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<p>I'm a beginner of QFT. Ref. 1 states that </p>
<blockquote>
<p><em>[...] The Lorentz group $SO(1,3)$ is then essentially $SU(2)\times SU(2)$.</em> </p>
</blockquote>
<p>But how is it possible, because $SU(2)\times SU(2)$ is a compact Lie group while $SO(1,3)$ is non-compact? </p>
<p>And after some operation, he says that the Lorentz transformation on spinor is complex $2\times2$ matrices with unit determinant, so Lorentz group becomes $SL(2,\mathbb{C})$. I'm confused about these, and I think there must be something missing. </p>
<p>References:</p>
<ol>
<li>L.H. Ryder, <em>QFT,</em> chapter 2, p. 38.</li>
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<p>I understand what three-phase power is. But when I look at some pictures of a double-circuit-three-phase-power-line I see two or three lines close together? What is the purpose of these lines close together?
(the wires are attached by smaller wires or connectors)</p>
<hr>
<p>Is there a separate alternator for the second group of three-phase? </p>
<hr>
<p><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Electric_Sails.jpg/450px-Electric_Sails.jpg" alt="Power line"></p>
<p>It has 2 lines instead of 1 line for one of the phases. So instead of having two sets of A, B, C it has AA, BB, CC? Or is that second line just a neutral line? </p>
<hr>
<p>This one has many wires! </p>
<p>is it now AAAAA, BBBBB, CCCCC?
<img src="http://tdworld.com/overhead_transmission/1200kV-Single-Circuit-line-1200kV-Double-Circuit-line-7.jpg" alt="power 2"></p>
<hr>
<p>This one is nice and simple! Just one line for each phase(x2)!
<img src="http://www.power-technology.com/projects/beaulydenny/images/1-transmission-line.jpg" alt="third power line"></p> | 3,543 | [
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<p>As a mathematics graduate student whose research area lies in low-dimensional topology (more precisely, invariants of 3-dimensional topological manifolds), I heard that there exist multiple applications of this theory to theoretical physics, and moreover, that many mathematical problems in the field actually arise from physical ones.</p>
<p>I would appreciate any examples of such applications/motivation, and references to textbooks (or articles which don't require a deep knowledge of physics) where I could read more on the subject.</p> | 99 | [
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<p>I woke up this morning thinking about spinning discs. Could someone verify whether my reasoning below is correct?</p>
<p><strong>Problem 1</strong></p>
<p>Suppose have two identical uniform discs constrained to move in a plane. Set disc $A$ spinning about its centre of mass, clockwise viewed from above. Now collide it with disc $B$.</p>
<p>Assume that friction is the only force acting, and the collision is elastic. I believe that I should be able to work out qualitatively what happens from conservation of linear and angular momentum.</p>
<p>The friction will provide a torque causing $B$ to spin anticlockwise about its centre of mass. Let $L$ be the line joining the centre of $A$ and $B$ at the moment of collision. But then by conservation of angular momentum $B$ must deviate to the right of $L$ after collision. And then by conservation of linear momentum disc $A$ will move to the left of $L$.</p>
<p>The other option for conserving angular momentum would be for the disc A to start spinning faster, but this is ruled out by conservation of energy. Correct?</p>
<p><em>Note</em>: this effect is observed in snooker when left hand side is imparted to the cue ball.</p>
<p><strong>Problem 2</strong></p>
<p>Now suppose that the discs are stood on end on a table and we do the same experiment, assuming no friction between table and disc. Then conservation of angular momentum must cause the first disc to jump in the air upon collision, by the same reasoning as before. Correct?</p>
<p><em>Note</em>: I guess this is the origin of the "kick" in snooker.</p>
<p>So really understanding how to prevent snooker kicks is the subtle problem of understanding precisely how much angular momentum is transferred between the balls. You ideally want to minimise this (i.e. have almost frictionless ball collisions, compared with the friction between cloth and ball).</p> | 3,544 | [
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<p>When an index of the Kronecker-delta tensor $\delta_a^b$ is lowered or raised with the metric tensor $g_{ab}$, i.e. $g_{ab}\delta^b_c$ or $g^{ab}\delta_b^c$, is the result another <a href="http://en.wikipedia.org/wiki/Kronecker_delta" rel="nofollow">Kronecker-delta tensor</a>?</p> | 3,545 | [
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<p>Two observers A and B, in different initial system describe the same physical event with their particular, different space time coordinates . Let the coordinate of the event be $x^\mu$ for observer A and ${x^\prime}^\mu$ for observer B .Both coordinates are connected by means of the Lorentz transformation.
$${x^\prime}^\mu = \sum_{\mu=0}^{3}a^{\nu}_{\mu}x^\mu\equiv a^{\nu}_{\mu}x^\mu\ = (\hat{a}\overset{\Rightarrow}{x})$$
Where $\hat{a}$ denotes the abbreviated version of the transformation matrix and $\overset{\Rightarrow}{x}$ is a 4 dimensional world vector .</p>
<p>I need to understand the Lorentz transformation equation that how it transformed .</p>
<p>EDITED :
How both coordinates are connected in that transformation .</p> | 3,546 | [
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<p>I'm in grad school and notice there are no prerequisites required for QFT in the physics department. In fact, the system allows me to sign up for the course just fine as a technical elective.</p>
<p>But... my field is chemical engineering and I've only taken basic quantum mechanics. I would really love to learn more about QFT though since it's always been something I've really been interested and lightly study in my free time.</p>
<p>From the perspective of someone who knows the physics required to take this course, is the material required to understand the subject outside the range of what I would have learned for an engineer (+QM)?</p> | 3,547 | [
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<p>My questions are in italics. In the article [1] a dimensional regularization is presented on an electrostatic example of an infinite wire with constant linear charge density $\lambda$. It is shown that the direct computation of the scalar potential gives infinity:
$$
\phi({\bf x})
= {\lambda\over 4\pi\epsilon_0}\int_{-\infty}^\infty { d l
\over |{\bf x} - {\bf l}| }
= {\lambda\over 4\pi\epsilon_0}\int_{-\infty}^\infty { d l
\over (x^2 + y^2 + (z-l)^2)^{1\over 2} } =
$$
$$
= {\lambda\over 4\pi\epsilon_0}\int_{-\infty}^\infty { d u
\over \sqrt{x^2 + y^2 + u^2} }
= \infty
$$
But with dimensional regularization in the modified minimal subtraction scheme we get eventually:
$$
\phi_{\overline{\rm MS}}({\bf x})
= {\lambda\over 4\pi\epsilon_0} \log{\Lambda^2\over x^2 + y^2}
$$
where $\Lambda$ is the auxiliary scale parameter. One can then calculate the electric field (let's set $y=0$ from now on) as follows:
$$
E_x = -{\partial \over \partial x} \phi_{\overline{\mathrm{MS}}}(x)
= -{\partial \over \partial x}
{\lambda\over 4\pi\epsilon_0} \log{\Lambda^2\over
x^2}=
$$
$$
= - {\lambda\over 4\pi\epsilon_0} {x^2\over\Lambda^2} \Lambda^2
\left(-{2\over x^3}\right)
= {\lambda\over 2\pi\epsilon_0} {1\over x}
$$</p>
<p>The article claims that the original scalar potential is scale invariant: $\phi(kx) = \phi(x)$. But since both $\phi(kx)$ and $\phi(x)$ are infinite, <em>I don't understand the argument.</em></p>
<p>The article claims that the dimensional regularization preservers translational symmetry. However, the only way to make $\phi_{\overline{\mathrm{MS}}}(kx)=\phi_{\overline{\mathrm{MS}}}(x)$ is to choose different $\Lambda$ for each side. <em>Are we allowed to do that?</em></p>
<p>I thought that we have to set $\Lambda$ once and for all and then just keep calculating with it and it must cancel at the end.</p>
<p>Update: based on Michael's comment below I realized that the article claims <em>translational</em> invariance of the original problem, i.e. $\phi_{\overline{\rm MS}}(x, y, z+h)=\phi_{\overline{\rm MS}}(x, y, z)$ and that is obviously true, because $\phi_{\overline{\rm MS}}({\bf x})$ does not depend on $z$. So I think that answers this particular question. Still a clarification from an expert would be nice.</p>
<p>[1] Olness, F., & Scalise, R. (2011). Regularization, renormalization, and dimensional analysis: Dimensional regularization meets freshman E&M. American Journal of Physics, 79(3), 306. doi:10.1119/1.3535586, available online <a href="http://www.ate.uni-duisburg-essen.de/data/postgraduate_lecture/AJP_2011_Olness.pdf" rel="nofollow">here</a>.</p> | 3,548 | [
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<p>In doing a little research into natural background radiation, I came upon a table from the National Council on Radiation Protection and Measurement (NCRP). It shows that inhaled radon gas is by far the largest contributor to average annual dose equivalent from background radiation, for people living in the United States. [<a href="http://www.physics.isu.edu/radinf/radrus.htm" rel="nofollow">1</a>] That table lists "other internally deposited radionuclides" as contributing only a small fraction of what inhaled radon gas contributes. Among those "other internally deposited radionuclides" is potassium-40.</p>
