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<p>How much knowledge of maths is required for learning <a href="http://en.wikipedia.org/wiki/Lagrangian_mechanics" rel="nofollow">Lagrangian mechanics</a>? Also from where can I learn this math?</p>
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<p>So I know that Einstein and general relativity had huge impacts on the way we view the world, but how crucial were these scientific advancements to the success of our space programs? Would Newtonian physics sufficed, or would using those formulas and methodologies when travelling off-earth and to the moon resulted in catastrophic failures?</p>
| 8,617 |
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<p>so this might have some duplicated inquiry that <a href="http://physics.stackexchange.com/questions/1586/what-if-physical-constants-were-increased-or-decreased">this question</a> <a href="http://physics.stackexchange.com/questions/78684/why-is-it-meaningless-to-speak-about-changes-in-a-dimensional-constant">or this question</a> had, and while i think i have some of <a href="https://en.wikipedia.org/wiki/Planck_units#Planck_units_and_the_invariant_scaling_of_nature" rel="nofollow">my own opinion</a> about it, i would like to ask the community here for more opinions.</p>
<p>so referring to <a href="http://arxiv.org/abs/hep-th/0208093" rel="nofollow">Duff</a> or <a href="http://www.coursehero.com/file/p2q03qm/It-has-the-value-k-B-1-381-10-23-JK-1-In-some-sense-there-is-no-deep-physical/" rel="nofollow">Tong</a>, one might still beg the question: why is the speed of light 299792458 m/s? don't just say "because it's defined that way by definition of the metre." before it was defined, it was measured against the then-current definition of the metre. why is $c$ in the ballpark of $10^8$ m/s and not in the order of $10^4$ or $10^{12}$ m/s?</p>
<p>similar questions can be asked of $G$ and $\hbar$ and $\epsilon_0$.</p>
<p>EDIT: to clarify a little regarding $c$. i recognize that the reason that $c\approx10^9$ m/s is that a meter is, by no accident of history, <em>about</em> as big as we are and a second represents a measure of how fast we think (i.e. we don't notice the flashes of black between frames of a movie and we can get pretty bored in a minute).</p>
<p>so light appears pretty fast to us because it moves about $10^9$ lengths about as big as us in the time it takes to think a thought.</p>
<p>so the reason that $c\approx10^9$ m/s is that there are about $10^{35}$ Planck lengths across a being like us ($10^{25}$ Planck lengths across an atom $10^5$ atoms across a biological cell and $10^5$ biological cells across a being like us). why? and there are about $10^{44}$ Planck times in the time it takes us to think something. why?</p>
<p>answer those two questions, and i think we have an answer for why $c\approx 10^9$ in anthropometric units.</p>
<p>EDIT #2: the other two questions referred do <strong>not</strong> address this question. <a href="http://physics.stackexchange.com/a/3666/37102">Luboš Motl</a> gets closest to the issue (regarding $c$) but does not answer it. i think in the previous EDIT and in the comments, i made it (the question) pretty clear. i was <strong>not</strong> asking so much about the <strong>exact</strong> values which can be attributed to historical accident. but there's a reason that $c \approx 10^9$ m/s, not $10^4$ or $10^{12}$.</p>
<p>reworded, i s'pose the question could be "<em>why are the anthropometric units (which are about as big as we are) as large as they are relative to their corresponding Planck units?</em>" (which <strong>is</strong> asking a question about dimensionless values.) if we answer those questions, we have an answer for not just why $c$ is what it is, but also why $\hbar$ or $G$ are what they are.</p>
| 283 |
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<p>If I understand Roger Penrose's theory, as the Universe expands and cools, matter is consumed by black holes. Eventually the black holes collide and evaporate so that there is only energy and the Weyl tensor (which relates to matter) heads to zero. He argues at zero, there is no effective space-time (my paraphrase) and the Universe 'reboots', turning that remaining energy into a new Big Bang. If this is correct-ish framing of his theory, (in a crude, layman's way) is there a lower bound for the Weyl tensor to allow a 'reboot'?
If there is such a non-zero value I presume that such a lower bound for Weyl tensor would be passed from a 'previous universe' and be part of the initial state the 'next universe'.<br>
Have I mangled Penroses's theory? If not, could the low Weyl tensor that would exist at T=0, explain any of the symmetry or fundamental constants that we observe in our Universe (Planks, fine structure etc)? </p>
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<p>I was told that the name 'Milky Way' first came about when people observered the milky looking stretch of sky; that is, before telescopes came about and we realised it wasn't a milky cloud, but rather a collection of stars, our galaxy.</p>
<p>So strictly speaking, Milky Way refers to that visible milky patch in the sky, rather than the collection of stars that is our galaxy, and that over time they've come to have the same name. </p>
<p>Is this the case? If so, does our Galaxy itself have its own name?</p>
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<p>In the text, it reads that the momentum of a particle will change if it is moving at speed close to light speed. In the general case, the wavelength is given as
$$
\lambda = \frac{h}{p}
$$
and
$$p = \frac{mv}{\sqrt{1-v^2/c^2}}$$
when $v \to c$, $p\to\infty$, so is it say that the wavelength is ZERO? I don't understand why the wavelength will change to zero if it is moving at speed very close to light speed?</p>
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] |
<p>Given a light pulse in vacuum containing a single photon with an energy $E=h\nu$, what is the peak value of the electric / magnetic field?</p>
| 742 |
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/11136/what-has-been-proved-about-the-big-bang-and-what-has-not">What has been proved about the big bang, and what has not?</a> </p>
</blockquote>
<p>I know the expansion of the universe is the most compelling but what else makes it so well liked and believed. I would appriciate the answer to this question soon.
Thank you.</p>
| 284 |
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<p>Would it be possible to create a habitable in terms of gravity planet that would rotate with the black hole acting as a center of gravity? The rotation of the structure would lessen the gravitational force, so it would be much harder to access it from outside. Would the rotation of the planet be sufficient to lessen the pull of the black hole?</p>
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<p>I'm trying to write a program to procedurally generate solar systems at a reasonably high level (I'm not interested in doing an n-body dust particle formation simulation).</p>
<p>Is there some sort of distribution that defines where I am most likely to find mass inside a solar system? i.e. should I expect heavier planets further out... or is it completely random?</p>
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<p>According to a book I'm reading, the <a href="http://en.wikipedia.org/wiki/Fourier_transform" rel="nofollow">Fourier transform</a> is widely used in <a href="http://en.wikipedia.org/wiki/Fourier_transform#Uncertainty_principle" rel="nofollow">quantum mechanics</a> (QM). That came as a huge surprise to me. (Unfortunately, the book doesn't go on to give any simple examples of how it's used!) So can someone provide one please?</p>
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<p>Suppose Winger's friend is placed into a black box, thoroughly isolated from the outside world.</p>
<p>He constantly observes an atom with a delay of some microseconds. According to Zeno effect, atom's lifetime will increase.</p>
<p>He writes his observations to a log.</p>
<p>After a day passed, the box is opened and Wigner's friend asked when the atom decayed.</p>
<p>Will the increased atom lifetime be seen by the observers who were outside of the box?</p>
| 8,624 |
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<p>Trying to understand Schutz's AFCIGR, where does the minus sign appear from in the metric tensor?</p>
<p><img src="http://i.stack.imgur.com/jXilu.gif" alt="metric"></p>
<p>I understand that this expresses the invariance of the spacetime interval. Schutz says (I think) that the metric is a (0,2) tensor. I assume that means it is the product of two one-forms, so presumably one of these one-forms has a -ve time component. What does that mean? Why don't both one-forms have a -ve time component? Looking at a Minkowski diagram what is a straightforward way to understand/visualise those one-forms? At my level, two things have been multiplied together to give a 4x4 matrix which has -1 in the top left corner. What are those two things and why do they give a -1 time component?</p>
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<p>I have often heard neighbours talking things like in a multi storied apartment, the upper flats are more hot in summer then lower flats (or vice versa?) and similarly for some comparison in winter? and similarly something for basement..</p>
<p>I have never understood these things well, even though people talk as if this is obvious.</p>
<p>So, what all factors cause such differences?</p>
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<p>I'm reading chapter 3 of Peskin and Schroeder and am stuck on page 43 of P&S. They have defined the Lorentz generators in the spinor representation as:
\begin{equation}
S^{\mu \nu} = \frac{i}{4}[\gamma^\mu,\gamma^\nu]
\end{equation}
such that a finite transformation is given by:
\begin{equation}
\Lambda_{1/2}=e^{-\frac{i}{2} \omega_{\mu \nu} S^{\mu \nu}}
\end{equation}
where $\gamma^\mu$ are the gamma matrices and $\omega_{\mu \nu}$ are the elements of a real and antisymmetric matrix. According to P&S on page 43 (between equation (3.32) and (3.33), they say that the adjoint of a Dirac spinor transforms as follows:
\begin{equation}
\psi^\dagger \rightarrow \psi^\dagger \left(1+\frac{i}{2} \omega_{\mu \nu}(S^{\mu \nu})^\dagger \right)
\end{equation}
