(2D) are a way to construct the bulk insulating gap, but with edge or surfaces with <strong>gapless fermions</strong>. Such gapless fermions are emergent, and which seems to be different than the <strong>High Energy Physics Lattice Fermions approach</strong>. </p>
<p>There in <strong>HEP Lattice Fermions</strong>, people try to discretizes the continuum Lagrangian on the lattice.</p>
<p>Here in <strong>Chern insulators</strong>, the lattice model is <em>NOT</em> written from discretizing the continuum Lagrangian, and the 1D edge gapless fermions fields $\hat{\psi}$ are emergent which degree of freedom does not directly mapped from the fermion hopping operator $f$ in the 2D bulk.</p>
<p>Questions-</p>
<ol>
<li><p>Can we compare the two kinds of schemes (Chern bands from 2D bulk $f$ to 1D $\hat{\psi}$, and HEP Lattice Fermions from 1D $\Psi$ fields to $\hat{\Psi}$) and their mapping more rigorously? How are their difference?</p></li>
<li><p>If we add <strong>interaction terms</strong> on the edge, such as $\Psi_L^\dagger \Psi_R^\dagger \Psi_L \Psi_R$; the HEP Lattice Fermions again just discretize the Lagrangian to $\hat{\Psi}_L^\dagger \hat{\Psi}_R^\dagger \hat{\Psi}_L \hat{\Psi}_R$; but in the Chern bands scheme, for a rigorous mapping, do we get more correction terms, beyond a simply adding $\hat{f}_L^\dagger \hat{f}_R^\dagger \hat{f}_L \hat{f}_R$ on 1D edge? (where $L$ and $R$ can be two different copies of Chern insulators.) Is there extra terms $...$, how are these terms derived.</p></li>
</ol>
<p>Any good and rigorous Ref on <strong>adding gapping terms on the edge of the Chern insulators</strong> and comparing the discretized lattice to a continuum theory is very welcome.</p> | 2,999 | [
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] |
<p>In <a href="http://web.physics.ucsb.edu/~mark/qft.html" rel="nofollow">Srednicki's QFT book</a>, eq. $14.27$ is a result used over and over again for computing loop correction. It is the following integral evaluated in terms of gamma functions:</p>
<p>$$
\int d^dq \frac{(q^2)^a}{(q^2+D)^b} =
\frac {\Gamma (b-a-\frac{1}{2}d)\Gamma (a+\frac{1}{2}d)}
{(4\pi)^{d/2}\Gamma(b)\Gamma(\frac{1}{2}d)} D^{-(b-a-d/2)}
$$</p>
<p>Where $q$ is a $d$-dimensional vector, and $q^2$ denotes the square of its norm. I want to know how to obtain the above result. </p>
<p>Since $q^2$ is the only variable in the integrand, we can use hyper-spherical coordinates, where the integral is non-trivial only for the radial component. The factor from the angular components is the volume of the unit $d$-sphere:
$$\frac {2\pi^{d/2}}{\Gamma(d/2)}$$
Then the above expression is then a equation for the radial component, let's call it $r$:
$$
\int dr \frac{r^{(2a+d-1)}}{(r^2+D)^b} =
\frac {\Gamma (b-a-\frac{1}{2}d)\Gamma (a+\frac{1}{2}d)}
{(8\pi)^{d}\Gamma(b)} D^{-(b-a-d/2)}
$$
Where the extra $r^{d-1}$ in the numerator comes from the volume element of the $n$-sphere. I would like to know how to obtain this result.</p> | 3,000 | [
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<p>Under a Galilean transformation, the coordinates and momenta of any system transform as:
$$ t \rightarrow t',\\ \vec r\:' = \vec r + \vec vt,\\ \vec p\:' = \vec p + m\vec v $$
where $\vec v$ is velocity of frame moving w.r.t it. Now, what will be unitary transformation that can that will carry out this transformation. Let us say the total momentum of the system is $\vec P$ and its mass $M$ and its position $X$.
I know how to write a single coordinate translation, but am not able to put all these together.</p>
<p><strong>An Attempt</strong> : The transformation should contain :</p>
<p>$ \bf e^{i \vec p.\vec x} $ for translations and $ \bf e^{iHt}$ for time translations, <strong>but what about generators of Velocity transformations ?</strong></p> | 3,001 | [
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<p>Both are feebly attracted by a magnetic field. I know the difference between these substances(on why these get attracted to magnetic field) but as both get feebly attracted how to find out whether a given substance is ferri-magnetic or para-magnetic?</p>
<p>Is it that all ferri-magnetic materials are compounds of different metals like magnetite and we can differentiate in this way? </p> | 3,002 | [
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<p>When we do a transformation (norm preserving one) for a given quantity, from what I have understood it seems like there is a representation of the group element for each quantity depending how they transform (eg : scalar, vector, rank 2 tensor spinor.. ).</p>
<p>Considering a normal rotation in 2-D plane (associated to $\mathrm{SO(2)}$ group), if a scalar field $\psi(x,y) \rightarrow \bar\psi(\bar x, \bar y)$ transforms, the representation for the group (which I derived from my arguements of infinitesimal rotations) :
$$ \psi(x,y) = (1+ L_z\delta\theta)\bar\psi(\bar x, \bar y) $$</p>
<p>Now I am just wondering what exactly remains unchanged here (since it is a scalar field) or am I just understanding it in the wrong way ? </p>
<p>Also is there a general way of finding a representation given a quantity (a field, vector, tensor ...) in group theory. Since I derived the above scalar representation unlike how find the representation in Lie groups.</p>
<p>PS : Is it probably the form of the field remains invariant, (like how Lorentz covariance gives us spinor transformations)</p>
<p>$$ x^2 +y^2 \rightarrow \bar x^2 +\bar y^2 $$</p>
<p>EDIT 1 : If I wanted to derive this infinite dimensional representation from its Lie group (like I do for the vector case), how can I do it ?</p>
<p>EDIT 2 : I am not able to see the Representation for transformation of Quantum mechanical operators from group directly. </p> | 3,003 | [
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<p>If a golf club strikes the ball out of the centre of the club face with the club path on the target line through impact, and the face square to target, the ball will move towards the target with no side-spin.</p>
<p>If the same shot is played but the impact is towards the toe of the club, the club face will open slightly as a result, and side spin will be imparted.</p>
<p>The question is: for a right handed golfer is the spin clockwise (ball path bends right) or anti-clockwise (ball path bends left).</p>
<p>I ask this question because my golf coach and I disagree on the answer. He is a very experienced and highly qualified coach. I know nothing about golf but I have a degree in physics. I'm looking for an answer with a link to a respected reference which backs it up.</p> | 3,004 | [
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<p>OK, this question is not your usual one: Last night while hiking solo from the mountains back to my car at the mountain/desert interface (Lone Pine, CA), I had a rather bizarre -- and downright spooky -- experience.</p>
<p>The last half-mile of my return was in total darkness, which wasn't a problem since I had prepared for that unintended possibility. Partway into that last portion of the hike, with my LED flashlight piercing the remote, desert darkness, I began hearing a slow, distinct and loud "breathing" sound, both inhaling and exhaling, which became more pronounced the closer I got to my car. The source seemed to be perhaps a couple hundred feet away. I'll skip the whole middle part which had a Blair Witch vibe to it -- at one point I froze in my tracks in the darkness for a minute or two, pondering what to do. Ultimately I realized the sound was coming from a large, steel, high-voltage power transmission tower. I had noticed earlier that that particular tower had been louder than the others in the daylight, buzzing and cracking, but nothing more than that. </p>
<p>The loud, rhythmic "breathing" noise began after the sun-baked tower began cooling down, with a modest 5 MPH wind present. It sounded EXACTLY like an animal slowly "breathing." I'm familiar with the corona discharge effect of such towers. But anyone have any insight into the pitch-black desert "breathing" phenomenon?</p> | 3,005 | [
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] |
<p>Simulations of the Bak-Sneppen Model of Species Evolution (introduced in <a href="http://link.aps.org/doi/10.1103/PhysRevLett.71.4083" rel="nofollow">http://link.aps.org/doi/10.1103/PhysRevLett.71.4083</a>) show that it exhibits Self-Organized Criticality where after a transient only mutation through barriers of height $B_i < B_C$ where $B_C = 0.67 \pm 0.01$ occur spontaneously.</p>
<p>As far as I can tell two studies attempt to show the SOC property of the Bak-Sneppen Model in the Mean Field approximation:</p>
<ol>
<li>Flyvbjerg et al. (1993, <a href="http://link.aps.org/doi/10.1103/PhysRevLett.71.4087" rel="nofollow">http://link.aps.org/doi/10.1103/PhysRevLett.71.4087</a>) formulate the evolution equation for the probability distribution of the barrier values $P(B, t)$ but the argument for the existence of a global attractor is given very tersely as:</li>
</ol>
<blockquote>
<p>Our mean field dynamics is an approximation to the master equation for the Markov process of the random neighbor model, both having one unique attractive fixed point. (Page 4088, last paragraph left column)</p>
</blockquote>
<ol>
<li>In de Boer et al. (1994, <a href="http://link.aps.org/doi/10.1103/PhysRevLett.73.906" rel="nofollow">http://link.aps.org/doi/10.1103/PhysRevLett.73.906</a>) the Markov Process hinted at in the previous publication is studied by deriving the Master equation $P_{n,\lambda}(t)$ where $n$ is the number of sites with a barrier value less than $\lambda$. However as $\lambda \rightarrow \frac{1}{2}$, $P_{n,\lambda} \rightarrow 0$, which I interpret as meaning that there exists a $B_C \ge \frac{1}{2}$. But I do not see how this proves that the critical state is an attractor.</li>
</ol>
<p>Therefore what is the argument for the critical state being a global attractor in the Mean Field Approximation?</p> | 3,006 | [
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<p>There has been recent activity by astrophysicists to determine whether a fourth flavor of neutrino, a sterile neutrino, exists. It would likely be more massive than electron, muon or tau neutrinos. However, it wouldn't be affected by the weak force, only by gravity. It would therefore have similar characteristics to dark matter. The LHC is looking for evidence of supersymmetry, and the existence of the stable neutralino, another dark matter candidate. Can the LHC be of any assistance in helping determine the existence of the hypothetical sterile neutrino? </p> | 3,007 | [
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<p>I recently saw cm^3/g as a unit for amount adsorbed. Usually, you see either kg adsorbate/kg adsorbent or mole adsorbate/kg adsorbent. Does anyone know the meaning of this unit?</p> | 3,008 | [
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<p>Electromagnetic waves travel in straight lines but do all waves travel in straight lines?</p> | 3,009 | [
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] |
<p>How do you obtain the spectral function for advection equation in one dimension?
