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<p>Given the <a href="http://en.wikipedia.org/wiki/Camera_matrix#The_camera_focal_point" rel="nofollow">camera matrix</a>, can I find the focal length of this camera ?</p>
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<p>What is the role of the resistor in e.g. an AND gate like this one? :</p>
<p><img src="http://i.stack.imgur.com/LirVA.png" alt="AND Gate"></p>
<p>One often sees lots of resistors in electric circuits, but I haven't really understood their role.</p>
| 7,222 |
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<p><strong>How are qubits entangled?</strong> </p>
<p>I understand the basics of entanglement but what I do not get is how it occurs in nature or in the lab. What causes entanglement to occur or what is done to the particle to make it occur.</p>
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<p>I really should know this off by heart (this is my field...) but I never really grasped the difference between the total wavefunction of a system and the wavefunctions of particles within it, so it only just dawned on me that perhaps the total energy of a system was simply the sum of the energies of the individual particles. </p>
<p>It's true, isn't it?</p>
<p>By 'energy' here, I really mean $\langle E \rangle$. So would the expectation value of the total energy equal the sum of the expectation values of all the component particles? Or is there some conditionality to it? I.e. in a quantum computer, if the states of two qubits are opposites, then the expectation value of the total energy would be the sum of the component energies for each possible scenario $|0\rangle|1\rangle$ and $|1\rangle|0\rangle$, multiplied by the probability of each. </p>
<p>Took me a long time to learn to ask the stupid questions.</p>
<p>[Edit: brief mathsing for two qubits:</p>
<p>$ \hat{H} \Psi = E \Psi $</p>
<p>$ \Psi = \psi_m \psi_n $</p>
<p>$ \psi_m = a_m |0\rangle + b_m |1\rangle \quad\quad\mathrm{(ditto}~~\psi_n \mathrm{)} $</p>
<p>$ \Psi = a_m a_n |0\rangle |0\rangle + a_m b_n |0\rangle |1\rangle \dots $</p>
<p>$ \langle E \rangle = a_m a_n E_{00} + a_m b_n E_{01} \dots $ </p>
<p>or time-independently</p>
<p>$ \langle E(t) \rangle = a_m(t) a_n(t) E_{00}(t) + a_m(t) b_n(t) E_{01}(t) $ ]</p>
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<p>I have been referring to a paper
<a href="http://arxiv.org/abs/physics/0405135" rel="nofollow">http://arxiv.org/abs/physics/0405135</a> to determine the effective resistance using random walks for an infinite square resistive lattice</p>
<p>Though the author seems to indicate this as a simple problem
(maybe i am missing something) i have been unable to prove this</p>
<p>$∆_{AB}$ = $\frac{1}{2p_{AB}}$ </p>
<p>where,</p>
<p>$∆_{AB}$ = $\sum_{n=0}^\infty$
$(P_{n}(A) − P{n}(B))$</p>
<p>$P_{n}(x):$Probability that a Random walker after n steps is found at x</p>
<p>$p_{AB}:$Probability that a
random walker, starting at A, gets to B before returning to A</p>
<p>Could someone please help me with this ? </p>
<p>(For more detailed description refer to the link)</p>
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<p>I heard from my GSI that the commutator of momentum with a position dependent quantity is always $-i\hbar$ times the derivative of the position dependent quantity. Can someone point me towards a derivation, or provide one here?</p>
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<p>Consider the Klein–Gordon equation and its propagator:
$$G(x,y) = \frac{1}{(2\pi)^4}\int d^4 p \frac{e^{-i p.(x-y)}}{p^2 - m^2} \; .$$</p>
<p>I'd like to see a method of evaluating explicit form of $G$ which does not involve avoiding singularities by the $\varepsilon$ trick. Can you provide such a method?</p>
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<p>Would it be possible to develop oculars that would enhance the vibrancy of color? I know there are many digital filters to improve vibrancy, but are there physical devices able to produce the same effect? Would it ever be physically possible to produce a device small enough to be worn like a contact lens?</p>
<p>This is quetion I developed while watching a Korean drama as I noticed the contrasting colors compared to the shows I normally watched. I feel environment and perception play a big part in emotional well-being. It is my thought that a device with this capability might serve as an aid to better emotional health.</p>
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] |
<p>What are some interesting classical systems for which the dynamics can be reduced to a many-body Schrodinger equation, at least in some useful regions of phase space, and in particular, with many variables.</p>
| 7,229 |
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<p>I recently read "An Introduction to Supersymmetry in Quantum Mechanical Systems" by T. Wellman (amongst other sources) in an effort to find out what a superpotential actually is and how it relates to the potentials of particles/fields). Here's the link: <a href="http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDkQFjAA&url=http%3A%2F%2Fphysics.brown.edu%2Fphysics%2Fundergradpages%2Ftheses%2FSeniorThesis_Wellman.pdf&ei=ulm-UPSCLZOY1AWjwYHYDw&usg=AFQjCNGrg_2jv5NZ7b6k4Fs7er34jgtw3w&sig2=yjQYy1Lf_gZVS-RRefUCsQ" rel="nofollow">http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDkQFjAA&url=http%3A%2F%2Fphysics.brown.edu%2Fphysics%2Fundergradpages%2Ftheses%2FSeniorThesis_Wellman.pdf&ei=ulm-UPSCLZOY1AWjwYHYDw&usg=AFQjCNGrg_2jv5NZ7b6k4Fs7er34jgtw3w&sig2=yjQYy1Lf_gZVS-RRefUCsQ</a></p>
<p>It occurred to me that the Fermionic Hamiltonian and the Bosonic Hamiltonian can be formulated without supersymmetry. On page 13, Wellman expresses these Hamiltonians in terms of the superpotential W in a way that is purely algebraic and doesn't require supersymmetry. In other words we have a bunch of terms that give us the two Hamiltonians; these terms are then simply replaced by W's (see equations 3.2 to 3.9). We only actually get supersymmetry when the separate assertion is made that Q operators exist that transform between our fermionic and bosonic states. </p>
<p>So would it be true to say that non-supersymmetric theories contain superpotentials, W, within their Hamiltonians in the same way that supersymmetric theories do? If this is the case the superpotential is just a useful function that is especially helpfully when we consider supersymmetric theories? I.e. superpotentials exist with or without supersymmetry. </p>
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<p>I am a physics groupie, so please excuse me if this question is stupid, but I am trying to better understand the particle/wave duality in quantum physics. It would seem that, in the double slit experiment or any similar experiment, there should be some method to tell the difference between two actual waves interfering (Schrodinger) and a probability wave (Einsteinian proposal) or a pilot wave (de Broglie proposal). If there are actually two waves interfering, there is both destructive and constructive interference. If not, there is just a distribution of particle hits. Is there not some way to design an experiment that would show which is actually happening?</p>
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<p>In the book <em>The Norton History of Astronomy and Cosmology</em> by the late John North I have found the following statement (page 514):</p>
<p>"The German mathematician Lejeune Dirichlet studied the law of gravitation in non-Euclidean space towards the end of 1850."</p>
<p>Does anyone perhaps know more about that?</p>
| 7,232 |
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<p>The part of the Einstein equations of general relativity referred to vacuum energy, introduce a repulsive term in gravity. This means that as the space become bigger and bigger, vacuum part become more and more important, leading to an undefined accelerated growth of the universe. Why vacuum energy does not violate the principles of thermodynamic? This is a sort of perpetual motion, isn't it?</p>
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] |
<p>I understand all the concepts of what voltage is using all the analogies but some things related to the drop of voltage across a circuit confuses me.</p>
<ol>
<li><p>If I had a short circuit and attached a voltmeter I would get a potential difference reading of 0 volts. How is current then going through the wire if it is 'X' volts at any point in the wire?</p></li>
<li><p>Let's say I have a DC 9V battery with a load in the middle. I read somewhere (probably mistaken here) that the voltage drop in this situation must be 9V or rather, that the sum of load resistances must be equal to voltage of the source. I mean, there is a variable amount of resistance to each load so at the base of the load I might have 9V and at the end of the load I might have 5V with a 4V potential difference.</p></li>
</ol>
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<p>Ok, so theoretically, is it possible to build a spaceship like the ones we see off of Star Trek or Prometheus or will physics not allow it? What are some challenge faces such an task. Also, is there other ways we can use to launch heavier payload from earth or are we just stuck with using tons of fuel to launch small object?</p>
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<p>I have seen many answers like: because we don't have infinite energy, because of gravity, because it is impossible, because of physics.</p>
<p>But they don't really answer my question.. I mean if there is no friction and at some points, even if just in theory, you could be so far away from other objects or at the right distance between many so that the total force vector is null... why is it still considered impossible?</p>
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<p>When a probe like Voyager 1 is sent into deep space they are able to point the camera at the planet and its moons and take pictures. </p>
<ul>
<li>How is the camera pointed at the object?</li>
<li>Is the camera fixed to the probe or do motors orient the camera independently?</li>
<li>Do they know the exact position of the probe with respect to the planet and pre-program orientations and exact times to take pictures?</li>
<li>Is there something on board to point the camera at a close gravitational mass of some kind?</li>
<li>Some other sensor to orient the probe? Light or infrared? How do they make sure it doesn't get confused by the sun?</li>
</ul>
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] |
<p>I am interested in modelling the trajectory of a rocket from the Earth to the Moon by solving a differential equation numerically. Below are some key facts and assumptions I am using. I want to make sure that I have not made any serious mistakes, nor disregarded any necessary facts.</p>
<p>We will consider the following equation,
$$
\vec{T} + \vec{c}(\vec{r})\dot{\vec{x}} + \vec{G}(\vec{r})= m(t) \ddot{\vec{x}},
$$</p>
<p>where $T$ is the <em><strong>constant</strong></em> rocket thrust, $c$ denotes air resistance and is a function of radial distance from the earth, and the rocket has mass that drops at a rate that is <em><strong>constant</strong></em> with respect to time (we are assuming that a constant amount of fuel is always used for constant rocket thrust -- is this a valid assumption?).</p>
<p>Now a question:</p>
<ul>
<li>The trajectory of the rocket is not straight; how do we incorporate parabolic motion into the numerics?</li>
</ul>
| 7,238 |
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<p>In the setting of general relativity, I came across a source term of the wave equation of the following form:</p>
<p>$$
\frac{1}{\sqrt{q}}\,\delta^{(3)}(p-\gamma(t))
$$</p>
<p>where $p\in M$ is a point in our 4d spacetime and $\gamma(t)$ is a trajectory that the source takes in the 4d spacetime. $\sqrt{q}$ is the 3d metric determinant of a preferred 3d slicing of $M$. $\delta^{(3)}(p-\gamma(t))$ is a 3d Delta distribution which means that we should have</p>
<p>$$
\int_M\,\delta^{(3)}(p-\gamma(t))\,f(p)\,d^3x=f(\gamma(t))\,.
