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<p>You age at a different rate depending on the force of gravity. Astronauts age fractions of fractions of fractions of a second less than earthlings.</p> <p>If you took a sphere of equal masses, separated by space, then found the exact center of the gravitational pulls of all masses. How would time react?</p>
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<p>I'm a non-engineer interested in the recent GP-B mission results: <a href="http://www.engadget.com/2011/05/06/nasa-concludes-gravity-probe-b-space-time-experiment-proves-e/#disqus_thread" rel="nofollow">http://www.engadget.com/2011/05/06/nasa-concludes-gravity-probe-b-space-time-experiment-proves-e/#disqus_thread</a...
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<p>In his book: <em>The Equation That Couldn't be Solved</em> Mario Livio explains the equivalence principle in laymen's terms. I took the statement on page 209: <em>The force of gravity and the force resulting from acceleration are in fact the same.</em> to mean that since our universe is accelerating, gravity is the ...
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<p>I have a circuit with capacitors on it:</p> <p><img src="http://i.stack.imgur.com/h5N90.jpg" alt="circuit figure 1"></p> <p>I am trying to figure out the charge on each capacitor.</p> <p>The following is given: </p> <p><img src="http://i.stack.imgur.com/YYXQN.jpg" alt="given"></p> <p>i know that parallel capaci...
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<p>Let's have Dirac spinor $\Psi (x)$. It transforms as $\left( \frac{1}{2}, 0 \right) \oplus \left( 0, \frac{1}{2} \right)$ representation of the Lorentz group: $$ \Psi = \begin{pmatrix} \psi_{a} \\ \kappa^{\dot {a}}\end{pmatrix}, \quad \Psi {'} = \hat {S}\Psi . $$ Let's have spinor $\bar {\Psi} (x)$, which transfor...
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<p>Say we had a particle moving in a frictionless funnel and was projected horizontally.</p> <p>If we had some initial conditions for the energy E, then would these conditions be the same always?</p> <p>For instance, in this particular question I got $$ E = 1/2m\dot r^2 - mgz, $$ and we were given that $z = b\left ( ...
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<p>Consider the situation when a cell of an unknown emf is being measured using a potentiometer. We slide the jockey so as to obtain the null point. Now, is there any current in the potentiometer wire at the null point? Since we know that there is no current in the arm containing the unknown cell, its terminals have ac...
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<p>Most sources say that <a href="http://en.wikipedia.org/wiki/Wigner_quasiprobability_distribution" rel="nofollow">Wigner distribution</a> acts like a joint phase-space distribution in quantum mechanics and this is justified by the formula </p> <p>$$\int_{\mathbb{R}^6}w(x,p)a(x,p)dxdp=&lt;\psi|\hat{a}\psi&gt;$$ as th...
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<p>I am learning about calculating decay rates from quantum field theory amplitudes from <a href="http://www.damtp.cam.ac.uk/user/tong/qft/three.pdf" rel="nofollow">David Tong's lecture notes</a> (page 74 in the notes, 24 in document). However, I have some doubts:</p> <ol> <li><p>When he says <em>the first is to integr...
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<p>How can one prove the Bohr-Sommerfeld quantization formula</p> <p>$$ \oint p~dq ~=~2\pi n \hbar $$</p> <p>from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation? </p> <p>With $S$ the action of the particle defined by Hamilton-Jacobi equation</p> <p>$$ \frac{\partial S}{\partial...
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<p>I'm trying to compute uncertainty for the density of the ball. </p> <p>I measured its radius 6 times, so I was able to compute the stastistical uncertainty (we call it uncertainty type A, I don't know, if that's common used designation) and I knew accuracy of the micrometer, so I got standatd uncertainty (we call i...
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<p>Can anyone explain to me why most articles describe chromium as an acceptor in titanium dioxide? In TiO<sub>2</sub>, titanium has the charge state Ti$^{4+}$ and oxygen has the charge state O$^{2-}$. When Cr substitutes for Ti, it does so as Cr$^{3+}$. Now, at first glance, Cr has atomic number 24 and Ti 22. Cr t...
