question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>Does spinning an object make it heavier? </p>
<p>A real-world example: </p>
<p>I was mowing the lawn in front of my house, a lawn that tends to have some steep inclines. I realized that the lawn-mower was easier to move, and much easier to pull up inclines when it was off than when it was running. The only difference between a lawn-mower that's running and one that is isn't is that the blade is rotating and there's some electricity running through it as it uses up gas. I guess the most significant of those would be the spinning blade.</p>
<p>Does the spinning blade make the lawn-mower heavier as a whole object, and would that mean that spinning objects are heavier than non-spinning objects?</p> | g12948 | [
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<p>To me it seems to come out to be kg/(m*s^2). Is this somehow equivalent to N/m^2?</p> | g12949 | [
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<p>Near a magnetar with $B>B_\rm{QED}$, the strong B field will suppress the Compton scattering cross section of photons with a specific polarization (E-mode). Some references I know deal this problem using time-dependent perturbation in quantum mechanics.</p>
<p>My question is there an intuitive way in QED to see how this takes place and why polarization is important in this case. The electron propagator will be modified. How can we include the background field in the filed theory calculation and derive it?</p> | g12950 | [
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<p>Following up on a comment by BlueRaja to <a href="http://physics.stackexchange.com/a/76758/8563">this beautiful answer of Ilmari Karonen</a>, I would like to phrase this follow up question:</p>
<p>How many air molecules hit your average human's skin during their lifetime? Actually, make that <strong>how many oxygen molecules do you breathe in your lifetime?</strong></p>
<p>(In case you want some motivation: Ilmari calculates that the chance for a random oxygen molecule in the atmosphere (though I note that local effects could actually play a role for this one) to have existed in that form since the time of <em>Homo erectus</em> is about one in 10<sup>14</sup>. However, there's a lot of them molecules, so maybe you <em>do</em> brush up with quite a lot of them often.)</p>
<p>Any takers?</p> | g12951 | [
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<p>It is obvious that there is no change in the mass of it and its radius. But the shape of the object does change. Does it mean its moment of inertia will also change?</p> | g12952 | [
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<p>I have a question relating to uncertinity.The equation used is period of a pendulum.<br>
<br>
T=2π √(l/g)<br></p>
<p>For example consider time to complete 10 cycles by the pendulum as 19.6 (+/- 0.2)s.<br>
I want to know how to calculate the <strong>uncertinity</strong> of
<br>1.period (T)
<br>2.T^2
<br>3.log T</p>
<p><br><br>Any help would be appriciated :)</p> | g12953 | [
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<p>Suppose i have some electrons stored in a empty shell container with a negative ion layer in the inner surface so the electrons keep bouncing inside without being able to leave the inner cavity.</p>
<p>I want to compute the electrostatic pressure that the electrons exert on the shell container. So i assume the electrons have a uniform volumetric charge density $\rho$, and the container has a radius $R_0$. My derivation is as follows:</p>
<p>electric field at radius $r$ is $$\frac{1}{3 \epsilon_0} \frac{\rho r^3}{r^2} = \frac{1}{3 \epsilon_0} \rho r$$</p>
<p>force on an element of charge $dQ = \rho dr dA$ is</p>
<p>$$F = p dA = \frac{1}{3 \epsilon_0} \rho^2 r dr dA $$</p>
<p>which means that the pressure satisfies</p>
<p>$$ \frac{dp}{dr} = \frac{1}{3 \epsilon_0} \rho^2 r $$</p>
<p>which by simple integration leads to</p>
<p>$$ p = \frac{1}{6 \epsilon_0} \rho^2 r^2 $$</p>
<p>evaluated at the shell this gives</p>
<p>$$ p(R_0) = \frac{1}{6 \epsilon_0} \rho^2 R_0^2 $$</p>
<p>Which looks reasonable. But the part that i'm not sure is if this result is sensitive to the assumption that the charge density is uniform inside the volume. The relaxed density of the electrons will tend to be maximum near $R_0$.</p>
<blockquote>
<p>How can i estimate the relaxed density radial function and/or how
will this change my result?</p>
</blockquote> | g12954 | [
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<p>As I remember long ago, in my physics classes, I always had a great trouble understanding the concept of <a href="http://en.wikipedia.org/wiki/Wave" rel="nofollow">waves</a>. Our professor used to explain, as if everything in this world is made up of waves.
However, with any logic, a normal person would always conclude that probably world is created of very small point like <a href="http://en.wikipedia.org/wiki/Particle" rel="nofollow">particles</a>. </p>
<p>So what are waves exactly? I think it's just a type of disturbance that is able to make particles jump up and down? So how come they become an entity? </p>
<p>I would appreciate explanation. (A simple explanation, in lay-man language. :) )</p> | g12955 | [
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<p>I was watching an old cartoon movie where a scientist makes a gadget, which when bound on the wrist, freezes the movement of the whole world. So, that one may do 100s of things in a single second. (The beagle boys later use the gadget to rob a whole bank in 1 second). </p>
<p>The scientist explains the working that the gadget helps in moving "very very fast". So fast that the person who wears it, sees the world, he finds everything frozen. As whatever he is doing is going on 1000s of times faster than the people in the world are doing. </p>
<p>The above explanation is quite logical and easily understandable actually.
So, with this logic, if movement occurs faster, time freezes. More the movement, more the time freezes. </p>
<p>With this thing in mind, how come then theory of relativity claims that
"moving faster may transport you ahead in time".</p>
<p>What I am assuming here is "transporting ahead in time" is probably something exactly opposite of "freezing the time". Am I right? </p> | g12956 | [
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<p>Some amateur scientist asked me that why can't one just simply apply the entire theory of QM at atomic scale to "quantize" celestial system with a different choice of $\hslash$, which he believed can be used to understand celestial orbital configurations, for example, the "discrete" distances from various Solar System objects to the sun, and to somehow "unify" the fundamental forces.</p>
<p>Well I'm pretty sure this has been done before and must turn out to be mathematically invalid. However, can anyone give me some intuitive arguments (not too technical) about why this would not work at all.</p> | g12957 | [
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<p>Consider a homogeneous isotropic universe filled with a perfect fluid with density $\rho$ and pressure $P = \rho/w$. E.g. for $w=-1$ we get a universe equivalent to one with "vacuum energy" or with the cosmological constant.</p>
<p>However, consider now that it is really a perfect fluid with which we can manipulate and $w$ is more or less arbitrary. Considering General relativity, could a <em>relative underdensity</em> of the fluid in the shape of a ring act as exotic matter powering a warp drive of an Alcubierre type? </p>
<p>Note that I want to ask only about the formal solution of Einstein equations and whether a similar metric to the one <a href="http://arxiv.org/pdf/gr-qc/0009013v1.pdf" rel="nofollow">proposed by Alcubierre</a> can be achieved without negative matter density. </p>
<hr>
<p>This question is one of the questions breaking up the discussion of <a href="http://physics.stackexchange.com/questions/128897/how-could-we-travel-to-the-nearest-supermassive-black-hole">this question</a> into smaller pieces.</p> | g12958 | [
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<p>In our everyday experience termperature is due to the motion of atoms, molecules, etc. A neutron star, where protons and electrons are fused together to form neutrons, is nothing but a huge nucleus made up of neutrons. So, how does the concept of temperature arise?</p> | g12959 | [
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<p>My mind has been busy recently by this question:</p>
<p>What is physics of Collision between solid and liquid (or gas)?</p>
<p>What is Conservation law's of such Collision?</p>
<p>Why, when we drop a solid object in water, water shows an Strange behavior (infact what is Conservation law's of energy and momentum when we drop a solid object in water )?</p>
<p>Figure 1: Strange behavior of water after impact</p>
<p><img src="http://wp.streetwise.co/wp-content/uploads/2012/05/water-drop.jpg" alt="Strange behavior of water after impact"></p> | g12960 | [
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<p>Let's assume a setup with a static linear molecule with three identical atoms connected by bonds and a single atom, identical to the other three, being shot at the molecule. Let's also assume that everything happens in 1D and can therefore be illustrated by this simple scheme:</p>
<pre><code>(projectile) A -> A-A-A (molecule)
</code></pre>
<p>Where the direction of the arrow is the direction of motion of the projectile and the dash signs in the molecule are the bonds between atoms. </p>
<p>Assuming a low-energy, non-relativistic, perfectly elastic collision, the projectile will stop dead in its track while the molecule will be set in motion at 1/3rd of the projectile's speed, as it has 3 times the projectile's mass (conservation of Momentum). Balancing also the equations for the Kinetic Energy easily reveals that 2/3rds of projectile's kinetic energy must have been locked away in internal vibrations of the molecule.</p>
<p>Now, it's easy for us to calculate these numbers by considering the projectile and the molecule as just two separate systems and conveniently attaching a total mass to each. But in reality the universe doesn't group atoms into molecules, does it? Each bond in the setup doesn't "know" about the existence of the other bond and each atom could be said to be unaware of all but the atoms bonded or colliding with it. </p>
<p>In this context, not "knowing" total masses, how does the universe "calculates" that in this case the molecule must store 2/3rds of the projectile kinetic energy into internal vibrations, no more, no less?</p> | g12961 | [
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<p>When I vary the action of the YM Lagrangian density $$L = -\frac{1}{4} F^a_{\mu \nu}F^{\mu \nu}_a + J_a^\mu A^a_\mu$$ with respect to the metric, I obtain:</p>
<p>$$T_{\mu \nu} = \frac{-2}{\sqrt{|g|}} \frac{\partial}{\partial g^{\mu \nu}} \left( \sqrt{|g|} L \right) = \frac{1}{4} g_{\mu \nu} F^a_{\sigma \alpha} g^{\alpha \beta} F^a_{\beta \rho} g^{\rho \sigma} - F^a_{\mu \alpha} g^{\alpha \beta} F^a_{\beta \nu} ,$$</p>
<p>where $$F^a_{\mu \nu} = \partial_\mu A^a_\nu - \partial_\nu A^a_\mu +f^a_{jk} A^j_\mu A^k_\nu. $$</p>
<p>$f^a_{jk}$ being the <a href="http://en.wikipedia.org/wiki/Structure_constants" rel="nofollow">structure constant</a> that embodies the properties of the symmetry group under consideration, here $SU(2)$ so that the index $a$ can run over three different values.</p>
<p>My question is, how do I go about showing that this stress energy tensor is invariant under rotations? I was able to show this for the $U(1)$ case with a scalar field, where I got $$T'_{\mu \nu} = R_{\mu i} R_{\nu j} T_{ij} = T_{\mu \nu}$$ using the <a href="http://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" rel="nofollow">FLRW metric</a> in its cartesian coordinate form, and assuming that the time component of the scalar field was zero and $A^a_i = \phi(t) \delta^a_i$ so that the terms arising from taking its derivative only yield diagonal elements. Note that the rotation matrix used was a standard 4 by 4 matrix with 1 as its (1,1) element and sine/cosine on the remaining 3 by 3 block.</p>
<p>Can I do something similar for the above tensor, that is, use the same rotation matrix?</p> | g12962 | [
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<p>I was watching a show on the science channel about gas giants; there is something I do not understand. I am not a scientist, so this may be obvious to some. I learned that there a three states of an given physical object; solid, liquid, and gas depending on how cold or hot the object is. An easy example is ice, water and steam from coldest to hottest. So the theory is that Jupiter has a super-heated solid and very dense core that is made up of hydrogen. How does a gas like hydrogen become a solid while being super-heated? Is it that the pressure is so much that the gas is compressed into a solid? If so how much pressure does it take to compress hydrogen into a solid? How does the heat play into the equation?</p> | g12963 | [
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<p>How about changing H atom to other kinds of atoms?</p> | g12964 | [
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<p>A cube has a side length of 20 cm. An atom in the gas moves around the cube as shown. It continually bounces off the four lateral walls of the cube. The atom has a mass of 6.6×10−27 kg. Because of the elastic collisions with the walls, the atom maintains its speed of 300 m/s as it moves around. The figure below shows the view from above looking down into the cube at the path of the atom.