2.How about 2D?
thanks a lot</p> | 3,010 | [
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<p>Let $B$ be the magnetic field.
If </p>
<p>$$\nabla \times B = 0$$ and of course $$\nabla \cdot B= 0$$</p>
<p>Can we conclude that $B=0$?</p>
<p>For a general field it is wrong because every constant vector will satisfy those conditions.</p>
<p>But for the magnetic field is it enough?</p> | 3,011 | [
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<p>Electron-phonon and electron-defect scattering clearly contributes to resistance, but pure electron-electron scattering conserves the total momentum (and energy) of all the electrons. Then, how is it possible for electron-electron interactions to contribute to electrical resistance?</p> | 3,012 | [
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<p>I am trying to understand and find a way to distinguish two same sounds of different people by some physics formula, so could you guys help me? </p>
<p><p>OK I'll try to explain my question in this way that, for example, there are two people A and B are reading this sentence aloud. <em>"Crackers are Cracking for Crown"</em>.
And if we want to find difference by applying any kind of physics, maths or computer science formula, so and then later we can say this was person A sound or B etc.
</P>
But while finding the difference these points should not matter:</p>
<pre><code>1- volume of the sound
2- pronunciation(obviously it understandable)
3- speed of the sound
4- same voice or different
</code></pre> | 3,013 | [
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<p>So the <a href="http://en.wikipedia.org/wiki/Geodesic_deviation_equation" rel="nofollow">geodesic deviation equation</a> gives the relative acceleration between two geodesics in motion. But given a pair of geodesic (let's say on the two sphere) that start at the equator, separated by some distance. Is there a way to compute their separation as a function of time without using the geodesic equation? Let's say they're moving at northward toward the pole along a line of constant longitude at unit velocity.</p> | 3,014 | [
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<p>I have the following equations</p>
<p>$$\ x′′(t)=−\frac km x′(t)$$</p>
<p>$$\ y′′(t)=−\frac km y′(t) - g$$</p>
<p>where $k$ is the drag, $m$ is the mass of the object and $t$ is the time. $g$ is the gravity constant.</p>
<p>After integrating the functions twice, I end up with the following equations</p>
<p>$$\ x(t) = C_1 e^{\frac {-kt} {2}} + C_2$$
$$\ y(t) = C_3 e^{\frac {-kt} {2}} + C_4 - \frac {gmt}{k}$$</p>
<p>How should I determine the constants $C_1$, $C_2$ etc? I want to be able to set the angle $\alpha$ and velocity $v_0$.</p>
<p>For example $y'(0) = 30 \sin(\alpha)$</p> | 3,015 | [
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<p>In the systems like photon gas in a cavity and phonon gas in a solid number of particles is not conserved and chamical potential is zero. Is this a general rule? If yes, how zero chemical potential is obtained from number non-conservation? </p> | 3,016 | [
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] |
<p><strong>Question:</strong></p>
<p>What isotope has the shortest half life?</p> | 3,017 | [
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<p>Let's assume that we build a giant steel hull in a shape of cube with open top (2km long edge) and lift it to the top of stratosphere and then pump air out of it. Would it float on the outer layer of stratosphere like a ship floats on the surface of water?</p> | 3,018 | [
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<p>A class 1 lever and a class 2 lever are connected in series, on the resistance end of the class one lever is a 500g weight. On the 2nd class lever sits a weight of an unknown mass. From the end of the 1st class lever to the center of the known mass is 46cm, from center of the known mass to fulcrum is 4cm. On the left side of the fulcrum the lever arm is 50cm. The 2nd class lever sits on the force end of the 1st class lever and their arms overlap 2cm. From the end of the 2nd class lever to the center of the known mass is 47cm. From the center of the unknown mass to the 2nd class fulcrum is 45cm. From Fulcrum to the right is 8cm. Calculate the unknown mass. (The answer should be 200g)</p>
<p>Picture representation:
<img src="http://i.stack.imgur.com/b4oBL.png" alt="Picture"></p>
<p>I can't seem to get this to work, I've tried using the $\frac{m_k}{d_k} = \frac{m_?}{d_?}$ with this but to no avail. I've discussed with some others about using the torque of the levers but I can't get that to work either. (Where $t = FL$ and $t_1-t_2 =0=t_3-t_4$ and I can't get that to work either.) Any help would be appreciated!</p> | 3,019 | [
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<p>There is a block of wood on a plank, with friction, and the block is moving down with <strong>uniform speed</strong>. They are asking what is the <strong>torque acting through the center of the block</strong>. </p>
<p><img src="http://i.stack.imgur.com/RicWP.jpg" alt="Force diagram of block on plank"></p>
<p>My doubt is that since the block is moving with <strong>uniform speed</strong> that means that downward force is exactly balanced by force upward due to friction so the <strong>net torque about the center should be zero</strong> but the answer they have given takes into account the downward force $mg \sin \theta$ to calculate the torque, friction is totally neglected.
<strong>And why is the net torque not zero?</strong></p> | 3,020 | [
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<p>I am a novice on this topic. However, I wonder if we use nuclear bombs against the tsunami, will it reduce the speed and impact of the tsunami. Is it possible to break the massive wall of waves using nuclear bombs? In other words, is it possible to create another opposite force which can neutralise/reduce the energy carried by Tsunami by creating an induced wave.</p> | 66 | [
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<p>If the Universe has two 'end points', one being the Big Bang, and the other being heat death, is there anything in the laws of physics which forbid a random fluctuation in the heat death state from being the reason for the Big Bang? My thinking is this: we know that moving along the time axis from the Big Bang to Heat Death, the various states of the Universe are separated by probabilistic quantum mechanical events. We also know from experience that moving in the opposite direction, the states are linked deterministically (if we prepare the state of an electron by measuring its spin along the x-axis, we find there is a 50/50 chance that the spin is +/-1/2. But once we make the measurement, we know that the outcome - say +1/2 with total certainty because it happened. If we then make a measurement along the y-axis, we again have a 50/50 chance of +/-1/2 but after the measurement we again know the result with 100% - say -1/2 for the 2nd measurement. But if we run the process in reverse, we know with 100% certainty the outcomes of both measurements because the future state of the Universe contains the information of the previous states). This is depicted in the picture below.</p>
<p><img src="http://i.stack.imgur.com/ttVDx.png" alt="enter image description here"></p>
<p>Each point is a possible state of the Universe at a given time. An infinite amount of time after the Big Bang, we end up in a state of Heat Death which looks the same no matter what path was taken. From what I understand, there is no sense of direction for the time dimension in space-time (i.e. in general relativity, all the events on the worldline 'exist' together - there is no 'flow of time', future states only contain the information of previous states). So I'm wondering is: Is there any fundamental physical law that prevents us from concluding that a random fluctuation in the Heat Death state, which would result in one of the infinite number of high entropy states that 'preceded' it, is the 'cause' of the Big Bang and the specific worldline of the Universe we experience (because if there is no sense that something 'happens', but rather all events are simply connected by a world line, if one of those states must exist due to a random fluctuation, then all states causally linked to it must also exist - i.e. trace the specific deterministic worldline back toward the Big Bang and you define the complete unique history of the Universe)? </p> | 3,021 | [
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<p>I am currently reading this <a href="http://journals.aps.org/pr/pdf/10.1103/PhysRev.104.563" rel="nofollow">Phys Rev paper</a> by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by
$$\mathbf j_{\pm} = n_{\pm} \mathbf V_{\pm} - D \nabla n_{\pm},$$
where $n$ is the number of spins(up/down). </p>
<p>Now the second term is clear, as this one comes from <a href="http://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion" rel="nofollow">Fick's first law</a>, but the first one is strange. He claims that $V_{\pm}$ is the velocity of positively(negatively) oriented spins (he restricts himself to spin 1/2). Does anybody know what this drift velocity could mean?</p> | 3,022 | [
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<p>The strain energy density is defined as
$$dU = \int_0^{\epsilon_{ij}} \sigma_{ij} d \epsilon_{ij}$$
(see Reddy "Energy Principles and Variational Methods in Applied Mechanics", 2nd Ed, 4.11). Assuming a linear stress-strain relationship, I get
$$U = \frac12 \sigma_{ij} \epsilon_{ij}$$
which is consistent with the literature. Now, if I do the summation and assume symmetry of the stress and strain tensors, I get
$$ U = \frac12 (\sigma_{11} \epsilon_{11} + \sigma_{22} \epsilon_{22} + \sigma_{33} \epsilon_{33} + 2 \sigma_{23} \epsilon_{23} + 2 \sigma_{13} \epsilon_{13} + 2 \sigma_{12} \epsilon_{12})$$</p>
<p>However, in Soedel "Vibration of Shells and Plates", 2nd Ed, 2.6.1, all the "shear terms" (i.e. terms with indices 23, 13, 12) are not multiplied by two. Did I make a mistake, is there some assumption in the Soedel book I might have missed or is this possibly a typo in the book?</p>
<p><strong>Edit:</strong> There is still some confusion on my part. For elastic materials the stresses can be derived from the strain energy
$$ \sigma_{ij} = \frac{\partial U}{\partial \epsilon_{ij} }$$
For orthotropic materials the constitutive relation is
$$ \begin{bmatrix} \sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \\ \sigma_{23} \\ \sigma_{13} \\ \sigma_{12} \end{bmatrix} =
\begin{bmatrix}
C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\
C_{12} & C_{22} & C_{23} & 0 & 0 & 0 \\
C_{13} & C_{23} & C_{33} & 0 & 0 & 0 \\
0 & 0 & 0 & C_{44} & 0 & 0 \\
0 & 0 & 0 & 0 & C_{55} & 0 \\
0 & 0 & 0 & 0 & 0 & C_{66} \end{bmatrix}
\begin{bmatrix} \epsilon_{11} \\ \epsilon_{22} \\ \epsilon_{33} \\ \epsilon_{23} \\ \epsilon_{13} \\ \epsilon_{12} \end{bmatrix} $$
So when I try to get $\sigma_{11}$, that works fine
$$ \begin{align}
\sigma_{11} = \frac{\partial U}{\partial \epsilon_{11} } &= \frac12 (\frac{\partial \sigma_{11}}{\partial \epsilon_{11}} \epsilon_{11} + \sigma_{11} + \frac{\partial \sigma_{22}}{\partial \epsilon_{11}} \epsilon_{22} + \frac{\partial \sigma_{33}}{\partial \epsilon_{11}} \epsilon_{33}) \\
& = \frac12 ( C_{11} \epsilon_{11} + \sigma_{11} + C_{12} \epsilon_{22} + C_{13} \epsilon_{33}) \\
& = \frac12 (\sigma_{11} + \sigma_{11} )
\end{align}
$$
However, for $\sigma_{12}$ I get
$$ \begin{align}
\sigma_{12} = \frac{\partial U}{\partial \epsilon_{12} } &= \frac12 \cdot 2 (\frac{\partial \sigma_{12}}{\partial \epsilon_{12}} \epsilon_{12} + \sigma_{12} ) \\
& = ( C_{66} \epsilon_{12} + \sigma_{12} ) \\