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<p>Suppose that it is given that the Riemann curvature tensor in a special kind of spacetime of dimension $d\geq2$ can be written as $$R_{abcd}=k(x^a)(g_{ac}g_{bd}-g_{ad}g_{bc})$$ where $x^a$ is a vector in the space.</p> <p>What condition can I impose on $d$ to guarantee that $k(x^a)$ is a constant? I have been tol...
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<p><img src="http://i.stack.imgur.com/DWU9K.jpg" alt="enter image description here"></p> <p>Light is the yellow arrow. Observer is the black arrow. Observer is moving at a constant speed of v, w.r.t to a Galilean frame of reference. </p> <p>Now from the point of view of the observer (O), how will the motion of the li...
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<p>The representation $(\frac{1}{2},\frac{1}{2})$ of the Lorentz group correspond to a four- vector or a spin-one object. Right? Does it imply that any four-vector is <em>identical to</em> a spin-one object or any scalar is <em>identical to</em> a spin-0 object? This can't be correct, right? Because although $A^\mu$ i...
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<p>Allow me to preface this by stating that I am a high school student interested in physics and self-studying using a variety of resources, both on- and off-line, primarily GSU's HyperPhysics website, Halliday &amp; Resnick's <em>Fundamentals of Physics</em>, Taylor's <em>Classical Mechanics</em>, and ultimately the F...
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<p>I always hear people saying symmetry is beautiful, nature is symmetric intrinsically, physics and math show the inherent symmetry in nature <em>et cetera, et cetera</em>.</p> <p>Today I learned that half of the quarks have +2/3 electric charge and other half have -1/3 magnitude electric charge. Is there any explana...
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<p>In atomic and molecular physics we quite often encounter with electric dipole approximation. The dipole approximation we do when the wave-length of the type of electromagnetic radiation which induces, or is emitted during, transitions between different atomic energy levels is much larger than the typical size of a l...
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<p>This <a href="http://www.youtube.com/watch?v=1TKSfAkWWN0">Veritasium video</a> explains how electromagnets can be explained by special relativity, and how the magnetic field surrounding a current-carrying wire can also be viewed as an electric field, if your frame of reference is moving with respect to the wire.</p...
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<p>I'm reading through Kardar's Statistical Mechanics of Particles; in the section 1.5 he says:</p> <blockquote> <p>A reversible process is one that can be run backward in time by simply reversing its inputs and outputs. It is the thermodynamic equivalent of frictionless motion in mechanics. <strong>Since time rever...
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<p>I came up last night with a talk given by <a href="http://www.sjcrothers.plasmaresources.com/index.html" rel="nofollow">Stephen J. Crothers</a> in which he claims that black holes and the Big Bang have no basis in general relativity. But is he really true? How legitimate are his claims?</p> <p>Here is the talk on Y...
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<p>Just like classical potential, it's stated that equilibrium is obtained when the corresponding thermodynamics potential reaches the minimum.</p> <p>Explicitly, according to <a href="http://en.wikipedia.org/wiki/Thermodynamic_potential" rel="nofollow">Wikipedia</a>, in particular: </p> <blockquote> <p>When the en...
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<p>I'm building an airplane (Super Baby Great Lakes) and I'm wondering something about <a href="http://en.wikipedia.org/wiki/Airfoil" rel="nofollow">airfoils</a>. In particular (this plane is fabric covered), I'm wondering about the lifting forces on the main wings. I've read something about it being very important tha...
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<p>Consider a system of $n$ undistinguishable particles moving in $d$-dimensional Euclidean space $E^d$. The configuration space is $M=((E^d)^n \setminus \Delta)/S_n$ where $\Delta$ is the diagonal (subspace where at least 2 particles have coincidental positions) and $S_n$ is the group permuting the particles</p> <p>Q...
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<p>Is there an entropy that one can use for the Wigner quasi-probability distribution? (In the sense of a phase-space probability distribution, not - just von Neumann entropy.)</p> <p>One cannot simply use $\int - W(q,p) \ln\left[ W(q,p) \right] dq dp$, as the Wigner function is not positively defined. </p> <p>The mo...