The repeated hits cause there to be a force applied to each of the four lateral faces. Find the force (in Newtons) that it applies to Face 1. Find the force it applies to Face 2.<img src="http://i.stack.imgur.com/mrgk6.jpg" alt="enter image description here"></p>
<p>I have tried the thing as F=change in momentum w.r.t time
for face 1 chnge inn momentum is 2mv sin(60') how to calculate change in time?</p>
<p>or is there any other approach to the problem??</p> | g409 | [
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<p>The problem is this:</p>
<blockquote>
<p>Consider an electron confined in a region of nuclear
dimensions (about 5 fm). Find its minimum possible
kinetic energy in MeV. Treat this problem as
one-dimensional, and use the relativistic relation between
E and p.</p>
</blockquote>
<p>From Heisenberg's uncertainty relation for position and momentum $\Delta x \Delta p\geq\frac{ℏ}{2}$, $\Delta pc= \frac{ℏc}{2\Delta x}=39.4\text{ MeV}$ where $2\Delta x=5\text{ fm}$ is the width of the region. Plugging this into the relativistic energy-momentum relation $E^2=(mc^2)^2+(pc)^2$, $E=39.4\text{ MeV}$ which is the correct answer.</p>
<p>However, in my book there is also an equation for the zero-point energy which is defined as the lowest possible kinetic energy for a quantum particle confined in a region (one-dimensional) of width $a$ and is given by $\langle K \rangle= \frac{ℏ^2}{2ma^2}$ and the answer I get here is about $1.52\text{ GeV}$.</p>
<p>Why are/should these answers be so different?</p>
<p>Also the questions says "The large value you will find is a
strong argument against the presence of electrons inside
nuclei, since no known mechanism could contain
an electron with this much energy."</p>
<p>How is this argument made exactly?</p> | g12965 | [
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<p>This is kind of hard to explain, because weird as it sounds, i have experienced a phenomenon that i would like to see if it exists and if i can explain it mathematically.</p>
<p>The longitudinal waves of photons( visible light spectrum) had a density and pressure.
It could be sound waves if they can produce light effects in the space( visible,white light), i dont know i am speculating ?.. but for this to happen, i quess, there would have to be very high frequencies of sound waves, which i quess would damage a living organism? I dont know.</p>
<p>I am sorry, for not being very specific, but this is everything i got.</p>
<p>So, my question is : Can there exist a longitudinal wave of light( white light) with density and pressure, that can be felt?</p>
<p>Thank you for your time.</p> | g12966 | [
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<p>A cube has a side length of 20 cm. An atom in the gas moves around the cube as shown. It continually bounces off the four lateral walls of the cube. The atom has a mass of 6.6×10−27 kg. Because of the elastic collisions with the walls, the atom maintains its speed of 300 m/s as it moves around. The figure below shows the view from above looking down into the cube at the path of the atom.
The repeated hits cause there to be a force applied to each of the four lateral faces. Find the force (in Newtons) that it applies to Face 1. Find the force it applies to Face 2.<img src="http://i.stack.imgur.com/mrgk6.jpg" alt="enter image description here"></p>
<p>I have tried the thing as F=change in momentum w.r.t time
for face 1 chnge inn momentum is 2mv sin(60') how to calculate change in time?</p>
<p>or is there any other approach to the problem??</p> | g409 | [
0.05019645392894745,
0.0376928485929966,
-0.012842357158660889,
-0.02513253316283226,
0.011574702337384224,
-0.02843109332025051,
0.050101686269044876,
0.009572552517056465,
-0.06799519062042236,
0.018668191507458687,
-0.012448008172214031,
0.019805409014225006,
-0.033127542585134506,
-0.0... |
<p>Suppose I have an wave source and light waves are radiating from it. If I have a point source, then after a time t, with a radius of ct I will have a circular wave front.By Huygens principle each point on the wave front acts like a secondary source. From this point again light can travel in all directions. So isn't the principle of rectilinear propagation of light violated?<img src="http://i.stack.imgur.com/ipOCi.png" alt="enter image description here"></p>
<p>Consider the light following the specified path shown with the arrow head.</p> | g12967 | [
0.011283093132078648,
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0.007022263947874308,
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0... |
<p>In quantum mechanics, one makes the distinction between mixed states and pure states. A classic example of a mixed state is a beam of photons in which 50% have spin in the positive $z$-direction and 50% have spin in the positive $x$-direction. Note that this is not the same as a beam of photons, 100% of which are in the state
$$
\frac{1}{\sqrt{2}}[\lvert z,+\rangle + \lvert x,+\rangle].
$$
It seems, however, that at least in principle, we could describe this beam of particles as a single pure state in a 'very large' Hilbert space, namely the Hilbert space that is the tensor product of all the $\sim 10^{23}$ particles (I think that's the proper order of magnitude at least).</p>
<p>So then, is the density operator a mathematical convenience, or are there other aspects of quantum mechanics that truly require the density operator to be a 'fundamental' object of the theory?</p>
<p>(If what I mean by this is at all unclear, please let me know in the comments, and I will do my best to clarify.)</p> | g12968 | [
-0.023592012003064156,
0.028184257447719574,
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0.05780902877449989,
0.013919868506491184,
0.0965084359049797,
-0.0027059896383434534,
0.01570364460349083,
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0.04740246757864952,
-... |
<p>How much energy would be necessary to slow down Earth rotation such that a year was 360 days long?</p>
<p>In the same spirit: how much energy would be necessary to make the Earth rotate faster around the Sun such that a year was 360 days long?</p>
<p><em>(Just for fun: how would you do it practically?)</em></p> | g12969 | [
0.04786628857254982,
0.04424848034977913,
0.011572492308914661,
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0.07643036544322968,
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0.015206079930067062,
-0.0263260155916214,
0.020752500742673874,
-0.01942765899002552,
0.017898980528116226,
-0.01... |
<p>Is it possible to unify the strong, weak, electric and magnetic field just by Maxwellian type equations?
(Maxwell by adding a small change - unified electric and magnetic field, then Einstein's equations - use it to create special and general theory of relativity, now maybe all we need is a little more change to unify all fields,)
When $B$ and $E$ are known magnetic and electric fields, then $W$ and $S$ are weak and strong fields, what are their units?</p> | g12970 | [
0.0020940559916198254,
-0.0000902072642929852,
-0.02774074487388134,
0.003210216760635376,
0.03263562172651291,
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0.003069402649998665,
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... |
<p>Let's say I have a uniformly-charged wire bent into a semi-circle around the origin. How can I find the electric field (magnitude and direction)</p>
<p>I'm not even sure if I should use Coulomb's or Gauss' law either. Kind of stuck setting up a solution and starting somewhere.</p> | g12971 | [
0.018406696617603302,
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0.0520038940012455,
0.013383118435740471,
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0.002317434176802635,
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0.00541... |
<p>A long space train's HAL 2000 computer goes wacko and drives the ship and its sleeping crew front first straight into a Black Hole. As it nears/crosses the event horizon, does the space train break up due to gravitational stretching from the rear first, the front first, or evenly ?</p>
<p>Contrary to depictions on YouTube which suggest the closest parts break up first, my quick calculations put the rear under most stress due to huge momentum forces from it being accelerated forward in its weaker gravitational field by the front of the train, as opposed to the front which is in free fall except for being held back by the rest of the space train's increasing momentum. </p>
<p>Think of a merry go round which simulates the increasing gravitational field. A long heavy rubber Bungy stretches more at the centre of the MGR where it is tethered than at the loose end because the tethered end carries the full weight of the Bungy. If it goes around fast enough the Bungy will break off at the tether not at the loose end or in the middle. Am I correct? </p> | g12972 | [
0.002196314511820674,
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0.010842004790902138,
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0.050494808703660965,
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0.006306811701506376,
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-0.051193900406360626,
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-0.00611150311306119,
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-0... |
<p>I got asked this question for my physics course at college, i'm not the best at airspeed velocities...</p>
<blockquote>
<p>What is the airspeed velocity of an unladen swallow?</p>
</blockquote>
<p>I still can't find anything to help me, i'm quite stuck and have been googling and asking about on a few forums.</p>
<p>Best help I found was <a href="http://style.org/unladenswallow/" rel="nofollow">this</a> page on the subject.</p>
<p>Thank you.</p> | g12973 | [
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0.005281577818095684,
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-0.019871020689606667,
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0.04580168053507805,
0.03732718154788017,
0.01... |
<p>New results published about photonic time travel, <a href="http://www.nature.com/ncomms/2014/140619/ncomms5145/full/ncomms5145.html" rel="nofollow">reference</a> here make quantum computers a reality in the near future? These results seem to indicate that there can be qubits that can exhibit nonlinear behaviour, and this in turn may have deep implications to quantum cryptography, and possible profound effects on the nature of unitary interaction, and the influence of decoherence.</p> | g12974 | [
-0.011752883903682232,
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0.030768554657697678,
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0.0... |
<p>I know that the <a href="http://en.wikipedia.org/wiki/Bohr%E2%80%93van_Leeuwen_theorem" rel="nofollow">Bohr-van Leeuwen theorem</a> shows that there could be not consistent pure classical explanation of dia- and paramagnetism. </p>
<p>Does the same theorem also rule out a consistent classical theory of ferromagnetism?</p>
<p>Do you have any realiable references for this?</p> | g12975 | [
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0.00304733170196414,
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0.012450069189071655,
0.012681878171861172,
... |
<p>Let's say $g=10\ \text{m/s}^2$ and it drops for $3$ seconds. For the first second it will drop $10\ \text{m}$, the second it will drop $20\ \text{m}$ ($10 + 10$) and the third second it will drop $30\ \text{m}$. Then if we add $10+20+30$ it equals $60$ but if you use the equation it equals $45$. </p>
<p>Whats the flaw in my thinking?</p> | g12976 | [
0.06998667865991592,
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0.015557383187115192,
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0.05562356114387512,
-0.05025672912597656,
0.03... |
<p>Many aircrafts depend on several types of static pressure sensors (barometers) to find the altitude. I assume this sensor need to be located outside the aircraft main body, so that it has a contact with the outside atmosphere to measure its pressure.</p>
<p>Now, won't the speed of the aircraft has an effect on this barometer? The fastest you are, the faster is the airflow in contact with the pressure sensor, which would cause (erroneous) increased pressure reading.</p> | g12977 | [
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0.02037080191075802,
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0.0271... |
<p>Given a beamsplitter drawn below, where $\hat{a}$ and $\hat{b}$ are input modal annihilation operators, transmissivity is $\tau\in[0,1]$, and output modal annihilation operators are $\hat{c}=\sqrt{\tau}\hat{a}+\sqrt{1-\tau}\hat{b}$ and $\hat{d}=\sqrt{1-\tau}\hat{a}+\sqrt{\tau}\hat{b}$, suppose the inputs $\hat{a}$ and $\hat{b}$ are in photon number (Fock) states $|m\rangle$ and $|n\rangle$, respectively. What are the states of the outputs $\hat{c}$ and $\hat{d}$?</p>
<p><img src="http://i.stack.imgur.com/KKwVy.png" alt="beamsplitter"></p>
<p>I understand that if one of the inputs is a vacuum state $|0\rangle$, then the output states are binomial mixtures of photon number states, with "probability of success" parameter being either $\tau$ or $1-\tau$ and the "number of trials" parameter being the photon number $n$ of the non-vacuum input (so, if $|0\rangle$ was input on mode $\hat{a}$ and $|n\rangle$ on mode $\hat{b}$, then mode $\hat{c}$ is in the state $\sum_{k=0}^n\binom{n}{k}(1-\tau)^k\tau^{n-k}|k\rangle$ and mode $\hat{d}$ is in the state $\sum_{k=0}^n\binom{n}{k}\tau^k(1-\tau)^{n-k}|k\rangle$). I am wondering how this generalizes to both input modes being in the non-vacuum states.</p> | g12978 | [
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0.028726447373628616,
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-0.007411855738610029,
0.03209709748625755,
... |
<p>First question here.