& = 2 \sigma_{12}
\end{align}
$$
which is obviously wrong. This works out fine if you leave out the 2s of the strain energy, as Soedel did. Any clarification would be greatly appreciated.</p> | 3,023 | [
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<p>Here's a question I got in my final exam this morning. "If in a Young's double slit experiment setup, the ratio of intensity of the bright spot to the dark spot is 25:9, what is the ratio of the width of the slits?"</p>
<p>Here's what I did. Since the ratio of intensity at the bright and dark spots is 25:9, the ratio of amplitudes there must 5:3. Which means the amplitude of one wave is 4 times the other. Now, knowing that the amplitude of light through the wider slit is 4 times the amplitude of light through the narrower slit, how can I determine the ratio of the slits' width? I'd appreciate any help even though I skipped the question in my exam, it's been bugging me all day.</p> | 3,024 | [
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<p>We can describe (some of) the dynamics of many systems using fluid mechanics. Of course these include classical fluids like water, more exotic fluids like photon gases and the universe as a whole and even solid(ish) things over long times, like glasses and ice. Further still we can treat general classical systems in phase space using a phase fluid, quantum systems (e.g. Madelung equations) and with a little bit of hand waving anything that happens on a symplectic manifold (which gives us a Hamiltonian and hence a flow and Louiville's theorem).</p>
<p>So what is it about a system that makes it obey a fluid model? Are there systems that definitely do not fit a fluid model?</p>
<p>(I realise that I haven't said exactly what I mean by "fluid model", this is somewhat deliberate. If you like you can take it to mean "having equations of motion which are (almost) identical in some form to the Euler equations".)</p>
<p><strong>edit:</strong>
Since admittedly, the original question wasn't quite clear I'll try to clarify a bit. I'm not looking for a high-school answer, or one which describes only actual literal physical fluids, e.g. "a fluid doesn't support a shear stress", "a fluid is something you can wash your hair with". I've given some examples above of situations that fit this description, and without further explanation I think it's non-obvious what a "mean free path" or similar would mean in a generalised fluid. What I'm really looking for (and there may not be any) is some overarching physical or mathematical principle, or failing that an argument as to why there isn't one. I'd even be quite happy to be directed to a book or more appropriate forum. I apologise for not being clearer before and appreciate the answers already given.</p> | 3,025 | [
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<p>Can a electrostatic field $\vec E=\vec E(x,y,z)$ (time-independent) or electrostatic potential $\phi=\phi(x,y,z)$ be quantized? If yes, will these quanta be photons again? But we don't have an electromagnetic field here.</p> | 3,026 | [
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<p>I once saw a demonstration where an electric current caused a drop of mercury to spin. The drop contained bits of iron, which could be seen flowing around in a circular pattern. As soon as the current was turned off, the spinning slowed fairly quickly. What caused the circular motion within the drop to slow? It seems to me that there would be very little friction within the drop, and that the motion should be similar to that of a gyroscope. Why was this not the case? </p> | 3,027 | [
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<p>I just broke a 120mm computer fan in name of science and now I'm pissed; can anyone explain why this doesn't work? :</p>
<p><img src="http://i.stack.imgur.com/rfwqo.jpg" alt="enter image description here"></p>
<p>The battery should create a potential difference across the motor, causing the fan to spin up, right?</p> | 3,028 | [
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<p>I am in search of a simplified version of the derivation of Newton-Euler equations of motion (both translational and rotational) for a rigid body (3D block) that has a body fixed frame and where the center of mass of the body is not at the center of gravity. I can find elementary derivations for the same system when the center of mass is at the center of gravity, but not for my system in question. </p>
<p>I am using the derivation as background research for a rotordynamics project that I'm working on.</p>
<p>Any help and or references would be greatly appreciated! :) </p> | 843 | [
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<p>A recent article, <a href="http://www.sciencenews.org/view/generic/id/350088/description/Counting_cracks_in_glass_gives_speed_of_projectile" rel="nofollow">Counting cracks in glass gives speed of projectile</a> (Andrew Grant, <em>Science News</em>, May 1 2013) indicates that the number of cracks in a broken glass can tell you information about the speed of the impact that broke it.</p>
<p><a href="http://www.sciencenews.org/view/generic/id/350088/description/Counting_cracks_in_glass_gives_speed_of_projectile" rel="nofollow"><img src="http://i.stack.imgur.com/w6h32.jpg" alt="enter image description here"></a> </p>
<p>However, I'm not quite clear on how this is done and what the physics behind this mechanism is. Can someone explain it to me?</p> | 3,029 | [
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<p>As far as I have read so far,
proper time is the time measured on the clock of an inertial frame moving uniformly with respect to another inertial frame. The concept and the mathematical expression for proper time is originated from the concepts of relativity of simultaneity and time dilation, both of which are evident from the fact that the quantity "interval" between two events remains constant in all the inertial frames. The conclusion is that the quantity proper time has a meaning only when we are talking about an inertial frame of reference. </p>
<blockquote>
<p>I encountered a question in my exam: $$ x(t) = \sqrt{(b^2)+((ct)^2)}
$$ The equation of motion of a particle in the ground frame of
reference is given by the above equation. Calculate the expression for
proper time. (This question is taken by Griffiths, Electrodynamics
book).</p>
</blockquote>
<p>I have two doubts about this question:</p>
<p><em>Does it make sense to define proper time for an accelerating object?</em></p>
<p>Assuming that the answer for Q1 is yes, then is it calculated by transforming coordinates into a new reference frame moving with velocity <strong>v</strong> for every small time <strong>dt</strong>? i.e., for every small change in dt there is a change in velocity of the particle as seen from ground frame. So, do I have to change my frame for every dt time, and sum up the <strong>dT</strong>?
<strong><em>dT</strong> - infinitesimal proper time.</em></p> | 3,030 | [
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<p>I thought that I understand the "Bragg's Law" understanding of crystal diffraction, but recently I read something that made me confused. I understand that if the planes in the crystal have sufficiently small spacing relative to wavelength (more specifically, such that $sin \theta$ in Bragg's Law >1 even for lowest order), then there would be no angles for which constructive interference occurs. Now, I read that if I shoot neutrons at the crystal of sufficiently large corresponding wavelength, then the neutrons will make it through. Why did I get confused by this statement?</p>
<p>Because, suppose we are shooting waves. I would think that scattering still occur, just that at every angle, the waves "cancel" each other out so nothing is observed. In particular, there is still nothing that makes it to the end of the crystal because the wave is scattered as it moves through the crystal. But apparently this is not the case for neutrons. So my question is:</p>
<ol>
<li>Is my understanding with shooting of waves correct? [That the waves are still scattered in all directions, but not observed due to destructive interference.]</li>
<li>Am I right to conclude that the wave model is therefore not an adequate description of neutrons? [I think I can see why neutrons make it to the end if I use probability amplitude analysis instead of thinking of the neutrons as waves.]</li>
<li>What about something like light which can be understood as a wave and as a stream of photons?</li>
</ol> | 3,031 | [
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<p>Is it possible to create matter? In a recent discussion I had, it was suggested that with enough energy in the future, "particles" could be created. </p>
<p>It seems like this shouldn't be possible due to conservation but perhaps I could be wrong. Would any of you Physics masters care to elaborate?</p>
<p>(Note... I will understand the basics, I am by no means an expert.)</p> | 67 | [
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<p>So I'm not OK with how some people derive this equation.</p>
<p>These people consider a pipe whose endings have cross-sectional areas and heights which are different. They then use the conservation of energy principle by saying $dW = dK + dU$ (Where $W$ is work, $K$ is kinetic energy, and $U$ is potential energy).</p>
<p>For this they consider that the work done on the system would be due to external pressure forces exerted on the whole system of water along the pipe. And here comes the part where I disagree: they use this Work to calculate the change in Potential and Kinetic energy for just a small slab of water within the whole system. This is completely invalid isn't it? I mean you would have to consider the entire system, I think.</p>
<p>My way of interpreting the derivation is if you consider just one slab the whole time. Is this a valid way of thinking?</p>
<p>Thanks!</p>
<p>edit: In fact, in one video I saw, the person just says "the middle chunk of water stays the same the whole time, so we can just ignore it".</p> | 3,032 | [
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<p><strong>Disclaimer.</strong> I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any misconceptions present in my question.</p>
<hr>
<p><strong>Background.</strong>
From readings I have done online (mainly on Wikipedia and online lecture notes),
I understand that according to the theory of quantum mechanics,
the possible energy levels of a quantum system are sometimes described using the eigenvalues of a Hermitian operator $H$ called the <strong>Hamiltonian operator</strong> on a (possibly infinite dimensional) Hilbert space,
which is (for convenience) sometimes approximated using a large $n\times n$ Hermitian matrix $\widehat{H}_n$ (i.e., with $n\gg0$).</p>
<p>Furthermore,
I understand that for many very complicated and rapidly fluctuating systems
(such as heavy atomic nuclei),
one is often mostly interested in a <em>generic</em> or <em>typical</em> hermitian operator,
which can be modelled by defining our approximation $\widehat{H}_n$ as a random hermitian matrix.</p>
<p>According to what I have written so far,
I understand at least partially the interest of studying the spectrum of large Hermitian matrices for applications in physics.</p>
<p>However,
when applications in physics are mentioned in <a href="http://en.wikipedia.org/wiki/Random_matrix" rel="nofollow">random matrix</a> theory,
there is usually a lot of emphasis on the <em>invariant</em> random matrix ensembles,
which are ensembles of random matrices $M$ whose distributions are invariant under conjugation by matrices from one of the classical matrix Lie groups.