$$</p>
<p>Of course, this is rather the physics short hand notation that $\delta^{(3)}(p-\gamma(t))$ is a map $C^\infty_c(M)\to C^\infty(\mathbb{R})$ that maps a function $f$ to $f\circ \gamma$.</p>
<p>We would like to show that the Lie derivative of the source along a certain vector field $T$ vanishes if $\gamma(t)$ is a Killing trajectory, that is $\gamma$ is an integral curve of $T$.</p>
<p>However, we are very confused about the rigorous treatment of this expression. Our intuition states the following:</p>
<ol>
<li><p>The delta distribution should transform as scalar density of weight 1 under changes of the 3d frames and as a scalar under changes of the frame along the forth direction. However, we are not sure how to make this rigorous, nor how to find the Lie derivative of such a combined expression.</p></li>
<li><p>The object $1/\sqrt{q}$ should be an inverse object, that is it is a scalar density of weight $-1$ under changes of the 3d frame and a regular scalar along the forth direction.</p></li>
<li><p>Combining these two statements, it would make sense that the original object
$$
\frac{1}{\sqrt{q}}\,\delta^{(3)}(p-\gamma(t))
$$
is a regular 4d scalar. This would also make a lot of sense because it serves as source term of a regular 4d scalar wave equation.</p></li>
<li><p>Finally, it makes somehow sense that the Delta distribution is invariant under the Killing vector field $T$ iff the trajectory $\gamma$ is an integral curve of $T$. But we are not sure how to prove this and how to deal rigorously with the delta distribution.</p></li>
</ol>
| 7,239 |
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<p>If it is impossible for matter to accelerate to $c$ (because doing so would take infinite energy), and if light can be deemed matter (because of wave-particle duality, photons are matter, right? And photons clearly have mass per solar radiation pressure), how does light manage to travel at $c$?</p>
| 195 |
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<p>I've been talking to a friend, and he said that it's impossible to travel at exactly the same speed as the speed of sound is. He argued that it's only possible to break through the sound barrier using enough acceleration, but it's impossible to maintain speed exactly equal to that of sound. Is it true? And if it's true, why?</p>
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<p>My field of study is computer science, and I recently had some readings on quantum physics and computation.</p>
<p>This is surely a basic question for the physics researcher, but the answer helps me a lot to get a better understanding of the formulas, rather than regarding them "as is."</p>
<hr>
<p>Whenever I read an introductory text on quantum mechanics, it says that the states are demonstrated by vectors, and the operators are Hermitian matrices. It then describes the algebra of vector and matrix spaces, and proceeds.</p>
<p>I don't have any problem with the mathematics of quantum mechanics, but I don't understand the philosophy behind this math. To be more clear, I have the following questions (and the like) in my mind (all related to quantum mechanics):</p>
<ul>
<li>Why vector/Hilbert spaces?</li>
<li>Why Hermitian matrices?</li>
<li>Why tensor products?</li>
<li>Why complex numbers?</li>
</ul>
<p>(and a different question):</p>
<ul>
<li>When we talk of an n-dimensional space, what is "n" in the nature? For instance, when <a href="http://en.wikipedia.org/wiki/Spin-%C2%BD#Mathematical_description">measuring the spin of an electron</a>, n is 2. Why 2 and not 3? What does it mean?</li>
</ul>
<p>Is the answer just "because the nature behaves this way," or there's a more profound explanation?</p>
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<p>What kind of global and causal structures does a Penrose diagram reveal?</p>
<p>How do I see (using a Penrose diagram) that two different spacetimes have a similar global and causal structure?</p>
<p>Also,</p>
<p>I have the following metric </p>
<p>$$ds^2 ~=~ Tdv^2 + 2dTdv,$$ </p>
<p>defined for </p>
<p>$$(v,T)~\in~ S^1\times \mathbb{R},$$ </p>
<p>e.g. $v$ is periodic.</p>
<p>This is the according Penrose diagram: </p>
<p><img src="http://www.matheplanet.de/matheplanet/nuke/html/uploads/8/8403_misner_penrose_2.jpg" alt=""></p>
<p>Is the Penrose diagram that I have drawn correct?</p>
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<p>In Chapters 34-36 of the Srednicki QFT book, 2 component spinors and their combinations in Dirac and Majorana spinors are carefully constructed. Specifically, in equations 36.14 and 36.15 the following left-handed spinors are defined:</p>
<p>$$
\begin{equation}
\begin{split}
&\chi = \frac{1}{\sqrt{2}}(\psi_1 + i\psi_2)\\
&\xi = \frac{1}{\sqrt{2}}(\psi_1 - i\psi_2)
\end{split}
\end{equation}
$$</p>
<p>A couple of pages later, charge conjugation is then defined as "Charge conjugation simply exchanges $\chi$ and $\xi$".</p>
<p>Now, I have read in other books (e.g. Georgi) that if a particle is defined in one SU(2) representation of the Lorentz group (e.g. as left handed spinor), then the corresponding anti-particle is in the other representation (e.g. as right handed spinor).However, in the above definition in Srednicki, both fermion and anti-fermion are left-handed spinors. </p>
<p>Have I got the this right? How can both of these statements be correct? Any help to clear up my confusion would be greatly appreciated. </p>
<p>As an aside, I have a more general issue understanding the intuition behind Dirac spinors. The state of a general fermion or anti-fermion is often given with a Dirac spinor $\Psi$. If this fermion has mass, then the fermion is a combination of a left-handed and right handed spinor, as in Srednicki:
$$
\Psi = \begin{pmatrix} \chi_c \\ \xi^{\dagger\dot{c}} \end{pmatrix}.
$$ </p>
<p>As helicity and handedness are frame depenendent, I can kind of understand how the Dirac fermion can be a combination of the two above. However, Dirac fermions can also by viewed as a combination of a fermion and anti-fermion in much the same way. This I do not fully understand. How can a fermion with mass be described by a field that is part particle and part anti-particle?</p>
<p>Again, any insights that the community could provide would be much appreciated.</p>
| 7,243 |
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<p>Assume an observer sent a beam of photons close to an event horizon, say at some distance x (a distance far enough to avoid the photons falling in.) This light would still be observable, albeit red shifted and with it's path curved appropriately. Now assume the black hole absorbs enough mass to expand it's event horizon beyond the distance x. This stream of photons would stop. Does the observer not have information about a process that occurred exactly at the event horizon, that is it's expansion? Isn't this a region that one should not be able to get any information about due to the fact that nothing could contact the event horizon and return to the observer?</p>
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<p>If particles are simply regions of space where certain quantum fields have non-zero divergence, are anti-particles simply the corresponding regions of opposite divergence?</p>
<p>This seems like the intuitive answer, especially when considering the process of annihilation. I have heard before that anti-particles are analogous to particles moving through time in reverse, which seems to indicate that an annihilation event is just a point of symmetry in that (arguably, single) particle's history. This analogy breaks down, however, when it comes to gravitation, since there seems to be no evidence of a negative-mass particle.</p>
<p>So what then is the meaning of an anti-particle, when their symmetry is preserved across certain fields, but not other?</p>
| 245 |
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<p>I watched a program of his in which it was claimed that since mass bends space in accordance to General Relativity, then in the case of very large stars it becomes a strong force to the point of being able to crush a star to a single nucleus (Neutron Stars) or less (Black Holes). </p>
<p>His argument is that Gravity is a force that <strong>scales</strong> and that it is not simply a matter of adding individual components and hence to claim it's weak, but that since space is bent in those areas, then gravity as a <em>fundamental force of nature</em> becomes stronger.</p>
<p>Now, I wonder not only about the claim's accuracy, but also if it's only a matter of interpretation and nobody is really wrong or right, as long as the discussion is framed properly.</p>
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<p>I was looking at pdf file of the presentation of a conference talk. The speaker discusses two types of "mechanisms" for stabilizing the weak scale and calls them "weakly coupled" and "strongly coupled". The examples are:</p>
<p>Weakly coupled: SM with a light Higgs, SUSY, Little Higgs, Twin Higgs, Large extra dimensions, Universal extra dimensions.</p>
<p>Strongly Coupled: Technicolor, Topcolor, Top See Saw, Composite Higgs, Randall-Sundurm warped extra dimension models.</p>
<p>I need to understand what makes one such beyond standard model theory to be weakly coupled and another to be strongly coupled, in general and especially why large/universal extra dimension and Randall-Sundrum models belong to two separate groups.</p>
<p>Perhaps I should emphasize where my doubt is: I understand why theories like technicolour are thought to be "strongly coupled" but I do not at all understand why theories involving say Randall-Sundrum extra dimensional models are also so. When we say Randall-Sundrum warped extra dimension model, we mean a particular kind of background on which different types of interactions take place. But why should all interactions taking place in such a background will have to be strongly coupled? How does background spacetime decide whether an (or all) interaction(s) will be strongly coupled? </p>
<p>Or does this have anything to do with the fact that in (classical) GR, spacetime is dynamically determined and is coupled with matter and energy content of the universe and may be due to quantum gravity effects this strong/weak nature of interactions are/is manifested. But what is the way to explain that? </p>
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<p>Suppose I am trying to formulate a multipoint model of fluid dynamics. I have a procedure for doing so the details of which is not important to this question, but only that it is based on a series expansion, the higher order terms in which series being dependent on larger number of spacial points. The equations for the first two terms in a Burger formulation is something like shown below:</p>
<p>\begin{align}
&\frac{\partial u^0}{\partial t}(x,t)+\frac{\partial^2 u^0}{\partial x^2}(x,t)
+ u^0(x,t)\frac{\partial u^0}{\partial x}(x,t)\\
&\qquad\qquad\qquad\quad\;\;+\int_0^1 u^1(x,t;x_1)\frac{\partial u^1}{\partial x}(x,t;x_1) dx=0\\
&\frac{\partial u^1}{\partial t}(x,t;x_1)+\frac{\partial^2 u^1}{\partial x^2}(x,t;x_1)+u^0(x,t)\frac{\partial u^1}{\partial x}(x,t;x_1)+u^1(x,t;x_1)\frac{\partial u^0}{\partial x}(x,t)=0
\end{align}</p>
<p>it is however an odd formulation, the point $x_1$ appears as a mere parameter in the second formulation while it appears only in the integrand of the first equation, so that apparently there is no enough restriction on the behavior of the function $u^1$ with respect to $x_1$, so it seems there s no unique solution for $u_1$. If the flow is a homogeneous flow but $u^1$ can be written as $u^1=u^1(x-x_1,t)$, so that derivation with respect to $x$ will also take into play the point $x_1$, so that $x_1$ will now behave like it is a more important variable. This will get more importance if we further consider the higher order terms like $u^2(x,t;x_1,x_2)$ which in a homogeneous flow will be writable as $u^2(x-x_1,x-x_2,t)$ and whose $x$-derivative becomes:
$$\frac{\partial u^2}{\partial x}=\frac{\partial u^2}{\partial(x-x_1)}+\frac{\partial u^2}{\partial(x-x_2)}$$
Such a treatment imports the variables $x_1$, $x_2$ and etc. in the second and higher order equations in a more proper manner, in such a way that hope to find unique solutions increase.</p>
<ol>
<li><p>The problem is that how the first formulation which was more general is lame in giving such unique solutions as the second formulation is apparently capable of?</p></li>
<li><p>Or maybe there is a must in every multi-point modeling of fluid dynamics (actually turbulence) to consider one of the following two procedures?</p>
<p>a- To expand the series in terms of functions of the form: $u^0(x,t)$, $u^1(x,x-x_1,t)$, $u^2(x,x-x_1,x-x_2,t)$ and etc. ?</p>