However, I would expect the transformation to be:
\begin{equation}
\begin{aligned}
\psi^\dagger & \rightarrow \psi^\dagger \left(1-\frac{i}{2} \omega_{\mu \nu}S^{\mu \nu} \right)^\dagger \\&
= \psi^\dagger \left(1+\frac{i}{2} (\omega_{\mu \nu})^\dagger (S^{\mu \nu})^\dagger \right) \\&
= \psi^\dagger \left(1-\frac{i}{2} \omega_{\mu \nu} (S^{\mu \nu})^\dagger \right)
\end{aligned}
\end{equation}
where in the last line I made use of the fact that $\omega$ is a real and antisymmetric matrix:
\begin{equation}
(\omega_{\mu \nu})^\dagger = (\omega_{\mu \nu})^T = \omega_{\nu \mu} = - \omega_{\mu \nu}
\end{equation}
This implies that according to my calculations, equation (3.33) of P&S should actually be:
\begin{equation}
\overline{\psi} \rightarrow \overline{\psi} \Lambda_{1/2}
\end{equation}
This equation must be wrong because it means that $\overline{\psi} \psi$ does not transform as a scalar and therefore the Dirac Lagrangian is not correct. However, I do not know where my mistake is and was hoping someone could help me out?</p>
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<p>How does a <a href="http://en.wikipedia.org/wiki/Tesla_coil" rel="nofollow">Tesla Coil</a> exactly work? I am currently making a Tesla Coil in school but before I start, I want to know exactly how does a Tesla Coil work? I understand the various electrical components used in it, but what I don't understand is how do those components together work to make something like Tesla Coil.</p>
| 8,628 |
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<p>I have been learning about time and the different dilation effects of gravity and relative velocity. I was wondering, are there any other factors that can affect time?</p>
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<p>Let's say you have two bodies at are held at rest relative to each other exchanging (real, not virtual) photons back and forth. Then we let them go (maybe push them apart slightly), so they will begin to move apart at some velocity. Now, if they have a relative velocity between them, the photons absorbed will be of longer wavelength and therefore lower energy than when the photons were emitted. This will result in a net energy decrease of the system. Would this energy decrease reduce the gravitational attraction between the particles, causing an increasing separation acceleration as long as there is an exchange of photons?</p>
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<p>Last year I attended an introductory particle physics course, in which the <a href="http://en.wikipedia.org/wiki/Eightfold_Way_%28physics%29">Eigthfold Way</a> for classifying hadrons has been discussed.</p>
<p>The main idea consists in grouping hadrons in <a href="http://en.wikipedia.org/wiki/Multiplet">multiplets</a> (i.e vectors) on which some (different) <a href="http://en.wikipedia.org/wiki/Representation">representation</a>s of the approximate symmetry $SU(3)$ <a href="http://en.wikipedia.org/wiki/Flavour_%28particle_physics%29">flavour</a> acts.</p>
<p>However, this part of the lectures was really sketchy and I always remained in doubt about how one actually does the classification.</p>
<p>Can someone give a reference or explain clearly how one constructs such multiplets from the <a href="http://en.wikipedia.org/wiki/Weight_%28representation_theory%29">weights</a> of various $SU(3)$ representations?</p>
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<p>Conservation of energy in an electrical circuit can be expressed by Ampere's law $$\nabla \times \textbf{B} = \mu_o
\textbf{J} + \epsilon_o \mu_o \frac {\partial \textbf{E}} {\partial t}$$ when both sides of the equation are dotted with $\textbf{E}$ and the input power is placed on the left side of the equation while the dissipated power (the output power) is placed on the right hand side of the equation</p>
<p>$$\textbf{E} \cdot (\nabla \times \textbf{B}) - \epsilon_o \mu_o \textbf{E} \cdot \frac {\partial
\textbf{E}} {\partial t} = \textbf{E} \cdot \mu_o \textbf{J}
$$</p>
<p>$$ \textbf{E} \cdot \frac {1} {\mu_o} (\nabla \times \textbf{B}) - \epsilon_o \textbf{E} \cdot
\frac {\partial \textbf{E}} {\partial t} = \textbf{E} \cdot \textbf{J}
$$</p>
<p>$$
\textbf{E} \cdot (\nabla \times \textbf{H}) - \epsilon_o \textbf{E} \cdot \frac
{\partial \textbf{E}} {\partial t} = \textbf{E} \cdot \textbf{J}
$$</p>
<p>The units of all terms are $\left[ \frac {W} {m^3} \right]$, which is energy per unit time per cubic meter. </p>
<p>If we now need to get the Poynting theorem from the above equation then we have to add on both sides of the equation the term $+\textbf{B} \cdot \frac {\partial \textbf{B}} {\partial t}$ which from Faraday's law dotted with $\textbf{B}$ is equal to $-\textbf{B} \cdot(\nabla \times \textbf{E})$</p>
<p>$$\textbf{E} \cdot (\nabla \times \textbf{B}) - \epsilon_o \mu_o \textbf{E} \cdot \frac
{\partial \textbf{E}} {\partial t} +\textbf{B} \cdot \frac {\partial \textbf{B}} {\partial t} = \textbf
{E} \cdot \mu_o \textbf{J} +\textbf{B} \cdot \frac {\partial \textbf{B}} {\partial t}$$</p>
<p>$$
\textbf{E} \cdot (\nabla \times \textbf{H}) - \epsilon_o \mu_o \textbf{E} \cdot \frac
{\partial \textbf{E}} {\partial t} -\textbf{B} \cdot(\nabla \times \textbf{E}) = \textbf{E} \cdot \mu_o
\textbf{J} +\textbf{B} \cdot \frac {\partial \textbf{B}} {\partial t}$$</p>
<p>$$
\textbf{E} \cdot (\nabla \times \textbf{H}) -\textbf{B} \cdot(\nabla \times \textbf{E}) =
\epsilon_o \mu_o \textbf{E} \cdot \frac {\partial \textbf{E}} {\partial t} +\textbf{B} \cdot \frac
{\partial \textbf{B}} {\partial t} + \textbf{E} \cdot \mu_o \textbf{J} $$</p>
<p>$$
-\nabla \cdot \textbf{S} = \epsilon_o \textbf{E} \cdot \frac {\partial \textbf{E}} {\partial t}
+ \frac {\textbf{B}} {\mu_o} \cdot \frac {\partial \textbf{B}} {\partial t} + \textbf{E} \cdot \textbf{J}
$$</p>
<p>where $\textbf{S} = \frac {1} {\mu_o} \textbf{E} \times \textbf{B} = \textbf{E} \times \textbf{H}$ $\left[ \frac {W} {m^2} \right]$ is the Poynting's vector. Doesn't the above make the Poynting vector redundant in proving CoE, the latter appearing to follow directly from Ampere's law alone?</p>
<p>Notice, it is not true that </p>
<p>$$
\textbf{E} \cdot (\nabla \times \textbf{H}) - \epsilon_o \textbf{E} \cdot \frac
{\partial \textbf{E}} {\partial t} = \textbf{E} \cdot \textbf{J}
$$</p>
<p>"just states some relation" between vector fields the way it is not true that</p>
<p>$$
\frac{\partial}{\partial t} \biggl[ \frac{1}{2} \biggl( \epsilon_0 \textbf{E}^2 + \frac{\textbf{B}^2}{\mu_0}\biggr) \biggr]
$$</p>
<p>"just states some relation" between vector fields. These state $\textit{change in energy density of electromagnetic field}$. As shown above, obtaining of the Poynting vector is only a result of a mathematical manipulation of an equation which already shows balance of these power densities and therefore the Poynting vector and the theorem connected with it are redundant.</p>
| 8,632 |
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<p>I am trying to compute the amount of oblateness that is caused by planetary rotation. I picture the force of gravity added to the centrifugal force caused by the rotation of the planet as follows:</p>
<p>$\hspace{4cm}$<img src="http://i.stack.imgur.com/Nfv6f.png" alt="forces"></p>
<p>That is, at the point in question, at latitude $\phi$, the distance from the axis of rotation is $r\cos(\phi)$. Thus, the centrifugal force would be $\omega^2r\cos(\phi)$ in a direction perpendicular to the axis of rotation. The radial and tangential components would be $\omega^2r\cos^2(\phi)$ and $\omega^2r\cos(\phi)\sin(\phi)$, respectively.</p>
<p>My assumption is that the surface of the planet would adjust so that it would be perpendicular to the effective $g$; that is, the sum of the gravitational and centrifugal forces. This would lead to the equation
$$
\frac{\mathrm{d}r}{r\,\mathrm{d}\phi}=-\frac{\omega^2r\cos(\phi)\sin(\phi)}{g-\omega^2r\cos^2(\phi)}
$$
We can make several assumptions here, and I will assume that $\omega^2r$ is small compared to $g$. Thus, we get
$$
\int_{\text{eq}}^{\text{np}}\frac{\mathrm{d}r}{r^2}
=-\frac{\omega^2}{g}\int_0^{\pi/2}\cos(\phi)\sin(\phi)\,\mathrm{d}\phi
$$
which leads to
$$
\frac1{r_{\text{np}}}-\frac1{r_{\text{eq}}}
=\frac{\omega^2}{2g}
$$
and
$$
1-\frac{r_{\text{np}}}{r_{\text{eq}}}
=\frac{\omega^2r_{\text{np}}}{2g}
$$
However, numerical evaluation and <a href="https://en.wikipedia.org/wiki/Earth_radius#Physics_of_Earth.27s_deformation">Wikipedia</a> seem to indicate that this should be twice what I am getting. That is,
$$
1-\frac{r_{\text{np}}}{r_{\text{eq}}}
=\frac{\omega^2r^3}{Gm}
=\frac{\omega^2r}{g}
$$
What am I doing wrong?</p>
| 8,633 |
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<p>If we consider a balloon full of air submerged in water then we all know that it will rise rapidly. I am having trouble understanding this at the level of individual molecules of air and water. What is a molecular/microscopic explanation for this phenomenon?</p>
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<p>For instance, if we choose the following scalar field Lagrangian, which is (I hope) Lorentz-invariant, where $l$ is a a length scale, and with a $(-1,1,1,1)$ metric: </p>
<p>$$ \mathfrak{L}(x) \sim l^{-6} \int d^4y \space e^{\frac{- y^2}{ l^2}} (\Phi(x + y)\Phi(x - y) - \Phi(x) \Phi(x)) $$</p>
<p>There are no explicit derivatives of fields in this expression. </p>
<p>Of course, if we develop this expression in orders of $l$, we will find, for instance, at the first order (in $l^0$), a term proportional to:</p>
<p>$$\partial_i \Phi(x) \partial^i \Phi(x).$$</p>
<p>And, of course, we will find higher order derivatives of fields with higher order development in $l$.</p>
<p>But the initial expression does not involve explicit derivative of fields.</p>
| 8,635 |
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<p>I'm looking for a reference, journal article, paper, etc. that supports the idea that classical mechanics, in particular rigid body dynamics, is largely <a href="http://en.wikipedia.org/wiki/Predictability" rel="nofollow">predictable</a>.</p>
<p>A view coming from the background of computer physics simulations would be an added bonus.</p>
| 8,636 |
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<p>I need to know the mathematical argument that how the relation is true $(C^{-1})^T\gamma ^ \mu C^T = - \gamma ^{\mu T} $ .