For example,
the random matrix $M$ is said to belong to a <em>unitary ensemble</em> if the probability distribution of $M$ is equal to the probability distribution of $UMU^*$ for every unitary matrix $U$.
This leads me to the following question:</p>
<hr>
<p><strong>Question.</strong> Is there a <em>physical</em> reason why physicists are especially interested in the invariant ensembles?
While researching this,
I came across the following paragraph in a paper which seems to address this question</p>
<blockquote>
<p>Physically, an invariant random matrix ensemble describes extended (but phase-randomized) states, where the localization effects are negligible. In contrast to that any non-invariant ensemble accounts for a sort of structure of eigenfunctions (e.g. localization) in a given basis which may be not the case in a different rotated basis (remember about the extended states in the tight-binding model which are the linear combinations of states localized at a given
site).</p>
</blockquote>
<p>but given my lack of knowledge of physics jargon,
I don't quite understand what is meant by "localization effects are negligible".</p> | 3,033 | [
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] |
<p>I recently read that:</p>
<blockquote>
<p>"A drop of water landing on a hot plate at $150^o C \:(300 F)$ evaporates in a few seconds.
A drop of water landing on a hot plate at $200^o C \:(400 F)$ survives a whole minute."</p>
</blockquote>
<p>How would you explain this observation using physics principles?</p> | 3,034 | [
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<p>So here is my question: Say we have measured something to be 15,67 mm and the <a href="http://en.wikipedia.org/wiki/Significant_figures" rel="nofollow">significant</a> error is $\pm 0,01$mm. then we convert the measurement to meter to be 0,01567m would the significant error then be $\pm 0.00001$m?</p> | 3,035 | [
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<p>In <a href="http://www.phys.ubbcluj.ro/~emil.vinteler/nanofotonica/PWM/pwmmanual_Guo.pdf" rel="nofollow">this document</a>, what does the line "Write $\vec{G}_i + \vec{G}_i' \rightarrow \vec{G}_i'$" after equation (25) actually mean?</p> | 3,036 | [
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<p>In the following I will give some arguments that will indicate that the gravitational coupling "constant" actually depends on the scale (space and time) of the interacting systems. The question is:</p>
<p>Question 1. Which of the following arguments are invalid?</p>
<p>The following arguments are inspired by the following article:</p>
<p>"Loops, trees and the search for new physics", by Zvi Bern, Lance J. Dixon and David A. Kosower, Scientific American, Special Edition, "Extreme Physics".</p>
<p>The unitarity method (presented in this article and others), is a way of analysing particle processes that bypasses the complexity of Feynman's technique. Virtual particles are the prime reason why Feynman diagrams get so complicated. Virtual particles have both real and spurious effects, but the spurious effects cancel out of the final result (we can call this interference). The key to the success of the unitarity method is that it avoids the direct use of virtual particles. In this approach, it seems that each graviton behaves like two gluons stitched together.</p>
<p>Heisenberg's uncertainty principle will allow transitory fluctuations of energy that would allow processes involving multiple virtual particle loops to occur. These processes will have a very low probability of occurrence p. The average waiting time for such a process to occur will be around 1/p (the less likely the process is, the longer we have to wait, on the average, for it to occur). we also note that there are also many possible combinations, for a fixed number of gravitons and a fixed number of loops.</p>
<p>In QCD, it has been noticed that at very short distances (including distances relevant for collisions at LHC), the coupling diminishes in value, so theorists can get away with considering only uncomplicated diagrams. </p>
<p>A similar phenomenon (but at different relative scales) will appear in quantum gravity (when following the unitarity method, for example), when estimating the gravitational coupling constant (through actual measurement). The waiting time for the occurrence of processes associated with complex Feynman diagrams (that will affect the calculated value of the gravitational coupling constant) will be much longer than for the simple processes. Here I assume that in a theory of quantum gravity, the gravitational coupling constant can be estimated through measurement, and calculated based on the theory (as is the case for the electromagnetic coupling constant in QED).</p>
<p>Related to the dark matter problem, when scientists study the rotational speed of stars in a galaxy as a function of their distance from the galactic center, the system involves distances around thousands of light years (or more), and observation time of months or years. In this case, the gravitational coupling constant will have a greater value than in the case of systems at a lower scale. These scales leave plenty of room for the processes associated to complex Feynman diagrams to occur, thus affecting the value of the gravitational coupling constant (as compared to the Planck length 10^(-35) m, and Planck time 10^(-43) s). The force of gravity will seem stronger at larger scales.</p>
<p>The conclusion is that the gravitational coupling constant actually depends on the scale (in space and time) at which the act of measurement (observation) is performed. This does not exclude the possible existence of massive compact halo objects, WIMP particles, or other attempts to solve the dark matter problem, but I think that it plays a major role in this.</p>
<p>Question 2. Could this solve that dark matter problem?</p> | 3,037 | [
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<p>As a mathematics student with almost no modern physics background (just an introduction to relativity when I was in secondary school) I find Leonard Susskind's lectures videos (freely available in Youtube) very interesting but I am wondering, in which order should I watch them? Which courses first? These are the ones I have found in Youtube:</p>
<ul>
<li>Modern Physics: Quantum Mechanics (<a href="https://www.youtube.com/watch?v=2h1E3YJMKfA" rel="nofollow">https://www.youtube.com/watch?v=2h1E3YJMKfA</a>)</li>
<li>Modern Physics: Special Relativity (<a href="https://www.youtube.com/watch?v=BAurgxtOdxY" rel="nofollow">https://www.youtube.com/watch?v=BAurgxtOdxY</a>)</li>
<li>String Theory and M-Theory (<a href="https://www.youtube.com/watch?v=25haxRuZQUk" rel="nofollow">https://www.youtube.com/watch?v=25haxRuZQUk</a>)</li>
<li>Einstein's General Theory of Relativity (<a href="https://www.youtube.com/watch?v=hbmf0bB38h0" rel="nofollow">https://www.youtube.com/watch?v=hbmf0bB38h0</a>)</li>
<li>Quantum Entanglements (<a href="https://www.youtube.com/watch?v=0Eeuqh9QfNI" rel="nofollow">https://www.youtube.com/watch?v=0Eeuqh9QfNI</a>)</li>
<li>Modern Physics: Classical Mechanics (<a href="https://www.youtube.com/watch?v=pyX8kQ-JzHI" rel="nofollow">https://www.youtube.com/watch?v=pyX8kQ-JzHI</a>)</li>
<li>Cosmology (<a href="https://www.youtube.com/watch?v=32wIKaLkvc4" rel="nofollow">https://www.youtube.com/watch?v=32wIKaLkvc4</a>)</li>
<li>The Theoretical Minimum (<a href="https://www.youtube.com/watch?v=iJfw6lDlTuA" rel="nofollow">https://www.youtube.com/watch?v=iJfw6lDlTuA</a>)</li>
</ul>
<p>I would also appreciate if you could give links to more lectures from him (I mean full courses, there are plenty of talks available)</p>
<p>P.D. Sorry about the bad Tags, but i couldnt find something like 'student, learning, modern-physics'</p> | 3,038 | [
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<p>Each person exists as an unchanging 4D worldtube in the block universe. At each slice of the worldtube there is a present, past and future.</p>
<p>However, there is a black box* which appears to exist in only one slice of the block universe at a time. How could this be explained?</p>
<p>I am not trying to attack the block universe concept, I am not trying to get into metaphysics and I am not trying to come up with my own crack-pot theory. </p>
<p>I would just like to know how a world tube can contain something, a black box, that exists throughout the whole worldtube, and yet creates the illusion of only existing in one slice of the universe at a time.</p>
<p>Is it an imaginary force like the centrifugal force? Or an emergent phenomena such as temperature? Something else?</p>
<p>*The black box is consciousness, but I don't want to use that word as it seems to make physicists run away screaming.</p> | 3,039 | [