Feel free to write if I posted in the wrong place.</p>
<p>While rotating a ship as accurately as we can around some point within the ship, we can calculate the point of rotation from GPS data collected by a GPS receiver on the ship (the GPS is positioned some distance away from the point of rotation).</p>
<p>From the GPS data we gather, we find the point of rotation to be an ellipse.
Of course due to inaccuracy we cannot find the exact point of rotation from GPS satellites, but is there some physical explanation as to why the point of rotation is an ellipse and not a circle?</p>
<p>For reference we used a Dynamic Positioning system to calculate the point of rotation.
This was a circle.</p> | g12979 | [
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0.0014850650914013386,
0.028965048491954803,
0.04856908693909645,
0.08514847606420517,
-0.0... |
<p>In Faraday's Induction Experiment, the e.m.f. induced in the induction coil becomes zero when the relative velocity of the coil and the magnet becomes zero. But one can also argue from a stationary observer's reference frame. Let's assume the magnet and the coil to be moving at an equal velocity.</p>
<p>For a stationary observer (who measures the induction apparatus in motion), there will be an induced e.m.f. in the region of space around the moving magnet, since there will be a relative velocity between any point in surrounding space and the magnet. Now since the coil moves through this region of space, it should therefore possesses an induced electric field as well.</p>
<p>I totally trust Relativity, and therefore this means that the stationary observer should compute a reverse e.m.f. that exactly cancels out the e.m.f. caused by the moving magnet, or maybe I am on the whole absurdly wrong (in which case I would like to know where my thought experiment went wrong).</p> | g12980 | [
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0.031149789690971375,
0.0054182019084692,
0.00973813... |
<p>The Universe's densest objects are black holes. In the second place, there are neutron stars.<p>
So, if a neutron star compresses to its Schwarzschild radius, would it appear as a black hole? That black hole would be one of the most dense objects in the universe?</p> | g12981 | [
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0.02438012883067131,
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0.006832521874457598,
0.0005386658594943583,
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<p>The aim of the Eötvös experiment was to "prove" that for every (massive) particle, the quotient $\frac{m_g}{m_i}$ is constant, where $m_g$ is the gravitational mass and $m_i$ is the inertial mass.</p>
<p><strong>The experiment:</strong></p>
<p>Consider two objects with coordinates $x(t)$, $y(t)$ and with masses $M_i$, $M_g$, $m_i$, $m_g$ (on the earth where the gravitational field $\mathbf g$ can be considered constant),
connected by a rod of length $r$, and suspended in a horizontal orientation by a fine wire. The Newton's second law says that
$$\ddot {\mathbf{x}}(t)=-\frac{M_g}{M_i}\mathbf g$$
$$\ddot {\mathbf{y}}(t)=-\frac{m_g}{m_i}\mathbf g$$
so if we experiment that the quantity $\eta:=\frac{2|\ddot {\mathbf x}(t)-\ddot{\mathbf y}(t)|} {|\ddot {\mathbf x}(t)+\ddot{\mathbf y}(t)|}$ is very small, then when can conclude that $\frac{M_g}{M_i}=\frac{m_g}{m_i}$ and so we are done. Now textbooks say that if $\ddot {\mathbf{x}}(t)\neq\ddot {\mathbf{y}}(t)$ then we will have a torque</p>
<p>$$N=\eta\, r(\mathbf g\times \mathbf{e_2})\cdot \mathbf{e_1}$$</p>
<p>and misuring this torque we can give an estimation of $\eta$.</p>
<p><img src="http://i.stack.imgur.com/F39RI.jpg" alt="enter image description here"></p>
<p><strong>My problem:</strong></p>
<p>Even if the two accelerations are different, I don't understand where is the torque, the point ${\mathbf{x}}(t)$ will move down and ${\mathbf{y}}(t)$ will move up in my opinion. The angular momentum is along $\mathbf{e_3}$, so the rotation is in the plane $\left<\mathbf{e_1},\mathbf{e_2}\right>$.</p> | g12982 | [
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0.02868252992630005,
-0.037... |
<p>I'm a Computer Engineering major, but when I was in high school I was a very poor student. I didn't pay attention and I didn't think I was capable of succeeding in classes like Math and Science so I just didn't care. I'm much older now and a bit wiser, and because I'm back in school, I realize I may have some potential. </p>
<p>I've always loved science and math but never appreciated it. I left high school knowing only pre-algebra. Now 8 years later I taught myself Algebra through reading and practice, and started attending a community college and placed directly into their Pre-calc class without any Algebra classes. I successfully passed Pre-Calc, Calculus 1 and currently in Calculus 2 all with A's. </p>
<p>I've never taken a Physics course before, but I'm extremely interested in the topic. Will my success in Math translate into success with my upcoming physics courses (calculus based physics is where I'll be starting)?</p>
<p>Is there anyway to prepare to learn physics so that I have a higher chance of succeeding in the course? How much of understanding physics is just natural ability?</p> | g12983 | [
-0.010992533527314663,
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0.018421193584799767,
0.03965916112065315,
0.049230437725782394,
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-0.0720762088894844,
0.01736895553767681,
0.005312808323651552,
0.017443453893065453,
-0.... |
<p>I was having a discussion with a friend about human tolerances of g-force. He believed that the maximum human tolerance of negative g-force is low, in the order of .5 g. I countered, saying that you're able to stand on your head and do not die. An interesting discussion ensued but there was one thing that we couldn't figure out:</p>
<p>Is there any difference between the negative g-force when you are standing on your head (i.e. you're stationary on the ground, just upside down, experiencing gravity) and negative g-force when you're in motion? For example, like when you are riding a roller coaster that has a bump in the track, and you're forced up from your seat?</p> | g12984 | [
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-0.06... |
<p>For one dimensional quantum mechanics $$[\hat{x},\hat{p}]=i\hbar $$</p>
<p>Does this fix univocally the form of the $\hat{p}$ operator? My bet is no because $\hat{p}$ actually depends if we are on coordinate or momentum representation, but I don't know if that statement constitutes a proof. Moreover if we choose $\hat{x}\psi=x\psi$ is the answer of the following question yes?</p>
<p>For the second one </p>
<p>$$(\hat{x}\hat{p}-\hat{p}\hat{x})\psi=x\hat{p}\psi-\hat{p}x\psi=i\hbar\psi $$</p>
<p>but I don't see how can I say that $\hat{p}$ must be proportional to $\frac{\partial}{\partial x}$. I don't know if trying to see that $\hat{p}$ must satisfy the Leibniz rule and thus it should be proportional to the $x$ derivative could help. Or using the fact that $\hat{x}$ and $\hat{p}$ must be hermitian</p>
<p>Any hint will be appreciated.</p> | g12985 | [
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0.0018987333169206977,
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-0.044918689876794815,
... |
<p>I find some variation in the values reported for ephemeris by the various sources I have access to. For example for 2012-11-27T03:31:55 UTC I get solar declination values of <a href="http://www.wolframalpha.com/input/?i=sun%20declination%20at%203:31:55%20AM%20GMT%202012-11-27" rel="nofollow">-21.1828°</a>, <a href="http://reference.wolfram.com/mathematica/ref/AstronomicalData.html" rel="nofollow">-21.18296°</a>, <a href="http://nancocad.com/sundec/sundec.htm" rel="nofollow">-21.1814°</a>, <a href="http://store.simulationcurriculum.com/products/pro-plus" rel="nofollow">-21.1834°</a>, <a href="http://www.stellarium.org" rel="nofollow">-21.1906°</a> and (again) <a href="http://www.celnav.de/longterm.htm" rel="nofollow">-21.1814°</a>. Are the differences among these values meaningful? Is there an "authoritative" source (ideally online) for ephemeris data?</p> | g12986 | [
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0.06253049522638321,
... |
<p>I mean, in the sense that the act of closing curtains would somehow reduce the amount of heat loss of the house to the outside, thus making it warmer <em>for a given supply of heating</em>. </p> | g12987 | [
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-0.04725472256541252,
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0.03253094106912613,
0.08... |
<p>Is there any example of a symmetry breaking phase transition in a system of particles under isothermal expansion?</p> | g12988 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/41291/why-i-think-tension-should-be-twice-the-force-in-a-tug-of-war">Why I think tension should be twice the force in a tug of war</a> </p>
</blockquote>
<p>For (A) in this image, I would think the tension should be should be 2mg.