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<p>The photon field is the non chiral piece of SU(2)xU(1), independently of symmetry breaking or not, isn't it? </p> <p>But before symmetry breaking, each gauge boson has only a chiral gaugino as superpartner. Is it still possible, <strong>and correct</strong>, to arrange two of them in order to form an electrically ...
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<p>Single particle states in quantum field theory appear as discrete components in the spectrum of the Poincare group's action on the state space (i.e. in the decomposition of the Hilbert space of quantum states into irreducible representations of the Poincare group). Classification of irreducible unitary representatio...
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<p>In all thermodynamics texts that I have seen, expressions such as $\operatorname{ln}T$ and $\operatorname{ln}S$ are used, where $T$ is temperature and $S$ is entropy, and also with other thermodynamic quantities such as volume $V$ etc. But I have always thought that this is incorrect because the arguments $x$ in exp...
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<p>Consider a point mass $x$ (like for example the earth in space) and let $A$ and $B$ be two sets of point masses which each hold the point mass $x$ in equilibrium, meaning the acceleration induced by $A$ on $x$ is zero, and the same for $B$. Now if I put the point masses of both $A$ and $B$ in space then (by superpos...
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<p>I am working through the derivation of an adiabatic process of an ideal gas $pV^{\gamma}$ and I can't see how to go from one step to the next. Here is my derivation so far which I understand:</p> <p>$$dE=dQ+dW$$ $$dW=-pdV$$ $$dQ=0$$ $$dE=C_VdT$$</p> <p>therefore</p> <p>$$C_VdT=-pdV$$</p> <p>differentiate the id...
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<p>Can you explain what happens when a particle and its antiparticle are created. Do they whiz away from each other at the speed of light or what? I suppose that they don't because otherwise they would never meet and annihilate each other, but then, if I had just been created with an antiparticle I would do all I could...
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<p>In bosonic string theory, to obtain the photon as the first excited state, the ground state must have a negative mass (tachyon). By applying $1 + 2 + 3 + \cdots = -1/12$, it can be shown (in a simplified way...) that a total of 26 spacetime dimensions are needed to obtain such a tachyonic ground state.</p> <p>Going...
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<p>The determinant of a two-qubit (4 x 4) density matrix lies between 0 and (1/2)^8. (A pure state has determinant zero, and the fully mixed [classical] state, determinant (1/2)^8.)</p> <p>The determinant of the partial transpose (transpose in place the four 2 x 2 blocks) of such a matrix (nonnegative values indicati...
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<p>I cannot seem to prove that the derivative of the duel tensor = 0.</p> <p>$$ \frac{1}{2}\partial_{\alpha}\epsilon^{\alpha \beta \gamma \delta} F_{\gamma \delta} = 0. $$</p> <p>Writing this out I get (for some fixed $\alpha$ and $\beta$),</p> <p>$$ \partial_{\alpha} (\partial_{\gamma}A_{\delta} - \partial_{\delta}...
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<p>Firstly I can say that I would love us to come up with a sustainable fusion solution. However with the latest estimates being 2050 at the earliest for an effective fusion solution and the planets energy needs growing by the year should we not be looking at alternatives?</p> <p>I understand that in the EU alone we ...
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<p>Is the opening of the NOVA program on PBS a Calabi-Yau space?</p>
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<p>I have a doubt about the electric field lines for a continuous distribution. Well, if there's only some point charges, I know that the field starts on the positive ones (or at infinite), ends at negative ones (or at infinity) and the number of lines is proportional to the number of charges. That's fine, but what are...
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<p>I have a problem that asks for the minimum energy of a wave that we will use to see a particle of size $.1\text{ nm}$. I understand that I can not see a $.1\text{ nm}$ particle with any wave length larger than $.1\text{ nm}$. I thought this would be easy, and I would use De Broglie's relation of electron waves,</p> ...
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<p>In <a href="http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect" rel="nofollow">Aharonov-Bohm effect</a>, how to derive that the wave function of a electric charge $q$ acquires a phase shift $\phi=\frac{q}{\hbar}\int \mathbf{A} \cdot d\mathbf{x}$ after travelling in the non-zero magnetic vector potential $\mat...