Where $C$ is defined by $U=C \gamma^0$ ; $U$= non singular matrix , $T$= transposition, $\gamma^0= $Dirac gamma matricx = $\beta$ </p>
<p>I need to know the significance of these equation in charge conjuration . </p>
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<p>I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free state. In particular, he argued the integral</p>
<p>$$\tag{1} \int d\alpha\frac{e^{-iE_{\alpha}t}g(\alpha)T_{\beta\alpha}^+\Phi_\beta} {E_\alpha-E_\beta+i\epsilon}$$</p>
<p>would vanish, where $d\alpha=d^3\mathbf{p}$ (also involves discrete indices like spin, but of no relevance here). In his argument, he used a contour integration in the complex $E_{\alpha}$ plane, in which the integral of central interest is the integration along real line</p>
<p>$$\tag{2} \int_{-\infty}^\infty dE_\alpha\frac{e^{-iE_{\alpha}t}g(\alpha)T_{\beta\alpha}^+\Phi_\beta} {E_\alpha-E_\beta+i\epsilon}$$</p>
<p>I don't see how to obtain (2) from (1), since the lower bound of energy is the rest mass, in the best case I could get something like $\int_{m}^\infty dE_\alpha\cdots$, but how could one extend this onto the whole real line.</p>
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<p>I have a sphere (mass = 3 kg), constrained to a fixed length rope, rotating (radius = 5 m) on a vertical plane.
My textbook ask me about the minimum speed in the highest point in order to keep the circular trajectory.</p>
<p>Now, I know that in the highest point (v=speed):</p>
<p>$$F_c=mg+T$$
$$\frac{mv^2}{r}=mg+T $$
$$ \frac{3}{5}v^2=29,43+T$$
I know that with a low speed I have a low Tension, so let's put T=0 and go on:
$$v^2=49,05 \rightarrow v=7$$</p>
<p>The result is correct, but I have a little doubt: if the Tension is 0, why the sphere doesn't go along the tangent or start falling down? Exactly what is forcing the sphere to preserve the circular trajectory?</p>
<p>In my ignorant opinion, the minimum speed is a little more than 7.00 m/s, because the tension mustn't be 0, even a very small number, but not null..</p>
| 8,639 |
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<p>The theory of QEC with stabilizer codes defines an alternative way to represent a quantum state in terms of operators.
To understand better what I am concerning about, let's consider the 7-qubit Steane code:</p>
<p>$$
\left|0\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|0000000\right\rangle + \left|1010101\right\rangle + \left|0110011\right\rangle + \left|1100110\right\rangle + \left|0001111\right\rangle + \left|1011010\right\rangle + \left|0111100\right\rangle + \left|1101001\right\rangle)
$$
$$
\left|1\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|1111111\right\rangle + \left|0101010\right\rangle + \left|1001100\right\rangle + \left|0011001\right\rangle + \left|1110000\right\rangle + \left|0100101\right\rangle + \left|1000011\right\rangle + \left|0010110\right\rangle)
$$</p>
<p>Papers and books directly define the relative generators as:</p>
<p>$$
K^1 = IIIXXXX
$$
$$
K^2 = XIXIXIX
$$
$$
K^3 = IXXIIXX
$$
$$
K^4 = IIIZZZZ
$$
$$
K^5 = ZIZIZIZ
$$
$$
K^6 = IZZIIZZ
$$
where I is identity matrix and X,Z Pauli's matrices.</p>
<p>Therefore, my questions are: how these generators have been calculated?
How can I calculate the generators for a generic superposition of n qubits?</p>
<p>Thank you</p>
| 8,640 |
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] |
<p>Has the <a href="http://www.enwp.org/Standard_Model_%28mathematical_formulation%29" rel="nofollow">Standard Model of Particle Physics</a> been experimentally verified? Or is it still waiting for experimental verification? OR,</p>
<p>What aspects/predictions of the Standard Model have been experimentally verified? </p>
<p>If not, what are some possible tests for it? </p>
| 8,641 |
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/12175/book-recommendations">Book recommendations</a> </p>
</blockquote>
<p>I am currently in the 11th grade (I am an Indian student) and I am looking forward to studying pure mathematics and theoretical physics in the future.</p>
<p>I therefore request you to tell me books/textbooks to study physics. I know some integration and differentiation and I plan to study Richard Courant's book "Introduction To Calculus And Analysis: Volume 1" from Tuesday onwards.Besides, I am studying Halliday-Resnick Walker for the moment.</p>
| 98 |
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<p>I have read about this and what I surmise is that when charged particles such as electrons accelerate they produce time-varying electric fields. These E-fields produce H-fields and the process goes on. </p>
<p>1.) Are the EM fields really moving. My textbooks says it's changes in field that is moving. I don't understand this part. </p>
<p>2.)
<del>The second question is hard for me to write down. I hope you guys can understand it.
If i have a string and i start a wave train and then stop after some time. The part of the string next to my hand eventually becomes stationary.
So similarly if i stop the accelerating charged particles which is radiating EM waves ,what happens to the electric and magnetic fields that it just produces. Do they disappear or continue with their movement.</del></p>
<p>It seems like a unnecessary question but I am not able to answer it at all.</p>
<p>Thanks.</p>
<p>Edit: So EM waves are just Changes in electric fields that seem to propagate along space.
But I have seen people on this site saying it happens because of continuous induction of Electric and Magnetic Field. How can I relate both of these?</p>
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<p>Why was the <a href="http://en.wikipedia.org/wiki/Luminiferous_aether" rel="nofollow">Ether Theory</a> refused by Modern Physics? If you please explain me, I just wanted to understand it more. </p>
| 761 |
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] |
<p>I know that if the integral is convergent we can always make a change of variable to make it better, however what happens with DIVERGENT integrals? can we make a change of variable into a divergent integral after having it regularized?</p>
<p>I mean we insert the regulator $(q+a)^{-s}$ or similar on each variable and then make the change of variable to polar, cilindrical or other</p>
| 8,643 |
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<p>I notice in the <a href="http://en.wikipedia.org/wiki/Electromagnetic_spectrum" rel="nofollow">EMS</a> chart that only half of the IR range will travel through the earth's atmosphere. So in the range of frequencies that penetrate the atmosphere what frequency travels farthest?</p>
| 8,644 |
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<p>I have been trying to find an equation (or some solution) of how to calculate the electric field strength (in N/C) of a conducting rectangular (nearly flat) plate which has non-zero potential to it, say the plate has a potential of 5V. </p>
<p>I have searched over the internet (and read Griffiths book on the method of images section), and it seems one would need to apply the method of images to solve the problem. However, since almost all examples regarding method of images is about "grounded" plates at 0V, it is very difficult for me to understand how to use method of images to solve for the electric field of a plate at 5V? </p>
<p>Also, I would like to mention that within the electric field of the 5V conducting plate, there is a small freely-moving positively charged particle in the vicinity (I assume because the charge on this small particle is the same as the charge on an electron/proton-- it can be regraded as a test charge and therefore, modification to the combined electric field between the conducting plate and the charge is not necessary?-please correct me here if I am wrong.)</p>
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<p>I really can't understand the power loss law. If we have a wire carrying a $15\:\mathrm{V}$ and $1\:\mathrm{ A}$ going into an inverter, giving $150\:\mathrm{V}$ and $0.1\:\mathrm{A}$, if we want to calculate the power loss as heat in wires, we use $P = I^2 R$ or simple $P=VI$, does that mean that all power is lost?</p>
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<p>In the standard model (omitting the QCD part), we start off with the set of generators </p>
<p>$T_1$, $T_2$, $T_3$, $Y$ </p>
<p>for the four-parametric gauge group $SU(2)_L \times U(1)_Y$.</p>
<p>We then define a new generator $Q= T_3+Y$ and make the transition to the four-parametric gauge group $SU(2)_? \times U(1)_Q$.</p>
<p>What are, aside from $Q$, the new generators for this "new" gauge group?</p>
<p>$?$ , $?$ , $?$ , $Q$ </p>
<p>Do we still use the $T$'s we used in $SU(2)_L$? That means the left factor in the group product is still the same as before the symmetry breaking?</p>
<p>My motivation for asking is the observation that in $SU(2)_L \times U(1)_Y$, the four generators are orthogonal and a basis for the space of all complex self-adjoint matrices.</p>
<p>The set of $T_1$, $T_2$, $T_3$, $Q$, while still a basis, is however not orthogonal, since</p>
<p>$( T_3| Q )$=$(T_3|T_3+Y)$=$(T_3|T_3) \neq 0$ </p>
<p>It would seem that we would probably want to preserve that orthogonality property and thus not use $T_3$ as a generator after symmetry breaking. </p>
| 8,647 |
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<p>I am not sure whether it is some well-known named model in statistical physics.
I could not find it in any standard text-book that I know of. </p>
<p>Let there be $N$ identical classical particles occupying a square lattice of $2N$ sites with at most one particle per site. Let the alternate sites be names $A$ and $B$. Let $p$ be the fraction of particles on $A$-type sites and assume that for a fixed value of $p$, all configurations are equally likely. (mean field approximation?) </p>
<ul>
<li>Then how does one calculate the entropy as a function of $p$? I guess there is some simplification that will happen if one works in the limit of $N$ being very large. (thermodynamic limit?) </li>
</ul>
<p>Let there be a repulsive interaction energy of $E_0$ whenever neighbouring $A$ and $B$ type sites are occupied. </p>
<ul>
<li>In that case the claim seems to be that the average total energy $E(p)$ is given by $4NE_0p(1-p)$. (..I am not sure whether here any large $N$ limit has been taken..but I guess this too is some asymptotic answer..)</li>
</ul>
<p>I would be glad if someone can help calculate/derive the above two bulleted questions.