<img src="http://i.stack.imgur.com/x7zBm.gif" alt="enter image description here"></p>
<p>However, my book says the weight in (A) should be only mg. I don't understand why the tension should not be the same as in (C) and double the tension in (B).</p> | g410 | [
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<p>We are given a graph of the position of a wave (amplitude).
How can we calculate the wavelength, frequency and the maximum speed of a particle attached to that wave?</p>
<p>We have </p>
<p><em>Speed = wave length $\times$ frequency</em>, </p>
<p><em>$W=2 \pi \times$ frequency</em> ,</p>
<p>$V_{max}=A\times W$.</p>
<p>So how to calculate A?</p>
<p><img src="http://i.stack.imgur.com/9vkUA.png" alt="enter image description here"></p> | g12989 | [
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<p>It is often seen that according to physics the light changes it's velocity according to the medium through which it is traveling. So can it be explained that why so happen?</p> | g298 | [
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<p>The title is slightly misleading. I really want to know if the randomness and probabilities observed in quantum mechanics is really just the result of a chaotic (yet deterministic) system.</p>
<p>If it is not simply a chaotic system, how do we know?</p> | g12990 | [
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<p>I'll start out with the cliche attempt in a protective shield of my dignity. I am a young highschool kid just eager to learn and understand. If I'm way off or this is already a known idea, or maybe this post is in the wrong area, I would appreciate a nonchalant and informative correction.</p>
<p>When I imagine space-time as a 3D fabric, I see actual threads of fabric, each weave is a certain length that can stretch or shrink. I'd also like to point out that I see space and distance as different things. As in a meter can still be a meter if no space-time fabric exists. So my question is; is time the rate at which one moves through the threads? </p>
<p>I have many reasons for why I thought this, I'll name a few:</p>
<ol>
<li>The universe (including space-time) is expanding, so if it is stretching and moving then that could be what causes time to flow forward.</li>
<li>When going the speed of light, time stops apparently, with my idea, I figured the speed of light could be = to the speed of the expanding space-time. Therefore if you move at the speed of light and are moving in-sync with space, then the rate at which you move through space is 0, meaning time is 0.</li>
<li>The speed of light could be constant relative to us inside the universe as $x = k/y$ where x = the speed of the expansion of space and y = time.</li>
<li>When approaching a black-hole, time slows down. This could be because it stretches space(the threads stretch out) making the same distance cover less threads, making a slower time.</li>
</ol>
<p>perhaps: $time = \frac{threads}{distance}$</p>
<p>and </p>
<p>$(speed of expansion of space) = \frac{(speed of light)(distance)}{(threads)}$</p>
<p>Ultimately my idea (not all here) has come to the conclusion that we live in a black hole.</p>
<p>I really just don't have anyone to discuss my physics questions with, so I would like to know what you all think, why this doesn't work, or really just any input. Thanks</p> | g12991 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/39165/linear-algebra-for-quantum-physics">Linear Algebra for Quantum Physics</a> </p>
</blockquote>
<p>Can you get all/most of the knowledge you need of Linear Algebra for QM in a one year course? I know for certain my course also includes eigenvectors and eigenvalues towards the end of the year..</p> | g53 | [
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<p>According to the paper:
A. S. Parkins and H. J. Kimble, Phys. Rev. A 61, 52104 (2000).
<a href="http://pra.aps.org/abstract/PRA/v61/i5/e052104" rel="nofollow">http://pra.aps.org/abstract/PRA/v61/i5/e052104</a></p>
<p>You can entangle position and momenta of two atoms by using entangled light. Atoms A and B are located at sites A and B. You get entangled light by parametric-down-conversion and send one photon to atom A and the corresponding entangled photon to atom B. You keep on sending entangled pairs until atom A and B come to a steady-state and they will be entangled with each other. Essentially what is happening is that "entanglement is transferred from a pair of quantum-correlated light fields to a pair of trapped atoms in a process of quantum state exchange."</p>
<p><img src="http://i.stack.imgur.com/ou0PZ.png" alt="enter image description here">
The atom is trapped in the x direction. The atom is stuck in a harmonic potential. The entanglement is only in x direction.</p>
<p>position are anti-correlated between two atoms: (q1 = -q2) and momentum are correlated (p1 = p2)</p>
<p>You can measure the position and momenta of each particle using homodyne measurement techniques. So, if I were to measure the position of atom A very very precisely, then its momentum would be very uncertain. Its distribution would be so smeared out that it'd be approaching a uniform distribution of momentum, if position is a sharp delta function. <em>At this point, there would exist a probability that the momentum is very large, and thus its kinetic energy would be very large too! KE = p^2/2m.</em> (Need a checking here) <strong>Would there be a non-negligible probability that the energy of the atom would be so large it would escape the harmonic oscillator trap?!</strong></p>
<p>Since the two atoms are entangled, p1 = p2, thus atom B would also have correlated momentum which translates to correlated kinetic energy. Atom B would also have enough energy to escape the harmonic trap as well.</p>
<p>If everything I have stated is correct, haven't I found a method to communicate via translational entanglement, because I can control the outcome of the measurement? (Unlike spin...) Let's say we have an ensemble of these entangled atoms. A scientist at Lab A can send a binary message by choosing to measure the position of an atom at Lab A to high precision thereby causing the atom at Lab B to escape the harmonic trap. Not measuring would keep the atoms trapped. The presence or absence would correspond to a 1 or a 0. Since there would exist chances that the momentum would not be large enough to cause an escape, then we could have batches of entangled atoms that would represent one bit. Very costly, but you can interact instantaneously over large distances...</p> | g12992 | [
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<p>brachistochrone problem: Suppose that there is a rollercoaster. There is point 1 ($0,0$) and point 2 ($x_2, y_2)$. Point 1 is at the higher place when compared to the point 2, so the rollercoaster rolls down from point 1 to point 2. Assuming no friction, we want to build a rollercoaster path from point 1 to point 2, so that the rollercoaster will reach point 2 from point 1 in shortest time. </p>
<p>So, time taken would be defined as $$\text{time (1} \rightarrow 2) = \int_1^2 \frac{ds}{v}$$</p>
<p>Then, the textbook says that v=$\sqrt{2gy}$.</p>
<p>Then, $ds = \sqrt{dx^2+dy^2} = \sqrt{x'(y)^2 +1} \, \, dy$</p>
<p>Then, $$\text{time (1} \rightarrow 2) = \frac{1}{\sqrt{2g}} \int_0^{y_2} \frac{\sqrt{x'(y)^2 + 1}}{\sqrt{y}} \, dy$$</p>
<p>Then, $f(x,x',y)$ is defined as $$f(x,x',y)=\frac{\sqrt{x'(y)^2 + 1}}{\sqrt{y}}$$</p>
<p>As per Euler-Lagrange equation,</p>
<p>$$\frac{\partial f}{\partial x} = \frac{d}{dy}\frac{\partial f}{\partial x'}$$</p>
<p>The left-hand would be zero, so
$$\frac{\partial f}{\partial x'} = \text{constant} = \frac{1}{2a}$$</p>
<p>Then $$x' = \sqrt{\frac{y}{2a-y}}$$ and $$x = \int \sqrt{\frac{y}{2a-y}} \, dy$$</p>
<p>The textbook then says that substituting $y=a(1-\cos\theta)$ would aid solving the integral.</p>
<p>How does this make sense?</p> | g12993 | [
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<p>How do I integrate the following?</p>
<p>$$\frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx$$</p>
<p>where $C$ is a constant.</p>
<p>I'm supposed to get a Gaussian function out of the above by integrating but don't know how to proceed.</p> | g12994 | [
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<p>It's an old-new question (I found only one similar question with unsatisfactory (for me) answer: <a href="http://physics.stackexchange.com/questions/68381/where-did-schrodinger-solve-the-radiating-problem-of-bohrs-model">Where did Schrödinger solve the radiating problem of Bohr's model?</a>)</p>
<p>It's strange for me how all books simply pass by such an important question, and mentioning strange and mathematically unsupported reasons such as:</p>
<ul>
<li><p>orbits are stationary (while as I know this is just idealization, there is no stationary orbits in reality even for Hydrogen) </p></li>
<li><p>electrons are actually not localized due to uncertainty principle, thus they have no acceleration (while obviously in a non-spherically symmetric orbits a kind of "charge acceleration distribution" always exist)</p></li>
<li><p>vacuum fluctuations play a major role (according to QED).</p></li>
</ul>
<p>I'm not interested in how Bohr or Schroedinger explained it, I want to see a rigorous proof with QM, QED or maybe even the standard model as whole. I would like to see how this question was <strong>closed</strong>.</p> | g770 | [
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<p>This might be a silly question, but if every atom has its own gravitational force could atoms or molecules be attracted to each other over vast distances in the void of space if there were no other greater forces being applied? Is this similar to the cooling/slowing theory?</p> | g12995 | [
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<p>I have a question about deriving the coordinate representation of momentum operator from the commutation relation, $[x,p]= i$.</p>
<p>One derivation (ref W. Greiner's Quantum Mechanics: An Introduction, 4th edi, p442) is as following:
$$ \langle x|[x,p]|y \rangle = \langle x|xp-px|y \rangle = (x-y) \langle x|p|y \rangle. $$
On the other hand, $ \langle x|[x,p]|y \rangle = i \langle x|y \rangle = i \delta (x-y)$. Thus
$$ (x-y) \langle x|p|y \rangle = i \delta(x-y). \tag{1} $$</p>
<p>We use $(x-y) \delta(x-y) = 0$. Take the derivative with respect to $x$; we have $\delta(x-y) + (x-y) \delta'(x-y) = 0$. Thus
$$ (x-y) \delta'(x-y) = - \delta(x-y). \tag{2} $$</p>
<p>Comparing Eqs. (1) and (2), we identify
$$ \langle x|p|y \rangle = -i \delta'(x-y). \tag{3} $$</p>
<p>In addition, we can add $\alpha \delta(x-y)$ on the right-hand side of Eq. (3), i.e.
$$ \langle x|p|y \rangle = -i \delta'(x-y) + \alpha \delta(x-y), $$
and $[x,p] = i$ is still satisfied. We can also add
$$ \frac{\beta}{\sqrt{|x-y|}}\delta(x-y)$$
on the RHS of Eq. (3). Here $\alpha$ and $\beta$ are two real numbers.</p>
<p>My question is, what is the most general expression of $\langle x|p|y \rangle$? Can we always absorb the additional term into a phase factor like Dirac's quantum mechanics book did?</p>
<p>Thank you very much in advance.</p> | g12996 | [
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<p>In section 3.4.1 of Griffiths' <em>Introduction to Electrodynamics</em>, he discusses electric multipole expansion.</p>
<p>He derives the formula or the electric potential of a dipole, which I follow, but right after, he begins talking about the electric potential at a large distance, which is as follows: </p>
<p>$$V( \vec{r}) = \frac{1}{4 \pi \epsilon _{0}} \int \frac{\rho (\vec{r}')}{ℛ} dV$$ </p>
<p>$ℛ$ is from some point inside the charge distribution to the point P. <strong>What exactly does $\vec{r}'$ denote?</strong> Is it the distance from the center of the charge distribution? </p>
<p>Next, he uses law of cosines to find the expression for $ℛ^{2} = r^{2}+(r')^{2}-2rr'\cos\theta'$. This gives the same question as above, what does the symbol $r'$ mean?