<p>According to another source, the typical activity of potassium-40 in the human body is about 0.1uCi. [<a href="https://www.orau.org/ptp/collection/consumer%20products/potassiumgeneralinfo.htm" rel="nofollow">2</a>] Typical activity of radon in outside air is said to be 0.4pCi/L, while for indoor air the average is 1.3pCi/L. [<a href="http://www.epa.gov/radon/pubs/citguide.html#risk%20charts" rel="nofollow">3</a>] Given that the typical volume of air the average adult inhales is 0.5L, at any given time an adult has about 0.4pCi of radon in their lungs. [<a href="http://faculty.stcc.edu/AandP/AP/AP2pages/Units21to23/respiration/volumes.htm" rel="nofollow">5</a>] Note that the stated activity levels for radon are about a million times lower than those for potassium-40 (0.4 pCi versus 0.1 uCi).</p>
<p>I also learned that radon typically decays via alpha decay. [<a href="http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/radon.html#c2" rel="nofollow">4</a>] Potassium-40, on the other hand, mostly decays via beta decay. [<a href="https://www.orau.org/ptp/collection/consumer%20products/potassiumgeneralinfo.htm" rel="nofollow">2</a>] I understand that alpha radiation is given more weight than beta radiation, generally by a factor of 20 or so, when estimating the biological effects of radiation. [<a href="http://ocw.mit.edu/courses/nuclear-engineering/22-55j-principles-of-radiation-interactions-fall-2004/lecture-notes/bakgrnd_radiaton.pdf" rel="nofollow">6</a>] However, a factor of 20 falls far short of the 10 million or so times higher effect stated for radon versus all other internally deposited radionuclides in the NCRP table. The table implies that the one million times greater activity of potassium-40 results in only about a tenth (or less) the equivalent dose. That seems way beyond what could be accounted for with just a weighting factor.</p>
<p>Why doesn't potassium-40 contribute much more to the equivalent dose? What am I missing?</p> | 3,549 | [
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] |
<p>I am trying to find the potential $V$ inside a sphere using the method of image charges.</p>
<p>I have a conducting spherical shell. The charge $q$ is inside the sphere. The sphere is ungrounded and is an equipotential because it is a conductor. </p>
<p>If I place an image charge $q'$ outside the sphere, I can make it equipotential if it is grounded i.e. potential$ V=0$ on the sphere. But since it is not grounded, there is some potential $V_0$ on the sphere. </p>
<p>To make the equipotential $V_0$ on the sphere, I can put another image charge $q''$ at the centre except that that is not allowed because I can't put image charges inside the space that I'm investigating.</p>
<p>Where else can I put the image charge? No matter where I put it outside the sphere it will not give me the $V_0$ equipotential on the sphere. How do I solve this?</p> | 3,550 | [
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<p>When I look at electric or magnetic fields, each of them has a constant that defines how a field affects or is affected by a medium. For example, electric fields in vacuum have a permittivity constant $ϵ_0$ embedded in the electric field expression of a point charge: $E = q/4π ϵ_0r^2$. However, if I put this point charge in some dielectric that has a different permittivity constant $ϵ$, the value of the electric field changes. On a similar note, magnetic fields behave very similar but have the permeability constant $μ_0$ instead. </p>
<p>From my understanding, I believe that this is not the case for gravitational fields since the universal gravitational constant $G$ is consider to be a fundamental constant. So I am assuming that even though gravitational fields do operate in different types of mediums, this somehow doesn’t affect the gravitational field value. My question is why is this the case, that is, why isn’t there a permittivity-type constant for gravitation?</p> | 3,551 | [
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<p>If I look at Hooke's law as it's defined in my textbook, it looks like:</p>
<p>$F = -k\Delta s$</p>
<p>Therefore, the restoring force of an ideal spring will be proportional to the displacement from equilibrium, where $k$ will be the constant of proportionality. From this equation, I believe that it can't be said that mass is proportional to the displacement from equilibrium (even though it seems to be the case implicitly).</p>
<p>However, if I substitute $ma$ for the restoring force:</p>
<p>$ma = -k\Delta s$</p>
<p>Is it then valid to say that mass is proportional to the displacement from equilibrium, as well as mass is inversely proportional to acceleration? I've been thinking about proportionality a lot lately and this one sort of threw me for a loop.</p> | 3,552 | [
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<p>I am having trouble understanding how centripetal force works intuitively.</p>
<p>This is my claim.</p>
<p>When I have a mass strapped on a string and spin it around, I feel the mass pulling my hand.
So, I want to say that the mass is trying to move away from the center of the circle, and yet centripetal force makes it move in a circle, i.e, centripetal acceleration towards the center.</p>
<p>Similarly, when I am driving a car and making a curve, I feel being pushed away from the center of the curvature rather than towards it.</p>
<p>I am having so much trouble with these types of problems because of this counter intuitive concept.
Can someone help me out?</p> | 727 | [
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<p>In <a href="http://en.wikipedia.org/wiki/Special_relativity" rel="nofollow">SR</a>, the interval $I$ between two spacetime events is called <em>light-like</em> if $I=0$.
Griffiths in his <em>Introduction to Electrodynamics</em> book says that [page 503],</p>
<blockquote>
<p><em>If $I=0$ we call the interval light-like, for this is the relation that holds when the two events are connected by a signal traveling at the speed of light.</em></p>
</blockquote>
<p>What does this statement mean?</p> | 3,553 | [
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<p>I have read that we need all operators in QM to be linear to confirm the principle of superposition which is experimentally well proven. I wonder how such an experiment could be made?</p> | 100 | [
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<p>Consider the following Hamiltonian which describes massless Dirac fermion on the surface of a topological insulator nanowire,
$$H = -i\hbar v_{F}\left[ \partial_{x}\sigma_{x} + \frac{\sigma_{y}}{R}\left( \partial_{\phi} + i\eta\right)\right]\ \text{.}$$
The nanowire has translational symmetry in $x$-direction and $\phi$ is the angle around perimeter. It has eigenenergies which can be written in the form,
$$E_{k,n} = \pm \hbar v_{F} \sqrt{k^{2} + \frac{1}{R^2}\left(l_{n} + \eta \right)^2}\ \text{,}$$
where $l_{n} = n-1/2$ is quantized in integers $n$. The wavefunction can be written like this,
$$\Psi^{\pm} = \frac{1}{\sqrt{2\pi L}}e^{\pm i k x}e^{i l_{n} \phi}\ \text{.}$$
Now, if You do the same thing but with the Bogoliubov-de Gennes equation You will get electron-like and hole-like solutions where the wavenumber $k$ woould depend on the total energy $\mathcal{E}$, transverse momentum $l_{n}$ and fraction of the magnetic flux quanta $\eta$. </p>
<p>I am wondering if the Andreev refelction at the boundary between normal-region and superconductor can take place between different modes $l_{n}$. Is there something which prevents from electron-electron, electron-hole etc. scattering processes between different modes at the N-S boundary? </p> | 3,554 | [
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<p>I feel disturbed by this question: Suppose $A$ and $B$ are POVM's with respective $\sigma$-algebras $\mathcal{F}_A$ and $\mathcal{F}_B$ and outcome spaces $\Omega_A$ and $\Omega_B$. Then why can't I take the following POVM $Z = A\cdot B$ defined on $\mathcal{F}_A \otimes \mathcal{F}_B$ as the joint measure? I mean it fullfills that </p>
<p>$$
Z(U, \Omega_B) = A(U) \cdot B(\Omega_B) = A(U), \quad \forall U \in \mathcal{F}_A
$$
and the same for $B$. And I guess you can define it to be $\sigma$-additive, at least in finite dimension of the outcome spaces? </p> | 3,555 | [
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<p>I'm developing an app that contains a 3D scene which the user can navigate. As the user moves it gives the illusion that you are browsing a real landscape but for the illusion to work I need to know two things:</p>
<ol>
<li>How to calculate the angular sizes of all the objects relative to their distances from the observer.</li>
<li>How to calculate the center of all the objects relative to the focal point as the user moves.</li>
</ol>
<p>The first one is easy but the second one still baffles me and I have no idea where to look for the answer. Let's examine the second one:</p>
<p>As the user navigates towards the focal point, the center of the object moves across the line that is created between the focal point and it's center.</p>
<p>Focal Point = $FP(x_0, y_0)$</p>
<p>Center 1 = $C_1(x_1, y_1)$</p>
<p>Center 2 = $C_2(x_2, y_2)$</p>
<p>The equation of the line is:</p>
<p>$y-y_0 = m(x-x_0)$ where $m=(y_1-y_0)/(x_1-x_0)$</p>
<p>The center 1 $(x_1,y_1)$ is known because it is the starting center.</p>
<p>Let's say the the object moved a distance $d$ from center1 to center 2.</p>
<p>(1) $d^2=y^2+x^2$</p>
<p>(2) $y_2=m(x_2-x_0)+y_0$</p>
<p>(1) (2) = ... you can find $y_2$ and $x_2$ if you know $d$.</p>
<p>Can you find $d$ from the illustration?