I would like to know if there is some general framework or class of models from which this comes. </p>
<ul>
<li><p>Apparently the interesting thing about this model is that it has a second order phase transition. How does one prove that? Or is it somehow supposed to be obvious? </p></li>
<li><p>Will some single unique value of $p$ get picked out in the high and low temperature limit? How does one determine that? </p></li>
</ul>
<p>For the last/above two of the questions one would obviously need to assume that the system is at a thermal equilibrium at a temperature $T$. Then I guess the value of $p$ gets determined by minimizing the ``free energy" $=F(p) = E(p) - TS(p)$. But to be able to do this calculation one would probably first need to find the answer to the first two questions in the large $N$/ thermodynamic limit. </p>
| 8,648 |
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<p>It's my understanding that <a href="http://en.wikipedia.org/wiki/General_relativity" rel="nofollow">General Relativity</a> abstracts away the concept of gravity as a force, and instead describes it as a feature of spacetime by which massive objects cause curvature. Then it follows that what we experience as a force is simply the difference between a geodesic on this curved surface and our perceived Euclidean space. What I am unsure of, exactly, is the implication of this. </p>
<p>$$S[q] \equiv \int L(q(t), \tfrac{ \delta q }{ \delta t }(t), t)dt$$
and <a href="http://en.wikipedia.org/wiki/Principle_of_least_action" rel="nofollow">Hamilton's Principle</a> states that
$$\tfrac{\delta S}{\delta q(t)} = 0.$$ </p>
<p>If
$$F(q(t)) = -\nabla U(q(t)) = \nabla (T(\tfrac{ \delta q }{ \delta t}(t)) - U(q(t))) = \nabla L,$$
which, as I understand is true for a conservative field like gravitation, then are these two statements not equivalent? </p>
<p>What additional insight do we gain by using principles of differential geometry versus classical potential theory?</p>
| 8,649 |
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<p>There is a small area element of size $da$ and normal vector $\hat n$. </p>
<p>I understand that the particles with speed $|\vec v|$ that hit this area element in the time interval $(t,t+\delta t)$ lie in a spherical shell with radius $r=|\vec v|t$ at $t=0$. Let the number of particles with energy $E(|\vec v|)$ within a solid angle $d\Omega$ be $dN$. Why then is the total number of particles hitting $\hat n da$ with velocity $|\vec v|$ (assuming isotropy of the velocity distribution) equal to $$\frac{(\vec v\cdot \hat n)}{|\vec v| 4\pi r}da \,\,dN$$? I don't quite understand how to get the factor $\frac{(\vec v\cdot \hat n)}{|\vec v| 4\pi r}$. Thanks.</p>
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<p>A naïve observational viewpoint doesn't automatically try to correct for signal delays. In other words, the time co-ordinate is <a href="http://en.wikipedia.org/wiki/Retarded_time" rel="nofollow">retarded</a>. </p>
<p>For example:</p>
<p>In popular expositions of relativity you'll find things like "moving observers see each other's clocks as running slow". If you're lucky it's made clear that "see" is not the everyday, well-understood meaning, but is technical jargon that involves correcting for signal delays. Often this point will be buried, sometimes it is not mentioned at all, and sometimes expositors just get confused on this point. (Even competent ones!)</p>
<p>Anyway, even if it makes it clear that this isn't what you actually see, it won't tell you what you do actually see. This is unfortunate because it doesn't seem like a very esoteric fact to me that <em>oncoming clocks run fast</em>. Is there a good low-level exposition that covers this, and other basic phenomena of special relativity, as they naïvely appear?</p>
| 8,651 |
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<p>I am unclear about the adjective "first" or "second" used in phase transitions. Take the liquid-gas transition for example. If we vary the volume of the system at constant T, at some point we will have two phases co-existing. The relevant free energy of the complete system (liquid+gas), the Helmholtz free energy $A$, varies continuously such that its second derivative is zero and first derivative is constant. On the other hand between the phases themselves $A$ is discontinuous, but intensities like T, P etc are same. If one studies the variation along a P-T isotherm (vary pressure of the system at constant temperature), the relevant free energy of the total system $G$ is continuous but non-differentiable at the transition. Exactly what is the criterion for calling this "first" order?</p>
<p>I have checked wikipedia and a few online lecture notes, and which free energy derivatives should one consider is not clear to me.</p>
<hr>
<p><strong>EDIT:</strong> I just realized a <a href="http://physics.stackexchange.com/q/52082/2451">similar question</a> has been raised a few days ago. Not sure how it slipped my attention. However, in light of that one, my question can be simplified to which free energy do I choose for deciding order? I can study a phase transition using different thermodynamic potentials, the free energy being the one that corresponds to my independent variables.</p>
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<p>There is a possible CP-violating term in the strong sector of the standard model proportional to $\theta_\text{QCD}$. In the absence of this term, the strong interactions are CP-invariant. In the weak interactions, there is CP-violation that comes from the lone phase $\delta$ appearing in the CKM quark-mixing matrix.</p>
<p>When the strong interactions are coupled to the weak interactions, and in the absence of new physics, do the weak interactions renormalize $\theta_\text{QCD}$? </p>
<p>My <strong>best guess</strong> by how this would show up diagrammatically is when the self energies of quarks pick up phases through loops, which via the U(1) anomaly could be interpreted as $\theta_\text{QCD}$. Is this guess correct?</p>
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<p>The other day in my string theory class, I asked the professor why we wanted to quantize gravity, in the sense that we want to treat the metric on space-time as a quantum field, as opposed to, for example, just leaving the metric alone, and doing quantum field theory in curved space-time. Having never studied it, it's not obvious why, for example, the Standard Model modified to work on a space-time with non-trivial metric wouldn't work.</p>
<p>The professor replied in a way that suggested that, once upon a time, this was actually a controversial point in the physics community, and there was a debate as to whether one should head in the direction of quantizing the metric or not. Now, he said, the general consensus is that quantizing the metric is the right way to go, but admitted he didn't have time to go into any of the reasons that suggest this is the route to take.</p>
<p>And so I turn here. What are the reasons for believing that in order to obtain a complete and correct quantum theory of gravity, we must quantize the metric?</p>
<p>EDIT: I have since thought about this more, and I have come up with an extension to the original question. The answers already given have convinced me that we can't just leave the metric as it is in GR untouched, but at the same time, I'm not convinced we have to quantize the metric in the way that the other forces have been quantized. In some sense, gravity isn't a force like the other three are, and so to treat them all on the same footing seems a bit strange to me. For example, how do we know something like non-commutative geometry cannot be used to construct a quantum theory of gravity. Quantum field theory on curved <em>non-commutative</em> space-time? Is this also a dead end?</p>
<p><strong>EDIT</strong>: At the suggestion of user <em>markovchain</em>, I have asked the previous edit as a separate <a href="http://physics.stackexchange.com/questions/55333/is-the-quantization-of-gravity-necessary-for-a-quantum-theory-of-gravity-part-i">question</a>.</p>
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<p>Firstly, I understand that we have no observational evidence for 'wormholes'. They are theorised solutions to general relativity equations.</p>
<p>That said, if macroscopic wormholes do exist---how do they work? I've been thinking about this for the past couple of days, and I have some questions.</p>
<ul>
<li>What does the mouth of a wormhole look like? I've seen <a href="http://www.spacetimetravel.org/wurmlochflug/wurmlochflug.html">this</a>; is that more or less accurate?</li>
<li>If I place one end of a wormhole in a high magnetic field, and the other end on my desk, will all my ferrous objects fly into the wormhole?</li>
<li>If so, with what force? What does the magnetic field look like at each end of the wormhole?</li>
<li>If the distance between the mouths of the wormhole was comparable to the force that the magnets exert, would the magnet 'pull' on itself and draw itself into the wormhole?</li>
</ul>
<p>Do any of these questions even make sense?</p>
| 8,655 |
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<p>I understand that the Biot number is essentially the ratio of the convective effects to the conductive effects in transient conduction but what if there is some sort of radiation from a heat source like a heat lamp (neglecting surface to ambient radiation)</p>
<p>Would the Biot number then be the ratio of the convective + radiative effects to the conductive effects? I have only ever used the Biot number for convection and conduction, not all 3.</p>
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] |
<p>Does photon have size measurement because of its particle nature like electron's 3.86*10^-13m etc..</p>
| 982 |
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<p>Consider the following experiment. I take a spin-$\frac{1}{2}$ particle and make a $\sigma_x$ measurement (measure the spin in the $x$ direction), then make a $\sigma_y$ measurement, then another $\sigma_x$ one, then $\sigma_y$, and so on for $n$ measurements. The formalism of quantum mechanics tells us that the outcomes of these measurements will be random and independent. I now have a string of completely random bits, of length $n$. Briefly, my question is <em>where does the information in this string come from?</em></p>
<p>The obvious answer is "quantum measurements are fundamentally indeterministic and it's simply a law of physics that you get a random string when you do that". The problem I have with this is that it can be shown that unitary evolution of quantum systems conserves von Neumann entropy, just as Hamiltonian evolution of a classical system conserves Shannon entropy. In the classical case this can be interpreted as "no process can create or destroy information on the microscopic level." It seems like the same should be true for the quantum case as well, but this seems hard to reconcile with the existence of "true" randomness in quantum measurement, which does seem to create information.</p>
<p>It's clear that there are some interpretations for which this isn't a problem. In particular, for a no-collapse interpretation the Universe just ends up in a superposition of $2^n$ states, each containing an observer looking at a different output string. </p>
<p>But I'm not a big fan of no-collapse interpretations, so I'm wondering how other quantum interpretations cope with this. In particular, in the "standard" interpretation (by which I mean the one that people adhere to when they say quantum mechanics doesn't need an interpretation), how is the indeterminacy of measurement reconciled with the conservation of von Neumann entropy? Is there an interpretation other than no-collapse that can solve it particularly well?</p>
<p><strong>addendum</strong></p>
<p>It seems worth summarising my current thinking on this, and having another go at making clear what I'm really asking.</p>
<p>I want to start by talking about the classical case, because only then can I make it clear where the analogy seems to break down. Let's consider a classical system that can take on one of $n$ discrete states (microstates). Since I don't initially know which state the system is in, I model the system with a probability distribution.</p>
<p>The system evolves over time. We model this by taking the vector $p$ of probabilities and multiplying it by a matrix T at each time step, i.e. $p_{t+1} = Tp_t$. The discrete analogue of Hamiltonian dynamics turns out to be the assumption that $T$ is a permutation matrix, i.e. it has exacly one 1 on each rown and column, and all its other entries are 0. (Note that permutation matrices are a subset of unitary matrices.) It turns out that, under this assumption, the Gibbs entropy (aka Shannon entropy) $H(p)$ does not change over time.</p>
<p>(It's also worth mentioning, as an aside, that instead of representing $p$ as a vector, I could choose to represent it as a diagonal matrix $P$, with $P_{ii}=p_i$. It then looks a lot like the density matrix formalism, with $P$ playing the role of $\rho$ and $T$ being equivalent to unitary evolution.)</p>
<p>Now let's say I make a measurement of the system. We'll assume that I don't disturb the system when I do this. For example, let's say the system has two states, and that initially I have no idea which of them the system is in, so $p=(\frac{1}{2},\frac{1}{2})$. After my measurement I know what state the system is in, so $p$ will become either $(1,0)$ or $(0,1)$ with equal probability. I have gained one bit of information about the system, and $H(p)$ has reduced by one bit. In the classical case these will always be equal, unless the system interacts with some other system whose state I don't precisely know (such as, for example, a heat bath).</p>
<p>Seen from this point of view, the change in von Neumann entropy when a quantum measurement is performed is not surprising. If entropy just represents a lack of information about a system then of course it should decrease when we get some information. In the comments below, where I refer to "subjective collapse" interpretations, I mean interpretations that try to interpret the "collapse" of a wavefunction as analogous to the "collapse" of the classical probability distribution as described above, and the von Neumann entropy as analogous to the Gibbs entropy. These are also called "$\psi$-epistemic" interpretations.</p>
<p>But there's a problem, which is this: in the experiment described at the beginning of this question, I'm getting one bit of information with every measurement, but the von Neumann entropy is remaining constant (at zero) instead of decreasing by one bit each time. In the classical case, "the total information I have gained about the system" + "uncertainty I have about the system" is constant, whereas in the quantum case it can increase. This is disturbing, and I suppose what I really want to know is whether there's any known interpretation in which this "extra" information is accounted for somehow (e.g. perhaps it could come from thermal degrees of freedom in the measuring apparatus), or in which it can be shown that something other than the von Neumann entropy plays a role analogous to the Gibbs entropy.</p>
| 288 |
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] |
<p>Suppose we have a 2D polymer model described by a set of 2D vectors {$\mathbf{t}_i$} ($i=1,2,\dots N$) of length $a$. </p>
<p>The energy of the polymer is given by:
$$
\mathcal{H}~=~-k\sum^N_{i=1}\mathbf{t}_i\cdot\mathbf{t}_{i+1}
~=~-ka^2\sum^N_{i=1}\cos\phi_i.