<p>b- To write the equations once at the point $x$, then once at the point $x_1$ available also in the arguments of $u^1$ and higher order functions, then once at the point $x^2$ available also in the arguments of $u^2$ and higher order functions, and etc., then consider all those equations in one place, for example by adding them together. As the series is truncated somewhere at a function $u^n$ this will not contain infinitely of equations but I am not very hopeful that this is the right path to take.</p>
<ul>
<li>any idea about these or other methods for multipoint formulations?</li>
</ul></li>
</ol>
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<p>This is a confused part ever since I started learning electricity. What is the difference between electric potential, potential difference (PD), voltage and electromotive force (EMF)? All of them have the same SI unit of Volt, right? I would appreciate an answer.</p>
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] |
<p>The graph of nuclear binding energy is relatively smooth going from H to U, except for He4 (alpha particle). Why is He4's binding energy so anomalously high compared to its neighboring isotopes?</p>
| 7,249 |
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<p>Consider a lift, which is at rest in an homogeneous gravity field. There is a thin layer(<strong>with thickness</strong> $h$) of water on the floor of the lift. At some moment a single cable, supporting the lift, breaks and the lift begins free falling(forever). It is easy to describe qualitatively what happens with water, i think: the formation of a drop begins. During this process the drop jumps up from the floor and once the total kinetic energy of the drop is dissipated into the heat, the center of the drop stands at some height $H$ from the floor. (All the kinetic energy of the drop is coming from the difference in surface tension energy of water between initial and end moments.)</p>
<p>Question: How to determine(approximately) $H$ ? </p>
<p>For simplicity let's assume that the cross-section of the lift is a disc-shaped with radius $R$. $(h<<R)$ </p>
<p>Remark: <strong>A key point is to determine how the total kinetic energy distributes between internal kinetic energy and translational kinetic energy of the drop, i think.</strong> With this the problem will be solved. </p>
<p>So it is convenient at the early stage of formation of the drop ignore viscosity effects of water and air resistance.</p>
<p><strong>Edit:</strong> </p>
<p>I would like to clarify that by internal kinetic energy i mean the kinetic energy of macroscopic motion of water inside the drop. At early stage there is no energy loss assumed, for simplicity. </p>
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<p>Sometimes old faulty CRT monitors generate nasty high-frequency squeal sound. What element might be responsible for generating such sound? I have heard that it might be dry electrolytic capacitor; is it? What is the physics of generating this sound (how it is generated)?</p>
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<p>The 2011 Nobel Prize in Physics, as far as I understand, concerns the expanding universe -- galaxies moving away from each other at ever increasing speed (that's what I think I read in newspapers). Now, the idea of expanding universe is not new. What is the novelty in this study? What was unexpected in it?</p>
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<p>What are the direct real life applications of general relativity other than nuclear technology? </p>
<p>What I meant was, was there any technology developed based on general relativity that can benefit mankind today? </p>
<p>Secondly, are there any adverse effects quantum technology today?</p>
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] |
<p>The average energy we receive from the Sun is 1,366 w/m^2, and this only varies by 0.1% from the activity peak to trough of its 11 year cycle. About 9% of the energy comes from wavelengths less than 400 nm. The 200-300 nm region varies on the order of a few percent, 150-200 nm by 10-20% and shorter regions by over 50% with maximums at the cycles peak activity. Energy above 400 nm is almost constant over the cycle. Why does solar energy variation over the Sun's activity cycle vary inversely with wavelength?
<a href="http://astro.ic.ac.uk/research/solar-irradiance-variation" rel="nofollow">http://astro.ic.ac.uk/research/solar-irradiance-variation</a></p>
| 7,254 |
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<p>Inspired by this question: <a href="http://physics.stackexchange.com/questions/8049/are-these-two-quantum-systems-distinguishable">Are these two quantum systems distinguishable?</a> and discussion therein.</p>
<p>Given an ensemble of states, the randomness of a measurement outcome can be due to classical reasons (classical probability distribution of states in ensemble) and quantum reasons (an <em>individual</em> state can have a superposition of states). Because a classical system cannot be in a superposition of states, and in principle the state can be directly measured, the probability distribution is directly measurable. So any differing probability distributions are distinguishable. However in quantum mechanics, an infinite number of different ensembles can have the same density matrix.</p>
<p>What assumptions are necessary to show that if two ensembles initially have the same density matrix, that there is no way to apply the same procedure to both ensembles and achieve different density matrices? (ie. that the 'redundant' information regarding what part of Hilbert space is represented in the ensemble is never retrievable even in principle)</p>
<p>To relate to the referenced question, for example if we could generate an interaction that evolved:</p>
<p>1) an ensemble of states $|0\rangle + e^{i\theta}|1\rangle$ with a uniform distribution in $\theta$</p>
<p>to</p>
<p>2) an ensemble of states $|0\rangle + e^{i\phi}|1\rangle$ with a <em>non-uniform</em> distribution in $\phi$</p>
<p>such an mapping of vectors in Hilbert space can be 1-to-1. But it doesn't appear it can be done with a linear operator.</p>
<p>So it hints that we can probably prove an answer to the question using only the assumption that states are vectors in a Hilbert space, and the evolution is a linear operator.</p>
<p>Can someone list a simple proof showing that two ensembles with initially the same density matrix, can never evolve to two different density matrices? Please be explicit with what assumptions you make.</p>
<p>Update: I guess to prove they are indistinguishable, we'd also need to show that non-unitary evolution like the projection from a measurement, can't eventually allow one to distinguish the underlying ensemble either. Such as perhaps using correlation between multiple measurements or possibly instead of asking something with only two answers, asking something with more that two so that finally the distribution of answers needs more than just the expectation value to characterize the results.</p>
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<p>I am a graduate student in a large experimental physics collaboration. Newcomers to the collaboration invariably complain about excessive use of jargon and insufficient documentation as barriers to their understanding and quick integration into the collaboration. Of course, jargon is unavoidable in any technical pursuit, and one should not expect to find comprehensive, polished documentation of what is essentially a work-in-progress, but there must be some effective techniques to communicate this stuff to new students with a minimum of frustration?</p>
<p><strong>What are some "best practices" in communicating institutional knowledge to new (graduate student and post-doc) members of a large scientific collaboration?</strong></p>
<p>Alternatively, what is the best way to prepare students for interaction with a big collaboration? Perhaps a few bits of advice at the beginning could help them become integrated and acquire institutional knowledge much more quickly(?).</p>
| 7,256 |
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<p>I was helping a friend of mine with the following question from Knight's book and I was not able to answer part (c).</p>
<p><img src="http://i.stack.imgur.com/G2AdB.jpg" alt="enter image description here"></p>
<p>Here is what I think I know:</p>
<p>(a) I expect $V_1 = V_2$; the two spheres are in equilibrium so no current flows between the two spheres. </p>
<p>(b) If $V_1 = V_2$, then $Q_1/R_1 = Q_2/R_2$. This implies that $Q_1 = Q_2 (R_1/R_2) > Q_2$. That is, $Q_1$ is larger than $Q_2$. </p>
<p>(c) Here is were I am unsure: I think that $E_2 > E_1$. </p>
<p>Question: Mathematically it makes since because if $V_1 = V_2$, then $E_1 = V_1/R_1$ and $E_2 = V_2/R_2$, then $E_2 > E_1$. But I don't see this physically. Can someone explain this?</p>
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<p>I've read from many sources that Dyson Air Multipliers are more efficient and quieter than normal fans. Now, with the proof of concept, is it possible to use its principles as a propulsion system for, say, a quieter helicopter? </p>
| 7,258 |
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<p>I have a problem with energy conservation in case of interfering waves.</p>
<p>Imagine two harmonic waves with amplitudes $A$. They both carry energy that is proportional to $A^2$, so the total energy is proportional to $2A^2$. When they interfere, the amplitude raises to $2A$, so energy is now proportional to $4A^2$ and bigger than before.</p>
<p>The equivalent question is what happens to the energy with the superposition of two waves that interfere destructively.</p>
<p>Also, if someone could comment on the statement about this problem in my physics book (Bykow, Butikow, Kondratiew): the sources of the waves work with increased power during the interference because they feel the wave from the other source.</p>
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<p>There is a known thought experiment, connected to quantum immortality: a duel between physicist and a philosopher. </p>
<p>Each turn physicist and philosopher fire at each other with a pistol. The quantum immortality predicts that each of the participants will find themselves alive and the opponent dead after a number of shots.</p>
<p>We can modify the experiment in the following ways:</p>
<ol>
<li><p>They do not fire at each other, but it is lightning that shots them. The outcome should not change.</p></li>
<li><p>There are not two but more participants.</p></li>
<li><p>They are located at separate islands in the ocean.</p></li>
</ol>
<p>It seems that even if there are hundreds of participants, each of them will eventually find all others killed by lightning. If he could not observe other isles directly, after he discovers and explores other isles, he will find them uninhabitable.</p>
<p>Now pretend that the participants actually live on separate planets, and in each million years there happens disaster that kills all inhabitants on 1% of all planets. It seems that after years the physicist that lives on one of the planets should discover that all other planets are uninhabitable. Even more: there is even no chance that organic matter on each other planet could actually evolve into anything resembling actual life.</p>
<p>That said the physicist will find out that there is no other inhabitable planet in the Uinverse. On the other hand, this does not mean that extraterrestrial life does not exist. It actually cannot not to exist. But it exists in parallel universes (in terms of MWI) and thus unobservable. Both physicist on planet A and philosopher on planet B exist, but will never meet in the same universe.</p>
<p>Thus, QI it seems predicts one concrete observable consequence that extraterrestrial life can be never detected.</p>
<p>What is your opinion?</p>
| 7,260 |
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<p>Just wondering about the definitions and usage of these three terms.</p>
<p>To my understanding so far, "covariant" and "form-invariant" are used when referring to physical <em>laws</em>, and these words are synonyms?</p>
<p>"Invariant" on the other hand refers to physical <em>quantities</em>?</p>
<p>Would you ever use "invariant" when talking about a law? I ask as I'm slightly confused over a sentence in my undergrad modern physics textbook:</p>
<blockquote>
<p>"In general, Newton's laws must be replaced by Einstein's relativistic laws...which hold for all speeds and are <strong>invariant</strong>, as are all physical laws, under the Lorentz transformations." [emphasis added]</p>
<p>~ Serway, Moses & Moyer. Modern Physics, 3rd ed.</p>
</blockquote>
<p>Did they just use the wrong word?</p>