Is there any other method?</p>
<p><img src="http://i.stack.imgur.com/3eefl.jpg" alt="Illustration"></p> | 3,556 | [
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] |
<p>Is there any optical component in existence that uniformizes randomly pointing rays?</p>
<p><img src="http://i.stack.imgur.com/IIXrV.jpg" alt="The component (greenish-yellow) takes in random light and uniformizes it. Light is traveling from left to right"></p> | 3,557 | [
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<p>I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force holding a subatomic particle together? What keeps mass in it's state? I hope this is not a silly question but I am clueless. Thanks </p> | 67 | [
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<p>I've seen plans for a pendulum oscillator water pump that is claimed to pump a large volume of water (100 gallons) from a well of 100 feet deep. The pendulum consists of a 100 pound weight raised 6 feet. A second 20 pound weight is hoisted up a pole 20 feet high. This second weight powers a mechanism which gives the pendulum a very slight push on every swing so that it does not lose any momentum on any stroke. The only energy inputs into this system are the act of raising the 20 pound weight 20 feet and raising the 100 pound weight 6 feet. This is supposed to pump 100 gallons (833 pounds of water) up 100 feet.</p>
<p>It seems to me that this is impossible, because we have applied a given amount of potential energy into this system:
20lbs x 20feet = 400 foot pounds
100lbs x 6 feet = 600 foot pounds
So 1000 foot pounds total</p>
<p>So this should be capable (at best) of raising 10 pounds of water (1.2 gallons) up 100 feet. </p>
<p>I've been told that I don't understand the engineering principles of oscillation, and I've been assured that the math checks out. However, based on the very limited physics I know (and I admittedly don't know much) - you can't get more work out of a system than you put in.</p>
<p>How is it possible to get more energy out of a system than you put into it?</p> | 3,558 | [
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<p>How can we show that the Einstein-Hilbert action is Parity invariant? $$
S_{EH}=\int \sqrt{-g}R d^4x $$ </p> | 3,559 | [
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<p>We can calculate the current density $\mathbf{j}$ of the electron in Hydrogen, and it is given by:
$$
j_\phi=-e\frac{\hbar m}{\mu r\sin\theta}\left|\psi_{nlm}\left(r,\theta,\phi\right)\right|^2
$$
(<a href="http://www.phys.spbu.ru/content/File/Library/studentlectures/schlippe/qm07-05.pdf" rel="nofollow">derivation found here</a> on page 6)</p>
<p>How can I calculate the magnetic field produced by this current density?</p>
<p>I could use the Biot-Savart law,
$$d\textbf{B} = \frac{\mu_0}{4\pi} \frac{1}{r^2} \int Id\textbf{s}$$
where the integration should be (at least classicaly) the along the current loop, and $I$ = $\int \textbf{J} \cdot d\textbf{S}$. What should I use as $d\textbf{S}$ and $d\textbf{s}$ for an electron in Hydrogen?</p> | 3,560 | [
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<p>The equations I'm using are:</p>
<pre><code>x = x + (DT * vx)
vx = vx * C
</code></pre>
<p>My DT is always 0.01 and the coefficient <code>C</code> (related to a linear drag coefficient, as mentioned in the comments) is greater than 0 and less than 1. The above will keep happening until x naturally reaches its limit. </p>
<p>What I want is an equation to find C given the other three inputs: initial x, initial velocity x and final resting x(this is where the object has come to a stop and vx = 0). Right now it's tedious because I have to plug in ix, ivx and C and run my simulation to see where the object stops. Then I have to do further tweaking to get exactly what I'm looking for.</p>
<p>Here are some samples:</p>
<pre>initial x = 3.5
velocity x = -12.0
acceleration = 0.92
final resting x = 2.0
initial x = 3.5
velocity x = -14.0
acceleration = 0.92
final resting x = 1.75</pre>
<p>For example(from the first dataset), we start at 3.5 we want to end at 2.0 and our velocity is -12.0 .. what do we need to use for C?</p> | 3,561 | [
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<p>Let me first say that I am not a physicist, but I am trying to make a simulation on my computer and I have the following question.</p>
<p><img src="http://i.stack.imgur.com/24umY.jpg" alt="enter image description here"></p>
<p>Let's consider that we have three free charges that somehow can change their charge in time.
$$
Q_1(t) = \sin(\omega t) \\
Q_2(t) = \begin{cases}1 & \mod(t,2)=1 \\ -1 & \mod(t,2)=0\end{cases} \\
Q_3(t) = 2\cos(2\omega t)
$$
where $t$ is the time measured in seconds. We say that all particles have same mass $m$. We also consider gravitational potential energy to be negligible.</p>
<p>I am trying to find </p>
<ol>
<li>potential energy in time</li>
<li>entropy variation in time</li>
</ol>
<p>I understand that this might not be solvable analytically, but as I said, I am trying to simulate this on a computer. I have the forces over time, but I really <em>don't</em> want to integrate them spatially to find the potential energy, as in my simulations, the particles can count thousands. Could you point me out an easier way, or a simplification that I could try? </p>
<p>About the entropy, do you think this has no sense as the system if far away from equilibrium, or for any other reason? If you think this is a valid thing to measure, could you tell me any ideas on how to do it?</p> | 3,562 | [
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<p>Given the formula</p>
<p>$$\frac{{\Delta}(KE)}{KE_i}=\frac{(KE_f-KE_i)}{KE_i}=\frac{-M}{(m+M)}$$</p>
<p>Now I know these that the conservation of momentum is always applicable. Also I understand that</p>
<p>$$KE=\frac{1}{2}mv^2$$
and
$$p=mv$$
When trying to solve it I get
$$\frac{m_2(v_2)^2}{m_1(v_1)^2}-1$$</p>
<p>Is their anything I am doing wrong? If so, what do I need to do to go about this equation? Also, what is the significance of this the negative value in M?</p>
<p><strong>Disclaimer: I am not looking for the complete answer, I am looking to find out how to solve it so I can be sure to know how to do this in future situations. Please edit this post as you see fit for the sake of the quality of the content in this site to help others understand the same problem as well. I thank you all in advance for your contribution.</strong></p> | 3,563 | [
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<p>Say I have a hollow cylinder and I wanted to strap it down to the bed of a truck. I would tension the strap on one end, and it would exert a force on the cylinder. My intuition tells me that the strap would crush the hollow cylinder down toward the truck bed, but when I think about it, there are inward forces perpendicular to the truck bed caused by the straps on the cylinder as well. Is this correct thinking, or are all of the forces only vertical?</p> | 3,564 | [
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<p>Looking directly at a welder is dangerous because large amounts of UV light is produced. What makes this light? Is it electrons from the current that excites metal atoms, and these atoms sends out UV light? Or does the extreme heat have anything to do with this?</p>
<p>Is it dangerous to look directly at a nail being melted (glowing brightly) by hundreds of amperes?</p>
<p>Is it dangerous looking at an oxyhydrogen explosion in itself, or could it be dangerous if the explosion touches other substances exerting UV light because of the extreme heat of the explosion?</p> | 3,565 | [
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<p>I know that I can use conservation of energy to find the velocity of a particle at a point when it's travelling in a vertical circle by saying</p>
<p>$$mgr(1-\cos{\theta})=\frac{1}{2}mv^2$$</p>
<p>then rearranging to get $v=\sqrt{2gr(1-\cos{\theta})}$</p>
<p>But I want to see this done 'the long way' using newtons second law directly and then probably solving a differential equation, but I'm not sure how to do it and nothing I've tried is getting very far.</p> | 3,566 | [
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<p>I have tried this question every way I can think but in the equation for particle $L$ $g$ cancels every time. Could someone show me how to do it correctly or tell me what I am doing wrong. Thanks,</p>
<p>The Question:</p>
<blockquote>
<p>A string with negligible mass passes over a smooth pulley V with a
particle A of mass $18kg$ on one end of the string and a pulley ($J$) of
negligible mass on the the other end</p>
<p>Another string with negligible mass passes over pulley $J$ and has a
particle $K$ of mass $12kg$ on one end and a particle $L$ of mass $9kg$ on
the other end.</p>
<p>Show the common acceleration of $A$ and $J$ then show the relative
acceleration of $K$ and $L$ to $J$.</p>
</blockquote>
<p>So far I have worked out that the tension in the top string is equal to twice the tension in the bottom string. $T-2S=0a$
$$T=2S$$</p>
<p>I then plug this into $18g-T=18a$ to get $18g-2S=18a$</p>
<p>From that equation I get $S=9g-9a$</p>
<p>After that I plug the value of $S$ into the equations for $K$ and $L$ then in the equation for $L$ $g$ is canceled out and I am stuck.</p> | 3,567 | [
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<p>I am reading Berkeley Physics Course, Volume 2 (Electricity and Magnetism
by Edward M. Purcell).</p>
<p>I am in chapter $3$ pg $92$, and the book discusses conductors.</p>
<p>The following is from the book:</p>
<p>Because the surface of a conductor [in Fig $3.2$] is necessarily
a surface of constant potential, the electric field, which is $-\nabla \varphi$
, must be perpendicular to the surface at every point on the surface</p>
<p>I have omitted the picture because it is not relevant.</p>
<p>Can someone please explain this reasoning ?</p>
<p>I understand that the potential $\varphi$ is a continuous function,
and since $E=0$ inside the conductor and since $E=-\nabla\varphi$
I get that $\varphi=0$ inside and on the surface (from continuity)
of the conductor.</p>
<p>However, I don't understand the reason the book gives for explaining
why the field is perpendicular to every point on the surface</p> | 3,568 | [
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<p>Is "second quantization" means system wich can contain variable, unknown, superposed and otherwise uncertain number of qubits?</p>
<p>Can "second quantized" system contain 0.5% of 1 qubit and 95% of 2 qubits?</p>
<p>Does this mean that quantum field state cannot be described with quantum computer with fixed number of qubits?</p>
<p>Or may be this is wrong and the "power" of qubit is sufficient?</p> | 3,569 | [
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<p>I have the transformation law of the Lorentz group for Pauli matrices:
$$
\tag 0 (\sigma^{\mu})_{a \dot {a}}{'} = \Lambda^{\mu}_{\quad \nu} N_{a}^{\quad c}(\sigma^{\nu})_{c \dot {c}}(N^{-1})^{\dot {c}}_{\quad \dot {a}},
$$
where
$$
N_{a}^{\quad c} = 1 + \frac{1}{2}\omega_{\mu \nu}\sigma^{\mu \nu}, \quad N^{\quad \dot {c}}_{\dot {a}} = 1 + \frac{1}{2}\omega_{\mu \nu}\tilde {\sigma}^{\mu \nu}.