$$</p>
<p>The constant $k$ is a measure of bending rigidity so that a probability of finding any configuration of the polymer is proportional to $e^{-\frac{\mathcal{H}}{k_BT}}$.</p>
<p>Essentially, this is a discrete version of the wormlike-chain model by Kratky and Porod.</p>
<ol>
<li><p>What is the expression for propability density $p(\mathbf{R})$, where $\mathbf{R}$ is an end-to-end vector $\sum_i\mathbf{t_i}$, for this model? Let's assume that $N \rightarrow \infty$.</p></li>
<li><p>How do I find linear force extension relation,when a force $\mathbf{F}$ is applied to the ends of the chain? Let's assume that the force is weak.</p></li>
<li><p>Can anyone point out useful literature?</p></li>
</ol>
| 8,657 |
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] |
<p>My test paper asked me which way a dipole should be orientated in an electric field to minimize its potential energy. My answer was that the dipole should lie parallel to the electric field with the positive end of the dipole pointing in the direction of the electric field because that way, the positive end would be closer to the negative "attracting" of the field, and similarly the negative end of the dipole would be closer to the positive side of the field (i.e. the side from which the electric field is coming). Is this the right way of thinking about it? </p>
| 8,658 |
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] |
<p>In the book "Kinetic theory in the expanding Universe" (J. Bernstein, 1988, Camb. Univ. Press), it was stated that </p>
<blockquote>
<p>"for nonstationary Robertson-Walker
matrixes [sic] there is no spacelike
Killing vector."</p>
</blockquote>
<p>(page 6, footnote.)</p>
<p>But we know this is not true, since one can see that the generators of spatial translations/rotations are manifestly space-like. (For example, see R. Maartens and S.D. Maharaj, Class. Quantum Grav. 3 (1986) 1005-1011, equation (1.7)).</p>
<p>Was the author of the book wrong, or was it a slip of the hand, where "spacelike" should have been "timelike" (but that would amount to tautology anyway, since "nonstationary" is defined in terms of the absence of a time-like Killing vector).</p>
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] |
<p>Given: Law of Conservation of Angular Momentum.</p>
<ul>
<li>Reverse spinning with dense atmosphere (92 times > Earth & CO2 dominant sulphur based).</li>
<li>Surface same degree of aging all over.</li>
<li>Hypothetical large impact is not a sufficient answer.</li>
</ul>
<p>Assuming any object large enough to alter a planets rotation or even orbit would likely destroy most of its shape, yet Venus has retained a spherical property with a seemingly flat, even terrain indicating no volcanoes,and few if any visible meteor impacts. It would be fragmented and dispersed for billions of years. Even the question of what meteor, comet, asteroid composition could survive traveling that close to the sun's temperature, radiation, electromagnetic energy, solar flares, or gravity to equal a mass reactionary change as to alter it's spin.</p>
| 231 |
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] |
<p>Critical point is the transition temperature of a second order phase transition. But what does tricritical point mean? <a href="http://en.wikipedia.org/wiki/Tricritical_point#cite_note-1" rel="nofollow">WIki</a> says that a tricritical point is a point in the phase diagram of a system at which three-phase coexistence terminates. But in <a href="http://iopscience.iop.org/0301-0015/7/5/002" rel="nofollow">this</a>
paper, it seems that the meaning of tricrital is different from Wiki. </p>
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<p>I want to calculate the tensor of the moment of inertia. Consider this situation:</p>
<p><img src="http://i.stack.imgur.com/lGUw1.png" alt="situation"></p>
<p>The dot represents a points mass, in size equal to $\frac{5}{4}m$. $m$ is the mass of the homogenous circle. I'm trying to calculate the tensor of inertia. Because this is in two dimensions, all components but $I_{xx}$, $I_{yy}$, $I_{zz}$ and $I_{xy}$ are zero. ($\bar{I}$ denotes the inertia around the mass center.)</p>
<p>$I_{xx}=\bar{I}_{xx}+m_{tot}R^2=\frac{mR^2}{4}+\frac{5mR^2}{4}+(m+\frac{5}{4}m)R^2=\frac{15}{4}mR^2$</p>
<p>But this is not the right answer. The right answer is supposed to be $\frac{10}{4}mR^2$, why?</p>
<p>$I_{zz}$ and $I_{yy}$ I can get for some reason, by the above method. For those it works.</p>
<p>$I_{zz}=\frac{mR^2}{2}+\frac{5mR^2}{4}+(\frac{5}{4}+1)mR^2=4mR^2$</p>
<p>$I_{yy}=\frac{mR^2}{4}+\frac{5mR^2}{4}=\frac{3mR^2}{2}$</p>
<p>These are correct. The last one is a bit easier because the axis passes through the mass center.</p>
<p>And then there's $I_{xy}$ which I cannot figure out how to calculate since I don't know the x and y position of the point mass, so I can't use the formula $I_{xy}=md_xd_y$. How would I calculate it? The answer is supposed to be $I_{xy}=-\frac{5mR^2}{4}$.</p>
| 8,661 |
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] |
<p>When talking about the rest energy of a composite particle such as a proton, part of the rest energy is accounted for by the internal kinetic energy of its constituent quarks. But what is physically meant by the rest energy of non-composite particles such as quarks?</p>
| 8,662 |
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<p>What is the definition of "precession"? How is it applicable to abstract objects such as Spinors? I understand the mathematics, but don't understand what one means by "precession angle" etc when it applies to abstract objects such as two spins?</p>
<p>In my (naive?) view, precession is defined as the rotation of a vector $\vec{v}_1$ about another vector $v_{2}$ in 3D space, with the following constraints:</p>
<ul>
<li>The norm of $\vec{v}_1$ is an invariant.</li>
<li>The projection angle of $\vec{v}_1$ on $\vec{v}_2$ is an invariant.</li>
</ul>
<p>I am stuck after this, because I know that there must be something else that has to do with the trajectory in the plane that is always orthogonal to both vectors (the cross product part of the equation).</p>
<p>Once you fix the definition, how to generalize it to quantum spin-systems? I am having a huge conceptual problem because in my view Spinors are not vectors and I don't know how they can be treated as such when we combine them with a magnetic field vector?</p>
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<p>Can there only be a critical temperature if there is some natural unit for an observable in the model, i.e. if there is a natural scale for something? Otherwise I don't see how for a system there could be a rule how the value of $T_c$ gets actually terminated. And do this transitions vanish from the model, if one does a limit where these units get irrelevant?</p>
<p>Is it a priori arbitrary which quantity (lenght, energy, charge,...) has to have the specified unit? And/Or have there to be more such units to make up a critical temperature? Lastly, can there only be a phase transition in a system if there is an associated critical temperature $T_c$? </p>
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<p>In <a href="http://pra.aps.org/abstract/PRA/v23/i5/p2673_1" rel="nofollow">this</a> paper it is described how the turbulent kinetic energy spectrum and the <a href="http://physics.stackexchange.com/q/59788/2751">flatness</a> (a measure for intermittency) are governed by the position of the (dominant) singularities of the solutions of the dynamic equations in the complex plane, as an approach to explain intermittency for example.</p>
<p>An alternative approach to investigate the UV behavior of a turbulent system is to analyze the renormalization group flow field and look at the UV fixed point(s). A possible reason for intermittency from this point of view could be the presence of more than one UV fixed point, as alluded to for example in <a href="http://arxiv.org/abs/1012.0461" rel="nofollow">this</a> paper about renormalization group analysis of turbulent hydrodynamics.</p>
<p>My question now is: What is the relationship between complex time singularities of the solutions of the equations of motion describing a turbulent system and the UV fixed point(s) of the renormalization group flow of the same system, if any? How can these two approaches to investigate the UV behaviour of a turbulent system be brought together?</p>
| 8,665 |
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<p>This is a problem that has bothered me for a couple of weeks now, and I can't seem to wrap my head around it and understand it.</p>
<p>Let's say we have a planet with a mass of <strong>m</strong>. We also have an object of relatively small mass (so small that its gravitational field would not affect the planet), and we know that at time 0 it is at position <strong>h</strong>.</p>
<p>If we know the acceleration due to gravity (<strong>g</strong>), we can calculate the position <strong>y</strong> at time <strong>t</strong>:</p>
<p>$y = h - { g \; t^2 \over 2 } $</p>
<p>And we know that the acceleration due to gravity could be calculated:</p>
<p>$g = G { m \over y^2 }$</p>