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<p>I assume that for a Lorentzian manifold (i.e. with Minkowski signature), the analog of an open ball is the interior of a light cone. My question is motivated by the observation that whereas any point on the boundary of an open ball on a Rimannian manifold (i.e. with Euclidean signature) can be considered to be simultaneously interior to an infinite number of other open balls (and exterior to an infinite number of others) the boundary of a light cone is associated with a metric interval that is distinct from the timelike and spacelike intervals. For that reason, I wonder whether this introduces additional subtleties/restrictions on constructing a spacetime topology. Related to this question is under what circumstances (if any) can individual points be associated with certain kinds of intervals (e.g. Spacelike, timelike, null).</p> | 3,040 | [
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<p>Two balls, first with the mass $m_1$ and the second with the mass $m_2$ are falling from the heigh $h$. Suppose all the collisions are perfectly elastic and do not consider the size of the balls. $m_1 < m_2$ and ball with the mass $m_1$ is on the top.</p>
<p><img src="http://i.stack.imgur.com/463dY.png" alt="enter image description here"></p>
<p>What height $h_1$ will the ball with the mass $m_1$ jump to and what height $h_2$ will the ball with the mass $m_1$ jump to? </p>
<hr>
<p>I think equations as $(m_1+m_2)gh=m_1gh_1+m_2gh_2$ and $(m_1+m_2)v=m_1v_1+m_2v_2$, where $v$ is the velocity of both balls falling, are correct, but I have no idea how to get $h_1$ and $h_2$ independent of each other.</p>
<p>It seems to me, like here is some common operation or relation, that I just don't know, that I have never seen or don't remember... Please don't describe me "you have to do this and this" and "think about what happen when...". I need to see the progress. I need to see these equations and what's happening.</p> | 928 | [
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<p>why airplanes are banned with use of cellphones? What were the impacts while we answer an call or make an call ,what was the <strong>physical</strong> reason behind the ban of using cellphone inside airplanes ?</p>
<p>I expect answer related to physics here</p> | 3,041 | [
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<p><img src="http://i.stack.imgur.com/Pik0X.jpg" alt="enter image description here"><img src="http://i.stack.imgur.com/LL2TD.jpg" alt="enter image description here"></p>
<p>I got confused about the difference between the last term of both pictures. In the first one, we have w x r, but in the second we have w x r underlined. Does anyone have a better explanation? They should be the same.</p> | 3,042 | [
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<p>Electromagnetism implies special relativity and then the universal constant "c". And if we set c=1, the coupling constant has units of angular momentum (so in relativistic quantum mechanics we divide by $\hbar$ and we get the adimensional coupling $\alpha$).</p>
<p>Question, loose, is: In which explicit ways does this angular momentum appear in the classical formalism? Has it some obvious, useful meaning?</p>
<hr>
<p>Edit: some clarifications from the comments.</p>
<p>More explicitly, I have in mind the following. In classical no relativistic mechanics a circular orbit under, ahem, a central force equilibrates $F = K / r^2$ equal to $F= m v^2 / r$, and then we have $K = m r v^2 = L v.$ Thus when introducing relativity we can expect that the angular momentum for a particle orbiting in a central force will have a limit, the minimum possible value being $L_{min} = K/c$. Note that this limit does not imply a minimum radius, we also have classically $K = L^2/ mr $, but m can be argued to be the relativistic mass, so when L goes towards its minimum, m increases and the radius of the orbit goes to zero.</p>
<p>More edit: Given that it seems that my derivation of the Sommerfeld bound $L_{min} = K/c$ risks to be wrong, I feel I should point out that failure, it it is, is completely mine. The original derivation of this relativistic (not quantum!) bound appears in section II.1 of <em>Zur Quantentheorie der Spektrallinien</em> (pages 45-47 <a href="http://zs.thulb.uni-jena.de/servlets/MCRFileNodeServlet/jportal_derivate_00152120/19163561702_ftp.pdf" rel="nofollow">here</a>) and also in Kap 5.2 of his <a href="http://www.archive.org/stream/atombauundspekt00sommgoog#page/n9/mode/2up" rel="nofollow">book</a>. The usual argument goes about generic ellipses and its stability properties.</p> | 3,043 | [
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<p>A familiar trope within science-fiction is that of a large relativistic object hitting a planet such as the earth. This is normally an interstellar spacecraft or a kinetic weapon with a mass in the range 10<sup>3</sup> - 10<sup>6</sup> kg. But what would actually happen?</p>
<p>The two scenarios seem to be: (a) the object creates a kind of conical tunnel through the earth with most of the material exiting on the far side; (b) the object dumps all of its kinetic energy within a few tens or hundreds of kilometres of the impact point and we have the equivalent of a conventional asteroid impact.</p>
<p>Light transit time through an earth diameter of 12,800 km is just over 40 milliseconds. There’s not much time for lateral effects as the object barrels in. So what would happen if a 1 tonne object hit the earth, square on, at 0.99995c (γ = 100)?</p> | 3,044 | [
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<p>Does anybody know the Fermi wavelength of graphene? I searched the Internet for a while without success. I found, by inspection with the Fourier transform of an S.T.M. image
$$
3.84e^{-10} \mathrm{m}.
$$
Is this value of the right order of magnitude?</p> | 3,045 | [
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<p>Is the Oort cloud blocking a substantial amount of light in the visual spectra, making it harder for observers seeing outside the solar system? </p> | 3,046 | [
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<p>Assume this question:
In a simple model of a monovalent metal consisting of point positive ion cores embedded in a uniform jellium of electrons, a value for the average energy for electron is:
$$E = \frac{9}{10} \frac{e^{2}}{r} + \frac{3\hbar^{2}}{10mr^{2}}\left(\frac{9}{4\pi}\right)^{2/3}$$
where r is the radius of a sphere containing one electron. Find the velocity of sound in terms of Fermi velocity.
I'm attempting to solve this question, but I only can find the equilibrium vaule of $r$. I cannot understand the relation between the velocity of sound and this question.</p> | 3,047 | [
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<p>I know that it is dust blocking the light. But what is this dust made of, gases or more heavy materials. If it is gas why is it not already drawn together in nebulas? </p> | 3,048 | [
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<p>From studying waves I find that I can visualise longitudinal waves where the wave propagates in the direction of the displacement. However I don't understand what causes the propagation perpendicular to the displacement in transverse waves. How is a perpendicular displacement caused in adjacent particles?</p> | 3,049 | [
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<p>$$F = \frac{\pi^2 EI}{(KL)^2}$$</p>
<p>Is Euler's buckling formula applicable for impact calculations, considering speeds relevant for a car or aircraft crash? </p>
<p>If there is a level where the formula becomes inapplicable or inappropriate in impact calculations, what determines this, and what behavior (and hence other formula) will then be relevant?</p> | 3,050 | [
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<p>In the context of producing a pulling force perpendicular to the 'spinning plane' of a propeller/fan, <br>
is it correct to say that a <strong>propeller</strong> mainly achieves it's force by being aerofoils producing lift and a <strong>fan</strong> mainly achieves it's force by utilizing Newtons third law?</p> | 3,051 | [
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<p>States of matter in physics are the distinct forms that different phases of matter take on. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma.
What is physics behind States of matter?</p>
<p><strong>For Example:</strong></p>
<p>I found a Trick to freeze water in about half a second, in this trick, When I open caps of a plastic bottle of cold water, cold Water freezes in a chain process, You can see the freezing process.</p>
<p>What is physics of The process of freezing water?</p> | 3,052 | [
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<p>What sense can be made of the natural logarithm, When appearing in a physical process?</p>
<p>For example, This integral in the thermodynamic $\int_i^f \frac {dV}{V}=Ln\frac {V_f}{V_i}$ when $V$ denotes Volume.