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<p>So I've been doing a lot of reading about the twin paradox and have encountered several different explanations that strive to resolve it. First off let me start by saying general relativity <em>is not</em> an adequate explanation and in fact has nothing to do with resolving the paradox. (That much has been made clear to me from what I have read, as it has been pointed out that believing general resolves the paradox is a common misconception) To drive that point home let me propose a slight variation on the twin paradox that removes acceleration all together. </p>
<p>Some ancient race of aliens long ago set up an experiment for us without our knowledge to help us understand space time. The experiment contains two space craft with clocks on board separated by a very large distance. The first clock, clock A, was accelerated to .866 speed of light millions of years ago (Thus time runs at half speed) and is set on a trajectory to fly past earth. As it flies past earth it resets its clock to 0 and continues on its way. (The aliens also left behind a clock on Earth, clock C, that starts ticking the moment Clock A passes earth and resets itself to 0) The other clock, clock B, was also accelerated to .866 the speed of light long ago and is on the same trajectory as clock A but in the opposite direction so that it heads towards Earth. The two ships and their respective clocks pass each other at a distance of four light years away from earth at which point clock A transfers its time reading to Clock B. Clock B flies past earth and relays its time measurement so as to be compared to Clock C. The time reads half the time elapsed by Clock C, but how could this be possible if time dilation is always symmetrical? </p>
| 249 |
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<p>This is potentially a very stupid question but I'm going to ask it anyway. With all these huge buildings such as the Abu Dhabi Mosque, where an unbelievable amount of materials such as marble was moved from one side of the earth to the other, is it possible that if we 'shift enough stuff' that we could change the earths centre of gravity, and potentially alter its orbit? </p>
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<p>We know that conducting materials can be heated by electromagnetic induction. Is it possible to generate current using a cooling process?</p>
| 7,263 |
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] |
<p>How are <a href="http://en.wikipedia.org/wiki/Fresnel_zone" rel="nofollow">Fresnel Zones</a> formed? What phenomena of light allow ellipsoid areas to be in phase? I've tried reading articles, but they more or less introduce me to characteristics of light, and then tell me that Fresnel Zones exist. How does the circular wave coming out of one antenna "bend back" to the other one in the shape of an ellipse?</p>
| 7,264 |
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<p>For the last few years, My friend worked on figuring out the "theory of everything". She is afraid of sharing her theory with well known physicists, because she doesn't want other people to take credit for her idea. So, my here's what I'm wondering:</p>
<p><strong>1) What is the best way for her to validate her theory with experienced physicists?</strong> and </p>
<p><strong>2) If the theory ends up being worth publishing, how can she go about publishing it considering the fact that she has no reputation in the field at the moment?</strong></p>
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<p>One of the classic stories in the annals of aerospace engineering is the development (and subsequent redesign) of the F-18 and its Leading Edge Extensions (LEX) due to fatigue problems, problems that were ultimately traced to the poorly-understood process of <a href="http://www.aerospaceweb.org/question/planes/q0176.shtml" rel="nofollow">vortex bursting</a>. This aptly named phenomenon is characterized by rapid increases in vortex diameter, mixing, and turbulent kinetic energy.</p>
<p><img src="http://i.stack.imgur.com/PMjQz.jpg" alt="enter image description here"></p>
<blockquote>
<p>As a vortex travels downstream, it enlarges and becomes weaker. If the rotational velocity of the vortex drops low enough, the increasing pressure within the vortex causes it to lose its tornado-like structure and break apart. This bursting behavior was found to occur just ahead of the F-18 vertical tails. The resulting air flow impinged directly on the tails causing severe buffeting and structural damage. <a href="http://www.aerospaceweb.org/question/planes/q0176.shtml" rel="nofollow">(Aerospaceweb)</a></p>
</blockquote>
<p>For a highly maneuverable fighter like the F-18, it was imperative that the LEX vortex remain intact and persist long enough in the flow-field to clear the vertical stabilizers, so vortex bursting was definitely an issue. For a commercial airliner like a 777, on the other hand, we have the exact opposite problem. The vortex pair trailing an aircraft in flight presents a very real and perilous hazard to any aircraft which happens to follow it. As a result, the more expeditiously these vortices can be dissipated the better. Vortex bursting breaks up the vortex and (presumably) reduces its presence downstream.</p>
<p><img src="http://i.stack.imgur.com/fpAIS.jpg" alt="enter image description here"></p>
<p>My question is, what are the physical variables which promote or inhibit vortex bursting and, if they can be controlled, can this phenomenon perhaps be used to reduce wake turbulence? Do all vortices experience bursting? If not, why not?</p>
| 7,266 |
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<p>During the winter we keep the basement door closed so that the cold air from upstairs won't flow into the basement. Then we heat the basement and the upstairs gets heated partially by conduction through the floor. But during the summer, the upstairs is heated while the basement (unfinished) is around 62 degrees F (16 degrees C). </p>
<p>How hot does it need to be upstairs before opening the basement door will actually heat the basement? I know hot air rises, but it seems that if there were a massive heat difference between upstairs and downstairs that air turbulence or diffusion would carry some of the heat. There's an 8' 7" height difference between upstairs and downstairs.</p>
| 7,267 |
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] |
<p>What was the density of the universe when it was only the size of our solar system? Did it approach neutron star density? Is it physically correct to even ask such a question? </p>
| 7,268 |
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<p>Now, I understand that when a an electron travels, it creates a magnetic field. If you put two wires with current traveling in the same direction they repel, and current traveling in opposite directions attract. I (somewhat) understand how this is caused by electrostatics and special relativity, but when I tried to get a better idea of the forces at work, I ended up with a result that said the force of attraction between to opposite wires was stronger than the force of repulsion between to wires with the same direction of current. Is this correct, or did I just mess up somewhere?</p>
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<p>According to the first and second law for a closed system containing different chemicals we have</p>
<p>\begin{align}
&\delta Q - \delta W = dU = T dS - p dV +\sum_i \mu_i d N_i\\
&\Rightarrow\;\delta W - p dV + \sum_i \mu_i dN_i = \delta Q - T d S \le 0\qquad\because\text{2nd law}\\
&\Rightarrow\;\delta W - p dV + dG\bigr|_{p,T} \le 0\\
&\Rightarrow\;\delta W - p dV \le -dG\bigr|_{p,T}\\
\end{align}</p>
<p>If $\delta W = p dV$ then $dG\bigr|_{p,T}\le 0$, that is, the condition $dG\bigr|_{p,T}\le 0$ coincides with the second law only if the only work done by the system is the pressure work and no other kind.</p>
<p>In addition, if $\delta W = p dV + \text{``other works"}$, then $\text{``other works"}\le -dG\bigr|_{p,T}$. This means the change in the "minus Gibbs function" is the maximum work attainable from the system beside the pressure work. This extra work can be positive or negative, in the form of electric work, friction work etc.</p>
<p>Therefore, it is clear that:</p>
<ol>
<li><p>A system cannot at the same be derived by $dG\bigr|_{p,T}\le 0$ and does e.g. an electric work $\delta W_{Electric}$;</p></li>
<li><p>If the system does have a $\delta W_{Electric}$ then its maximum value would be equal to $dG\bigr|_{p,T}$ but if so, then the process is already assumed reversible and all the inequalities should be substituted by equalities.</p></li>
</ol>
<p>However, according to <a href="http://www.mhhe.com/physsci/chemistry/chang7/ssg/chap19_4sg.html" rel="nofollow">this Mc Graw-Hill link</a> during a spontaneous reduction-oxidation chemical reaction the Gibbs Free Enthalpy must decrease and at the same time the change in the Gibbs Free Enthalpy is the maximum <em>electric work</em> that the reaction can do:
$$\Delta G = W_{max}\le 0$$
I cannot understand this and have a number of problems with this derivation:</p>
<ol>
<li><p>First of all, the maximum work that a system can do on its surrounding equals minus the change of the Gibbs Free Enthalpy, so the equality $\Delta G = W_{max}$ doesn't hold?</p></li>
<li><p>If the work has attained its maximum value, then the process must be assumed as reversible, but the inequality in the formula above holds for irreversible processes!</p></li>
<li><p>If there is an Electric work done by the system then decreasing Gibbs free energy is no longer necessary due to the second law?</p></li>
<li><p>When both the donor and acceptor of electron in the chemical reaction lay inside the system the electric work will nowhere enter the formulation as the electric work is an internal work that does not crosses the boundary of the system!? But the whole formulation is here to study $W_{electric}$ in the system as spontaneity of the reaction should be related to the electromotive force of the reaction which has a chance to appear in $W_{electric}$ only! So what should be taken as system here?</p></li>
</ol>
<p><strong>Hint.</strong> In the books on thermodynamics that I have seen that discuss the electric works they are usually dealing with the problem of Electrochemical cells. But electrochemical cells work in an outer electric circuit and so if one assume the cell as the closed system yet the electric work will enter the discussion. Only one book was talking about open-circuit Emf but again I have the problems listed above with that as well.</p>
<p>[<em>I have asked the same question at the Chemistry.SE <a href="http://chemistry.stackexchange.com/q/14011/6980">here</a> but have not been convinced with the single answer given there.</em>]</p>
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<p>Total noob here.</p>
<p>I realize that photons do not have a mass. However, they must somehow occupy space, as I've read that light waves can collide with one another.</p>
<p><strong>Do photons occupy space?</strong> and if so, does that mean there is a theoretically maximum brightness in which no additional amount of photons could be present in the same volume? </p>
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<p>Imagine I exist at time $t_1$ and my mass is $m$. At time $t_2$ I time travel back to $t_1$. At time $t_1$ there is now a net increase of mass/energy in the universe by $m$.</p>
<p>At time $t_3 = t_2 - x$ where $x < t_2 - t_1$, I travel back to t1 again. The net mass in the universe has now increased by $2 \times m$.</p>
<p>Properly qualified, I can do this an arbitrary $n$ number of times, increasing the mass in the universe by $n \times m$. This extra mass, of course, can be converted to energy for a net increase in energy.</p>
<p>Does this argument show that traveling back in time violates the conservation of mass/energy?</p>
| 7,272 |
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] |
<h1>Scenario description</h1>
<p>Lets assume both containers have a capacity of 300 litres.</p>
<p>One is a vertical tube as shown in pic 1</p>
<p>Other one is more or less a V shaped containers as shown in pic 2</p>
<p>Both are at ground level</p>
<h1>Question</h1>
<p>No doubt that whole weight of 300 litres will act on the base of the tube (pic 1). But will the weight of the whole 300 litres act on the base of the container as shown in pic 2?</p>
<p>I.e if you keep both the containers on a weighing scale, for sure, it will show a weight of approx. 300 kg each.</p>
<p>But what I'm asking is whether the weight of whole 300 litres acts on the <strong>base</strong> of container 2 (since the container's walls are slanting, as opposed to the walls of the tube in pic 1).</p>