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<p>Which of two objects at the same tempreature can cause more intense burns when you touch it: the one with the greater specific heat capacity or the one with the smaller specific heat capacity and why?</p>
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<p>Suppose one inertial observer measures a rod at rest w.r.t. him and another observer is moving w.r.t. rod. We then say that length will be shorter for moving observer but at the instants the first observer is measuring the length, the second observer doesn't even get the length of the rod, he just gets distance betw...
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<p>I know the famous beta function of asymptotic free, but that seems describe the running coupling beyond confinement/QCD scale so that a perturbative analysis can apply. But how coupling runs below that scale? Any comment or references are greatly appreciated.</p>
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<p>Different authors seem to attach different levels of importance to keeping track of the exact tensor valences of various physical quantities. In the strict-Catholic-school-nun camp, we have Burke 1980, which emphasizes that you don't always have a metric available, so it may not always be possible to raise and lower...
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<p>I am working on this lab that involved gathering data from two different sources. It involved gathering reaction times from a device and from a web application which was put into our data sets.</p> <p>It is asking about anticipated events and if they agreed with the experimental uncertainty. After Googling these te...
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<p>In the movie <em>Transporter 3</em> a submerged car is floated to the surface by filling a large bag with air from the tyres.</p> <p>I know that movies are about the worst places to get examples of physics in action, and my first thought was that if the air from the tyres was enough to inflate the bag and lift the ...
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<p>I am a high school student doing an IB Extended Essay investigation concerning the resonant frequencies of <a href="http://en.wikipedia.org/wiki/Ernst_Chladni" rel="nofollow">Chladni</a> plates of differing materials and sizes. Would someone please explain the definition of radial and diametric nodes ($n$ and $m$),...
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<p>Yesterday my brother asked me how orbits work. Suppose for the sake of the question that you are trying to put a rocket in orbit around the Earth. I explained that orbiting is essentially being in free fall while going very fast sideways, so that by the time you fall, there's no ground anymore and you keep going.</p...
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<p>What is theory behind free energy perturbation? Is it way too difficult to understand? Can someone explain it in simple terms.</p>
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<blockquote> <p>I want to calculate the expectation value of a Hamiltonian. I have a wave function that is $$\psi = \frac{1}{\sqrt{5}}(1\phi_1 + 2\phi_2).$$</p> </blockquote> <p>I want to know if I set this up properly. The Hamiltonian is $\hat H \left(x, \frac{\hbar \partial^2}{2m\partial x^2}\right)$. To get an ex...
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<p>Suppose that completely stopping a subatomic particle, such as an electron, could happen under certain conditions. What would be likely ways to get an electron to be perfectly still, or even just stop rotating the nucleus and collapse into it by electromagnetic forces? What would likely be required, below absolute-z...
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<p>if I have a not necessarily homogenous electric field of a charge distribution in an electrolyte and i want to find out what the electric field at some position in the electrolyte is. is there any equation that i could use to consider also electric screening by the ions, so that I will get a different electric field...
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<p>I am a class 9 student in India. I want to become a physicist. What should I study after class 10? What are my options for colleges and universities? What should I do after my education? What are the fields to do research in post-graduation?</p>
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<p>I know that if a star collapses into a volume with radius less or equal to the Schwarzschild radius $r_s=\frac{2GM}{c^2}$ then a black hole is created and it has the same mass of the star that gave it origin. But is there a way to calculate the mass of a black hole without knowing the volume of the star?</p>
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<p>This is a question about an historical theory of gravitation, studied by Einstein quite a bit <em>before</em> he settled on General Relativity. At that time, Einstein did not know that gravity was a consequence of curved space-time. He identified the variations of gravity with the variations of light speed in a grav...
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<p>Does gravity slow the speed that light travels? Can we actual measure the time it takes light from the sun to reach us? Is that light delayed as it climbs out of the sun's gravity well?</p>
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<p>Is it more efficient to stack two Peltier modules or to set them side by side? And why?</p> <p>I have a small box that I want to cool down about 20 K below ambient -- cold, but not below freezing. (I want to keep my camera cool, so I'm putting in this cool box. The camera looks through a flat glass window on one si...