<p>But since the acceleration depends on the position of the object relative to the planet, and the position of the object is dependent on the acceleration, this would obviously mean that the first formula won't work when we are working with displacement so large that it would change the acceleration significantly.</p>
<p>So, in essence, my question is, what formula can we use to calculate the position of an object, taking into consideration the change in acceleration due to gravity?</p>
| 8,666 |
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] |
<p>The shuttle craft "Galileo" travels at a constant velocity of $2.73*10^3$ m/s up for $34.0$ min. and then turns around to travel $1.45*10^3$ m/s down for $15.0$ min.</p>
<p>a) Find its average speed.</p>
<p>b) Find its average velocity</p>
| 8,667 |
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<p>I have this problem:</p>
<blockquote>
<p>If the constant of gravity is measured to be $g_0$ in an earth fixed
coordinate system, what is the difference $g-g_0$ where $g$ is the
real constant of gravity as measured when the earth stands still.</p>
</blockquote>
<p>The earth fixed coordinate system is rotating, so that the absolute acceleration $g$ is given by</p>
<p>$g=g_0+2\vec\omega\times\frac{d}{dt}\vec r+\vec\omega\times (\vec \omega\times \vec r)$</p>
<p>This is the Coriolis term and the Centrifugal term, the other ones disappear since earth rotates in a steady pace and does not itself accelerate.</p>
<p>I know the answer is supposed to be</p>
<p>$g-g_0\approx g_0\frac{x^2-2x}{2}\cos^2(\phi)$</p>
<p>Where $x=\frac{R \omega^2}{g_0}$. How can I come to this conclusion? My attempts so far have been to try to evaluate the expression given earlier. But I cannot for my life figure out how that yields the supposed answer.</p>
<p>(Note: I've edited the "correct" answer, multiplying what was written originally with g_0 after some of the answers were written)</p>
| 8,668 |
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<p>In some PSE questions or answers such as <a href="http://physics.stackexchange.com/questions/67037/is-it-possible-to-have-uniform-proper-acceleration-along-a-large-object-without/68733#68733">here (and comments below)</a> there appears the notion of "<i>accelerating frame</i>" or (more or less equivalently) "<i>noninertial frame</i>". </p>
<p>What's the definition of this notion?,<br>
<i>i.e.</i><br>
How are given participants (or, if you prefer, "<i>point particles</i>"$\,\!^{(*)}$) who "keep sight of each other" supposed to determine whether they (pairwise) belonged to the <b>same</b> "<i>noninertial frame</i>", or not?</p>
<p>$(*$: Cmp. the notion of "inertial frame", in distinction to "inertial coordinate system", of <a href="http://www.scholarpedia.org/article/Special_relativity:_kinematics" rel="nofollow">http://www.scholarpedia.org/article/Special_relativity:_kinematics</a><br>
<blockquote>We should, strictly speaking, differentiate between an inertial frame and an inertial coordinate system, although in sloppy practice one usually calls both IFs. An inertial frame is simply an infinite set of point particles sitting still in space relative to each other.</blockquote>$)$.</p>
<p>Follow-up:<br>
The new (follow-up) question to be asked to fully address this question has been submitted as <a href="http://physics.stackexchange.com/questions/69831/how-should-observers-determine-whether-they-can-be-described-as-being-defined-o">How should observers determine whether they can be described as being "defined on a Lorentzian manifold"?</a></p>
| 285 |
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<p>If we consider an object undergoing who has an acceleration proportional to the displacement of the object, it is going simple harmonic motion.</p>
<p>In terms of Newton's second law, this is $$ -\dfrac k mx = \dfrac{d^2 x}{dt^{2}} $$ where $k/m := \omega^2$, the frequency. </p>
<p>For an object floating because of the buoyant forces, Netwton's second law looks like $F_B - F_g = ma$. Why can we consider this SHM as they do here (for example: <a href="http://vhcc2.vhcc.edu/ph1fall9/lectures/ph_98116_981204/ph1_1130/class_notes.htm" rel="nofollow">SHM of floating objects</a>)?</p>
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<p>I'm reading some literature on mass loss in the RGB/AGB branches and so far I'm getting a lot of information regarding mass loss via dusty-winds/pulsations but almost no explanation of mass loss by 'chromosphere activity'. I asked my mentor about it and he couldn't come up with anything so I'm turning to whomever might be able to throw a few references or explanations my way.</p>
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<p>I have just got a query about how this equation works if its right.</p>
<p>We have <em>Newtonian Physics</em> saying $F=ma$,</p>
<p>According to the '<em>Mass in special relativity</em>' the mass changes according to
$$m= \dfrac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}.$$</p>
<p>So, our </p>
<p>$$F=\dfrac{m_0}{\sqrt{1-\frac{v^2}{c^2}}} \cdot \dfrac{dv}{dt}.$$</p>
<p>$v^2$ isn't constant. It is moving with an uniform acceleration. So, I find out the average velocity, </p>
<p>Since the $v=at$, Cause: $ u=0$</p>
<p>$$\dfrac{\int_{t_1}^{t_2}f(t)dt}{t_2-t_1}=v_{avg}$$</p>
<p>$$\dfrac{a(t_2^2-t_1^2)}{2(t_2-t_1)}=v_{avg}$$</p>
<p>My Force equation becomes
$$F=\dfrac{m_0}{\sqrt{1-\frac{\dfrac{a^2(t_2^2-t_1^2)^2}{4(t_2-t_1)^2}}{c^2}}} \cdot \dfrac{dv}{dt},$$ </p>
<p>or simply </p>
<p>$$\dfrac{m_0}{\sqrt{1-\frac{v_{avg}^2}{c^2}}} \cdot \dfrac{dv}{dt}.$$</p>
<p>What happens when I travel faster than light? Or equal the speed of light. My mass doesn't become '$\infty$' for sure. What will be the correction factor if my <strong>acceleration</strong> is not uniform.</p>
| 8,671 |
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<p>Suppose we have an operator $Q$ with eigenvalue $q$. Expectation value is $\langle Q \rangle$ and dispersion $D(Q) = \sqrt{\langle \left( Q - \langle Q \rangle \right)^2 \rangle} $. I want to find values for the expectation value and dispersion.</p>
<p><strong>Attempt</strong></p>
<p>Expectation value is simply the average value of the observable associated with $Q$ right? Dispersion is the variance of the observable associated with $Q$ right?</p>
<p>$$ \langle Q \rangle = \langle \psi | Q |\psi \rangle = q \langle \psi|\psi \rangle = q $$</p>
<p>$$ D(Q) = \sqrt{\langle \left( Q - \langle Q \rangle \right)^2 \rangle} = \sqrt{ \langle Q^2 -2Q \langle Q\rangle + \langle Q \rangle^2 \rangle } = \sqrt{ \langle Q^2 - 2Qq + q^2 \rangle } $$ </p>
<p>Now $\langle Q^2 \rangle = q^2 $ by applying $Q$ twice.</p>
<p>Does this mean that $$D(Q) = 0 $$?</p>
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<p>Consider a canonical ensemble of $N$ ideal gas atoms, which could have spin up or spin down. Why is it that the probability of finding the particle in a spin up state generally only involves the single partition function?</p>
<p>In a canonical ensemble, $P_i = \frac{e^{-\frac{E_i}{kT}}}{Z}$.</p>
<p>$$P_{up} = \frac{e^{-\frac{h}{kT}}}{e^{-\frac{h}{kT}}+e^{\frac{h}{kT}}} $$</p>
<p>Why do we only use the one-particle partition function here and not the $N$ particle partition function?</p>
<p>I tried this using a sample Hamiltonian:</p>
<p>$$H = \sum_{i=1}^N \frac{p_i^2}{2m} - h s_i$$</p>
<p>I got:</p>
<p>$$Z = \frac{1}{N!} \left(\frac{V}{\lambda^3} (e^{\beta h} + e^{-\beta h}) \right)^N$$, where $\lambda = \frac{h}{\sqrt{2 \pi m k_B T}}$</p>
<p>Is it possible to reproduce $P_{up}$ from the $N$-particle partition function. Can one do this using the binomial theorem, $(1+x)^n = \sum_{k=0}^n {n \choose k} x^k$?</p>
<p>I'm trying to understand how the single particle and many particle partition functions are related.</p>
| 8,673 |
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<p>The Rabi model describes a two-level system interacting via a linear coupling with a quantized harmonic oscillator, and it is described by the hamiltonian
$$
H_{\rm{Rabi}}=\hbar\omega\, a^\dagger a +\hbar\omega_0\,\sigma_3+\hbar g\,\sigma_1(a+a^\dagger). \tag1
$$
Here $[a,a^\dagger]=1$, $\sigma_i$ are the Pauli matrices on the two-level system, and $g$ represents the coupling. When deriving such a model for a physical system, one typically needs to assume that (i) there are only two atomic energy levels involved in the experiment, (ii) there is only one mode of the relevant bosonic field (e.g. the laser field inside a cavity) that's close enough to resonance to matter, (iii) the coupling is linear and that quadrupolar-like terms like $(a+a^\dagger)^2$ either don't couple or couple too weakly, and (iv) that the two-level atom has no permanent dipole moment. Under those assumptions, equation (1) follows.</p>
<p>Most physical systems, on the other hand, admit a further approximation, called the rotating-wave approximation (RWA). Here the coupling term is decomposed into slow- and fast- rotating terms, in the form
$$
\sigma_1(a+a^\dagger)=(\sigma_++\sigma_-)(a+a^\dagger)=(\sigma_+ a+\sigma_-a^\dagger)\quad+\stackrel{\rm counter-rotating\, terms}{\overbrace{(\sigma_-a+\sigma_+a^\dagger)}}.