<p>If the whole weight will not act on the base of the container, can you state the reasoning and also the principle, so that I can further get to know about it?</p>
<p>Pic 1</p>
<pre><code> | |
| |
| |
| |
| |
| |
|_________|
</code></pre>
<p>Pic 2</p>
<pre><code> \ /
\ /
\ /
\________/
</code></pre>
| 7,273 |
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<p>While reading Peskin and Schroeder (page 64) I come across this</p>
<blockquote>
<p><em>Although any relativistic field theory must be invariant under the proper orthocronous Lorentz group, it need not be invariant under P, T, or C. What is the status of these symmetry operations in the real world? From experiment, we know that three of the forces of Nature the gravitational, electromagnetic, and strong interactions are symmetric with respect to P, C, and T. The weak interactions violate C and P separately, but preserve CP and T. But certain rare processes (all so far observed involve neutral K mesons) also show CP and T violation. All observations indicate that the combination CPT is a perfect symmetry of Nature.</em></p>
</blockquote>
<p>The question is this. As is stated above all known interactions preserve T, yet it is said that there are processes that violate it. How is this possible? Via which interactions do these processes happen?</p>
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<p>I have read somewhere that for <a href="http://en.wikipedia.org/wiki/Particle_in_a_ring" rel="nofollow">particle on a ring</a> problem you don't have to solve eigenvalue equation $H\psi=E\psi$ you can instead solve eigenvalue equation $P\psi=p\psi$ where P is momentum operator. Why?</p>
| 7,275 |
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<p>This action reads
$$S=-\frac{1}{4g_{D9}^2}\int d^{10}x F_{MN} F^{MN}-\frac{1}{4g_{D5}^2}\int d^{6}x F'_{MN} F'^{MN}- \int d^6 x \left[ D_{\mu} \chi^{\dagger} D^{\mu} \chi + \frac{g_{D5}^2}{2}\sum\limits_{A=1}^{3}(\chi_i^{\dagger}\sigma_{ij}^A \chi_j)^2\right]$$</p>
<p>My question is about the $\chi$. The field content of the theory is : 2 vector multiplets (one from the $5-5$ strings and one from the $9-9$ strings) and 3 hypermultiplets (one from the $5-5$ strings, one from the $9-9$ strings, one half from the $5-9$ and another half from the $9-5$). </p>
<p>In the action, the first two integrals are the kinetic terms for the vector multiplets. If I understand correctly, $\chi$ is a doublet describing the $5-9$ and $9-5$ hypermultiplet scalars. The first term in the square brakets is the kinetic term for those, but then the second term looks like the potential <strong>for the $5-5$ hypermultiplet</strong> (see eq. B.7.3) ! </p>
<p>So here is my question : what is $\chi$ really, and how is the action above obtained ? </p>
<p>Edit : my guess would be that $\chi$ is a generic notation for the scalars of all the hypermultiplets. But then there would be something like another index, because I assume that the range of $i$ is $1,2$ if $\sigma_{ij}^A$ are the usual Pauli matrices. </p>
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<p>Is there anyway to see by inspection that a form like
$$a(x^2 )^{-3} (g _{μσ} x_{\rho} x_{ ν} + g_{μρ} x_{σ} x_{ ν} +g_{νσ} x_{ρ} x_{ μ} + g_{ νρ} x_{ σ} x_{ μ} ) $$
may be equivalent to (i.e reduced down to or reexpressed) $$
b(g _{μν} x_{ ρ} x_{ σ} + g_{ ρσ} x_{ μ} x_{ ν} )(x^2 )^{ −3} ?$$ where $g_{\mu \nu}$ is the metric tensor (diagonal).</p>
<p>I have tried to put in various permutations of $\mu \nu \rho \sigma$ and from $1111$ and $2222$ for example, I obtained the constraint that $a/b = 2$ but I am not really sure what this means. If I try the combination $1221$ e.g then it implies $b=0$, which seems to contradict my first result.</p>
<p>Does this mean that the two forms are not equivalent?</p>
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<p>According to my book, "tension is the reaction of a rope when it is stressed". Then it also said when the string is massless, tension is same everywhere. However in a,let, pulley-rope system,when there is friction between the pulley & the rope, the tensions are not same. Why the tension is not same in this case? Does tension arise due to Newton's third law? When a block is attached to the rope ,the rope gets streched and can I say tension then arises due to Newton's third law or only to undo the deformation? If Newton's 3rd law is cause, then how can there be different tensions in a same rope? Plz explain.</p>
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<p>I'm looking for the pure mathematical definition of <a href="http://en.wikipedia.org/wiki/Work_%28physics%29" rel="nofollow">work</a>, but I haven't yet learned line integrals.</p>
<p>My book says that the work due to a force ${\bf F}$ from point $A$ to point $B$ is
$$
W= |AB|\cdot |{\bf F}|\cdot\cos(\angle AB,{\bf F})
$$</p>
<p>but it also says this only applies for constant forces.</p>
<p>I am assigned a problem which asks me to determine the work of from a point $A$ to $B$ with gravitational force $$F=GmM/R^2.$$ I don't think that I can apply the normal rule above, since it only works for forces that don't change their pointing. Am I mistaken?</p>
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] |
<p>How would the universe be modified if protons (as we know them) have negative charge and electrons (as de know them) have positive charge.</p>
| 7,280 |
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<p>I learned that electron absorbs a photon and goes into higher energy state. But also all electrons are identical. </p>
<p>What is a difference between the electron in low orbital energy state? and the high one?</p>
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<p>For quite sometime there has been a claim that the firewall paradox has been resolved (via lasers). For instance, <a href="http://global.ofweek.com/news/Lasers-to-solve-the-black-hole-information-paradox-9867" rel="nofollow">http://global.ofweek.com/news/Lasers-to-solve-the-black-hole-information-paradox-9867</a> . I was wondering what the physics community thought about it? I haven't heard much of a reaction of the physics community. Why is this?</p>
<p>His paper: <a href="http://arxiv.org/abs/1310.7914" rel="nofollow">http://arxiv.org/abs/1310.7914</a></p>
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<blockquote>
<p>Even if the system is isolated and there is no heat exchange with surroundings, shouldn't the decrease/increase of pressure result in increase/decrease of entropy?</p>
<p>Does this property of an isolated system means that increase of pressure means equivalent decrease in volume, so after the process the $pdV$ i.e. the work is still the same?</p>
<p>Can someone explain this in more detail?</p>
</blockquote>
<p>Quoted text above was original question.</p>
<p>Please read on further, I clarified the question.</p>
<p>To be more specific, situation is this.</p>
<p>We have an adiabaticaly isolated system and (for example) a piston inside it. If there is piston, that means that volume work or $PdV$ can be done.</p>
<p><strong>So if we do work on the system, by some force from surroundings which pushes piston(compresses the gas) we would get increase of the pressure inside the system... right?</strong></p>
<p><strong>If we increase the pressure in the system, the entropy will decrease as well, altough we haven’t bring in the heat .. right?</strong></p>
<p>So if we increased the pressure and mutually decreased the volume, the molecules of the gas are packed more tightly and they have lesser space to move in...This is followed by system having more internal energy now, then it had before process...Since the activity of molecules inside is higher, they are moving at higher speeds(cause of smaller volume)...
<strong>That means that system should have more internal energy after the process, right</strong>?</p>
<p>Taking that into consideration, and if we follow the rule that increase in pressure is also increase in temperature, that is molecules have higher activity on higher pressure and that kind of activity is measured with temperature...<strong>that means that system also has more amount of heat?</strong>
<em>Correct me if I am wrong.</em></p>
<p><strong>And even if it is adiabatically isolated (dQ=0) shouldn't the internal energy increase and thus amount of heat in the system increase as well when we do the work on the system (move the piston to compress the gas )?</strong></p>
<p>I am talking that higher activity leads to more heat inside the system even if it is prevented (isolated) to exchange heat with its surroundings.</p>
<p>I hope you understand me now.</p>
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] |
<p>My textbook explains Newton's Third Law like this:</p>
<blockquote>
<p>If an object A exterts a force on object B, then object B exerts an equal but opposite force on object A</p>
</blockquote>
<p>It then says:</p>
<blockquote>
<p>Newton's 3rd law applies in all situations and to all types of force. But the pair of forces are always the same type, eg both gravitational or both electrical.</p>
</blockquote>
<p>And:
If you have a book on a table the book is exerted a force on the table (weight due to gravity), and the table reacts with an equal and opposite force. But the force acting on the table is due to gravity (is this the same as a gravitational force?), and the forcing acting from the table to the book is a reaction force. So one is a gravitational, and the other is not. Therefore this is not Newton's Third Law as the forces must be of the same type.</p>
| 7,284 |
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<p>If an object is acted on by equal and opposite forces then it will be in equilibrium, and it's acceleration or velocity (and so direction as well) will not be changed.</p>
<p>So when a ball bounces, it exerts a force on the floor, which matches the magnitude of the force in the opposite direction (the ball is bouncing perfectly vertical), up. So how is it's velocity/direction changed? If the forces are equal and opposite to each other. In order for it bounce, surely the force acting from the floor to the ball must be greater than the force acting from the ball to the floor?</p>
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/22700/about-binary-stars-and-calculating-velocity-period-and-radius-of-their-orbit">About binary stars and calculating velocity, period and radius of their orbit</a> </p>
</blockquote>
<p>I am given the non-redshifted wavelength of the EM radiation from one of the stars, the wavelengths at minimum and maximum redshift, and the interval between minimum and maximum redshift (which is presumably half the orbital period). It is assumed that the stars' orbits are on the same plane as the Earth.</p>
<p>How would one calculate the radius of the given star's orbit?</p>
| 246 |
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<p>To get from point $A$ to $B$, a river will take a path that is $\pi$ times longer than as the crow flies (I think this result is from Einstein). What is the proof of this, and how well does it hold water against experiment?</p>
<p>What assumptions are made during the proof?</p>
<p><strong>Edit:</strong> I was also sceptical when I first heard this, asking this question in part to potentially mythbust. To be clear, I assumed that the statement was:</p>
<blockquote>
<p>For a river that is formed in the 'usual way' on a flat plain under 'usual conditions' (whatever those are, assume the conditions of Princeton as Einstein was possibly involved), as the arc length of the river from a starting point tends to infinity, $\frac{\text{arc length}}{\text{crow's length}}\rightarrow \pi$.</p>
</blockquote>
<p>I am aware this is equivalent to the hypothesis that the meandering of the river can be well approximated as semi-circular as the length increases above a certain value.</p>
| 7,286 |
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<p>Four questions: (To start off, I know very little about physics it isn't even funny (I probably use a ton of wrong terms here and leave out vital information, if so I will try to edit it in as you point it out!), Anyways, I have been always curious about this scenario though so I finally figured I'd ask some people who actually know what they are talking about)</p>
<p>First question: Theoretically speaking, if I have a vacuum that is a closed system, it's made of walls that are 100% nonreactive and have no electromagnetic force, strong force, weak force, gravitation force, or anything, but they can still restrain things placed inside the box (without any interaction on the particles, but instead just by the laws of this system)</p>
<p>If I place 1 particle in the box will it stay exactly where I placed it, or will it somehow move to the center of the box thus distancing itself as far as possible away from each wall?