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<p>If we are to take two Hydrogen atoms and subject them to the same potential, then wouldn't both Hydrogen atoms be in the same exact quantum state? This bother me because no two identical fermions can be in the same quantum state! This seems to contradict the principle. This applies to any two elements or molecules t...
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<p>Every so often,* we get a question about what would happen should there be a change in a physical constant that contains dimensional information, such as $\hbar$, $c$, $G$, or often "the scale of the universe", and we often wind up reinventing the wheel to explain why this is not a well-posed question. I would there...
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<p>We all use deodorant and they always feel cold, why is that?</p> <p>Is it because it is liquid inside the bottle and a gas when it is released?</p>
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<p>The firewall paradox is a very hot topic at the moment (1207.3123v4). Everyone who is anybody in theoretical physics seems to be jumping into the action (Maldacena, Polchinski, Susskind to name a few). </p> <p>However, I am unable to see the paradox. To me Hawking's resolution of the information paradox (hep-th/050...
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<p>My physics teacher talked about the meeting of 2 parallel lines, and he said that it may occur in the infinity or something. I know that 2 parallel lines can meet in spherical geometry, (thanks to math stackexchange), but can such a thing occur in physics? (I really want to know so I could tell him).</p>
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<p>Do Earth's rotation/revolution is regulated by other planets (and vice versa) in any way? How?</p>
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<p>Recently, I was doing my homework and I found out that Torque can be calculated using $\tau = rF$. This means the units of torque are Newton meters. Energy is also measured in Newton meters which are joules.</p> <p>However, torque isn't a measure of energy. I am really confused as why it isn't measured in Joules.</...
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<p>Roughly speaking, we define a <a href="http://en.wikipedia.org/wiki/Manifold" rel="nofollow">manifold</a> $M$ to be covered by a set of charts $\{(U_i , \varphi_i)\}$ such that locally the $n$-dimensional manifolds looks like $\mathbb{R}^n$. One of the conditions is that all the $U_i$ are open sets of the topology o...
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<p>When an electron absorbs a photon, does the photon become electron "stuff" (energy); or, is it contained within the electron as a discrete "something"?</p>
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<p>I'm trying to understand the definition given on my electromagnetism course for the current density. More specifically, I want to know why, as defined below, the current density is given the name "current density."</p> <p>On my course, the current density is $\vec{j}(t,\vec{x}):=\rho (t,\vec{x}) \vec{v} (t,\vec{x})...
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<p>When resistances connected in series then why through each resistances the different potential difference occurs? </p>
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<p>If space is not actually a void, then there's something shooting around in it, I'm guessing a lot like molecules in a gas. Could we apply a $(PV/T = k)$ -like gas law to it. Obviously we're not measuring a regular everyday gas but some theoretical "fluid" that we don't know enough about yet. Also regular radiatio...
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<p>Does the resistance of an analog current meter increase or decrease when it is set to a more sensitive scale (lower range)?</p>
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<p>Since the $\vec{E}$ field inside a "perfect" conductor is zero, do the electrons(the current) flow only on the outer surface? This has bothered me since I studied electromagnetism. </p> <p>Thank you for your time.</p>
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<p>Are there any QM effects that have been/could be measured from interactions involving non-charged particles? </p> <p>Elementary QM is all about the electron energy levels in the atom, photon - atom interactions, etc. </p> <p>When one looks at the nucleus, its all about quark interactions - which are also charged p...
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<p>So I was reading about <a href="http://www.nasa.gov/mission_pages/spitzer/news/spitzer20111221.html" rel="nofollow">GN-108036</a> this morning and for some reason I thought of something which I can't quite wrap my head around and make sense of. It's early morning so maybe coffee hasn't kicked in yet.</p> <p>If it ...
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<p>In <a href="http://en.wikipedia.org/wiki/Catching_Fire" rel="nofollow">Catching Fire</a>, the second episode of the Hunger Games trilogy, one of the characters (Beetee) proposes a plan to kill some of the remaining tributes. He proposes wrapping a special wire that he has designed to withstand the vast energy of lig...