$$
In an interaction picture, the oscillations of the terms in the first bracket, at frequencies $\omega_0$ and $\omega$, cancel out (at least approximately), whereas the so-called counter-rotating terms oscillate at frequency $\omega+\omega_0$, which is <em>very</em> high in usual experiments, so their effect is typically very small. Neglecting such terms leads to the Jaynes-Cummings hamiltonian,
$$
H_{\rm{JC}}=\hbar\omega\, a^\dagger a +\hbar\omega_0\,\sigma_3+\hbar g\,(\sigma_+ a+\sigma_-a^\dagger), \tag2
$$
which is <em>much</em> easier to handle than the full Rabi one, and which has proved to be extremely successful in describing a wide variety of different experimental systems.</p>
<hr>
<p>The rotating-wave approximation, however, tends to break down as the coupling increases. This has led to at least three different regimes beyond the weak coupling, Jaynes-Cummings region:</p>
<ul>
<li>The "strong coupling" regime at $g/\omega\lesssim0.01$</li>
<li>The "ultrastrong coupling" regime at $g/\omega\gtrsim0.1$</li>
<li>The "deep strong coupling" regime at $g/\omega\approx1$.</li>
</ul>
<p>(List taken from A. Moroz, <a href="http://dx.doi.org/10.1016/j.aop.2013.10.014" rel="nofollow"><em>Ann. Phys.</em>, in press, 2013</a>, <a href="http://arxiv.org/abs/1305.2595" rel="nofollow">arXiv:1305.2595</a>.)</p>
<p>I've seen these terms used before but I've never quite understood what they mean. <strong>What are the different characteristics of these three regimes?</strong> What physics should one expect, or what parameters are important, in each of them? Is there a specific reason to consider that $g/\omega\sim10^{-2}$ is already strong enough to drive very new physics, or is this simply a reflection of the fact that strong couplings are (very) hard to do experimentally? Why are there so many different regimes in between $g/\omega\ll1$ and $g/\omega\approx1$?</p>
| 8,674 |
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<p>I'm reading the following paper:</p>
<blockquote>
<p>Intercomparison of Bulk Aerodynamic Algorithms for the Computation of
Sea Surface Fluxes Using TOGA COARE and TAO Data</p>
</blockquote>
<p>and am having trouble working through some of the equations, I have copied these equations below:</p>
<p><img src="http://i.stack.imgur.com/ymp8m.png" alt="enter image description here"></p>
<p>Would someone be able to show me the process of how integrating (1) to (6) gives (7)?</p>
<p>Any help would be appreciated. </p>
| 8,675 |
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<p>Say I have one LED in a flashlight, it produces some light. </p>
<p>Now, if I have 3 of those LEDs in the same flashlight, <em>each</em> LED receiving the same amount of energy than the single LED was receiving in the model described above (thus producing, individually, the same amount of light), will I get (perceive) more light? Will it be brighter? (considering the 3 LEDs very close to each other, same direction, etc.)</p>
<p><strong>Quickly said</strong>: does the perceived light "sum up"?</p>
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] |
<p>Confinement of antihydrogen might help provide a future answer. <a href="http://arxiv.org/abs/1104.4982" rel="nofollow">http://arxiv.org/abs/1104.4982</a></p>
| 286 |
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<p>When we introduce minimal coupling for the Dirac spinor field, we introduce terms into the Lagrangian, by the substitution $i\frac{\partial}{\partial x^\mu}\mapsto i\frac{\partial}{\partial x^\mu}+eA_\mu$, so that the Lagrangian is invariant under arbitrary changes of phase at every point of space-time, $$\psi(x)\mapsto e^{-ieG(x)}\psi(x),\qquad A_\mu\mapsto A_\mu+\partial_\mu G(x),$$ where $G(x)$ is a scalar function.
We don't make this substitution, however, in the anti-commutator $$\left\{\psi_\xi(x),\overline{\psi_{\xi'}(x')}\right\}=\left(i\gamma^\mu\frac{\partial}{\partial x^\mu}+m\right)_{\xi\xi'}i\Delta(x-x'),$$
which, <em>it seems</em>, is therefore not invariant under the transformation $\psi(x)\mapsto e^{-ieG(x)}\psi(x)$,
$\psi(x')\mapsto e^{-ieG(x')}\psi(x')$.
Presumably the path-integral formalism doesn't care about this, but does this have consequences in subsequent derivations in the canonical approach?</p>
<p>I expect that in fussing about this I'm missing something very obvious. Am I? What is it?</p>
<p>EDIT: So it appears from the Answers, for which Thanks, that the anti-commutator given is valid for both space-like and time-like separation for the free Dirac field, and it's valid for space-like separation in QED, but it's nae valid for time-like separation in QED. Put somewhat loosely, this is OK in the canonical formalism because this anti-commutator is valid for the phase space. I'd rather like to know what a valid expression for the anti-commutator is at time-like separation in QED, but since that would, in a sense, be a solution of the theory I guess I'll have to whistle for it. I'll be grateful for Comments if this is an obviously obtuse reading of the Answers, though I ask that you consider that I would like a manifestly covariant version (so to speak, perhaps obscurely) of the canonical formalism before leaping in.</p>
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/9371/why-would-antimatter-behave-differently-via-gravity">Why would Antimatter behave differently via Gravity?</a> </p>
</blockquote>
<p>Regarding the following statement in <a href="http://www.technologyreview.com/blog/arxiv/26709/" rel="nofollow">this article</a>:</p>
<blockquote>
<p>Most important of these is whether ordinary gravity attracts or repels antimatter. In other words, does antihydrogen fall up or down?</p>
</blockquote>
<p>Is this a seriously considered hypothesis? What would be the consequences on general relativity?</p>
<p>If this is seriously studied, can you point to some not-too-cryptic studies on the (anti ;-)matter?</p>
| 286 |
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<p>How to show that if two masses($m_1$ and $m_2$) are connected($r_1<r_2$) with a string moving around a point A( circular motion), they move with same angular velocity? In this special case if $r_1=0.5 m$ and $r_2=0.9 m$, $m_1=m_2=0.15 kg$ => $ \omega = 6.9 rad/s$.</p>
<p>Picure below depicts the situation besides that you have two objects in same wire, so the other "ball" has moved to next wire nearer($r_1$) than $r_2$. </p>
<p><img src="http://i.stack.imgur.com/N4DcG.jpg" alt="picture which depicts almost the situation"></p>
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<p>According to black hole complementarity, for an external observer, the interior of the black hole is replaced with a stretched horizon at a Planck distance above where the horizon ought to be. Is this stretched horizon an end-of-space boundary with a Gibbons-York term, or does it have an interior a la fuzzball complementarity? Is fuzzball complementarity different because it has an interior according to external observers?</p>
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<p>I'm curious whether I can find the overlap $\langle q | p \rangle$ knowing only the following:</p>
<ol>
<li>$|q\rangle$ is an eigenvector of an operator $Q$ with eigenvalue $q$.</li>
<li>$|p\rangle$ is an eigenvector of an operator $P$ with eigenvalue $p$.</li>
<li>$Q$ and $P$ are Hermitian.</li>
<li>$[Q,P] = i \hbar$.</li>
</ol>
<p>I'm asking because books and references I've looked in tend to assume that $Q$ is a differential operator when viewed in the $P$-basis, then show that it satisfies the commutation relation. (I haven't read one yet that proves that the form given for $Q$ is the only possible one.) I've heard, though, that we can work purely from the hypothesis of the commutation relation and prove the properties of $Q$ and $P$ from it.</p>
| 8,680 |
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<p>There is no timelike Killing vector for FRW cosmologies. In the path integral formalism, is it possible to Wick rotate for quantum cosmology in quantum gravity? If yes, how? If no, how does one work with nonconvergent Lorentzian path integrals?</p>
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<p>In my experiment, I am filling liquid crystal between two glass plates. Nn AC voltage is applied on them. The thickness of the liquid crystal cell is around $200 \mu m$. One glass plate is with +V and another with -V. Liquid crystal is aligned perpendicular to the electric field direction. Now I am inserting a metal coated fiber in the liquid crystal cell (between the glass plate filled with liquid crystal). </p>
<ol>
<li>Is this metal coated fiber has any effect on electric field? </li>
<li>If yes, then what happens to the electric field orientation and strength. </li>
<li>Is it still transverse? </li>
</ol>
| 8,682 |
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<p>Suppose to have a chain (of size $L$) with bosons, and $\hat{a}_i^\dagger$,$\hat{a}_i$ are the associated creation and annihilation operators at site $i$. A Fock state can be written as:
\begin{equation}
| n_1 \dots n_L \rangle = \prod_{i} \frac{1}{\sqrt{n_i!}} \left( \hat{a}_i^\dagger \right)^{n_i} |\rangle
\end{equation}
where $|\rangle$ is the empty state. Now we define a new set of bosons:
\begin{align}
\hat{b}_{k} &= \frac{1}{\sqrt{L}} \sum_{j} e^{-ikj} \hat{a}_j &
\hat{b}_{k}^\dagger &= \frac{1}{\sqrt{L}} \sum_{j} e^{ikj} \hat{a}_j^\dagger
\end{align}
where $k$ are such that some boundary condition is fulfilled. Now a Fock state can be written as:
\begin{equation}
| \dots \tilde{n}_k \dots \rangle = \prod_{k} \frac{1}{\sqrt{\tilde{n}_k!}}
\left( \hat{b}_k^\dagger \right)^{\tilde{n}_k} |\rangle
\end{equation}
The question is: is there a simple formula to express or compute the scalar product
$\langle \dots \tilde{n}_k \dots | n_1 \dots n_L \rangle$? </p>
| 8,683 |
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<p>Imagine I throw a ball straight upwards with some velocity $v_1$, and filming the ball with a camera, I can estimate a velocity $v_2$ (along the same vector) after the ball has moved a distance $D$. Using the difference between $v_1$ and $v_2$, and assuming constant friction due to air, how well can I estimate the initial velocity necessary to toss the ball some height $H$?</p>
<p>For fun - provided some $v_1$, $v_2$, and $D$, can we estimate an upper-bound for the Earth escape velocity with air friction/drag? Or is there unpredictable scaling of friction with velocity?</p>
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<p>I'll be doing Introductory General Relativity and Graduate Quantum Mechanics II next semester. I still need to choose 2 (or maybe 3, but I don't want to overload too much) from the following:</p>
<ul>
<li><p>Algebraic Topology I: Sounds useful in both mathematical physics, and things like string theory, so leaning towards taking this one.</p></li>
<li><p>Number Theory: Sounds interesting, not sure if very useful though. Things like the Riemann-Zeta function will be discussed, and other topics may include elliptic curves etc.</p></li>
<li><p>Graduate Complex Analysis: My fear is that it may be too focused on proofs, so not sure how useful it'll be as far as use in physics goes. I'm already familiar with the usual complex analysis methods that physicists use, but sharpening my understanding of it can't hurt. How useful would this be to learning the sort of complex geometry stuff that seems indispensible these days (reimann surfaces and complex manifolds etc)?</p></li>
<li><p>Lie Algebras and Representation Theory: Same concern as the one with complex analysis, i.e offered by the math department and designed for math grad students, so not sure how useful it will end up being.</p></li>
<li><p>Graduate Statistical Mechanics: Haven't had an undergrad class yet so it may be a bit tough going. Also, its at the same time as the Lie Algebras class.</p></li>
</ul>
<p>I would really appreciate it if someone with experience in fields such as string theory, quantum gravity, mathematical physics etc can comment on the relative usefulness of these courses and give their recommendations on which ones to choose. I know that all these topics are potentially useful and I would have to learn them all eventually if I am serious about these fields but which ones are the most immediately useful ones in terms of progressing to the next stage.</p>