(I've drawn a 2D demonstration)
<img src="http://i.stack.imgur.com/DX2s1.png" alt="enter image description here"></p>
<p>Now, if I place a second particle in, will they both stay where I placed them, will they divide the box in half in some way (I just gave 1 example, there are many) and then both move to the center of those halves, will they space themselves as far apart as possible (pushing themselves against the nearest corners of the box), or is there some ring of energy around particles that I don't know about that has a statistical radius and they would just distance themselves as much as the "reach" of this ring so that the rings aren't touching?
<img src="http://i.stack.imgur.com/KdhRb.png" alt="enter image description here"></p>
<p>Or will something else happen?</p>
<hr>
<p>Second question: I'm assuming different things will happen if the particles are different things, for example if Particle A was a proton and Particle B was an electron they would just pull together? Or the electron would begin orbiting the proton (Or would they even both start orbiting each other?) (If either of these are the case what determines if the orbiting is clockwise or counter-clock-wise (Or whatever the 3D equivalent of these would be, does spin determine?)? What are some particles that would react different ways, for example 2 photons, a proton and a proton, a proton and an electron, etc. Or would it not matter? </p>
<hr>
<p>Third and Fourth questions: What would happen in the same scenario except the walls are reactive, they are made of steel, or carbon fiber, or something strong enough to support a vacuum?</p>
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<p>From Wikipedia on how a <a href="http://en.wikipedia.org/wiki/Salisbury_screen" rel="nofollow">Salisbury Screen</a> works:</p>
<blockquote>
<p><em>1. When the radar wave strikes the front surface of the dielectric, it is split into two waves.</em> </p>
<p><em>2. One wave is reflected from the glossy surface screen. The second wave passes into the dielectric layer, is reflected from the metal surface, and passes back out of the dielectric into the air.</em> </p>
<p><em>3. The extra distance the second wave travels causes it to be 180° out of phase with the first wave by the time it emerges from the dielectric surface.</em></p>
<p><em>4. When the second wave reaches the surface, the two waves combine and cancel each other out due to the phenomenon of interference. Therefore there is no wave energy reflected back to the radar receiver.</em></p>
</blockquote>
<p>The Wikipedia article focuses on use to absorb radar, but the same concept can be applied to other wavelengths of light.</p>
<p>The energy of a photon is found with the equation $E=hc/\lambda$</p>
<p>My question is: When the waves cancel each other out, is the energy converted to heat, or is it expressed some other way?</p>
| 7,288 |
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<p>I'm trying to calculate the <em>released energy from a reaction</em>.
The radioactive substance polonium decays according to this formula:
$$^{210}_{84}\mbox{Po} \rightarrow \mbox{X}+^4_{2}\mbox{He} $$
At first I solved X to be: $^{206}_{82} \mbox{Pb}$</p>
<p>Now when I have the whole reaction, what formula should I use? </p>
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<p>In the multiverse as it is described by eternal inflation, it is not clear to me what is its causal structure and in particular if the bubble-universes are causally connected. We start from a de-Sitter space-time and a scalar field whose almost constant potential plays the role of a positive cosmological constant, but after decay of the scalar field in certain regions it is not clear to me what becomes of the causal structure. If they are considered universes on their own, it should mean that the bubble are causally disconnected from everything else; however I already heard of bubble colliding and leaving hypothetical imprints in the CMB. There also the different probability measure defined in inflationary cosmology, are there probabilities seen by an observer in one of the bubbles, or by an outside (super)observer seeing the whole space-time foliation and every bubble, no matter the causal structure of the space-time?</p>
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] |
<p>Given the definition of unix timestamp as the number of seconds elapsed since January 1st, 1970 as GMT+0, without leap seconds, is it possible to create a universal clock that will generate the correct timestamp?</p>
<p>Is the current definition of a second </p>
<blockquote>
<p>the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.[1] In 1997 CIPM added that the periods would be defined for a caesium atom at rest, and approaching the theoretical temperature of absolute zero (0 K), and in 1999, it included corrections from ambient radiation.[1] Absolute zero implies no movement, and therefore zero external radiation effects (i.e., zero local electric and magnetic fields).</p>
</blockquote>
<p>sufficient for this?</p>
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<p>I'm having problems solving for the electric field and the current that an electric eel generates. Would I use Gauss's law and treat it as a long charged wire? How would I find the charge of the electric eel? I'm really confused about what I can do and where to start. </p>
<p>In the second part of the project I need to find the current and electric field that affects the prey of an electric field also. Would this calculation be like adding a (human) resistor in a circuit? </p>
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] |
<p>I recently read <a href="http://newsoffice.mit.edu/2013/you-cant-get-entangled-without-a-wormhole-1205" rel="nofollow">this</a> article from MIT News. I then started thinking about how a particle accelerator creates a temporary <a href="http://press.web.cern.ch/backgrounders/safety-lhc" rel="nofollow">microscopic black hole</a>.</p>
<p>My question is: </p>
<blockquote>
<p><em>If quantum entangled pair $A$, consisting of $A_1$ and $A_2$, and a second pair $B$, consisting of $B_1$ and $B_2$, were collided, $A_1$ collides with $B_1$, and $A_2$ collides with $B_2$, would this create a temporary wormhole?</em></p>
</blockquote>
| 7,293 |
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] |
<p>I'm an undergraduate reading up on some quantum physics so that I can help out more in the lab that I'm working in this summer. In the book I'm reading (Shankar's "Principles of Quantum Mechanics") I just came across the term <a href="http://www.google.com/search?as_q=interaction+hamiltonian" rel="nofollow">interaction Hamiltonian</a> in describing how orbiting electrons interact with a magnetic field.</p>
<p>I have an idea of what it might mean, but I can't find a good explanation anywhere. What is an "interaction Hamiltonian", and how does it differ from a standard Hamiltonian?</p>
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<p>I haven't yet gotten a good answer to this: If you have two rays of light of the same wavelength and polarization (just to make it simple for now, but it easily generalizes to any range and all polarizations) meet at a point such that they're 180 degrees out of phase (due to path length difference, or whatever), we all know they interfere destructively, and a detector at exactly that point wouldn't read anything.</p>
<p>So my question is, since such an insanely huge number of photons are coming out of the sun constantly, why isn't any photon hitting a detector matched up with another photon that happens to be exactly out of phase with it? If you have an enormous number of randomly produced photons traveling random distances (with respect to their wavelength, anyway), that seems like it would happen, similar to the way that the sum of a huge number of randomly selected 1's and -1's would never stray far from 0. Mathematically, it would be:</p>
<p>$$\int_0 ^{2\pi} e^{i \phi} d\phi = 0$$</p>
<p>Of course, the same would happen for a given polarization, and any given wavelength.</p>
<p>I'm pretty sure I see the sun though, so I suspect something with my assumption that there are effectively an infinite number of photons hitting a given spot is flawed... are they locally in phase or something?</p>
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<p>Given a (closed or not) surface and a point emitting a spherical sound wave, how can I calculate the wave amplitude in any point of space, considering reflections on this surface ?</p>
<p>The idea is to determine the response of the cavity to a dirac impulse, for use in <a href="http://en.wikipedia.org/wiki/Convolution_reverb" rel="nofollow">convolution reverb</a> afterwards (and also mainly because the question interests me). The main idea is answering the question "If I am at this point of the cavity and say 'Hello World', what echo will I hear ?".</p>
<p>Remembering some lessons on waves some years ago, I tried to go with <a href="http://en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle" rel="nofollow">Huygens-Fresnel principle</a>, by computing the value of wave after exaclty 1, 2, 3 etc.. reflexions and summing up everything, but I couldn't find out how to properly formulate it in this case.</p>
<p>Going deeper into Wikipedia, the <a href="http://en.wikipedia.org/wiki/Kirchhoff_integral_theorem" rel="nofollow">Kirchhoff integral theorem</a>, but my attempts to use it where quite unsuccessful as well.</p>
<p>Is there some formula of this kind that would stand for my problem (and maybe that could be exactly resolved in cases with a lot of symmetries), or should I just get down to the wave equation and compute numerically the value (and thus, how should it be done with a dirac impulse as initial conditions) ?</p>
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] |
<p>I'm aware of the critical constants for gas-liquid transition but is there such constants for liquid-solid transition? Like the maximum temperature above which a liquid cannot be solidified.</p>
| 7,297 |
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<p>As in, if I'm accelerating away from the Earth, then does the Earth <em>also</em> appear to be accelerating away from me at the same rate? Or is there something to "break" this type of symmetry?</p>
<p>My question is inspired by the below discussions:</p>
<p><a href="http://www.quora.com/Special-Relativity/When-I-am-traveling-at-high-speed-near-speed-of-light-am-I-time-traveling-or-slowing-my-aging-slowing-my-particles-speed-interactions/answer/Anthony-Yeh" rel="nofollow">http://www.quora.com/Special-Relativity/When-I-am-traveling-at-high-speed-near-speed-of-light-am-I-time-traveling-or-slowing-my-aging-slowing-my-particles-speed-interactions/answer/Anthony-Yeh</a></p>
<p><a href="http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity" rel="nofollow">http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity</a></p>
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<p>Let be a dimensional regularized integral</p>