in general $Ln\frac {Q_f}{Q_i}$ when the $Q$ denotes Physical quantities.</p>
<p>or this one
$S=k_BLn\Omega$</p>
<p>Why sometimes natural logarithm can be interpreted as a physical process? What are the odds of that happening?</p> | 3,053 | [
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<p>How does Einstein got equivalent mass- energy equation E=mc2 ?</p> | 68 | [
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<p>I'm reading about uncertainty principle, and something has been bothering me for quite a while. There is the formula: </p>
<p>$$\sigma_x \sigma_p \ge \frac{\hbar}{2}$$</p>
<p>I know what this means: <em>the more you know about the position, the less you know about the momentum, and vice-versa.</em> </p>
<p>As an implication of this principle, I see this kind of image: </p>
<p><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/6/62/P_vs_Q_2.svg/640px-P_vs_Q_2.svg.png" alt="image"></p>
<p>And thats my point: as we narrow the hole, we know more about the position, so we are uncertain about... about what? The trajectory? But the state is that <strong>we know more about the position, we know less about the momentum</strong>. So that means: </p>
<p><em>Momentum = Trajectory</em> ?</p>
<p>I don't think so, once momentum is mass times velocity. The mass must be constant - I assume - so the velocity must be changing, and that will make the bean spread out after passing through the hole? How is that? </p> | 3,054 | [
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<p>A <a href="http://www.cnn.com/2013/02/15/world/europe/russia-meteor-shower">report</a> on the Chelyabinsk meteor event earlier this year states </p>
<blockquote>
<p>Russian meteor blast injures at least 1,000 people, authorities say</p>
</blockquote>
<p>My question is </p>
<ul>
<li>Why do meteors explode? </li>
<li>Do all meteors explode?</li>
</ul> | 3,055 | [
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<p>In Kaluza-Klein theories I often see that the compact space is assumed to be an Einstein manifold, that is, its Ricci tensor is proportional to its metric. </p>
<p>So, why is this done?</p> | 3,056 | [
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<p>From the <a href="http://en.wikipedia.org/wiki/Closed_timelike_curve" rel="nofollow">Wikipedia article</a>, it seems that physicists tend to view closed timelike curves as an undesirable attribute of a solution to the Einstein Field Equations. Hawking formulated the <a href="http://en.wikipedia.org/wiki/Chronology_protection_conjecture" rel="nofollow">Chronology protection conjecture</a>, which I understand essentially to mean that we expect a theory of quantum gravity to rule out closed timelike curves.</p>
<p>I am well-aware that the existence of closed timelike curves implies that time travel is technically possible, but this argument for why they should not exist isn't convincing to me. For one, if the minimal length of any closed timelike curve is rather large, time travel would be at least infeasable. Furthermore, this is essentially a philosophical argument, which is based, at least in part, on our desire to retain causality in studying the large scale structure of the universe.</p>
<p>So far, the best argument I've heard against CTCs is that the 2nd law of thermodynamics wouldn't seem to have a meaningful interpretation in such a universe, but this isn't totally convincing. A good answer to this question would be some form of mathematical heuristic showing that in certain naive ways of combining quantum mechanics and gravity, CTCs are at least implausible in some way. Essentially, I'm trying to find any kind of an argument in favor of Hawking's conjecture which is not mostly philosophical. I realize that such an argument may not exist (especially since no real theory of quantum gravity exists), so other consequences of the (non)existence of CTCs would be helpful.</p> | 3,057 | [
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<p>Under the Lorentz transformations, quantities are classed as four-vectors, Lorentz scalars etc depending upon how their measurement in one coordinate system transforms as a measurement in another coordinate system.</p>
<p>The proper length and proper time measured in one coordinate system will be a calculated, but not measured, invariant for all other coordinate systems.</p>
<p>So what kind of invariants are proper time and proper length?</p> | 3,058 | [
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<p>I've seen the claim made several placed; Terning's "Modern Supersymmetry" p. 5 on N=1 SUSY algebra states it as well as anyone:</p>
<blockquote>
<p>The SUSY algebra is invariant under a multiplication of $Q_\alpha$ by a phase, so in general there is one linear combination of $U(1)$ charges, called the $R$-charge, that does not commute with $Q$ and $Q^\dagger$:</p>
<blockquote>
<p>$[Q_\alpha,R] = Q_\alpha, \;\;\;[Q^\dagger_\dot{\alpha},R]=-Q^\dagger_\dot{\alpha}$ </p>
</blockquote>
</blockquote>
<p>The first statement is straightforward to see. But</p>
<p>(1) Why is there is one linear combination of charges that does not commute?</p>
<p>(2) How do we arrive at these commutators? (I imagine that the generators can be rescaled to give the coefficient $\pm1$, but I would like a clearer explanation.)</p>
<p>I spoke to a peer who said that the commutation relations could be found in a very general, mathematically heavy treatment of the most general possible SUSY algebra. Is there some easier way to understand?</p> | 3,059 | [
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<p>In the definition (in one spatial dimension) of $\Delta \tau$ there is the relation:</p>
<p>$(\Delta \tau)^2 = (\Delta t)^2 - (\Delta x)^2$ which is invariant. If $(\Delta x)^2 > (\Delta t)^2$ then there is the characterization "spacelike."</p>
<p>In this case $\Delta \tau$ will be an imaginary number.</p>
<p>My question is: what is the intuitive physical or geometric meaning of imaginary in this context?</p>
<p>(Just a guess; is it related to hyperbolic functions and the Lorentz transformations?)</p>
<p>Thanks</p> | 3,060 | [
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<p>In the <a href="http://en.wikipedia.org/wiki/Quantum_eraser_experiment" rel="nofollow">quantum eraser double slit experiment</a>, does the photon (or wavefunction) pass through one slit or both slits when different polarizers are placed over the slits?</p> | 3,061 | [
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<p><img src="http://i.stack.imgur.com/XvaWP.gif" alt="enter image description here"></p>
<p>Imagine the sliding part of the mirror is controlled by computer and opens on intervals.</p>
<p>Is it possible to increase the power of the beam by making it bounce between the mirrors thus going through the lens and then releasing it resulting in beam with more power ?</p> | 3,062 | [
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] |
<p>The largest Mercury mirror telescope is the Large Zenith Telescope in Vancouver, Canada. When spinning the Mercury is spread out in a layer that is about 2 milimeter thick at every point on the dish.
<br>
<br>
<br>
I want to examine the following simple case: a Mercury mirror located on the equator, spinning counterclockwise. </p>
<p>To form a perfect paraboloid surface the Mercury must experience the same gravitational acceleration at every point on the dish. Then the incline of the dish gives rise to just the right centripetal force towards the center of the dish.</p>
<p>Given the equatorial location the relevant rotation-of-Earth-effect is the <a href="http://en.wikipedia.org/wiki/E%C3%B6tv%C3%B6s_effect" rel="nofollow">Eötvös effect</a>. Let's distinguish between a 'southern half' and a 'northern half' of the Mercury mirror. The Mercury in the southern half experiences too little gravitational acceleration; it will tend to slide outward, up the incline. Conversely, the Mercury in the northern half experiences too much gravitational acceleration, and it will tend to slide down the incline.</p>
<p>To mitigate the distorting effect you could try a tilt of the mirror's spin axis. However, you can counteract the rotation-of-Earth-effect only partially.</p>
<p>The magnitude of the effect is proportional to the velocity relative to the Earth, hence the magnitude of the effect is different at different distances to the center of the mirror. A level of tilt that is just right for the outer rim of the Mercury mirror will be too large for the rest. The best you can do is a compromise that minimizes the effect averaged over the entire dish.</p>
<p>It seems to me that the above qualitative reasoning is unassailable. While distortion due to the rotation-of-Earth-effect can be counteracted, it cannot be eliminated.
<br>
<br>
<br>
However, Paul Hickson, director of the Large Zenith Telescope, has come to an altogether different conclusion.
In a 2001 article titled <a href="http://arxiv.org/abs/astro-ph/0108306" rel="nofollow">Eliminating the Coriolis Effect in Liquid Mirrors</a> he states that the rotation-of-Earth-effect can be eliminated entirely.</p>
<p>I have difficulty following the steps of Hickson's derivation, so much so that I cannot pinpoint the error that I feel must be there.</p>
<p>There is a another article by Hickson on the same subject, published in 2006. <a href="http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-45-31-8052" rel="nofollow">Hydrodynamics of rotating liquid mirrors</a> (Unlike the 2001 article not a free download; I don't have that article). In the abstract it is stated that the shape of the mirror is highly sensitive to the tilt of the axis.</p>
<p>The question is the title of this post: <br>
Mercury mirror telescopes: is it possible to eliminate the rotation of Earth effect?</p> | 3,063 | [
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<p>I just read about a team of physicists at the University of Darmstadt, Germany, that managed to completely slow down a beam of light that traveled through an opaque crystal (article <a href="http://www.newscientist.com/article/dn23925-light-completely-stopped-for-a-recordbreaking-minute#.UfG1bG1ZTJt" rel="nofollow">here</a>).</p>
<p>How is it possible for a beam of light come to a complete stop? In the article they mentioned that they fired a laser at the crystal causing the atoms to go into a quantum superposition. How does this affect the stopping of the light? Also if the uncertainty principle applies to photons (which I do not know if it does), how does this not violate the uncertainty principle if the photons aren't moving?</p> | 3,064 | [
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<p>I was reading a webpage on <a href="http://www.astro.umd.edu/~miller/nstar.html" rel="nofollow">neutron stars</a>, and it mentioned that a neutron star's gravitational mass is about 20% lower than its baryonic mass due to gravitational redshift. I understand the basics of what the terms mean, but I do not see why gravitational redshifting would cause the gravitational mass to be reduced.</p> | 3,065 | [
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<p>There is a charge q at a perpendicular distance z = d from an infinite conducting plate z=0. We use the image method and place -q on the other side of the plate and calculate the field. This field points outwards from the charge q and inwards towards the -q and the field at z = 0 on the x-y conducting plane is $E_{x,y,z=0}=0$ . By this, I mean to say, that if I draw a Gaussian pillbox near the plate, the field points downwards for both the upper and lower sides of the pillbox and thus the closed integral of $E.dA$ goes to zero ? Is that not true ? What I saw that textbooks use the formula $E = \sigma/\epsilon$ and calculate the surface charge density ? How does that work out ? Is it also possible to say intuitively that the net charge induced on the conductor is -q ?</p> | 3,066 | [
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<p>This question is about the Hamiltonian for more than one particle (non-relativistic).</p>
<p>Griffiths (Introduction to Quantum Mechanics, 2e) seems to imply that it is $\displaystyle H=-\frac{\hbar^2}{2}\left(\sum_{n=1}^N\frac{1}{m_n}\nabla_{\mathbf{r}_n}^2\right)+V(\mathbf{r}_1,\dots,\mathbf{r}_N,t)$, but wikipedia isn't so clear: <a href="https://en.wikipedia.org/wiki/Hamiltonian_%28quantum_mechanics%29#Many_particles" rel="nofollow">https://en.wikipedia.org/wiki/Hamiltonian_%28quantum_mechanics%29#Many_particles</a>. </p>
<p>Initially the article quotes that formula, but it quickly gets confusing: </p>
<blockquote>
<p>However, complications can arise in the many-body problem. Since the potential energy depends on the spatial arrangement of the particles, the kinetic energy will also depend on the spatial configuration to conserve energy. The motion due to any one particle will vary due to the motion of all the other particles in the system. For this reason cross terms for kinetic energy may appear in the Hamiltonian; a mix of the gradients for two particles:<br>