$$
Also I have the relation
$$
\tag 1 \gamma_{\mu} = \begin{pmatrix} 0 & \sigma_{\mu} \\ \tilde {\sigma}_{\mu} & 0 \end{pmatrix}, \quad (\tilde {\sigma}_{\mu})^{\dot {a} a} = \varepsilon^{ab}\varepsilon^{\dot {a} \dot {b}}(\sigma_{\mu})_{d \dot {b}}.
$$
How exactly can I get the transformation law
$$
(\gamma_{\mu}){'} = \Lambda_{\mu}^{\quad \nu}\hat {S}\gamma_{\nu}\hat {S}^{-1}, \quad \hat {S} = 1 + \frac{1}{2}\omega_{\mu \nu}H^{\mu \nu},
$$
$$
H_{\mu \nu} = \frac{1}{4}\gamma_{[\mu} \gamma_{\nu ]}
$$
from $(0)$?</p>
<p>I failed when I tried to write explicitly transformations of Pauli matrices in $(1)$: I can't pick out $\hat {S}^{-1}$, because I entangled in the indices.</p> | 3,570 | [
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<p>An answer to the question <a href="http://physics.stackexchange.com/q/133301/25794">If we could build a neutrino telescope, what would we see?</a> contains a <a href="http://apod.nasa.gov/apod/ap980605.html">link to a neutrino image of the sun </a> by the Super-Kamiokande neutrino detector. </p>
<p><img src="http://i.stack.imgur.com/dSed3.jpg" alt="neutrino image of the sun"></p>
<p>There it says that the image actually covers a large part of the sky of about 90x90 degrees. As the diameter of the sun from earth is around one half of a degree, it must be that many of the neutrinos didn't come straight at us. This seems surprising (to me), as neutrinos should hardly interact with the atmosphere. Maybe the central few pixels of the image are extremely much brighter than the others, but this image doesn't show the difference between those and the surrounding pixels? Or is something else going on?</p> | 3,571 | [
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<p>In quantum optics, the output from a laser is modelled using a coherent state; what are some orders-of-magnitude for the complex parameter (usually denoted $\alpha$) of the coherent state corresponding to real laser fields used in experiments?</p> | 3,572 | [
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<p>I am somewhat confused about this topic. </p>
<p>It is usually explained how magnetic fields avoid breaking time reversal symmetry by the example of a field produced by a circulating charge current - run time backwards, the current direction is reversed and so is the field.</p>
<p>But what about the moment associated with the electron spin? Is the spin of an electron not an intrinsic property? So why (if indeed it does) would running time backwards change the sign of the spin?</p> | 3,573 | [
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<p>My car has proximity sensors to help me park. I've noticed that when motorcycles whiz past me the proximity alarm goes off. I originally though that the motorcycles were just too close, but now I have observed that that isn't the case; cars or other road uses at a similar distance and speed do not set off the sensors. What's special about the movement of a motorcycle that sets off the alarm?</p> | 3,574 | [
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<p>Does the subadditivity (and <a href="http://en.wikipedia.org/wiki/Strong_Subadditivity_of_Quantum_Entropy" rel="nofollow">strong subadditivity</a>) of quantum entropy hold for infinite dimensional quantum systems as well? Unfortunately the books in my hand give proof for finite dimensional cases only and I could not extend them to infinite dimensional cases. Please give some reference or some outline of approach. </p> | 3,575 | [
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<p>There is some porous dielectric membrane with strictly vertical cylindrical pores. I would like to find theoreticaly optical transmission spectra of this membrane, depending on the bulk material optical dispersion, radius and height of cylindrical pores and the distance between their centers.</p>
<p>In result I want to find a formula for optical transmission spectra depends on wavelength (to compare with experiments). The material is dielectric, so it's only about complex diffraction and Beer–Lambert–Bouguer law, but I don't know how to start with porous system.</p> | 3,576 | [
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<p>If we have two inertial frames $S$ and $S'$ and $S'$ is moving to the right w.r.t. $S$ with a velocity $v$. Suddenly $S$ undergoes negative acceleration (no longer being inertial) and after some time the acceleration stops when the frame has reversed its velocity. How much will be the time difference between two, previously synchronized, clocks in $S'$ separated by a distance $x$ (as measured by $S$) after the acceleration has been ceased and will it depend on the history of acceleration or just on the initial and final velocity?</p> | 3,577 | [
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<p>I want to make a finite element analysis of a cold airflow through warmer pipes. In particular I want to see how the pipes cool down and the air heats up, as it travels through the pipes. Wich are the equations and boundary conditions that I have to consider?</p>
<p>I assume that the velocity field is already given, call it $v$.