<p>$$ \int d^{4-\epsilon}kF(k,m,s)= \frac{2}{\epsilon}+\frac{m^{2}}{3}(\gamma +log(4\pi)-\frac{1}{\epsilon}))$$</p>
<p>then formally if we elmiinate the divergent quantities we may have</p>
<p>$$ \int d^{4-\epsilon}kF(k,m,s)_{reg}= \frac{m^{2}}{3}(\gamma +log(4\pi)+log\mu) $$</p>
<p>here $m$ and $s$ are parameters and $ \mu $ and energy scale </p>
<p>but is it that enoguh is renormalization simply 'deleting' teh divergent quantities proportional to $ \frac{1}{\epsilon ^{k}} $ ?</p>
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<p>Well, the Possion bracket:</p>
<p>$ \{ A(q,p),B(q,p) \} \equiv \sum_{s} \left( \dfrac{\partial A}{\partial q_{s}} \dfrac{\partial B}{\partial p_{s}} - \dfrac{\partial A}{\partial p_{s}} \dfrac{\partial B}{\partial q_{s}} \right) $</p>
<p>is a coordinate transformation according to the words of this Wikipedia page: (link: <a href="http://en.wikipedia.org/wiki/Poisson_bracket" rel="nofollow">http://en.wikipedia.org/wiki/Poisson_bracket</a>)</p>
<p><em>...".It places mechanics and dynamics in the context of coordinate-transformations: specifically in coordinate planes such as canonical position/momentum, or canonical-position/canonical transformation."...</em></p>
<p>The Jacobian of, for example, $ A(q,p) $ and $ B(q,p) $ has the same form as the terms in the parenthesis. From what to what coordinates does the bracket transform? Does it make any sense to make comparison (Poisson bracket and the Jacobian)? </p>
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<p>I was asking myself if there is a closed formula for the following product of gamma matrices:</p>
<p>$$\gamma_\mu\gamma_\nu \gamma_5.$$</p>
<p>I would like to express this matrix in terms of the basis </p>
<p>$${\mathbb{1}, \gamma_{5}, \gamma_{\mu}, \gamma_{\mu}\gamma_{5},[\gamma_{\nu},\gamma_{\mu}]} .$$</p>
<p>Thank you very much for any help.</p>
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<p>The <a href="http://www.phys.uconn.edu/~dunne/dunne_schwinger.html">Schwinger effect</a> can be calculated in the world-line formalism by coupling the particle to the target space potential $A$.</p>
<p>My question relates to how this calculation might extend to computing particle creation in an accelerating frame of reference, i.e. the <a href="http://en.wikipedia.org/wiki/Unruh_effect">Unruh effect</a>. Consider the one-loop world-line path integral:</p>
<p>$$Z_{S_1} ~=~ \int^\infty_0 \frac{dt}{t} \int d[X(\tau)] e^{-\int_0^t d\tau g^{\mu\nu}\partial_\tau X_\mu \partial_\tau X_\nu},$$</p>
<p>where $g_{\mu\nu}$ is the target space metric in a (temporarily?) accelerating reference frame in flat space and the path integral is over periodic fields on $[0,t]$, $t$ being the modulus of the circular world-line. If the vacuum is unstable to particle creation, then the imaginary part of this should correspond to particle creation.</p>
<p>Since diffeomorphism invariance is a symmetry of the classical 1-dimensional action here, but not of $Z_{S^1}$, since it depends on the reference frame, can I think of the Unruh effect as an anomaly in the one-dimensional theory, i.e. a symmetry that gets broken in the path integral measure when I quantize?</p>
<p>This question would also apply to string theory: is target space diffeomorphism invariance anomalous on the worldsheet?</p>
| 7,302 |
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<p>In the cosmic history of the universe, does the dark energy comes before the radiation epoch, or only now, in the 'matter' universe (matter dominated era)? </p>
<p>Because, we now know that like 75% of our visible universe is made up of dark energy, about 20% is dark matter and the rest is the 'ordinary matter', but does that mean that this dark energy came after the radiation and matter domination of the universe or was it there in the beginning, at the BB, and then was just spread out via inflation, while radiation era and matter domination era followed?</p>
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<hr>
<p>Consider a dielectric slab waveguide (lossless, isotropic) illuminated transversally from the vacuum (with coherent, monochromatic light).</p>
<p>We define the <em>base bandwidth</em> of a waveguide (or optical fiber), $AB$, to be the inverse of the time retardation, $\Delta t$, at 1 km of the waveguide between the energy of a guided mode (transmitted following the <em>zig-zag</em> model) with a $\theta_{c}$ critical angle and the energy transmitted without total internal reflections. Let $n_{f}$ and $n_{s}$ be the refractive indexes of the film and the substrate respectively. Prove that if $\Delta n=n_{f}-n_{s}<<1$, then:</p>
<p>$$
{\rm{AB}} = {\left( {\Delta t} \right)^{ - 1}} \simeq \frac{{2c{n_s}}}{{{{\left( {{\rm{AN}}} \right)}^2}}} = \frac{c}{{{n_f} - {n_s}}}
$$</p>
<p>where $AN$ is the numerical aperture of the guide.</p>
<hr>
<p>This problem has been on my mind for 2 days now and it seems I can't find a method to calculate that time difference... Any ideas?</p>
<p><em><strong>My thinking so far:</em></strong></p>
<p>We have to look at the Ray Optics picture of Dielectric Waveguide Theory (see e.g. Tamir et al: <em>Integrated Optics</em> (chapter 2)). A guided mode is propagated through the waveguide following a series of total internal reflections at an angle $\theta_{c}$ with the normal to the film-substrate or film-cover surfaces, and therefore its energy is "trapped" in the film. A mode which is <em>not</em> a guided mode will travel through the waveguide suffering reflections and refractions and therefore radiating some energy to the cover and substrate.</p>
<p><img src="http://i.stack.imgur.com/9LTzS.png" alt="Dielectric slab waveguide"></p>
<p>The rays travel through the film at the same speed $c/n_{f}$ but follow different paths, so it will take different times for them to advance 1 km in the waveguide. We could then try to find the components of these velocities in the direction of propagation ($z$ axis), $v_{i}$, and use the simple relation $t_{i}=d/v_{i}$. The trouble with this, is that the problem doesn't specify the angle at which the non-guided mode incides in the surfaces of the film. Am I missing something here?</p>
<p><img src="http://i.stack.imgur.com/24Kix.png" alt="Total internal reflection in the slab waveguide"></p>
<p>On the other hand, the numerical aperture of the waveguide is:</p>
<p>$$
n\sin \left( {{\theta _{\max }}} \right) = {n_f}\sin \left( {90 - {\theta _{\rm{c}}}} \right) = {n_f}\cos \left( {{\theta _{\rm{c}}}} \right)
$$</p>
<p>where n=1, and $\theta_{\max}$ is the angle of incidence of the illumination beam with the normal to the $x-y$ plane so that doing some work we find:</p>
<p>$$
{\rm{AN}} = \sin \left( {{\theta _{\max }}} \right) = \sqrt {{n_f}^2 - {n_s}^2}
$$</p>
<hr>
<p><strong>UPDATE:</strong> Some calculations:</p>
<p><img src="http://i.stack.imgur.com/7mSHt.jpg" alt="Rays"></p>
<p>The effective refractive indexes of the 3 rays (ray 1: guided mode, ray 2: radiation mode, ray 3: no reflection at all) are:</p>
<p>$$
{N_1} = \frac{{{\beta _1}}}{{{k_1}}} = \frac{c}{{{V_1}}} = {n_f}\sin \left( {{\theta _{\rm{c}}}} \right)
$$
$$
{N_2} = \frac{{{\beta _2}}}{{{k_2}}} = \frac{c}{{{V_2}}} = {n_f}\sin \left( \theta \right)
$$
$$
{N_3} = {n_f} = \frac{c}{{{v_3}}}
$$</p>
<p>So that the retardations would be: ($d=1km$)</p>
<p>Between rays 1 and 2:
$$
\Delta {t_{1 - 2}} = {t_2} - {t_1} = d\left( {\frac{1}{{{V_2}}} - \frac{1}{{{V_1}}}} \right) = \left[ {...} \right] = \left( {d\frac{{{n_f}}}{c}} \right)\left( {\sin {\theta _c} - \sin \theta } \right)
$$</p>
<p>Between rays 1 and 3:</p>
<p>$$
\Delta {t_{1 - 3}} = {t_3} - {t_1} = d\left( {\frac{1}{{{v_3}}} - \frac{1}{{{V_1}}}} \right) = \left[ {...} \right] = \left( {d\frac{{{n_f}}}{c}} \right)\left( {\sin {\theta _c} - 1} \right)
$$</p>
<p>And the respective base bandwidths:</p>
<p>$$
{\rm{A}}{{\rm{B}}_{1 - 2}} = \frac{{\frac{c}{{d{n_f}}}}}{{{\rm{AN}} - \sin \theta }}
$$</p>
<p>$$
{\rm{A}}{{\rm{B}}_{1 - 3}} = \frac{{\frac{c}{{d{n_f}}}}}{{{\rm{AN}} - 1}}
$$</p>
<p>Are any of these results equal to the equation given at the beginning for $AB$? How would one use the approximation $n_{f}-n_{s}<<1$?</p>
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<p><img src="http://i.stack.imgur.com/CvXe0.png" alt="Look at this."></p>
<p>I'm trying to work out a model for the system above, that is, $N$ particles of unitary mass subject to the constraints: $$1=\varphi _i(\mathbf r _1,\mathbf {r}_2,...,\mathbf r _n)=|\mathbf r_i-\mathbf r_{i-1}|^2,\qquad 1\leq i \leq n+1,$$
and limited to the $xy$ plane ($\mathbf r_0$ and $\mathbf r_{n+1}$ are two fixed point on the $x$ axis). I'd like to write the Lagrangian of the above system (the particles are subject to gravity). </p>
<p>I thought that one good choice for the coordinates could be to take, for $1\leq i\leq n+1$, the angle $\theta _i$ that $\overrightarrow{P_{i-1}P_i}$ makes with the $x$-axis. Note that there are $2n-(n+1)=n-1$ degrees of freedom and so $n-1$ angles should suffice. With this choice we can write the positions as $$\mathbf r_{i}=\mathbf r_{i-1}+(\cos \theta _i, \sin \theta _i)=\mathbf r_0+\sum _{k=1} ^i(\cos \theta _k ,\sin \theta _k).$$</p>
<p>In this line of reasoning, the two constraints are given by: $$\mathbf r_{n+1} -\mathbf r_0=\sum _{k=1} ^{n+1} (\cos \theta _k,\sin \theta _k),$$
that are equivalent to: $$\cos \theta _n+\cos \theta _{n+1}=\ell - \sum _{k=1} ^{n-1} \cos\theta _k,$$
$$\sin \theta _n+\sin \theta _{n+1}=-\sum _{k=1}^{n-1}\sin \theta _k,$$
assuming that the system is solvable for those two (by the implicit function theorem and the second equation it must be solvable locally for a couple of $\theta$s).</p>
<p>Given this, I don't know how to go further. The velocities $\mathbf v_i$ and generalized velocities $\dot \theta _i$ satisfy similar relations to those of the positions, but I don't see any way to use these facts to write down the kinetic energy.</p>
<p>So my question is: is it possible to write the lagrangian of this system without some sort of approximations (i.e. small angles etc.)? Is it possible to do it following my line of reasoning, completing my analysis? Or maybe a totally different approach would work?</p>
<p>Thank you in advance.</p>
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<p>For a given system, how can you tell which one is kinetic energy for center of mass and which one is internal kientic energy?</p>
<p>K = Kcm + K int</p>
<p>For example, "A 150 g trick baseball is thrown at 63 km/h. It explodes in flight into two pieces, with a 39 g piece continuing straight ahead at 85 km/h. How much energy do the pieces gain in the explosion?"</p>
<p>I found the answer using conservation of momentum. I solved for the velocty and then taking the difference in kinetic energies before and after, the change was .984 J. However, relative to the equation, how do I know which one is internal kinetic energy and which is center of mass kinetic energy. Does K in the equation mean to total energy? How would you find Kcm and Kint?