Then he defines $ℛ = r(1+ \epsilon)^{1/2}$, where $\epsilon \equiv \left(\frac{r'}{r}\right)^{2}\left(\frac{r'}{r}-2\cos\theta^\prime\right)$.
The proceeding part is where I really get lost:</p>
<blockquote>
<p>For points well outside the charge distribution, $\epsilon$ is much
less than 1, and this invites a binomial expansion.
$$\frac{1}{ℛ} = \frac{1}{r}\left[1- (1/2) \epsilon+ (3/8) \epsilon ^{2} - (5/16) \epsilon ^{3}+\ldots\right]$$ </p>
</blockquote>
<p><strong>What is going on in this last step?</strong></p>
<p>And finally, we eventually derive the formula
$$V(\vec{r}) = \frac{1}{4 \pi \epsilon _{0}} \sum ^{\infty}_{n=0}\frac{1}{r^{n+1}} \int(r')^n\,P_{n}(\cos \theta)\,\rho( \vec{r}')dV $$</p>
<p>Why did we go for all this trouble? If this is supposed to be the electric potential at a large distance, <strong>couldn't we have just used $V( \vec{r}) = \frac{1}{4 \pi \epsilon _{0}} \int \frac{\rho (\vec{r}')}{ℛ} dV$</strong>? I don't understand what this equation <em>actually means</em> in physical terms. </p>
<p>And in regards to the actual equation, <strong>what is $P_{n}$</strong>? </p>
<p>Any help is much appreciated. </p> | g12997 | [
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<p>I'm reading <em>Quantum Liquids</em> by A.J. Leggett and became confused by the following statement in the first chapter.</p>
<blockquote>
<p>Consider now a pair of such identical atoms. In the absence of appreciable coupling between the hyperfine and (atomic center-of-mass) orbital degrees of freedom, the energy eigenfunctions can always be written as a product of a “spin” function (i.e. a function of the hyperfine degrees of freedom) and an orbital function (i.e. a function of the coordinates of the atomic nuclei). The symmetry of the orbital wave function under exchange of the two atoms is $ (−1)^L $ where $L$ is the relative orbital angular momentum. As to the spin wave function, the combination of two atomic (intrinsic) angular momenta each equal to $F$ yields possible values of the total dimer intrinsic angular momentum $K \equiv \left| F_1 + F_2 \right| $ equal to $0, 1, \ldots , 2F$.</p>
</blockquote>
<p>$F$ here is the total atomic spin.</p>
<p><strike>I have trouble understanding how the relative phase of the wave function results from the <em>difference</em> between the magnitude of the angular momenta when their $z$-projections ($z$ being the quantization axis) are not known.</strike></p>
<p><strike>Does anyone know how $L$ and $K$ are determined?</strike></p>
<p>Ok, so "relative" here had to do with "relative motion" and not "difference".<br/>
Now... does anyone know the reasoning behind the factor of $(-1)^L$ ?</p> | g12998 | [
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<p>I understand that combining deuterium and tritium will form helium and a neutron. There are three methods to do this (1) tokamak (2) lasers and (3) cold fusion. I would like to know after helium is formed. How is that energy extracted from tokamak and stored? </p> | g12999 | [
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<p>Up until now I've explained relative time to myself as looking at the 3D world from different four-dimensional perspectives, analogous to how looking at a 2D-ish object (eg. a sheet of paper) from different angles makes it appear to change shape.</p>
<p>Also, I've used this representation below to explain how the time at which an event occurs could change depending on the body's reference system. This representation uses two bodies that move relative to each other, $B1$ and $B2$, to represent the time of occurrence of events $E1$ and $E2$.</p>
<p><img src="http://i.stack.imgur.com/KsZ2r.png" alt=""></p>
<p>(<em>Not very precise — blame MS Paint :P — but my intent should be clear.</em>)</p>
<p>I am not sure, but as far as I know $t(E1) \le t(E2)$ should hold true for any reference system (order should be preserved), which means that the drawing is correct. But I just realized that in certain cases, it is possible for $E2$ to occur before $E1$ (according to my representation): </p>
<p><img src="http://i.stack.imgur.com/8X5n9.png" alt=""></p>
<p>Here you can see that $B3$ and $B2$ have entirely different perceptions on the order of the two events, but that would break causality, so it cannot be true. What is wrong in my representation of relative systems of reference?</p> | g13000 | [
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<p>I don't understand the following reasoning that I found in a set of lecture notes from a physics course, it's about Perrin's stimate on $N_{a}$ Avogadro's number via the bariometric formula</p>
<p>In order to stablish that formula, the reasoning begins with Boltzmann distribution</p>
<p>$$\frac{n(E)}{n(0)}=\exp\left(-\frac{E}{k_{B}T} \right) $$</p>
<p>For a single particle, under the action of the Earth's gravitational field</p>
<p>$$E=\frac{p^2}{2m}-mgz $$</p>
<p>In the equilibrium</p>
<p>$$E=-mgz$$</p>
<p>substitution upon Boltzmann's distribution</p>
<p>$$\frac{n(z)}{n(0)}=\exp\left(-\frac{-(mgz)}{k_{B}T} \right) \propto \exp(z) $$</p>
<p>completely wrong</p>
<p>In the lectures notes that problematic minus sign is omitted. Where is (are) the error(s)?</p> | g13001 | [
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0.0300041... |
<p>Topological order are sometimes defined in opposition with the order parameter originating from a symmetry breaking. The latter one being possibly described by a Landau theory, with an order parameter. </p>
<p>Then, one of the distinctions would be to say that <em>topological order can not be described by a <strong>local</strong> order parameter</em>, as <em>e.g.</em> in <a href="http://physics.stackexchange.com/a/34175/16689">this answer by Prof. Wen</a>. I thus suppose that a Landau theory describes a <em>local order parameter</em>. </p>
<p>I have deep difficulties to understand what does <em>local</em> mean ? Does it mean that the order parameter can be inhomogeneous (explicit position dependency), as $\Delta\left(x\right)$ ? Does it mean that one can measure $\Delta$ at any point of the system (say using a STM tip for instance) ? (The two previous proposals are intimately related to each other.) Something else ?</p>
<p>A subsidiary question (going along the previous one of course) -> What is the opposite of <em>local</em>: is it <em>non-local</em> or <em>global</em> ? (Something else ?) What would <em>non-local</em> mean ? </p>
<p>Any suggestion to improve the question is warm welcome.</p> | g13002 | [
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0.0... |
<p>I've seen many Young-Earth Creationists attempt to <a href="http://crev.info/2012/01/cosmologists-forced-to-in-the-beginning/">discredit</a> Big Bang cosmology. For example, an article by Cal Thomas in the 1990's stated that it meant there was a "pre-eternally existing 'cosmic egg' that decided to explode." A new refrain I keep hearing that there was pre-eternally existent energy.</p>
<p>My layman's understanding of Big Bang cosmology is that there was a "start" to matter, space, time, <strong>and energy</strong>. The Young Earth retelling, in contrast, would say "pre-eternally existent energy, then turning into these other things."</p>
<p>Even the theme song for Big Bang Theory says:</p>
<blockquote>
<p>Our whole universe was in a hot dense state, </p>
<p>Then nearly fourteen billion years ago expansion started, wait</p>
</blockquote>
<p>Which, seems to be a popular re-telling of what I presumed was the YEC distortion of the Big Bang model itself. Temperature and density pre-existed, according to the song.</p>
<p><strong>QUESTION: What references or very short articles explicitly define the Big Bang model in terms of "what-was-before"? <em>Was there energy sitting around?</em></strong> </p> | g13003 | [
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<p>Why does there have to be a singularity in a black hole, and not just a very dense lump of matter of finite size? If there's any such thing as granularity of space, couldn't the "singularity" be just the smallest possible size?</p> | g13004 | [
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<p>Let's say that a hot gas is trapped in a metal box. This metal box is magnetically suspended in another structure with a low temperature. The inner box does not touch anything. And there is a void in the structure. To me there seems to be no way for heat transfer to occur. Will the gas change its temperature with time? </p> | g13005 | [
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<p>Since l=0 for a valence electron in 5s state of silver, L=0 and therefore magnetic dipole moment is also 0 which means that the beam should not have deflected at all. So, we introduced the property of an electron called spin which explains the deflection. However, my problem is How the introduction of spin explains the splitting of beam into two parts ?</p> | g13006 | [
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<p>I was looking in New Scientist the other day when I saw something to do with the Higgs boson, energy levels, entropy, space/time, quantum oscillations and many other things. It was in a feature to do with symmetry. I have read up about this and I know that the magazine does not accept original works, so I guess that this is mainstream physics.</p>
<p><img src="http://i61.tinypic.com/28sltnm.jpg" alt="higher energy levels are brighter"></p>
<p>The above is a diagram of what I'm talking about. This is how it appears in the magazine:</p>
<p><img src="https://scontent-b-lhr.xx.fbcdn.net/hphotos-xfp1/t1.0-9/q71/s720x720/10255610_10152371905339589_1518379512515532344_n.jpg" alt="Their diagram..."></p>
<p>According to NS, a ball (like the blue one above) that is sitting at the top of a piece of space/time warped like this has an unstable energy level and position. Given the slightest nudge, it will "fall" into a lower energy state and quantum oscillations (which occur as is "rolls" up and down the "pit") caused by the uncertainty principle create Higgs bosons in the Higgs field.</p>
<p>I have pondered this repetitively, and it still looks like nonsense (even in the eyes of quantum physics). What I want to know is: has this been regarded as true or is this "complete nonsense"? And if so, how can the uncertainty principle cause such things to happen?</p>
<p>--ADDITION TO QUESTION--</p>
<p>What I do not understand is how a vacuum generates Higgs particles if it has no mass - unless it's trading it with energy.</p>
<p>What is actually happening (the magazine hasn't described it in enough detail for me to understand)?</p>
<p>(It's hard for me to visualise; it's an entirely new concept to visualise for me.)</p> | g13007 | [
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<p>So in my engineering statics course we have been doing a great deal of work with trusses and machines, and a part of the physics behind it has really been confusing me. Just as a note, I also have been trying to use matrices/inversion once I have my family of equations since I also like trying to use linear algebra to solve problems. While I find this topic interesting I keep having problems creating my family of equations to solve from. One thing in particular I noticed that if I try to use 2 moments from one of my free body diagrams and I start trying to solve my equations I typically get a singular matrix. For example:</p>
<p><img src="http://i.stack.imgur.com/FpKpQ.png" alt="enter image description here"></p>
<p>Determine reactions on member ABCD at A and D.</p>
<p>If I take this whole body as a FBD, I did the sum of the x-component forces, y-component forces, and the moment about F. However, since this has 2 reactions at A an d2 at F I need four equations to solve the final FBD. But when I tried using the moment about A I get a linear combination of the other variables, and when I tried the moment about E the same result occurred. </p>