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<p>While reading with my son about how a Mars-like planet collided with the early Earth that resulted in our current moon, it said the initial debris also formed a ring, but that ring ended up getting absorbed by the Earth and the Moon.</p> <p>I couldn't answer his question then why Saturn still has rings. Shouldn't ...
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<p>In my particle physics lecture, <a href="http://en.wikipedia.org/wiki/Faddeev%E2%80%93Popov_ghost" rel="nofollow">ghost fields</a> were briefly mentioned. </p> <p>As far as I understand, these come up when computing cross sections by the path integral method, to compensate for equivalent contributions due to gauge ...
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<p>In the YouTube video <a href="https://www.youtube.com/watch?v=_yEu2R1gYSs" rel="nofollow">Monster magnet meets computer</a>, the south pole of a 1 T (roughly) neodymium magnet is held in front of a CRT. Assuming the CRT produces electrons of 30 keV, and that the screen is 0.2 m from the end of the electron gun, how ...
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<ol> <li><p>What is the meaning <a href="http://en.wikipedia.org/wiki/Generalized_coordinates" rel="nofollow">generalised coordinates</a> in Classical Mechanics?</p></li> <li><p>How is <a href="http://en.wikipedia.org/wiki/Lagrangian_mechanics" rel="nofollow">Lagrangian formalism</a> different from <a href="http://en.w...
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<p>Recently I read <a href="http://blogs.discovermagazine.com/badastronomy/2011/11/17/huge-lakes-of-water-may-exist-under-europas-ice/">this entry</a> by Dr. Phil Plait (a.k.a. The Bad Astronomer). He is talking about a lake of water contained within the ice layer of Europa.</p> <blockquote> <p>the lake is complete...
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<p>I understand now how I can derive the lowest energy state $W_0 = \tfrac{1}{2}\hbar \omega$ of the <a href="http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator" rel="nofollow">quantum harmonic oscillator</a> (HO) using the ladder operators. What is the easiest way to now derive possible wavefunctions - the ones ...
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<p>There is a section of my notes which I do not understand, hopefully someone here will be able to explain this to me. The notes read (after introducing the uncertainty operator):</p> <blockquote> <blockquote> <p>If the state $\chi_A$ is an eigenstate of $\hat O_A$ then the uncertainty is zero and we measure it...
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<p>I thought electronics is mainly discussed in engineering majors. But in my university Electronics and Digital Electronics is also compulsory for physics majors.I searched other's syllabus, but I didn't found any electronics course. In MIT opencourseware also there is no electronics course in physics.</p> <p>Is ther...
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<p>In <a href="http://arxiv.org/pdf/1003.1366.pdf">this</a> paper on p42, it is explained that when starting with a bare action that contains a standard kinetic term, this kinetic term attains a correction in the course of the RG flow which can be denoted by $1/Z_{\Lambda}$, such that the effective kinetic term at a sc...
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<p>When solving the heat equation, $$ \partial_t u -\Delta u = f \text{ on } \Omega $$ what physical situations are represented by the following boundary conditions (on $\partial \Omega$)?</p> <ul> <li>$u=g$ (Dirichlet condition),</li> <li>$n\cdot\nabla u = h$ (Neumann condition),</li> <li>$n\cdot\nabla u = \alpha u$...
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<p>In the context of this <a href="http://physics.stackexchange.com/questions/1428/a-question-on-evolution-of-mass-and-velocity-distributions-rhor-t-and-v">question</a> should mass distribution $\rho(r,t)$ and momentum distribution $p(r,t)$ be well behaved ? By 'well behaved' it is meant that derivatives of all orders ...
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<p>Since any source of light will have a finite duration, the light emited won't have a particular frecuency. It will be a sum of different frequencies (infinite, I think) if we apply Fourier's series (integral).</p> <p>Would this mean that any photon's frequency will have some uncertainty or something like the photon...
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<p>Assume the time standard clocks and any memories about the time standard are destroyed. Can we recover the time standard again exactly?</p> <p>Recovering the time standard again means we can determine the date and time that are exactly the same as the destroyed time standard clocks will show (if they are not destr...
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<p>I work on a drilling rig as a roughneck and we had a lecture today (at the office) about mechanical advantage in pulley systems. Now, I know that my boss is well educated in oil drilling, but my instincts tell me that he may have this one wrong.</p> <p>A drilling rig works sort of like a crane in that it has a tall...