Currently I solve the following equation
$$
\rho c_p(\frac{\partial T}{\partial t} + v\cdot \nabla T) - k \Delta T = 0
$$
($T\ $ temperature, $\rho\ $ density, $c_p\ $ heat capacity at constant pressure, $k\ $ heat conductivity) over the whole domain, where inside the pipes I use the given velocity field and in the pipe material I assume $v = 0$. The constants like $\rho\ $ jump on the boundary. I have an initial condition of the same temperature everywhere and then apply a Dirichlet BC at the pipe inlet of a colder temperature.</p>
<p>I know that this describes convective heat transfer and for $v=0$ the equation reduces to conduction heat transfer. But does it describe my problem correctly? I do not have a boundary condition on the pipe/air boundary. Do I need one? Which one?</p>
<p>The heatflow inside the metal pipe seems to be very slow, I expected it to be somewhat faster. The thermal diffusivity, i.e. the term $\frac{k}{\rho c_p}$ is of the magnitude $10^{-5}$, I took this value from the literature. However this makes the diffusion part of the equation very slow. Is this correct?</p>
<p>Thank you!</p> | 3,578 | [
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<p>Is there any good software for construction optical path's in geometrical optics. More specifically I want features like:</p>
<ul>
<li><p>draw $k \in \mathbb{N}$ objects $K_1,\dots,K_n$ with indices of refraction $n_1,\dots,n_k$ and light sources $l \in \mathbb{N}$ light sources $L_1,\dots,L_l$</p>
<p>-- draw for each some of these light sources light rays and the program constructs the optical path of those rays through $K_1,\dots,K_n$. </p>
<p>-- instead of drawing the light rays, draw a point and the program construction the optical path between the light sources and the given point</p></li>
<li><p>draw some specific optical elements like lenses, (concave, convex) mirrors and do things like above</p></li>
<li><p>construct automatically virtual images</p></li>
<li>3D drawings would be fine</li>
</ul>
<p>I would prefer free software for linux.</p> | 812 | [
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<p>Can we say that we are crystals because just like crystals we are made up of very small unit (cell) making up almost the same shape (our body) everywhere.</p> | 3,579 | [
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<p>Why massless particles have zero chemical potential?</p> | 93 | [
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<p>I made a metal cylinder that is the <strong>SAME</strong> size as my 400g propane cylinder (picture: <a href="https://2ecffd01e1ab3e9383f0-07db7b9624bbdf022e3b5395236d5cf8.ssl.cf4.rackcdn.com/Product-800x800/7a66c8cb-d697-4680-9321-fcb73ede75c9.jpg" rel="nofollow">here</a>). I want to transfer <strong>ALL</strong> (or almost all) of the propane from the propane cylinder to my metal cylinder, preferably without using an air compressor or something like that. The reason why I'm doing this is because I'm building a rocket and I can't get the propane to flow out of the propane cylinder fast enough. </p> | 3,580 | [
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<p>This refers to the discussion about <a href="http://en.wikipedia.org/wiki/Gravitational_wave" rel="nofollow">gravitational waves</a> for the YouTube video <em><a href="http://www.youtube.com/watch?v=RzZgFKoIfQI" rel="nofollow">LIGO Gravitational Wave Observatory</a></em>.</p>
<p>I have two questions:</p>
<ol>
<li><p>When the gravitational wave passes through the space where the light is traveling, the light beam will itself be distorted as per the distortion of space (because the gravitational wave distorts <em>everything</em> in its path) and the slight change they expect to detect should be nullified. For instance, suppose the wave shrinks one of the pipes by half and increases the other by double, the waves inside would be distorted similarly, resulting in no overall change in the interference. Am I missing something here?</p></li>
<li><p>It takes a huge amount of energy to distort something (for example, a block of iron). If the gravitational wave distorts <em>everything</em> it passes through (such as the Earth, the Sun and space itself), it will lose its energy at a very high rate in trying to do this distortion (much more than what the inverse square law implies) when it passes through solid objects. The current understanding is that gravitational waves do not get effected by anything and pass through a solid as if was vacuum. How is this possible? </p></li>
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<p>When using the ray trace methodology to solve a given thin lens question, does the arrow (commonly used as the example object when tracing) represent the literal height of the object or the perceived height of the object relative to the lens? Refresher image below:
<img src="http://boson.physics.sc.edu/~rjones/phys153/raytracelens.GIF" alt="a generic ray trace"></p>
<p>Same for the equation methods. When using below equation for magnification, derived from the thin lens equation, does $h_0$ represent the the literal height of the object or the perceived height of the object relative to the lens?
$$
\frac{i}{o}=\frac{h_i}{h_o}
$$
Note: in the event that these aren't the standard notations, $i$ is the image's distance away from the lens, $o$ is the object's distance away from the lens, $h_i$ is the height of the image, and $h_o$ is the perceived or literal height of the object. </p> | 3,582 | [
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<p>I am in grade 10.
I have developed an interest in physics but unfortunately I do not know/ have not studied calculus yet as my school board does not recommend it in grade 10.
I have a copy of fundamentals of physics, <a href="http://www.google.com/search?as_q=halliday+resnick+walker" rel="nofollow">Halliday Resnick Walker</a>, I read chapter's one and two briefly and I understood the conceptual part.
But when it came to derivation's of the equation's I couldnt understand it.
Please, can you recommend any book/video lecture to solve this problem.
Thanks</p> | 3,583 | [
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<p>As Galaxies travel through the universe, how do they orient? </p>
<p>And, does this orientation apply to stars and their satellites?</p>
<p>that is to ask if the movement of a galaxy or star is perpendicular to its satellites and its rotation.. </p>
<p>One might even compare this proposed action to that of a tornado in that the planets or stars would 'follow' in the 'wake' of the star or blackhole like debris.</p> | 3,584 | [
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<p>I read somewhere that part of Minkowski's inspiration for his formulation of Minkowski space was Poincare's observation that time could be understood as a fourth spatial dimension with an imaginary coefficient.</p>
<p>Clearly, taking the Euclidean norm of the vector $$(i \Delta t, \Delta x, \Delta y, \Delta z)$$ gives the correct spacetime interval (assuming appropriate units), but I don't really know where it goes from there (possibly something to do with Moebius transforms?)</p>
<p>I think this is mentioned in Taylor and Wheeler's book, but I may have read it elsewhere. After the historical note, the author (whoever it was) said it was "preferable" to use Minkowski geometry straight off, rather than mucking about with time as an imaginary space coordinate.</p>
<p>Could anyone elaborate on Poincare's formulation? Why is Minkowski's methodology better?</p> | 3,585 | [
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<p>The strong force acting between quarks and responsible for holding protons together is 100 times stronger than the electromagnetic force. How come the nuclear binding energy derived from the strong force is millions time stronger than chemical energy. (rather than 100 times)</p> | 3,586 | [
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<p>I wish to understand <a href="http://arxiv.org/pdf/1008.0654v2.pdf">the statement in this paper more precisely</a>:</p>
<blockquote>
<p>(1). Any 3d Topological quantum field theories(TQFT) associates an inner-product vector space $H_{\Sigma}$ to a Riemann surface $\Sigma$. </p>
</blockquote>
<p>-</p>
<blockquote>
<p>(2) In the case of abelian Chern-Simons theory $H_{\Sigma}$ is obtained by geometric quantization of the moduli space of flat $T_{\Lambda}$-connections on ${\Sigma}$. The
latter space is a torus with a symplectic form</p>
</blockquote>
<p>$$ ω =\frac{1}{4π} \int_{\Sigma} K_{IJ} \delta A_I \wedge d \delta A_J.$$</p>
<blockquote>
<p>(3) Its quantization is the space of holomorphic sections of a line bundle $L$ whose curvature is $\omega$. For a genus g Riemann surface $\Sigma_g$, it has dimension $|\det(K)|^g$.</p>
</blockquote>
<p>-</p>
<blockquote>
<p>(4) The
mapping class group of $\Sigma$ (i.e. the quotient of the group of diffeomorphisms of $\Sigma$ by its identity component) acts projectively on $H_{\Sigma}$. The action of the mapping class group of $\Sigma_g$ on $H_\Sigma$ factors through the group $Sp(2g, \mathbb{Z})$.</p>
</blockquote>
<p>We are talking about this abelian Chern-Simons theory:
$$S_{CS}=\frac{1}{4π} \int_{\Sigma} K_{IJ} A_I \wedge d A_J.$$</p>
<blockquote>
<p>Can some experts walk through this (1) (2) (3) (4) step-by-step for focusing on this abelian Chern-Simons theory?</p>
</blockquote>
<p>partial answer of (1)~(4) is fine.</p>
<p>I can understand the statements, but I cannot feel comfortable to <strong>derive them myself</strong>.</p> | 3,587 | [
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<p>A simple boost in the $x$ direction is given by:
$$ \Lambda = \begin{pmatrix}
\cosh(\rho) & \sinh(\rho) & 0 & 0 \\
\sinh(\rho) & \cosh(\rho) & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{pmatrix} $$</p>
<p>Which get linearized to the following transformation:
$$
x^0 \mapsto x^0
, \quad
x^1 \mapsto x^1 + \frac vc x^0
$$</p>
<p>How come the zeroth component is not linearized to $x^0 \mapsto x^0 + \frac vc x^1$? Is that because there is another factor $c$ in the time components? Since $x^0 = ct$, that would mean the time is transformed like
$$ t \mapsto t + \frac v{c^2} x,$$
and $c^{-2}$ is just so small that is ignored?</p>
<p>Or is it just to fit the Galilei transformation?</p> | 3,588 | [
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<p>I have a doubt about how double slit experiment is made.</p>
<p>Let's think about the perforated wall, what are the requirement for it?</p>
<p>Can a photographic plate could be used as a wall ?</p>
<p>I see a problem here, as a photographic plate serve also as a detector, then the single photon experiment could end up with a single point in <em>the wall that contains the slits</em> and not in the plate located <em>behind the slit's wall.</em></p>
<p>Of course the "one photon count", is knowing the emition before the slits (if this count were made after, it will be a detector making a measurement and would simply reflect the particle effect)</p>
<p>The wall with the slits could absorb the photon(removing electrons from the material) before something happen on the other side, if that happened, there would be no experiment, the photon won't pass through the slits, just because its energy was already used (supposing all energy is used and the photon doesn't split).</p>
<p>There must be some kind of specification about the material of the wall, need to be special, in the sense of needing a higher energy (than the test photon) to pickup electrons, then the light won't stop there, for that, I think the wall can't be made of a photosensible material, but I don't know, and here I am asking..</p>
<p>thanks for any answer</p> | 3,589 | [
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<p>Hubble's law states that $v=Hx$</p>
<p>Age of the universe is calculated by $T= \frac{x}{v} = \frac{1}{H}$</p>
<p>but the velocity is not constant; it changes with distance, so I think that this equation cannot be applied because simply the velocity is NOT uniform</p>
<p>$v$ should have been replaced with $\frac{\mathrm{d}x}{\mathrm{d}t}$, so it gives this differential equation $\frac{\mathrm{d}x}{\mathrm{d}t}=Hx$.</p>
<p>Nevertheless, when this differential equation is solved, and we substitute for initial condition ($x=0$ when $t=0$), it appears that there are no solutions, because it will be an exponential function, which can't take the value $0$ ever. </p>
<p>What is wrong with my understanding? </p> | 3,590 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/9354/question-about-time-dilation">Question about Time Dilation..</a> </p>
</blockquote>
<p>I have a question about special relativity which was bothering me for a while now. I know that as one approaches the speed of light, time moves slower for him. So, if I start moving as fast as 99% of the speed of light and travel away from Earth for 1 day and come back, I'll see that (suppose) about 1 year has passed on Earth.</p>
<p>But my question is, if everything is relative, then how can we say that I was the one moving and Earth was the one staying? I mean if I consider myself as the center o the coordinate system, then I can say that Earth went on a travel with the speed of light and came back. So why is that the time slows down for me and not for the Earth? How do we distinguish between the moving and the static object according to relativity?</p> | 101 | [
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<p>Is there a good chance that gravitational waves will be detected in the next years?</p>
<p>Theoretical estimates on the size of the effect and the sensitivity of the newest detectors should permit a forecast on this.</p> | 357 | [
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] |
<p>After spending hours understanding what exactly Black Body radiation and Ultraviolet catastrophe is, I cannot help myself asking what was the reason that make scientists such as Wilhelm Wien and Max Planck to study Black Body Radiation at the first place? What intrigue them to study a hypothetical situation? What they were looking for exactly that make them in studying this phenomenon. </p> | 3,591 | [
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] |
<p>Given the Hubble slow-roll parameters $\epsilon=-\frac{\dot{H}}{H^{2}}$ and
$\eta=\frac{\dot{\epsilon}}{H\epsilon}$, can they assume negative values? For inflation to occurr they are required to be small but what about their sign?