<p>I might be making a mistake in the following way, but if not then theres an even bigger question at hand:</p>
<p>I have simplified the pressures into resultant forces that gives the total magnitude of force applied, and placing this force at the center of application (@ point E for the uppoer 2kN m rectangle and @ point C for the 2kN m triangle). Are these resultant forces not usable for moment calculations?</p>
<p>currently I had these equations I was using (sorry don't know latex yet)</p>
<pre><code>sum Fx = Ax - Fx + 3kN = 0
sum Fy = Ay + Fy - 4kN = 0
sum Mf = -Ay - 3kN*2m - 4kN*1m = 0
sum Ma = 1m*Fy - 3kN*2m = 0
sum Me = -Fx*3m + Ax*3m - 3kN*1m - Ay = 0
</code></pre>
<p>only 1 moment equation provides any new information to the system. If I am not making a mistake the core question I have is why? Why does looking at a different moment not yield any new information about the system?</p> | g13008 | [
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... |
<p>Let suppose that $\vec{F}$ is the velocity vector field of of a fluid in space, and $\vec{s}$ is a straight path of arbitrary length. Let's suppose that $\vec{F}$ and $\vec{s}$ are parallels and point in the same direction, so that $\vec{F} \cdot \vec{s} = F s$. How can we account for the total amount of fluid that moves along the path (per unit of time).</p>
<p><a href="http://math.stackexchange.com/questions/849581/line-integral-as-circulation-but-why#comment1752006_849611"><strong>Related question</strong></a></p> | g13009 | [
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<pre><code>Firstly, I am sorry if this seems like a joke. It is not.
</code></pre>
<p>I have always loved the Dragon Ball series, so this question has been on my mind for a while.
Can any of you figure out why time would move slower in a " 'hyperbolic' time chamber?" (this seems like a relevant physics question for a fan of the show). Does it have anything to do with the fact that hyperbolic inverse tangent is utilized in special relativity? In addition, if one could survive for months in 10x earth's gravity, would one actually get that much stronger? It does seem like they would, just by drawing a free body diagram.. But would this ever be a logical method to use for strength training? Would your entire body get proportionally stronger? (also, all of my tags are just guesswork for this question, as any of them may apply)</p> | g13010 | [
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0.00183... |
<p>This isn't a question of how a wing works -- vortex flow, Bernoulli's principle, all of that jazz. Instead, it's a question of why we need a wing at all. A wing produces lift, but why is that necessary?</p>
<p>I got to this by thinking of an airplane at a coarse level. The wing produces lift through <a href="http://physics.stackexchange.com/questions/290/what-really-allows-airplanes-to-fly">some interesting physics</a>, but it needs energy to do this. The engine is what ultimately provides all of this energy (let's assume no headwind, and in "ultimately" I'm not including chemical energy in the fuel, yadda yadda "it all comes from the sun"). That means the engine pushes enough air, and fast enough, to (a) offset gravity and (b) still propel the plane forward. So the question is: <strong>why can't we just angle the engine down a bit and get the same effect?</strong></p>
<p>To slightly reword: why do wings help us divert part of an engine's energy downward in a way that's more efficient than just angling the engine?</p>
<p>One answer is that we can do exactly that; I'm guessing it's what helicopters and VTOL airplanes like the Harrier do. But that's less efficient. Why?</p>
<p>One analogy that comes to mind is that of a car moving uphill. The engine doesn't have the strength to do it alone, so we use gears; for every ~2.5 rotations the engine makes, the wheel makes one, stronger rotation. This makes intuitive sense to me: in layman's terms, the gears convert some of the engine's speed-energy into strength-energy.</p>
<p>Is this analogy applicable -- is the wing on a plane like the gearbox in my transmission? And if so, what's the wing doing, more concretely? If a gear converts angular speed to increased force, what X does a wing convert to what Y?</p>
<p>None of the answers I could guess at satisfied my intuition. If the wing converts horizontal speed to vertical speed, tipping the engine downward would seem to have the same effect. If it's changing the volume/speed of the air (more air blown slower, or less air blown faster), it would still have to obey the conservation of energy, meaning that the total amount of kinetic energy of the air is the same -- again suggesting that the engine could just be tipped down.</p>
<p><strong>EDIT</strong></p>
<p>In thinking about this more from the answers provided, I've narrowed down my question. Let's say we want a certain amount of forward force $S$ (to combat friction and maintain speed) and a certain amount of lift $L$ (to combat gravity and maintain altitude). If we tilt our engine, the forces required look like this:</p>
<p><img src="http://i.stack.imgur.com/lIIVr.png" alt="vectored thrust"></p>
<p>The total amount of force required is $F = \sqrt{S^2 + L^2}$. That seems pretty efficient to me; how can a horizontal engine + wing produce the same $S$ and $L$ with a smaller $F'$?</p> | g13011 | [
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0.... |
<p>I'm hearing a guy ( Tom Cassidy ), which supposedly has a master in physics, saying that what we expect in a physical experiment ( for example, observing some particle ) can actually interefere with the workings of the experiment. Is he distorting quantum mechanics terms and facts to use it with his purpose ( what we think internally can actually interfere with the external world ) ? </p>
<p>Here is more or less of what he said : </p>
<p>We can measure an electron to be at two different places at the same time.And we can also observe an electron as a particle or as a wave depending on what we set the experiment to observe.. It makes no sense but WHAT we are actually looking for, creates the result. Because its all the experiment, it's not humans thinking "oh, it would be nice if the results came that way ... ".
What we expect to see, we see ... then we design the experiment in a different way and expect something else ... and thats what we see ! It makes no sense, thats why we don't understand Quantum Mechanics.
The scientists know this. When you are doing a quantum mechanics experiment, you are looking to observe somthing as a particle, you open up a box ( figurative ) and what you see is a particle. What you are looking for, it knows you are looking for .. thats how quantum mechanics works .. An electron will exist in the bottom of an energy well, it has really low probability of getting outside of that energy well ( the energy required is insane ) but every so often electroncs magically tunnel into the walls ( energy walls ) .. Why do they do it ? I don't know ... and anyone who says they know why it works, they are lying ... they don't know, nobody knows why quantum mechanics is the way it is ... </p>
<p>Then some people might directly think that Quantum Mechanics is like Law of attraction : "You think and it happens ". But it's not as simple as that.What we found is that this is the way of how results are found in quantum mechanics. Quantum mechanics works for the very very very very small , but recently , just last week i was reading a study which says that Quantum Mechanical entanglement effects have been observed in much larger things ... groups of atoms as high as fifty. Last week, there was a study in the New Scientist in the UK which reported that quantum mechanical effects have been observed between pairs of diamond crystals. And the relation of size between Diamond crystals and our brain is a lot smaller than the difference between particles and diamond crystals. Now, the final question is ... how big are thoughts ? It's so when you start thinking " its actually real ". You talk of people between the law of attraction and they say, oh its so mambo-jambo, now they can think its ideas are actually based on science ...</p>
<p>So, is there at least some truth to it ( even if its not true that quantum mechanical effects work for a pair of diamonds ) ?</p>
<p>Thanks a lot in advance.</p>
<p>EDIT :
Just did some search and it seems like the final part of the top answer in this link <a href="http://physics.stackexchange.com/questions/54975/quantum-entanglement-whats-the-big-deal">Quantum Entanglement - What's the big deal?</a> might suggest some kind of influence of one electron in another electron, physically distant from it"</p> | g13012 | [
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0.0038782558403909206,
0.01062000822275877,
-0.029... |
<p>What does it take to become a top physicist?</p>
<p>Why do so many extremely talented young upstarts totally flop as they move to more advanced physics?</p> | g13013 | [
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-0.005... |
<p>So I was given the following homework problem:</p>
<blockquote>
<p>You land on an unknown planet somewhere in the universe that clearly has weaker gravity than Earth. To measure g on this planet you do the following experiment: A ball is thrown upward from the ground. It passes a windowsill 15.0 m above ground and is seen to pass by the same windowsill 2.00 s after it went by on its way up. It reaches the ground again 5.00 s after it was thrown. Calculate the magnitude of g (the acceleration due to gravity) at the surface of this planet.</p>
</blockquote>
<p>I found a solution on answers.yahoo.com, but I still don't really understand it as well as I would like.</p>
<p>I drew a picture and know that after 15m it takes 2secs to fall back to 15m and then an additional 5secs until it hits the ground. I can't assume that the velocity is uniform for entire trip can I? (e.g. 6secs travel time going both up and down/quadratic curve, for total 12secs) I have the 4 equations of kinematics and usually I just look where I can plug in values and simply get the answer, but obviously that's not going to help me to solve slightly more advanced problems such as this!</p>
<p>Could someone please give me advice on how to approach this problem (and/or physics problems in general). Anything that can help me conceptualize these better. I just want to be able to solve these without staring at it for 5hrs...Thanks in advanced.</p> | g13014 | [
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0.0020928706508129835,
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-0.0077527971006929874,
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0.04981311410665512,
0.04285876825451851,
0.0... |
<p>At this website:</p>
<p><a href="http://heasarc.gsfc.nasa.gov/docs/swift/analysis/threads/uvot_thread_afterglows.html" rel="nofollow">http://heasarc.gsfc.nasa.gov/docs/swift/analysis/threads/uvot_thread_afterglows.html</a></p>
<p>The passage at the bottom states that a V-band magnitude of 17.62, with an error $\pm$0.02 is a 49.4-$\sigma$ detection significance.</p>
<p>How is this value calculated? Could you provide the working? I have a similar problem, with a set of magnitudes and errors, and would like to know at what magnitude limit I can claim a statistically significant (6-sigma) detection.</p>
<p>Thanks</p> | g13015 | [
0.03600624203681946,
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0.07973369210958481,
0.04977789893746376,
0.... |
<p>Are strange metals described by a quantum critical theory?</p> | g13016 | [
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0.03913949802517891,