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<p>Since I don't know the proper physical terms for this, I describe it in everyday English. The following has kept me wondering for quite some time and so far I haven't found a reasonable explanation.</p> <p>When you fill a ceramic cup with coffee and you click with the spoon at the bottom (from the top, through the ...
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<p>Assuming a frictionless / "perfect" environment, and given a ball held in an elastic sling (like a hand-held catapult) <em>where the pocket is lighter than the projectile itself</em>, <strong>what is the point at which the ball separates from the sling pocket? At the start of the shot, or as the sling-pocket passes ...
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<p>Given a stationary 1-D wave function $\psi(x)$, how is the derivative in the momentum operator interpreted?</p> <p>$$ \int_{-\infty}^\infty \psi^*(x) \hat{p} \psi(x) dx = \int_{-\infty}^\infty \psi^*(x) (-i\hbar\nabla) \psi(x) dx $$</p> <p>Should the integral be interpreted as</p> <p>$$-i\hbar\int_{-\infty}^\i...
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<p>Let’s consider this equation for a scalar quantity $f$ as a function of a 3D vector $a$ as:</p> <p>$$ f(\vec a) = S_{ijkk} a_i a_j $$</p> <p>where $S$ is a tensor of rank 4. Now, I’m not sure what to make of the index $k$ in the expression, as it doesn’t appear on the left-hand side. Is it a typo, meaning there is...
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<p>Let's consider a situation: we have distant point source of unpolarized light in certain non-zero range of wavelengths (it's polychromatic). Let's divide this light into 2 beams depending on polarization direction with e.g. Wollaston prism. Then let's rotate the polarization plane of one of these beams by angle 90 d...
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<p>When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity:</p> <p>$\Delta t = \pm \sqrt{2h/g}$</p> <p>$\Delta v = \pm \sqrt{2gh}$</p> <p>One ignores the "unphysical" negativ...
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<p>I heard once in a TED talk how Fizeau measured the speed of light in the 19th century. Here is the link </p> <p><a href="https://www.youtube.com/watch?v=F8UFGu2M2gM" rel="nofollow">https://www.youtube.com/watch?v=F8UFGu2M2gM</a></p> <p>You can read about it here in Wikipedia:</p> <p><a href="http://en.wikipedia.o...
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<p>I have a very simple question.</p> <p>Everyone must have seen the rainbow after rain. According to the theory the <a href="http://en.wikipedia.org/wiki/Rainbow#Explanation" rel="nofollow">rainbow</a> is created due to the passing of sunlight from small drops of water in the atmosphere(means by dispersion of light)....
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<p>As I understand, the kinetic energy of the proton beam in a hadron collider is quite large. Can you build a space propulsion system that is based on accelerating a proton bean to relativistic speeds and then using the resulting kinetic energy to propel a space vehicle? </p> <p>Edit: In the large hadron collider, th...
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<p>This is Problem 2.6 (b) in Griffiths, <em>Intro to QM:</em></p> <blockquote> <p>A particle in an infinite square well has its initial wave function an even mixture of the first two stationary states:</p> <p>$\Psi(x,0) = A[\psi_1(x) + \psi_2(x)]$.</p> </blockquote> <p>Here is the part of the problem that I a...
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<p>Heat Flux= 10 MW Inlet water temperature = 28 degree centigrade for cooling purpose through a tube passing through the centre of retangular block of length 50 mm,height 30 mm and width 30 mm inner diameter of tube=10mm and outer diameter=12 mm tube is made of copper.</p> <p>Find out the heat transfer coefficient of...
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<p>Assuming the following</p> <ol> <li><p>A universe is the surface from a bubble in hyperspace. Inside a bubble there is nothing, only the surface represents a universe. The size of the bubble is time.</p></li> <li><p>Dark matter is from bubbles different then our own bubble that only shares gravity.</p></li> <li><p>...
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<p>Is it possible to deduce the Archimedes' law of the lever using only the laws of conservation of the classical mechanics? I never saw (which is strange), but I think that it's possible. </p>
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