Thanks in advance.</p> | 3,592 | [
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<p>I was wondering if someone can explain why E is the way it is in cases 2,3,4 in page 9 of these <a href="http://www.maths.gla.ac.uk/~drf/courses/mhd/lect4.pdf" rel="nofollow">notes</a> ?</p>
<p>In case 2 "Short Circuit", do I just have to assume that for a perfect conductor E = 0 for short circuit ?</p>
<p>I don't really get why current density is negative in this case (or the 3rd case for that matter) and what it means physically, for current density to be negative...</p>
<p>Any extra comments on what is going on in there would also be appreciated.</p> | 3,593 | [
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<p>It is well know that planewaves are a complete basis for solutions to the wave equation. Let us assume a 2D space, and at fixed temporal frequency, the equation reduces to the Helmholtz equation. In cylindrical coordinates, the most appropriate solutions are the two kinds of Hankel functions, representing outgoing and incoming wave solutions. Actually, the Hankel functions should be multiplied by $e^{i m \theta}$ to produce cylindrical harmonics, which are a complete basis. My question is this:</p>
<p>If cylindrical harmonics are a complete basis, is there a closed form expression relating them to planewaves?</p>
<p>I know that 1st kind Bessel functions $J_m$ have a planewave decomposition by way of the Jacobi-Anger identity. However, a Hankel function's real part is a bessel function while its imaginary part is a 2nd kind Bessel function (Neumann function) with a singularity at the origin. I can't find an analogous expression for expression Neumann functions in terms of planewaves.</p> | 3,594 | [
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<p>When two tuning forks stand near one another and one is excited, the other rings as well. When high notes are struck on a piano, lower notes are also heard. If I understand correctly, this is called <a href="http://en.wikipedia.org/wiki/Sympathetic_resonance" rel="nofollow">sympathetic resonance</a>.</p>
<p>What is the principle behind this effect, and how can it be described mathematically? I've seen it used in analogy with quantum entanglement--is such an analogy accurate?</p> | 3,595 | [
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<p>Consider a supersonic plane (mach 2) aproaching a stationary sound source (e.g a fog horn on a boat).</p>
<p>If I understand it correctly, the passengers in the plane can hear the sound twice. First at a 3 times higher frequency, and then (after they passed the source) a second time at normal frequency but backwards. None of the textbooks or web sites mention this backwards sound. Yet I am quite sure it must be there.</p>
<p>Am I correct? And if so, is it actually observed (e.g. By fighter pilots) and why do textbooks never mention this?</p> | 3,596 | [
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<p>My son who is 5 years old is asking me a question about how the earth moves around the sun. What answer should I give him?</p> | 3,597 | [
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<p>I'm working on an article about propagators from int. representations of Green`s functions for several N-dimensional potential(all this is done in an N-dimensional Euclidian space). Potentials like the free-particle, harmonic oscillator, Coulomb and Poschl-Teller. I started from the radial equation which is satisfied by the Qth partial-wave Green's function</p>
<p>$$\biggl[E+\frac{1}{2r^{N-1}}\frac{\partial}{\partial r}r^{N-1}\frac{\partial}{\partial r}-\frac{Q(Q+N-2)}{2r^{2}}-V(r)\biggr]G_{Q}^{N}[r,r',E]=\frac{\delta(r-r')}{(rr')^{N/2-1/2}}$$</p>
<p>As the usual procedure goes, the construction of the Green's function is </p>
<p>$$G[r,r',E]=\frac{u(r_{-})v(r_{+})}{\frac{1}{2}r^{N-1}W[u,v]}$$</p>
<p>obviously, here the u and v are solutions of the homogeneous equation with the appropiate boundary conditions and W is the Wronskian.
With the first three potential I had no problem to arive at the N-dimensional form of the propagator.</p>
<p>But I don't know what method to use for the Poschl-Teller potential, I can't even find the solutions for the homogeneous equation with this given potential. Do you have any pointers on this problem?I tried the classical method used to solve the Schrodingers eq. with this potential but I got nowhere with it.</p>
<p>Thanks.</p> | 3,598 | [
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<p>I'm looking at Kopfermann H., Ladenburg R., Nature, 122, 338-339 (1928) and it appears Ladenburg in Ladenburg R., Z.Physik, 4, 451-468 (1921) was the first to discover the phenomenon of "negative dispersion" and/or "negative absorption" which is at the basis of the laser theory. That idea is present in as early as Planck's 1901 paper but apparently Ladenburg was the first to see it. Unfortunately, I can't read German, so the 1921 paper is off-limits for me and therefore I'm missing most of the derivation. I'm, however, seeing the formula $$ f_{kj} N_j \frac{g_k}{g_j} \left( 1 - \frac{N_kg_j}{N_j g_k} \right) $$ in Kopfermann H., Ladenburg R., Nature, 122, 338-339 (1928), which appears later in Fabrikant's dissertation but because only two pages from that dissertation are available I can't tell if Fabrikant has cited Ladenburg in it. Anyway, Ladenburg claims that the refractive index should be proportional to the above formula which isn't at all obvious to me. Further, it should be said that the above formula is arrived at from $$ \frac{f_{kj}}{g_j} \left( N_{jgk} - N_kg_j \right) .$$ This can be obtained only if $N_{kgj} = N_j g_k$ leading to a formula $$ f_{kj} N_j \left( \frac{g_k - g_j} {g_j} \right) , $$ equivalent to the first one presented here. Now, let me not forget to mention that $N_j$ and $N_k$ are the number of atoms per cm$^3$ in the states $j$ and $k$, $g_j$ is the statistical weight in the state $j$ and $f_{kj}$ is the probability coefficient for the transition $j \rightarrow k$. Can anyone tell how the second equation is derived and what the physical meaning of the third formula might be? Also, how it would follow from the first formula naturally that there may be "negative dispersion" other than speculating that somehow the term $\frac{N_kg_j}{N_j g_k} $ might be of a certain value to achieve "negative dispersion" and then test that hypothesis experimentally?</p> | 3,599 | [
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<p>Consider a field redefinition
$$
\phi \rightarrow \phi' = \phi+\lambda \phi^2
$$
Find the Feynman rules for this theory and work out the $2\rightarrow 2$ scattering amplitude at tree level (The result should be zero).</p>
<p>$$
\mathcal{L}_0 = -\frac{1}{2}(\partial^\mu \phi \partial_\mu \phi + m^2 \phi^2) \implies \text{EOM: } \Box\phi - m^2\phi=0
$$
Preforming the field redefinition on the Lagrangian I obtain:
$$
\mathcal{L}_0 \rightarrow \mathcal{L}'= \mathcal{L}_0 -2\lambda\phi \partial^\mu \phi \partial_\mu \phi - 2 \lambda^2 \phi^2 \partial^\mu \phi \partial_\mu \phi -\lambda m^2 \phi^3 - \frac{\lambda^2}{2} m^2 \phi^4
$$
I then rewrote the two terms with partial derivatives as
$$
-2\lambda\phi \partial^\mu \phi \partial_\mu \phi = -\lambda \partial^\mu (\phi^2 \partial_\mu \phi)+\lambda \phi^2 \Box \phi
$$
which gets rid of the total derivative. Then I used the EOM to replace $\Box \phi$ with $m^2 \phi$ to get
$$
\mathcal{L}' = \mathcal{L}_0 + \lambda (m^2 - 1)\phi^3 + \lambda^2 \left( \frac{m^2}{3}-\frac{1}{2} \right) \phi^4
$$
Now this looks like a normal scalar field theory with a cubic and quartic vertex. Now it wants a tree level diagram for two to two scattering, so I should put these two vertices in all the combinations that have no loops and result in two in, and two out? Then subsequently work out the scattering amplitude from the said diagrams using the Feynman rules I put together with the above Lagrangian?</p> | 3,600 | [
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<p>In perspective of thermodynamics,a person can survive a temperature of twenty degrees Celsius in air, but a person cannot survive in water with same temp.(it's not because he can't breathe) why is that in perspective of thermodynamics??</p> | 3,601 | [
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<p>I have this graph of a gas:</p>
<p><img src="http://i.stack.imgur.com/DMQlN.jpg" alt="gas graph"></p>
<p>Now, I need to calculate work of it, based on ABCD cycle of changes (that's a bit confusing to me, do I calculate AB, BC, CD separately?). How do I do it?</p>
<p>Also, how can I calculate heat of this gas needed to exchange with enviroment, in order to maintain it's internal energy?</p> | 3,602 | [
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<p>When water freezes continuous translational symmetry is broken. When a metal becomes superconducting, what is the symmetry that gets broken?</p> | 3,603 | [
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<p>I realize that the question a rather large paradox, but I do wonder if such a thing were true what would happen. Assuming that neither of these "objects" can be destroyed by each other. </p> | 3,604 | [
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<p>Please explain from:
mathematical point of view "laws of mathematics", and, physical point of view "laws of physics"? Or is there any bound on number of dimensions?</p> | 3,605 | [
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<p>A system of solar panels are fixed on top of a large water tank of height $40m$ and area $10m^2$. Atmospheric pressure is $100kPa$. What is the pressure at the bottom of the tank? The density of water is $\rho =1000kg/m^3$ and $g=10m/s^2$.</p>
<pre><code>a 10kPa
b 1000kPa
c 2000kPa
d 200kPa
e 1kPa
</code></pre>
<p>My doubt: why is the answer not $100kPa+\rho gh$? explanation of concept will be appreciated.