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0.062478236854076385,
0.009015468880534172,
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<p>In General Relativity, a totally rigid body cannot be accelerated. It will behave like something of infinite mass. </p>
<p>Similarly a body of two separated particles which connected to each other with a highly rigid bond, will be difficult to accelerate. The more rigid bond is, the more difficult will it be to accelerate the system.</p>
<p>As such, my question is, can any particle's mass be a measure of rigidity of the bonds of its fundamental components?</p> | g13017 | [
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<p>I need to verify that the solution for vanishing <a href="http://en.wikipedia.org/wiki/Weyl_tensor" rel="nofollow">Weyl tensor</a> is conformally flat metric $g_{\mu\nu} = e^{2\varphi}\eta_{\mu\nu}$. The most convenient way to show this is to prove that Weyl tensor is invariant under conformal transformation of the metric. How to prove this fast?</p>
<p>I have the idea to build 4-rank tensor which include terms with curvature tensor, Ricci tensor and scalar curvature and then use the requirement on invariance under infinitesimal conformal transformations. If I can show that it is Weyl tensor, I can also prove the statement. But do some alternatives exist?</p> | g13018 | [
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<p>The energy level of an electron could be shifted by an electric field. $\langle n, l,m|[L_z,z]|n^{\prime},l^{\prime},m^{\prime}\rangle=(m-m^{\prime})\hbar \langle n, l,m|z|n^{\prime},l^{\prime},m^{\prime}\rangle$. Because $[L_z,z]=0$, we must have $m= m^{\prime}$ for non-vanishing $\langle n, l,m|z|n^{\prime},l^{\prime},m^{\prime}\rangle$. This is one selection rule in Stark effect.</p>
<p>Then how to rigorously prove $l^{\prime}=l\pm1$ is the other selection rule for $\langle n, l,m|z|n^{\prime},l^{\prime},m^{\prime}\rangle\neq0$?</p> | g13019 | [
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-0.04491506144404411,
0.0... |
<p>If we cannot define a proper time (or synchronize clocks in different positions) in an inertial frame (independent with the theory of relativity), there seems to be no direct way to confirm the 2 postulates of Einstein. Is that true?</p>
<p>Consider an inertial frame, which is associated with a proper coordinate $(t,x,y,z)$. It seems like there is no way for observers in different positions of this frame to synchronize their clocks. If they move to 1 position to do so, they must accelerate, and they have completely destroyed their inertial frame.</p>
<p>If there is no way one can measure the time in different positions of an inertial frame, how real is the $t$ coordinate of the frame?</p>
<p>Is there any convention to measure such $t$? If there is, how true it is compared with the "real" inertial time?</p>
<p>However, in the end I feel like there is no way we can measure $t$ in different positions without destroying the inertial frame. Therefore it seems like we cannot truly measure the velocity of anything.</p>
<p>I ask this question because there may be a request for proving the constancy of the speed of light, and to measure the speed of light (from A to B) we have to synchronize 2 clocks, which is a very subtle process.</p> | g13020 | [
0.025083839893341064,
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0.028872476890683174,
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0.0... |
<p><img src="http://i.stack.imgur.com/oCVEr.jpg" alt="block-spring system"></p>
<p>I am reviewing for an exam next week, and this is one of the questions I am stuck on. I have the mass-spring system above with spring constant $k$ on a frictionless incline. I would like to find the total energy of the system at any time $t$.</p>
<p>I know that the total energy of the system is going to be the sum $E = K + U_g + U_s $</p>
<p>My first question is that I am confused about how to approach the problem. If I take my axes along the ramp, then the problem becomes one dimensional. My idea was set up my coordinate system like that so I could describe the displacement of the mass around it's equilibrium position on the ramp so I could find $K + U_s$, and then switch back to a more traditional coordinate system where I take my axes along the perpendicular sides of the ramp to find $U_g$. Does this approach work? If not what should I be doing?</p> | g13021 | [
0.06987330317497253,
0.025563977658748627,
0.015773888677358627,
0.00914650410413742,
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0.008835997432470322,
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0.0... |
<p>I am doing msc physics. And we are studying major part of scattering theory. I used <em>Quantum Mechanics</em> by Davydov, Griffiths, etc, to study scattering theory. But I am not understanding it properly, hence I want a specific book which will explain scattering theory very clearly. </p> | g98 | [
0.028845831751823425,
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0.02557862363755703,
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0.052097026258707047,
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0.013902057893574238,
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<p>Having a layman level of logic about probability ( read about it 10 years ago, so pardon if it's still not right completely) what i know that the calculation requires some knowledge about the number of total possibilities vs outcomes. Say for a coin there are total 2 and 1 outcome each time. So "50%" .
So, if the same math needs to be applied to know the ( accurate ) probability about the existence of life or a similar planet like earth, what would be the prerequisite knowledge ? And how a mathematician will proceed to do the math on it ? </p>
<p>Also, the number of outcomes from big-bang is quite large. In that way the probability to have something similar to earth must too be large. But then why, practically this probability is still zero ? </p> | g411 | [
0.042809225618839264,
0.05104576423764229,
0.03018752671778202,
0.00957148801535368,
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0.054401248693466187,
0.02640... |
<p>In Landau Mechanics (third edition page 4), why does adding Lagrangians of two non interacting parts remove the indefiniteness of multiplying each Lagrangian by a different constant?</p>
<p>If both systems are completely non-interacting, I can perfectly create a new Lagrangian L = a*L1 + b*L2 and still maintain validity of the Euler-Lagrange equations and make the action integral perfectly stationary, with a and b different. Can't I?</p>
<p>Here's the original statement:</p>
<blockquote>
<p>It is evident that the multiplication of the Lagrangian of a mechanical system by an arbitrary constant has no effect on the equations of motion. From this, it might seem, the following property of arbitrariness can be deduced: the Lagrangians of different isolated mechanical systems may be multiplied by different arbitrary constants. The additive property, however, removes this indefiniteness, since it admits only the simultaneous multiplication of the Lagrangians of all the systems by the same constant.</p>
</blockquote>
<p>I kind of understand that, of course, after you create L = L1 + L2, xL = xL1 + xL2 but nothing stops me from multiplying each Lagrangian of each non interacting part by <em>different</em> constants a and b and <em>then</em> summing, like: xL = xaL1 + xbL2</p>
<p>So the statement seems without meaning for me. Could anyone clarify? Thanks!</p>
<p>One addition: I see that, if both systems are interacting externally, the constants must be equal (and the proportion of masses becomes relevant). My goal is exactly that: to understand, conceptually, how he derives the role of ration of masses later on in page 7. Going back to the text, what confused me is that the whole thing starts with the assumption that both system are <em>closed</em> so any external interaction is dismissed:</p>
<blockquote>
<p>Let a mechanical system consist of two parts which, if closed (..), and the interaction between them may be neglected, the Lagrangian of the whole system tends to: lim L = La + Lb.</p>
</blockquote> | g13022 | [
0.0625402182340622,
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0.024768516421318054,
0.0013105020625516772,
0.0... |
<p>MY thoughts: I think it will not be as the expression for RMS value is dependent only on the peak value of current. Is my thinking correct? </p> | g13023 | [
-0.006730858702212572,
-0.002482370473444462,
0.0033937846310436726,
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0.01079921331256628,
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0.08620309829711914,
-0.05483182147145271,
... |
<p>We know that when we strike a metal, it usually has a characteristic "sharp" sound, unlike when we strike wood, say.</p>
<p>What characterizes this "metallic sound"? Does it have a well-defined power spectrum? What are its generic properties?</p>
<p>Also, why do metals have a metallic sound?</p>
<p>My best guess would be that metals have high Young's / Bulk modulus and so the resonances for typically sized metals should be at fairly high frequencies, and since they are very elastic, they wouldn't dissipate energy all that easily, so the resonances would have small FWHM and hence be sharp. So my guess is that a "metallic sound" has distinct resonance peaks in its power spectrum, whereas for a piece of wood, for example, these peaks merge into each other to create a continuum.</p> | g13024 | [
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0.039870485663414,
0.0168869998306036,
0.0098... |
<p>Very simple homework question which I managed to get wrong:</p>
<blockquote>
<p>"The weight of a box sitting on the floor points directly down. The normal force of the floor on the box points directly up. Need these two forces have the same magnitude? (y/N)"</p>
</blockquote>
<p>My answer was yes, the correct answer is no. I must be missing some important concept here, may someone help me think of a realistic scenario in which the magnitudes are not equal?</p> | g13025 | [
0.06338206678628922,
0.04934851452708244,
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0.0018765830900520086,
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0.012148461304605007,
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-0.0030337399803102016,
-0.026... |
<p>If I only know $x$- and $y$- coordinates of every point on a trajectory without knowledge of time information, is there any way to approximate Cartesian acceleration angle at each point? Time interval between every two points is very small, ~0.03 second. </p> | g13026 | [
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0.0361... |
<p>Step #1 Imagine one preforms an electron based Double-slit-experiment and one does so with only one electron being fired at a time. </p>
<p>Step#2 Also included in the experiment is an unobserved alternating opening of the double slits such that there is only one slit open at a time, and that each individual alternating ( the single process of closing of 1 slit and the opening of the other ) occurs during the gap time period that is present between the individual electrons being fired. </p>
<p>Knowledge of which slit each electron goes through is therefore NOT being observed.</p>
<p>Thus does an interference pattern still arise over time here to ?</p>
<p>If so, could you please present any data concerning proof of this in particular experiment, thus in turn eliminating any assumption.</p>
<p>Note:<em>Time is required to accumulate an interference pattern in the double slit experiment, just like it is in the Kim et al Delayed Choice Quantum Eraser experiment of the year 2000.</em></p>