| 8,685 |
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<p>What would be the speed of a hypothethetical object created during the big bang, and that has been moving around in the universe and that is now close to the earth, so the time elapsed (from the hypothetical object's perspective) is around 6,500 years, that is the age of the universe according to some people?. </p>
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<p>What is the furthest object from which non-electromagnetic cosmic rays were detected?</p>
| 8,687 |
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<p>Say I have an ideal gas that has a known $P_1$, $P_2$, $T_1$, and $T_2$ undergoing a reversible adiabatic process. I want to find the work done so I must use $PV = RT$ to get the change in $V$, so that's $$\frac {P_1V_1}{T_1} = \frac {P_2V_2}{T_2}$$, and also $$W = \int PdV = P(V_2 - V_1)$$.</p>
<p>My problem is, these are only 2 equations and 3 unknowns. How do I solve $V_1$, $V_2$, and $W$? Also, in the second equation, is the value of $P$ equal to $P_1$ or $P_2$?</p>
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<p>If I have the following metric: </p>
<p>$$ds^2=(1-2\phi)c^2 dt^2 - (1-2 \phi)(dx^2+dy^2+dz^2)$$</p>
<p>$\phi$ being the gravitational potential with $|\phi| << 1$ everywhere. </p>
<p>How do I find a coordinate transformation to a locally inertial coordinate system to first order in $\phi$?</p>
<p>One method that I know of is writing $\phi$ as an equivalent acceleration $g\sqrt{x^2+y^2+z^2}$, and then make a coordinate transformation such that the particle is accelerating with this acceleration in the new frame. Is this correct?</p>
<p>But, more importantly, I am looking for an <strong>alternative method</strong>. E.g. Is it possible to make a coordinate transformation such that the christoffel symbols are zero? </p>
<p>How can I write any general metric in a locally inertial frame?</p>
<p>Note: I am actually studying this in an SR course which introduces GR very very briefly. But, I know the basic definitions of manifolds, such as differential forms, and tangent spaces. So, I won't mind a technical answer, but it would be great if you could talk about any terms that I am not likely to know in a couple of lines. (or I can find it out for myself, if it is too much hardwork for you). I have studied GR uptil the geodesic equation. </p>
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<p>Suppose we have a helicopter that is able to stay stationary in flight for extended periods of time. If such a helicopter stayed at point A in the sky for 12 hours straight, would it reach the other side of the globe?</p>
| 162 |
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<p>The movement of several metronomes <a href="http://www.youtube.com/watch?v=Aaxw4zbULMs" rel="nofollow">can be synchronised</a> when a movable floor is utilised which couples the movement of the different metronomes.</p>
<p>Is it possible to apply this sort of synchronisation to several swings occupied by people (the ones you have on children playgrounds)? </p>
<p>I visualise this as several swings connected to a rigid platform that is free to move parallel to the ground. I assume that the length of each swing line ($L$) is the same and that the length of the swing line is the only factor that influences the swing period ($T$) according to:</p>
<p>$$T = 2 \cdot \pi \cdot \sqrt\frac{L}{g}$$</p>
<p>I understand that the metronome is driven by a wound spring and that this part is not present in a swing. People can move their c.o.g. back and forth during the swing, emulating the effect of the spring.</p>
<p>Can the principles present in the metronome sync be carried over to swing sync such that swings start swaying together after a certain amount of time?<br>
Are my assumptions correct? Which additional assumptions do I need to make this work?</p>
| 8,690 |
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/10852/how-are-these-balls-reflected-after-they-hit-each-other">How are these balls reflected after they hit each other?</a> </p>
</blockquote>
<p>I was wondering what sort of physics equations would I need in order to build a top down billiards game? I tried using Box2D (a 2D physics engine for games) but it has issues with objects going through other objects when the velocity is too fast. So I decided to do all the physics by scratch. </p>
<p>So, what would be all the physics I need to create a top down 2D billiards game?</p>
<p>Thanks!</p>
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<p>I'm a retired Physics Professor, but I admit I'm puzzled by this... </p>
<p>Consider two loops of wire, 2 small dipoles B and C , with a common axis z (facing each other) and (say) 30 cm apart B to C. At the speed of light, information (including a change in magnetic field) will require about 1 nanosecond to travel from C to B.</p>
<ol>
<li>Have the current on in coil B for some period of time at the start, so the B-fields at C is established in the +z-direction.</li>
<li><p>Turn loop B off rapidly (fall time < 0.3 ns, say) at the same time that a current in loop C is turned ON (rapidly, rise time <0.3ns, and current in opposite sense with respect to the previous current in loop B).</p></li>
<li><p>In this way, as the current is turned on in loop C, it is immersed in the field from loop B and therefore it receives an impulse to the right, in the +z-direction. </p></li>
</ol>
<p>However, loop B will be "off" (and open so no effective eddy currents) when the "return" field from loop C arrives.</p>
<p><strong>Thus, loop C (which is free to move) will experience a force giving it momentum in the +z direction (to the right), whereas loop B will not experience a force to the left. It seems that Newton's Third Law is violated.</strong><br>
(The question can also be posed in momentum terms, but I chose to consider forces and the Third Law. )</p>
| 8,691 |
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<p>At the Advanced Photon Source, they use two accelerators before injecting the electrons into the large storage ring. Is the addition of particles to the storage ring done in "batches" (however small/short they may be), or continuously? </p>
<p>By a "batch", I'm thinking where the LINAC would throw however many electrons into the booster ring, which would then accelerate them all together, then dump them all into the storage ring when they're at the appropriate energy.</p>
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<p>After taking a basic signals & systems class and learning about the frequency domain, I started wondering:</p>
<h3>How the heck do scientists still communicate with Voyagers I and II??</h3>
<p> <br>
Do they send/receive signals in a frequency that is otherwise unusually silent? If not, then how do they send and receive faint signals from something <em>10 billion</em> miles away, when the spacecraft has so little energy and where it seems practically impossible to aim everything 100% correctly (since things are so distant and moving at the same time)?</p>
<p>(I wasn't sure what to tag this, so please retag as appropriate, thanks!)</p>
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] |
<p>Material density is given by $ \rho =m/V$, where $m$ is mass and $V$ is volume.
Again number density given by $n=N/V$, where $N$ is the total number of particle. How can I calculate number density $n$ from material density $ \rho $.</p>
| 8,694 |
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<p>I haven't ever studied fluid dynamics before and may mix something here, so please, be patient :). </p>
<p>Given flow potential of the form (homogeneus flow over a dipole): </p>
<p>$$ \phi = u_\infty x -\frac{M}{2\pi} \frac{x}{x^2 + y^2} $$</p>
<p>how do I calculate pressure field? I know the answer is like below, and it's derived using Bernoulli's principle. I just don't know how to get there analytically.</p>
<p><img src="http://i.stack.imgur.com/NI2t9.jpg" alt="enter image description here"></p>
<p>In my materials the answer is:</p>
<p>$$ C_p = \frac{p-p_\infty}{\frac{1}{2} \rho u_\infty^2} = 1 - \left( \frac{u}{u_\infty}\right)^2$$</p>
<p>but I don't understand where it comes from.</p>
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] |
<p>Why or when does it occur in a circuit? What does it imply when you speak of a voltage drop across a resistor? (Obviously, it probably means that the current's voltage before the resistor is higher than the voltage after the resistor, but why does this drop occur?)</p>
| 8,696 |
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<p>If electric field lines cannot terminate in empty space, in the simple example of two equal charges what happens to the line starting from one of the charges toward the other in the middle? </p>
| 8,697 |
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] |
<p>I know this probably varies quite a bit from place to place on earth. But just some rough estimates: if I were to pull power via multiple antennae tuned to a variety of different frequencies, how much "ambient" power could I draw from the atmosphere? Perhaps I'm not asking the right question, but I'm just trying to understand how much unused energy is floating around me right now and if I could use it to say, recharge batteries slowly without an active power source.</p>
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<p>Could anyone help me work through the following set of equations:</p>
<p><img src="http://i.stack.imgur.com/LVAjt.png" alt="enter image description here"></p>
<p>I found these online at</p>
<p><a href="http://marian.fsik.cvut.cz/~bodnar/PragueSum_2012/Staquet_1-2.pdf" rel="nofollow">http://marian.fsik.cvut.cz/~bodnar/PragueSum_2012/Staquet_1-2.pdf</a></p>
<p>and I'm trying to work through them. I get the basics from this i.e. that if a water particle moves vertically it will be subjected to a buoyancy force due to it being surrounded by water of different density. However, I don't understand how the solution has worked i.e. how they went from one stage to the next. Could anyone provide more information about how this solution works? </p>
<p>My main aim here is to figure out how the Brunt vaisala buoyancy frequency is derived. </p>
| 8,699 |
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<p>I am on my way to a <a href="http://en.wikipedia.org/wiki/Shimla" rel="nofollow">shimla</a>, and as it is one of the coldest places of India.</p>
<p>Previously I lived in a warm environment of <a href="http://en.wikipedia.org/wiki/South_India" rel="nofollow">southern india</a>. What would be the correct way to live in a cold environment? I mean to say that would keeping our body warm every time will prevent us from loosing temperature. Or no expenditure of energy would be better?</p>
| 8,700 |
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] |
<p>Why 21cm line observations is more helpful compared to other radiation?
Is it only because of its abundance in whole universe or anything else?</p>
| 8,701 |
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<p>Whenever I add milk to my morning coffee I often enjoy watching the patterns which are created. These patterns have a striking resemblance to certain fractals and my question is, "Why?" Oh dear, that is never a good question, so let's try "Why shouldn't they?"</p>
<p>The obvious observations are that the water is very hot when the milk is added, so we expect the "coffee particles" (non-milk part) to have a higher velocity relative to the "milk particles". Secondly, the coffee part, having been recently stirred, is often still rotating (clockwise in my case). Finally, the image we observe is a projection of some distinct portion of a "top layer" of the milk and coffee mixture.</p>
<p>Add diffusion into the mix and it really seems like some crazy stuff should go down! But I'm afraid I'm not satisfied. Why physics.SE... why? </p>
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] |
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