What I did was simply atmospheric pa +pressure due to water.
The confusion lies in the fact that will we only consider the pressure due to water as the solar panel roof will balance the atmospheric pressure?</p> | 3,606 | [
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<p>Connes's noncommutative geometry program includes an <a href="http://www.alainconnes.org/docs/einsymp.pdf">approach to the Standard Model</a> that employs a noncommutative extension of Riemannian metric. In recent years I've heard physicists say that this approach does not hold significant interest in the physics community. </p>
<p>Is this, in fact, the case? If so, why?</p>
<p>I do not mean for this question to be argumentative, but instead would like clarification. </p> | 3,607 | [
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<p>Prove <a href="http://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law" rel="nofollow">Biot-Savart law</a>, assuming that
$$\vec{A}=\frac I c\int \frac{d\vec{L}}{r}$$
$$\vec{B}=\nabla\times \vec{A}$$
Any hint on what to do next?</p> | 3,608 | [
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] |
<p>The collision term in the Boltzmann equation can be derived from the BBGKY hierarchy. </p>
<p><a href="http://en.wikipedia.org/wiki/BBGKY_hierarchy" rel="nofollow">Wikipedia</a> says:</p>
<blockquote>
<p>In statistical physics, the BBGKY hierarchy [...] is a set of equations describing the dynamics of a system of a large number of interacting particles. The equation for an s-particle distribution function (probability density function) in the BBGKY hierarchy includes the (s + 1)-particle distribution function thus forming a coupled chain of equations.</p>
</blockquote>
<p>Does this mean, if I have a system consisting of s particles, that there is an interaction with a particle outside my system? So my system is not closed?</p> | 3,609 | [
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<p>How do I calculate the angle of Inclination for a specific location on the Earth? The only Information I've got is the longitude and latitude in degree, so I do not understand. I now <code>I=arctan(Z/H)</code> if I have three components <code>X(=north), Y(=east) and Z(=down=vertical intensity)</code>.
But then, how do I calculate the vertical intensity from what I've got? I would need to get all three components, but I do not now how these are calculated. I tried to fiend it on google, but I only got a bunch of calculators, which do not explain what is happening. Can someone help out?</p> | 3,610 | [
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<p>It seems I am stuck with a (at a first sight) trivial problem. </p>
<p>It's from the <em>"Quarks and Leptons" (Halzen, Martin)</em> book page $141$, where one considers the following integral: </p>
<p>$$\tag{1} T_{fi} = -i\int \!d^4x \, J_0^A(t_A,\vec{x}_A)\,J_0^B(t_A,\vec{x}_A)\frac{1}{|\vec{q}|^2}. $$
In equation $(1)$, $J_0^A$ and $J_0^B$ are the zeroth component of two electron currents:
$$J_\mu(x) = j_\mu\mathrm{exp}[(p_f-p_i)\cdot x].$$</p>
<p>Now, according to the authors, one can rewrite $(1)$ by making use of the Fourier transform </p>
<p>$$\tag{2} \frac{1}{|q|^2} = \int\! d^3x\, e^{i\vec{q}\cdot\vec{x}}\frac{1}{4\pi|\vec{x}|}, $$
to the following
$$ \tag{3} T_{fi}^{Coul} = -i\int \!dt_A\int d^3x_A\int d^3x_B \, \frac{J_0^A(t,\vec{x}_B)\,J_0^B(t,\vec{x}_B)}{4\pi|\vec{x}_B-\vec{x}_A|}. $$</p>
<p>Equation $(3)$ is then interpreted as the instantaneous$^1$ Coulomb interaction between the charges of the particles, $J_0^A$ and $J_0^B$. </p>
<p>The derivation of this is given in the answer below. </p>
<hr>
<p>$^1$I.e. interaction without retardation at time $t_A$. </p> | 3,611 | [
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<p>my question concerns the kinematics of 2 to 2 particle scattering. I refer to Peskin and Schroeder eq.17.59 going from this expression</p>
<p>$\frac{d^3\sigma}{dy_3dy_4dp_T}=x_1f_1(x_1)x_2f_2(x_2)\;2p_T\frac{d\sigma}{d\hat{t}}(1+2\to3+4)$</p>
<p>to this</p>
<p>$\frac{d^4\sigma}{dy_3dy_4d^2p_T}=x_1f_1(x_1)x_2f_2(x_2)\;\frac{1}{\pi}\frac{d\sigma}{d\hat{t}}(1+2\to3+4)$</p>
<p>He uses $2\pi\,p_T\,dp_T=d^2p_T$ but I fail to see how that is true?</p>
<p>Thank you for your insight!</p> | 3,612 | [
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] |
<p>In <a href="http://en.wikipedia.org/wiki/Quantum_mechanics" rel="nofollow">Quantum mechanics</a> , a <a href="http://en.wikipedia.org/wiki/Quantum" rel="nofollow">quantum</a> of energy called <strong>Quanta</strong> is origin of everything.</p>
<blockquote>
<p>In physics, a quantum (plural: quanta) is the minimum amount of any physical entity involved in an interaction.</p>
</blockquote>
<p>$E=n.h.\nu$</p>
<p>$\epsilon=h.\nu$.</p>
<p>But it's properties and characteristics is unknown</p>
<p>What is properties and characteristics of a single Quanta?</p> | 507 | [
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<p>I am new to electron spectroscopy. I have a basic question regarding the molecular transition. I have learned about the states $\Sigma_g^+$ $\Pi_g$.. etc electronic states. But I could never find in any books the states like $a^3B_2$, $b^3A_2$ and $A^1A_2$ states! For example, I am attaching a part from from the page 770 of the article (Analyst, 2003,128,765-772). Can anyone please explain me what are these states mean? Or any books/reference suggestions to learn will also be good.