$-\frac{\hbar^2}{2M}\nabla_i\cdot\nabla_j$<br>
where <em>M</em> denotes the mass of the collection of particles resulting in this extra kinetic energy. Terms of this form are known as <em>mass polarization terms</em>, and appear in the Hamiltonian of many electron atoms (see below).</p>
</blockquote>
<p>Unfortunately, the author wrote nothing below which might explain where the mass polarization terms come from.<br>
Could I get some mathematical background, maybe a derivation, of why these terms are present in the Hamiltonian, and why they are sometimes omitted/forgotten?</p> | 3,067 | [
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<p>Can I create a device that moves in one direction with a design like Figure 1? I suspect that the forces cancel each other by the recirculation. It is a simple exercise of action and reaction, but I can not figure out the math to explain. </p>
<p>Maybe my problem is of type <a href="http://meta.stackexchange.com/questions/66377/what-is-the-xy-problem">XY problem.</a> </p>
<p>My intention is to create a device that produces movement from a <strong>closed container</strong>, something like a black box. (which would be added energy)</p>
<p>Figure 1.</p>
<p><img src="http://i.stack.imgur.com/dt1NI.png" alt="enter image description here"></p> | 3,068 | [
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<p>For instance, this image: </p>
<p><img src="http://i.stack.imgur.com/6uN1dm.jpg" alt="enter image description here"></p>
<p>shows human eyelashes close up. </p>
<p>The lashes look green, in fact the whole surface area has a strange tint of green Why is this?</p> | 3,069 | [
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<p>I've seen numerous examples where the De Broglie wavelengths of macroscopic objects such as bullets and baseballs have been calculated. However, in each case, the objects are moving fast and the corresponding momentums are large, resulting in tiny De Broglie wavelengths. What happens if you slow the bullet down to almost a stop. It's momentum is now small, so why doesn't it have a measurable wavelength?</p> | 3,070 | [
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<p>I was watching a <a href="http://www.youtube.com/watch?v=P8ZOf8xp1no" rel="nofollow">video</a> and when the car did blow up I asked to me... what happens with the atoms and their bonds when an object blows up of this way? what is the behavior of the atoms and their bonds when an object is on fire? what is the atomic structure of the fire?</p>
<p>thanks in advance :)</p> | 3,071 | [
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<p>The simplest magnetic field is that of an infinitely long wire with uniform current. It does enjoy radial symmetry about the wire and has the variation as 1/r.</p>
<p>To find the direction of the resulting magnetic field you use the right hand grip rule (for conventional current). This rule repeats the experimental fact. But it is a asymmetry. We get a bit less asymmetry calculating the magnetic field for a "anti"wire with positrons. Now we have to use the left hand grip rule.</p>
<p>Where this asymmetry comes from?</p> | 3,072 | [
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<p>So I was reading this: <a href="http://physics.stackexchange.com/questions/11885/invariance-of-lagrange-on-addition-of-total-time-derivative-of-a-function-of-coo?newreg=6fd794fac6bd4ee7beaa30633f9484f5">Invariance of Lagrange on addition of total time derivative of a function of coordiantes and time</a> and while the answers for the first question are good, nobody gave much attention to the second one. In fact, people only said that it can be proved without giving any proof or any.</p>
<p>So, if I have a Lagrangian and ADD an arbitrary function of q', q and t in such a way that the equations of motion are the same, does this extra function MUST be a total time derivative? </p>
<p><strong>EDIT</strong> Ok, I feel really dumb now. I guess the most voted answer of the question I posted was kinda wrong. So, I changed my question a little bit:</p>
<p>If I have a function that obeys the Euler-Lagrange equation off-shell, this implies that my function is a time derivative? This was used in the most voted answer of this other question: <a href="http://physics.stackexchange.com/questions/23098/deriving-the-lagrangian-for-a-free-particle?lq=1">Deriving the Lagrangian for a free particle</a> , equation 7.</p>
<p>Also, why people only talk about things that change the lagrangian only by a total derivative? If this is not always the case that keeps the equation of motion the same, so why is it so important? And why in the two questions I posted about the same statement on Landau's mechanics book only consider this kind of change in the lagrangian? </p> | 3,073 | [
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<p>I have to calculate<br>
$$ i_\rho \times i_\phi $$ it should be $$ i_\theta $$ but in my notes I have $$ - i _\theta $$</p>
<p>Which one is correct? How can I do this kind of operations without mistakes?</p> | 3,074 | [
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<p>Most quantum mechanics texts include a phrase such as 'any ket can be written as a sum of eigenkets of a given observable'.</p>
<p>I have problems with the generalities of <em>any</em> ket.</p>
<p>Does this literally mean <em>any</em> ket, or does it mean any ket of the same observable? It seems odd that any ket, say an eigenket of position, should be expressible as a sum of eigenkets of a different observable?</p>
<p>Edit:
Unless of course a general state is dependent on more than one summation of eigenkets of more than one observable, but the measurement of one of those observables does not depend on the other summations. </p> | 3,075 | [
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<p>Plenty of material on the web will tell you what to expect when you run a 50/60Hz 3-phase induction motor at 60-80Hz, but what if you would like to run it at 140Hz? or 250Hz? Or at any frequency?</p>
<p>Currently we have a 50Hz motor which drives a conveyor via a chain arrangement that gears up by a factor of 2.8 (not by design; more by putting together what was readily available). Since our conveyor represents (as we understand it) a constant torque load, would we not be better off eliminating the chain arrangement with its friction losses, and just directly driving the motor at 140Hz? Would the loss of torque at higher frequency be cancelled out by the elimination of the gearing? Is there anything (dangerously) wrong with trying this?</p> | 3,076 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/1639/whats-the-difference-between-running-up-a-hill-and-running-up-an-inclined-tread">What's the difference between running up a hill and running up an inclined treadmill?</a> </p>
</blockquote>
<p>I want to know how a system can give so many small steps of inclination and so strong to against impact from people running. Thanks</p> | 69 | [
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<p>I have a book saying,</p>
<blockquote>
<p>$\int \delta(x-x')\psi(x)dx = \psi(x')$ where $\psi(x) = \langle x\lvert\psi\rangle$, so our definition of delta function would be $\langle x'\lvert x\rangle = \delta(x-x')$.</p>
</blockquote>
<p>However I could find some documents (<a href="http://hitoshi.berkeley.edu/221a/delta.pdf" rel="nofollow">example</a>; refer to 3. Position Space) saying,</p>
<p>$$\delta(x'-x'') = \langle x'\lvert x''\rangle$$</p>
<p>which corresponds to $\delta(x-x') = \langle x\lvert x'\rangle$.</p>
<p>So the result should be</p>
<p>$$\delta(x-x') = \langle x\lvert x'\rangle (=) \langle x'\lvert x\rangle \tag{1}$$</p>
<p>I think neither of them is an error, because my book uses the definition many times and I have found many documents explaining as $\delta(x-x') = \langle x\lvert x'\rangle$. Is (1) correct?</p> | 3,077 | [
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<p>In a question <a href="http://physics.stackexchange.com/questions/30524/does-a-interstellar-spacecraft-traveling-at-relativistic-velocity-require-contin">here</a> Ron Maimon comments that "relativistic mass makes gravity, not rest mass."</p>
<p>If so, does that mean that the faster that stars orbit the galaxy the larger the relativistic mass of the galaxy therefore more gravity therefore the stars orbit even faster therefore the gravity gets even more therefore the stars keep on getting faster ...</p>
<p>So the speed of stars and mass of galaxy would be correlated with age and history of the galaxy or galaxy clusters and that's why calculations of galaxies' masses don't add up.</p> | 3,078 | [
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] |
<p>Some of the distant galaxies appear to be receding from us faster than the speed of light due to stretch of the space between us and those galaxies.</p>
<p>By an analogy with the <a href="http://en.wikipedia.org/wiki/Ant_on_a_rubber_rope" rel="nofollow">ant on a rope</a> paradox, the light emitted from those galaxies can actually reach us. Is it true that, at one point of time, those galaxies suddenly disappear from our view, and then after sufficiently large times (which may be more than the lifetime of the universe), they come into view again? And by the same reasoning, would more previously hidden galaxies will become visible at some time?</p> | 3,079 | [
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<p>$\newcommand{\ket}[1]{\left|#1\right>}$
I have the next protocol:</p>
<ol>
<li><p>$A$ tosses a fair coin $a\in \{0,1\}$, if $a=0$, $A$ sends to $B$ $\ket{\psi_0}=\ket0$, if $a=1$ $A$ sends to $B$, $\ket{\psi_1}=\ket{+}$.</p></li>
<li><p>$B$ now picks randomly $b\in \{0,1\}$.</p></li>
<li><p>$A$ sends to $B$, the value of $a$.</p></li>
</ol>
<p>After step 1., $B$ measures the state he gets in the basis $\{\psi_a, \psi^{\perp}_a\}$, if he doesn't get $\psi_a$ he wins, otherwise the score is $a\oplus b$, i.e if it's $0$ then $B$ wins, if it's $1$ then $A$ wins.</p>
<p>The question is to find the best strategy for $B$ to win if he's dishonest and $A$ is honest, and it's probability, and when B is honest and $A$ is dishonest to show that there exist a constant positive prob for which $B$ can win the game.</p>
<p>My attempt at solution is as follows:</p>
<p>For the first question:
a. Well, as far as I can see $B$ can only cheat on choosing between b=0 or 1, but still he's left with 50/50 chance of winning, I don't see better strategy.</p>
<p>b. Here when $A$ cheats and $B$ is honest, if $A$ picks $a = 0 \ or \ 1$, and $\psi$ he sends is different than $\phi_a$, then by the criterion of the game $B$ wins. In case $A$ doesn't cheat $B$ has 0.5 chance of winning the game.
So the probability should be (prob. A is dishonest)<em>(prob B to win)+(prob A is honest)</em>(prob B to win)= 0.5*1+0.5*0.5=0.75.</p>
<p>But then again, I might be wrong here. :-(</p> | 3,080 | [
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<p>I'm new here, loving this website and I'm having some difficulty with the wilson-loop operator in kitaev's honeycomb model.</p>
<p><strong>problem statement</strong>
The Kitaev model (<a href="http://arxiv.org/abs/cond-mat/0506438" rel="nofollow">Kitaev, 2006</a> is the original paper) consists of spins residing at the lattice sites of a honeycomb lattice with separate nn couplings for the three directions that are identified for the bonds.
The wilson-loop operator is $w_p=\sigma^x_1 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6$, where the indices $i \in\{1,...,6\} $ indicate the $6$ lattice sites involved in the hexagonal loop (see picture).</p>
<p><img src="http://i.stack.imgur.com/aiT0X.png" alt="Kitaev honeycomb loop"></p>
<p>In Jiannis K. Pachos' book (Introduction to topological quantum computation, 2012) the author states that $(w_p)^2=1$, which I'm trying to find myself. Actually this should be not at all hard, but I'm stuck unfortunately.</p>
<p><strong>attempt at solution</strong> I've tried the following
$$
(w_p)^2 = \sigma^x_1 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \sigma^x_1 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \\
= -\sigma^x_1 \sigma^x_1 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \\
= -\sigma^y_2 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \\
= + \sigma^z_3 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \sigma^x_4 \sigma^y_5 \sigma^z_6 \\
= + \sigma^x_4 \sigma^x_4 \sigma^y_5 \sigma^z_6 \sigma^y_5 \sigma^z_6 \\
= - \sigma^y_5 \sigma^y_5 \sigma^z_6 \sigma^z_6 \\
=-1
$$</p>
<p>Where I've pulled $\sigma_1$ through first, next the $\sigma_2$, etc.