Can someone please clarify? </p>
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<p>While analysing a problem in quantum Mechanics, I realized that I don't fully understand the physical meanings of certain integrals. I have been interpreting: </p>
<ul>
<li><p>$\int \phi^\dagger \hat A \psi \:\mathrm dx$ as "(square root of) probability that a particle with state $|\psi\rangle$ will collapse to a state $|\phi\rangle$ when one tries to observe the observable corresponding to $\hat A$"</p></li>
<li><p>$\int \phi^\dagger \psi \:\mathrm dx$ as "(square root of) probability that a particle with state $|\psi\rangle$ will collapse to a state $|\phi\rangle$".</p></li>
</ul>
<p>All integrals are over all space here, and all $\phi$s and $\psi$s are normalized.</p>
<p>Now, I realize that interpretation of the first integral doesn't really make sense when put side by side with the second one. </p>
<p>For example, when $|\phi\rangle$ is an eigenstate of $\hat A$, I get two different expressions for "the square root of probability that one will get the corresponding eigenvalue of $\psi$ when one tries to observe the observable corresponding to $\hat A$". As far as I can tell, $\int \phi^\dagger \hat A \psi \:\mathrm dx \neq\int \phi^\dagger \psi \:\mathrm dx $, even if $|\phi\rangle$ is an eigenstate of $\hat A$. I am inclined to believe that the second integral is the correct answer here (it comes naturally when you split $|\psi\rangle$ into a linear combination of basis vectors). But I am at a loss as to the interpretation of the first integral.</p>
<p>So, my question is, <strong>what are the physical interpretations of $\int \phi^\dagger \hat A \psi \:\mathrm dx$ and $\int \phi^\dagger \psi \:\mathrm dx$?</strong></p>
<p>(While I am familiar with the bra-ket notation, I have not used it in this question as I don't want to confuse myself further. Feel free to use it in your answer, though)</p>
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<p>Given two (or more) observables $A, B$ which commute one can construct a third observable $C= A \circ B$. If $\psi$ is a common eigenvector of $A, B$ with eigenvalues $\lambda_1, \lambda_2$ then it is clear that the measurement of $C$ of the state $\psi$ gives the measurement result $\lambda =\lambda_1 \lambda_2$, i.e. the result of the measurement of the observable $C$ is the result from the measurement of $A$ times the result from the measurement $B$. But what if $\psi$ is an eigenvector of $C$, but not of $A$ and $B$? Is there any connection between the measurement results of $A$, $B$ and $C$?</p>
<p>Example: Let there be three observers which measure a spin state with the corresponding observables
$A = \sigma_x \otimes \mathbb{I} \otimes \mathbb{I}$,
$B=\mathbb{I} \otimes \sigma_y \otimes \mathbb{I}$ and
$C=\mathbb{I} \otimes \mathbb{I} \otimes \sigma_y$.
They commute and we can construct $D= A \circ B \circ C = \sigma_x \otimes \sigma_y \otimes \sigma_y$.
Now the GHZ-state $\psi = \frac{1}{\sqrt{2}} ( | +z, +z, +z \rangle - | -z, -z, -z\rangle)$ is an eigenvector of $D$ with eigenvalue $\lambda =-1$ but it is not an eigenstate of $A, B$ or $C$.</p>
<p>Each of the observers will get a result $\pm 1$. Is there any connection between this individual results and the eigenvalue of $\psi$ (respectively the expectation value $\langle \psi | D | \psi \rangle = -1$)? Intuitively I would say that the product of the results should give the eigenvalue of $\psi$ but I can't see how this should follow from any quantum mechanical postulate or mathematical reasoning like in the case of the common eigenvector.</p>
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<p>In the movie <a href="http://www.imdb.com/title/tt1454468/" rel="nofollow"><em>Gravity</em></a> the two astronauts (Bullock and Clooney) are hit <em>twice</em> by the fast moving debris that bring havoc to their locations. I think this is a bad scientific mistake in the movie plot.</p>
<p>Indeed, different objects cannot travel the <em>same</em> orbit at different speeds. The shape of the orbit is defined by the total energy which depends essentially on velocity. So, objects that happen to be at the same point with different velocities will follow different orbits.</p>
<p>It is true that orbits are closed (in classical mechanics, not counting disturbing effects) so that an object will go over and over again through the same points, and the speedier objects will be again at the point where it met the slower one, but in the meantime the slower has also moved and the two won't pass through the meeting point at the same time again.</p>
<p>Any further meeting would occur only after a certain number of orbits, which makes way more than the mere 90 minutes claimed in the movie.</p>
<p>Is there a scientifically sound explanation for this?</p>
| 7,309 |
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<p>Imagine a source of photons at the center of a spherical shell of detectors at radius $R$.</p>
<p>Assume the photons are emitted one at a time.</p>
<p>Now if photons are particles that are highly likely to travel on straight paths at velocity $c$ then one would expect the following behavior:</p>
<p>At time $t=0$ as the photon is emitted in a particular direction the source recoils in the opposite direction.
Later at time $t=R/c$ the photon is absorbed by one of the detectors which recoils as it absorbs the photon.</p>
<p>But quantum mechanics says that the photon is actually emitted at time $t=0$ as a spherical wave that expands out to the detectors at the velocity $c$.</p>
<p>While the spherical wave is in transit from the source to the detectors the source cannot recoil in any particular direction as no direction has been picked out yet by the photon detection.</p>
<p>So does the source only recoil when the photon is absorbed at time $t=R/c$ or is its recoil somehow backdated to $t=0$ to be consistent with the particle picture?</p>
| 7,310 |
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<p>Imagine a point process defined by the passage time of purely brownian particles through a given point (in 1D), line (2D) or plane (3D). I'm interested in the variance of the counts (number of particles passing the points) as a function of sampling time.</p>
<p>Unlike brownian motion, I expect my signal to show non-vanishing correlation, because a particle that just crossed the point, has a high probability to cross it again. Thus the correlation should look like a dirac delta function (classic for discrete point process) plus a decreasing time function. </p>
<p>However, I'm a bit confuse with the way to calculate it analytically. I search in areas of photon counting, geiger counter, and gaz dynamics, but I didn't find any explicit calculation of the variance.</p>
<p>Two idea I had:</p>
<p>1/ Studying the Spatio-Temporal correlation function of a field of Brownian particles (see Gardiner, Stochastic Methods, eq. 13.3.22 for instance):</p>
<p>$G(x,t)=\frac{1}{\sqrt{4\pi Dt}}\exp\left(-x^2/(4Dt)\right)$</p>
<p>in 1d. We should have:
$Var(T)=\lim_{x\rightarrow 0} \int_T\int_T G(x,t) dt dt'$. However, the last expression is hard to compute.</p>
<p>2/ Using the probability of return time to origin of Brownian motion (the correlation arise from successive passage of the same particle)</p>
<p>Any idea or suggestions would be welcomed !</p>
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<p>The identification of an electron as a <em>particle</em> and the positron as an <em>antiparticle</em> is a matter of convention. We see lots of electrons around us so they become the normal particle and the rare and unusual positrons become the <a href="http://en.wikipedia.org/wiki/Antiparticle">antiparticle</a>.</p>
<p>My question is, when you have made the choice of the electron and positron as <em>particle</em> and <em>anti-particle</em> does this automatically identify every other particle (every other fermion?) as normal or anti?</p>
<p>For example the proton is a <em>particle</em>, or rather the quarks inside are. By considering the interactions of an electron with a quark inside a proton can we find something, e.g. a conserved quantity, that naturally identifies that quark as a <em>particle</em> rather than an <em>antiparticle</em>? Or do we also just have to extend our convention so say that a proton is a <em>particle</em> rather than an <em>antiparticle</em>? To complete the family I guess the same question would apply to the neutrinos.</p>
| 686 |
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] |
<p>Wikipedia has articles on <a href="https://en.wikipedia.org/wiki/Two-photon_absorption" rel="nofollow">two photon absorption</a>. And a lot of NMR literature refers to <a href="https://www.google.com/search?q=double+quantum+transitions&client=ubuntu&channel=cs&oq=double+quantum+transitions&aqs=chrome.0.69i57j69i59j69i61j69i62l3.5671j0&sourceid=chrome&ie=UTF-8" rel="nofollow">double quantum transitions</a>. But is there a difference? </p>
<p>As far as I can tell, a double quantum transition is has an intermediate step. $m = 1 \rightarrow m=2 \rightarrow m=3$. But two photon absorption just absorbs two photons and skips the $m = 2$ state. </p>
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<p>I've done this before, but it's been a long time.</p>
<p>Using trigonometric functions, I've been asked to solve the following problem. However, I'm at a complete loss as to how to do it. I have 5 questions similar that I know I can figure out if given an example.</p>
<p>A plane moving at $180$ mi/hr comes down to a $300$ ft elevation, flying straight and level. It releases a package to be caught in a net on the ground. Neglecting air friction, what should the horizontal distance between the plane and the net be at the time of release?</p>
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<p>It's a somewhat theoretical question. In special relativity, The energy of a photon is given by $E = pc$. But, my argument is that, since photons have no mass, how can they have a momentum $p$? The energy $E$ turns out to be 0 always. So, why does this equation hold?</p>
| 195 |
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<p>Is the earth's magnetic field strong enough to hold a quantum locked superconductor, or the superconductor wouldn't be able hold its own weight?</p>
<p>How strong should be the earth's magnetic field to hold quantum locked superconductors?</p>
| 7,314 |
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