<img src="http://i.stack.imgur.com/s4u2M.jpg" alt="enter image description here"></p> | 3,613 | [
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<p><img src="http://i.stack.imgur.com/nk6qd.png" alt="parabolic profile"></p>
<p>How do I compute the velocity field around the parabolic body using Navier-Stokes? I want to solve it like Poiseuille's law. </p>
<p>I have no slip at the wall boundary and a free shear layer at the boundary between the parabola and the outer fluid. </p>
<p>How do I integrate over the parabolic surface? I am interested in the velocity of the falling film, given the rising velocity of the parabolic body.</p> | 3,614 | [
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<p>Do static charge in a strong insulator flow to a weaker insulator when both stay in contact with each other? For example, when an insulator weaker than air placed in a medium of air, would the static charges on the insulator be absorbed to the air slowly and finally the insulator becomes neutral? If so then what is the rate of flow from the insulator to air?</p> | 3,615 | [
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<p>I am a math grad student who would like to learn some classical mechanics. The caveat is I am not to interested in the standard coordinate approach. I can't help but think of the fields that arise in physics are actually sections of vector bundles (or maybe principal bundles) and would love an approach to classical mechanics or what have you that took advantage of this.</p>
<p>Now for the questions:</p>
<ol>
<li>Is there a text book you would recommend that phrases the constructions in classical mechanics via bundles without an appeal to transition functions? </li>
<li>What are the drawbacks to this approach other than the fact that it makes computations less doable? (if it does that) </li>
<li>Are there benefits to thinking about things this way, ie would it be of benefit to someone attempting to learn this material to do it this way? </li>
</ol>
<p>thanks for your time,
sean</p> | 277 | [
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<p>I have always wondered about applications of Algebraic Topology to Physics, seeing as am I studying algebraic topology and physics is cool and pretty. My initial thoughts would be that since most invariants and constructions in algebraic topology can not tell the difference between a line and a point and $\mathbb{R}^4$ so how could we get anything physically useful?</p>
<p>Of course we know this is wrong. Or at least I am told it is wrong since several people tell me that both are used. I would love to see some examples of applications of topology or algebraic topology to getting actual results or concepts clarified in physics. One example I always here is "K-theory is the proper receptacle for charge" and maybe someone could start by elaborating on that. </p>
<p>I am sure there are other common examples I am missing.</p> | 99 | [
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] |
<p>I've seen several popular reports of a new count of low-mass stars in elliptical galaxies (<a href="http://www.usatoday.com/tech/science/space/2010-12-01-dwarf-stars_N.htm" rel="nofollow">here's one</a>).</p>
<p><strong>Edit:</strong> Pursuant to several correct comments I've changed the title to agree with the actual report which is that the recount concerns elliptical galaxies---and I don't know where I got the notion that it concerned dwarf galaxies---but I am leaving my comments below intact as they represent the way I was thinking before I was corrected. Note that we are in fact talking about relatively few very massive galaxies instead of many very light ones, but the questions are largely unchanged.</p>
<p>My first instinct was to dismiss it as mostly interesting to those who specialize in galactic dynamics, but then it occurred to me that there must be a <em>lot</em> of those galaxies, and I began to wonder about the baryonic-matter/dark-matter/dark-energy balance.</p>
<p>My guess is that this makes little difference to the matter/dark energy part of the equation because the total matter fraction is derived from large scale measurements of cluster dynamics. But even if I am right about the matter/dark-energy thing, that leaves the question of baryonic vs. dark matter fraction.</p>
<p>Can anyone shed some light on this?</p>
<p>Also, links to pre-prints or journal articles related to this measurement would be welcome.</p> | 3,616 | [
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<p>I saw this equation today when calculating energies of photons of different frequencies, and noticed that the change in energy is a product of plank's constant and frequency. $$\Delta e = h * \nu $$ but what is the change in energy with respect to? since a change would be having some initial state $ e_f - e_i$ e sub f being final, e sub i being initial. What are these two initial and final states?</p> | 3,617 | [
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<p>In a <a href="http://physics.stackexchange.com/questions/134533/measuring-more-accurately-the-distance-of-remote-galaxies">previous question</a>, one issue was related to the potential energy
of cosmic structures. This raised in particular the question of
whether these structures are gravitationally bound.</p>
<p>If you consider a group of say, 50 galaxies, I guess one can decide
whether they are gravitationally bound by comparing their positions
and velocities, even if the galaxies considered do not constitute the
whole group thus bound.</p>
<p>Considering a group of very remote galaxies, I presume (is it
correct?) that all one can measure only angular distance, and their
redshift which is due to their peculiar velocity and their distance
(through universe expansion).</p>
<p>Given a set of such measurements for each member of a group of
galaxies, is it possible on that limited basis to determine whether these
galaxies are gravitationally bound, and to infer from that more
precise information about these galaxies?</p>
<p>Are there other measurements that can be made to help that
determination?</p> | 3,618 | [
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] |
<p>Yes in a recent paper I have derived Lorentz force from Maxwell equations. This is available at <a href="http://cpb.iphy.ac.cn/EN/abstract/abstract52454.shtml" rel="nofollow">http://cpb.iphy.ac.cn/EN/abstract/abstract52454.shtml</a>
best wishes</p> | 3,619 | [
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<p>Very basic question.... I know that GAMESS can be used to compute localized molecular orbitals, using for example Boys equation; how does one use the program to get the resulting coefficients used to mix the basis functions. </p> | 3,620 | [
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<p>I heard that at Quantum level events can happen out of order making causality invalid. Thus the future can happen in present and the present in the future. Is this true?</p> | 3,621 | [
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<p>What is the speed of a car going v=1.000 mile per hour in SI units? You can do each conversion separately. Use the facts that 1mile=1609 meters and 1hour=3600 seconds.
Express your answer in meters per second to four significant figures.</p>
<p>Okay first I set the problem to the right conversions.
I do this</p>
<p>$(1000 miles / 1 hour)$ * $(1609 meters / 1 miles)$ * $ *(1hour/ 3600 seconds)$ </p>
<p>Thus I get 446.9 m/s however this is not the right answer. I could use some guidence towards where I went wrong.</p> | 3,622 | [
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<p>You see the poles of a magnet on every magnet picture, and they are said to be in the direction of magnetic field lines, but what does that mean? Is the number of electrons different on one side of the magnet? If electrons only repel each other how do they act like magnets?</p> | 3,623 | [
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<p>I was reading some <a href="http://physics.stackexchange.com/search?q=postselect%2a">questions here</a>. </p>
<p>I couldn't understand what it means by postselection.</p>
<p>What is postselection? What is its use/significance? Where did it came from? </p> | 3,624 | [
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<p>Feynman says in his book "QED" that the square root of the fine structure constant is the probability for a charged particle to emit a photon. But for which wavelength? Or is it an average over all wavelengths? </p>
<p>Note: I meant <em>virtual</em> photon, and I meant a stable charged particle, like the electron. One way to rephrase it would be: how many virtual photons (per unit volume) are there in the Coulomb field around an electron?</p> | 3,625 | [
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<p>Did anyone ever heard about this?I've never seen any serious physicist talk about "mass fluctuations".</p>
<p>Here is the man in his own words: <a href="http://www.intalek.com/Index/Projects/Research/woodward1.pdf" rel="nofollow">http://www.intalek.com/Index/Projects/Research/woodward1.pdf</a></p>
<p>And what about this guy: <a href="http://aetherwavetheory.blogspot.com/" rel="nofollow">http://aetherwavetheory.blogspot.com/</a></p>
<p>He claims his theory can explain virtually every unsolved problem in contemporary physics.</p> | 3,626 | [
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<p>What is the underlying reason that the same pairs of conjugate variables (e.g. energy & time, momentum & position) are related in <a href="http://en.wikipedia.org/wiki/Noether%27s_theorem" rel="nofollow">Noether's theorem</a> (e.g. time symmetry implies energy conservation) and likewise in QM (e.g. $\Delta E \Delta t \ge \hbar$)?</p> | 3,627 | [
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] |
<p>Is there a convention for chemical symbols of mu-mesic atoms, at least for ones bound to light atomic nuclei?</p> | 3,628 | [
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<p>When listing energies for the purposes of keeping track of conservation, or when writing down a Laplacian for a given system, we blithely intermix mass-energy, kinetic energy and potential energy; they are all forms of energy, they all have the same units, and so this looks OK. For example, in the LHC, turning kinetic energy into new particles of mass-energy is routine. We just converted "energy which does not gravitate" (kinetic energy) into "energy which does gravitate". Isn't it a bit peculiar that this same thing called energy can manifest into two different kinds of forms - those forms which gravitate, and those which do not?</p>
<p>How about potential energy? It would be of course ridiculous to calculate your potential in relation to the galactic centre and expect that huge (negative, by convention) quantity of energy to gravitate; and yet if we allow its conversion into kinetic energy, and thence into particle creation, lo and behold we end up with something that does gravitate.</p>
<p>We know that the massless photon gravitates, because it can be "bent" around a star, per GR. A photon also expresses energy in the form E = p c. So clearly finite rest mass is not a requirement for certain forms of energy to gravitate.</p>
<p>So what's the rule here? When does energy gravitate, and why? Isn't it all supposed to be "just energy"?</p>
<p>Then there's the flip side of the equivalence principle - inertia. Do fields have inertia? - they do gravitate, so if they possess no inertia, doesn't that break EEP?</p> | 3,629 | [
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<p>Position is relative, as it depends on the reference frame. We usually visualize the sun at the center of the solar system. BUT, we can also visualize the Earth at the center of the solar system, with the sun orbiting around it and the planets orbiting around the sun. Therefore, shouldn't we be theoretically be able to see a star orbiting around a planet? (given that the planet happens to be stationary relative to the Earth)?</p> | 102 | [
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