And I've used $\{\sigma^\alpha_i , \sigma^\beta_j \}= 2 \delta_{i,j}\delta_{\alpha,\beta} I_2 $ (so that every swapping of unequal $\sigma$'s gives a minus sign and $\sigma^\alpha_i\sigma^\alpha_i =I_2$ ).</p>
<p>So I get $(w_p)^2=-1$, which is not what I wanted to find. All text on the subject state that $w_p$ acting on a lattice configuration yield $w_p=\pm1 $ which can be easily concluded from $(w_p)^2=1$ (the expression I didn't get).</p>
<p>My guess is that my commutation relations are not correct, but I'm unsure. Who can help me out? A big thanks in advance!</p>
<p>Best,
L</p> | 3,081 | [
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<p>Suppose I have two triangles relatively close together (so they probably shouldn't really be treated as point masses). I want to calculate the gravitational force (and potentially torque?) generated between the two bodies in the 2D plane.</p>
<p>For spheres/circles you can just treat them as point masses and go from there, but can you do that for arbitrary triangles (or tetrahedrons in 3D)?</p>
<p>I know the answer is probably to do a spatial integral across both triangles, but it's been a long time since I knew how to do that :)</p>
<p>The end goal is to be able to compute the gravitational force between arbitrary polygons/polyhedra. I figured decomposing it in to triangles/tetrahedrons would be a good start.</p>
<p>...</p>
<p><strong>UPDATE:</strong></p>
<p>Okay, my multidimensional calculus is a bit rusty, but I think this is a promising direction:</p>
<p>Let:
$\vec{f} = (a - c) \mu_1 + (b - c) \upsilon_1 - (x - z) \mu_2 - (y-z) \upsilon_2 - (z - c)$
be the separation vector between two points on either triangle,</p>
<p>where $a, b, c$ are the vertices of triangle 1, and $\mu_1, \upsilon_1$ are the barycentric coordinates (corresponding to $a$ and $b$) for the point on triangle 1. Likewise for $x, y, z$ and $\mu_2, \upsilon_2$ for triangle 2. Using the barycentric coordinates let's us form the spatial integral to arrive at an answer.</p>
<p>So the (linear, non-torque) force between them is proportional to:</p>
<p>$\vec{F_G} = \displaystyle\int_0^1 \int_0^{1-v_2} \int_0^{1} \int_0^{1-v_1} \! \frac{f}{||{f}||^3} \, \mathrm{d} \mu_1 \mathrm{d} \upsilon_1 \mathrm{d} \mu_2 \mathrm{d} \upsilon_2 $</p>
<p>I think this admits a closed form solution, though I'm still wrestling with Mathematica. I'd really be surprised if this integral hasn't been done somewhere before, though.</p> | 3,082 | [
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<p>The stature and design of the human body. Is it possible that the best physical structure belongs to a human being? If not. What are the flaws in it and what improvements could be done?
Is there actually a perfect physical design in terms of strength and agility?</p> | 3,083 | [
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<blockquote>
<p>If a projectile is launched at a speed $u$ from a height $H$ above
the horizontal axis, and air resistance is ignored, the <strong>maximum</strong>
range of the projectile is $R_{max}=\frac ug\sqrt{u^2+2gH}$, where $g$ is the
acceleration due to gravity.</p>
<p>The angle of projection to achieve $R_{max}$ is
$\theta = \arctan \left(\frac u{\sqrt{u^2+2gH}} \right)$.</p>
</blockquote>
<p>Can someone help me derive $R_{max}$ as given above?</p>
<p>I have tried substituting $y=0$ and $x=R$ into the trajectory equation</p>
<p>$$y=H+x \tan\theta -x^2\frac g{2u^2}(1+\tan^2\theta),$$</p>
<p>then differentiating with respect to $\theta$ so that we can let $\frac {dR}{d\theta}=0$ (so that $R=R_{max}$), but this would eliminate the $H$, so it won't lead to the expression for $R_{max}$ that I want to derive.</p> | 3,084 | [
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<p>When we measure a physical quantity multiple times, we can calculate several values which should help us understand the whole measurement better: Standard deviation, variance, median, average, and so on.
What Im interested in: How many measurements should I take to get a representative number?
Clearly it depends on the variance of the measurable itself...</p>
<p>The following equation gives a starting point, but im unsure how to use it. $\sigma$ is the standard deviation, $e$ the accuracy and $z$ a value that has different values for different wanted certainties.
$$ n \geq \left(\frac{z\sigma}{e}\right)^2 $$</p> | 3,085 | [
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<p>On the Wikipedia page on <a href="http://en.wikipedia.org/wiki/Superfluidity" rel="nofollow">superfluidity</a> one can find the sentence</p>
<blockquote>
<p>not all Bose-Einstein condensates can be regarded as superfluids, and not all superfluids are Bose–Einstein condensates.</p>
</blockquote>
<p>So I was wondering if someone here can give me an example of a system which is superfluid, but not a Bose-Einstein condensate.</p> | 3,086 | [
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<p>This one has been in my mind for years, but I simply can not find any reason for this event.</p>
<p><strong>The Situation</strong></p>
<p>Imagine yourself sitting in the living room while watching television. It's 9 p.m and the news are on. Suddenly the news presenter announce of an event and contacts a field reporter, and start asking him questions or delivers us the exposition for the story.</p>
<p><strong>The Problem</strong></p>
<p>In these cases, most of the times, because that particular event is pretty far away from the studio, there is a time gap between the speech of the news reporter until it gets to the field reporter. Now, naturally you can think - well, thats make sence - the voice, usually travelling through some kind of electromagnetic force by using an antena or a satellite, takes time to travel long distances, thus creating this time gap between it's emerging from the studio and it's arrival to the reporter. And this is where I get to the point - When the field reporter answers back, and start talking, this time gap magically disappears, and you can see that his lips are synchronized with his voice. </p>
<p><strong>The Questions</strong></p>
<ul>
<li>Why is this happening?</li>
<li>Both the studio and the reporter uses the same method to tranfer their voices? If not, why? If yes, why there is a time gap only in one direction?</li>
</ul>
<p>I hope this question is physics related :)</p> | 3,087 | [
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<p><a href="http://en.wikipedia.org/wiki/Ostwald_ripening">Ostwald's Ripening</a> is a phenomenon where the surface area to volume ratio of droplets causes small particles to shrink until they disappear and for droplets above a certain volume to continuously grow. This is due to mechanisms of evaporation and condensation, which I don't fully understand in this specific case. My first thought upon hearing this is "this sounds like black holes".</p>
<p>Hawking Radiation is a mechanism through which a black hole emits matter-energy from its event horizon. The power of this radiation is related to surface area, and in a naive sense, surface area is proportional to mass. This is as opposed to a 2/3rds power in the case of an incompressible drop held together by surface tension, but it's still monotonic and increasing which is what matters for the law to apply. Thus, all black holes are radiating, but small ones are doing so at a much greater rate relative to their mass. There is also a certain cutoff beyond which the temperature of the black hole is lower than the Cosmic Microwave Background (CMB) so the radiative balance can only permit it to grow bigger.</p>
<p>I'm surprised to not find any real mention of Ostwald's Ripening and black holes in the same paper. <strong>Has this terminology ever been entertained by physicists?</strong> I think Ostwald's Ripening is a <em>physical</em> law, although I might be trying to apply it in a cross-disciplinary sense.</p>
<p>Perhaps it's also valid to ask if this applies for cosmology in a larger sense. If the current thinking is to accept an apparent inevitability of a big rip, would the swelling and consolidation of black holes continue indefinitely, or would a lowering of the CMB due to the universal acceleration cause all black holes to evaporate way in the future? Is this question trivial or non-trivial?</p> | 3,088 | [
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<p>Let's say it's a laptop charger not connected to a laptop, and it is frayed near the tip. I am guessing about 20Volts runs through that area. Now if a person touches a bit of plastic below the frayed area, and they receive a painful shock in the finger but not enough to throw them back, about how much percentage of that 20V would they receive? Assume the person was standing barefooted and was reasonably dry.</p> | 3,089 | [
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<p>I don't have any physics background (except the material we did in high school-long time ago).<br>
I was watching a documentary with Stephen Hawking about whether God created the Universe and I could not follow one of the arguments.<br>
<strong>Note:</strong> This is <strong>not</strong> a theological question. I am not trying to determine if the conclusion about God is right or wrong, I am trying to understand the argument from the physics perspective. </p>
<p>One of the arguments (at least as much as I was able to understand it) was that: </p>
<blockquote>
<p>For each positive energy in the universe (plannets etc) there is
an equal negative energy. So the sum of both adds up to nothing. As a
result there is no need for a God.</p>
</blockquote>
<p>To make the argument more clear, the following analogy was presented:<br>
A man on a flat area of sand or dirt wants to make a hill. So the man starts to dig and pile up the sand (or dirt) which is increasing and piling up as a hill.<br>
In the end a hill has been created BUT at the same time a hole has also been created taking equal space as the hill in the oposite direction.<br>
In this example it is clear that both do add up to nothing since if you reverse the process then you return to the original flat area. </p>
<p>What I can not understand are the following: </p>
<p>How can in the analogy and in reality things add up to nothing?I
mean in the analogy with the pile of sand(dirt) the hill and the
hole don't add up to nothing since you always have the original flat
area with sand you started with. So how is this starting state
ignored and it is stated that the 2 opposite forms add up to nothing? Why is the original flat area of sand which is a prerequisite for the existence of both the hole and the hill being ignored?</p>
<p>If someone could help me understand these, but explain it in layman's terms (as I have no physics background) it would be much appreciated.</p> | 3,090 | [
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