<p><em>But in this Delayed Choice Quantum Eraser experiment, what makes the experiment possibly astonishing is that, unlike in the classic double-slit experiment, the choice of whether to preserve or erase the which-path information of the idler was not made until 8 ns after the position of the signal photon had already been measured by detector D0.</em> </p>
<p><em>Thus this Delayed choice experiment raised questions about time and time sequences.</em> </p>
<p><em>Two separate events, the position detecting of the signal photon and the determining of the which-path information of the idler photon, occurred at two different times, yet despite being separated by time, both were taken into account to produce a single final outcome.</em></p>
<p><em>Thus my above double-slit experiment arises. Does one electron interfere with another electron despite being displaced by time, or does a single electron interfere only with itself.</em></p> | g13027 | [
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0.010595... |
<p>Why are <a href="http://en.wikipedia.org/wiki/MHV_amplitudes">MHV amplitudes</a> so important? How/where are they used and why do people keep trying to rederive them in many different ways?</p> | g13028 | [
0.03832569345831871,
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0.096... |
<p>I'm just learning about relativity, and every equation I see for a galilean transformation of frame $S'$ (moving with uniform velocity in the $x$-direction with respect to frame $S$) is $x'=x-vt$, $y'=y$, $z'=z$, $t'=t$. My question involves the $x'$ term. Don't these equations assume that frames $S$ and $S'$ align together (origins $O$ and $O'$ are the same point) at $t=0$? This assumption is not explicitly stated in my textbooks, and it seems like the general formula should be $x'=x-x_0-vt$, where $x_0$ is the distance (in $x$-direction) the $S'$ frame is away from the $S$ frame (along the $x$-axis) ath $t=0$. This wouldn't change the velocity transformation formula, because $x_0$ is constant. Am I right about this? If so, why doesn't the canonical form for a galilean transformation include this initial displacement term?</p> | g13029 | [
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0.029907220974564552,
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0.004535219632089138,
0.04416964575648308,
-0.05565... |
<p>Let's say you are observing the movement of the Sun and Earth from very far away. After year 1, the Earth creates an orbital plane around the Sun. Since the objects in the universe induce forces of different magnitudes on the Earth and Sun, you will observe the Sun and Earth moving differently, although the Earth will always orbit the Sun. My question is, what is the time frame under which the Earth moves out of the orbital plane it created after year 1. After how long does this orbital plane rotate? Will this change in orbital plane have any visual or physical effect for an observer on the Earth?</p> | g13030 | [
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0.02683664858341217,
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<p>Unitary Groups is the most mysterious thing for me when studying physics. All my physics endeavor ends when author starts talking about unitary groups. This is often the case because in a lot of the texts or papers the author would throw terms like $SU(3)$, $SU(5)$ without any background motivation. </p>
<p>When you search for some more answers online, you will often get a purely mathematical treatment (i.e. Wiki article: <a href="http://en.wikipedia.org/wiki/Special_unitary_group" rel="nofollow">http://en.wikipedia.org/wiki/Special_unitary_group</a>) or something related to quantum field theory. Now remind me how many years of studying physics will one reach QFT? </p>
<p>Could someone qualitatively explain or provide a good article that motivates the concept of unitary group with examples drawn from ... every day experience or basic physics. Could someone at least explain what an element of an unitary group physically mean?</p> | g13031 | [
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0.014247557148337364,
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... |
<p>We created a table in my physics class which contained the strength of gravity on different planet and objects in space. At altitude 0(earth), the gravitational strength is 100%. On the moon at altitude 240,000 miles, it's .028%. And on the International Space Station at 4,250 miles, the gravitational strength compared to the surface of the earth is 89%.</p>
<p>Here's my question:
Why is the strength of gravity compared to the surface of the earth 89% even though it appears like the ISS has no gravity since we see astronauts just "floating" around?</p> | g13032 | [
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0.01... |
<p>Is there a term referring to space that is inside the plane of a galaxy, but not part of the center/bar/arms/spurs, etc? What's the filler called?</p>
<p>The space between two spiral arms (if it isn't a spur or anything) would be called... I really feel like there should be a word for this, but I can't find one.</p> | g13033 | [
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<p>The question is: </p>
<blockquote>
<p>A 90kg disc is floating in a frictionless vacuum. A 150N force is
applied to the outer rim of the disc. The disc has a radius of 0.25m
and a radius of gyration of 0.16m. What is the acceleration and
angular acceleration of this disc?</p>
</blockquote>
<p>To solve it I set up these equations:</p>
<p>\begin{equation}
\mathbf{F}_{a} = \mathbf{m}\times\mathbf{a}\tag{1}
\end{equation}
\begin{equation}
\mathbf{F}_{\alpha} = \frac{\mathbf{I}\times\mathbf{\alpha}}{0.25}\tag{2}
\end{equation}
\begin{equation}
\mathbf{F}_{a}+\mathbf{F}_{\alpha} = 150 N\tag{3}
\end{equation}</p>
<p>You can find I and plug it in along with m, but that still leaves 4 unknowns and only 3 equations. I need a 4th equation but I'm not sure what else is known about the problem. </p> | g13034 | [
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0.0... |
<p>So I am building a circular accelerator (like a slightly oversimplified model version of CERN) as a physics project, and I'm at a dead end. I believe I need to know how to work out differential equations to answer this, but I'd like to know if there's any other way to get the answer.</p>
<p>Okay. I am calculating the velocity of a projectile after passing through a solenoid. I have a system using an photo-interrupter to switch the coil on when a projectile passes through it.</p>
<p>I know the force of a solenoid can be calculated using $F = (NI)^2\mu_0A/2g^2$ So the first part of my question should be fairly simple I believe. Since the gap between projectile and coil ($g$) changes as the projectile accelerates, the force acting on the projectile become stronger (because the magnetic field diminishes with the square of the distance.)</p>
<p>Can I use the average distance between coil and projectile or must I learn how to work differential equations?</p>
<p>My second question involves the length of time the force from the solenoid is applied. As I have my formulas set up, I know the distance between the photo-interrupter and the coils, I know my starting velocity, and I know the acceleration applied to the projectile (assuming I can use the average force applied).</p>
<p>I made a python program to run through the equation for displacement as a function of time, adding a set amount of time in each run-through, until the displacement was equal to the distance between my interrupter and my coils. I then had it record the number of second it took, rearranged $F=ma$ to get $\frac{F}{m}=a$, used this instead of $a$ in $V = \frac{a}{\Delta t}$ to get $$V=\frac{\frac{F = (NI)^2\mu_0A/2(g_{avg})^2}{\text{Mass of projectile}}}{\Delta t} \,.$$
Is this an accurate way to calculate the velocity?</p> | g13035 | [
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0.00495834369212389,
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0.... |
<p>I heard capacitors affect the valleys and mounds of voltage sine curves, so that you get DC from AC. It's related to Graetz bridge, flipping signs of sine waves and seemingly afterwards smoothing sharp points, see pictures below.</p>
<p>How can that be derived and interpreted from electronics? What is the math behind capacitors in a parallel configuration of an AC source $U_\text{ext}$ leveling to give flater the output voltage? </p>
<p>For example the images suggest the capacitor provides the current at the right time, but I don't know why. If charges when the current is high, but how to compute the current at the vertex at the parallel capacitor and the partition to the three paths. The picture suggest the process is periodic and so I guess there might be a closed form for the time behaviour of the relevant functions. </p>
<hr>
<p><img src="http://i.imgur.com/yEt8IMe.gif" alt="enter image description here"></p>
<hr>
<p><img src="http://i.imgur.com/sw5QI7u.gif" alt="enter image description here"></p>
<hr>
<p>My approach: </p>
<p>$I_{U_\text{ext}}=I_C+I_R$</p>
<p>$U_R=I_R\ R$</p>
<p>$U_C=\frac{1}{C}\int I_C \mathrm dt$</p>
<p>$U_\text{ext}\overset{?}{=}I_{U_\text{ext}}\cdot \frac{1}{1/Z_C^{???}+1/R}$</p>
<p>$U_\text{ext}\overset{?}{=}\pm U_C\overset{?}{=}\pm U_R$</p>
<p>$U_R=\ ???$</p> | g13036 | [
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0.11539295315742493,
0.07103648781776428,
0.014900... |
<p>Two twin sisters synchronize their watches and simultaneously (from the earth frame) depart earth in different directions. Following a predetermined flight plan, each sister accelerates identically to 99.9%c and then returns home at the same time (again in the earth frame). The observers on earth see each twin as having aged identically, as the symmetry of the problem dictates. Each twin however should see the other as having aged... What gives?</p> | g84 | [
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0.006... |
<p>It is said in textbooks that if the $SU(2)_f$ or $SU(3)_f$ flavor symmetry were exact for sstrong isospin, then all members of the multiplets would be exactly equally massive. By looking at quark masses then one can conclude that the symmetry is not exact. But how does the argument work with the weak force ? It is said to be an exact symmetry, yet electron and neutrino have different masses even though they are in the same doublet. What is the difference ?</p> | g13037 | [
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-0.028882503509521484,
-0.027375342324376106,
-0.05099419131875038,
0.009161551482975483,
... |
<p>How would you proof that
$$ \mathrm {Tr} (\mathbf{S\cdot \bar S })=0$$
where $\mathbf S$ is an element of area delimited for the 4-vectors $\mathbf u$ and $\mathbf v$ given by
$$S^{\alpha \beta}\equiv u^\alpha v^\beta-u^\beta v^\alpha$$
and
$$\bar S^{\alpha \beta}\equiv \frac{1}{2}\epsilon^{\alpha \beta \gamma \delta} S_{\gamma \delta}$$
is the dual of $\mathbf S$.</p>
<p>I used an analogy with the Maxwell field tensor $\mathbf T$. I know that $\mathrm {Tr} (\mathbf{T\cdot \bar T })=\frac{4}{c}\mathbf E \cdot \mathbf B$. Building the analog vectors $\mathbf E$ and $\mathbf B$ but with $\mathbf S$ I get that $ \mathrm {Tr} (\mathbf{S\cdot \bar S })=0$. But I'm looking for a more ilustrative solution to this problem. Any ideas?</p> | g13038 | [
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0.03356276452541351,
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0.10703782737255096,
0.050119612365961075,
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-0.02251254767179489,
-0.058050598949193954,
0.026287619024515152,
0.025173773989081383,
-0.... |
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