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<p>A molecule consists of two atoms whose centers are located at $\mathbf{r}_1$ and $\mathbf{r}_2$ respectively. The atoms are connected by a bond that can be approximated by a
harmonic spring, so that its energy as a function of the separation between the atoms $\mathbf{r}=\mathbf{r}_1-\mathbf{r}_2$
is $$U(r) = (akTr^2)/2$$</p>
<p>Assuming that the molecule lives in one dimensions, what will be the overdamped <a href="http://en.wikipedia.org/wiki/Langevin_equation" rel="nofollow">Langevin equation</a>(s) for the motion of the molecule?</p>
| 4,551 |
<p>I'm having some trouble with successfully working out a rotation about the $z$-axis on the <a href="http://en.wikipedia.org/wiki/Bloch_sphere" rel="nofollow">Bloch sphere</a>.
Now, I know how this is performed, in principle.
A rotation of the Bloch-sphere around an axis $\boldsymbol n$ by an angle $\theta$ is given by
$$ R_{\boldsymbol n}(\theta)=e^{-i\theta \boldsymbol \sigma\cdot \boldsymbol n/2} $$
where $\boldsymbol \sigma$ is the vector of Pauli-matrices.</p>
<p>So for example if I start in \begin{pmatrix}
1 \\
0 \\
\end{pmatrix}</p>
<p>And I want to rotate by pi/2 around the x-axis, I simply compute the product with </p>
<p>\begin{pmatrix}
\frac{1}{\sqrt{2}} & \frac{-i}{\sqrt{2}} \\
\frac{-i}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>And I end up with
\begin{pmatrix}
\frac{1}{\sqrt{2}} \\
\frac{-i}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>However, now I want to rotate this around the z-axis, by an angle theta. Now from what I can tell this simply corresponds to the matrix multiplication with
\begin{pmatrix}
e^{\frac{-i\theta}{2}} & 0 \\
0 & e^{\frac{i\theta}{2}} \\
\end{pmatrix}</p>
<p>so that I end up with the vector</p>
<p>\begin{pmatrix}
\frac{e^{\frac{-i\theta}{2}}}{\sqrt{2}} \\
\frac{-ie^{\frac{i\theta}{2}}}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>However, here things go wrong. For example, I know that if I rotate by $2\pi$, I should end up back at the same spot, but instead I end up at
\begin{pmatrix}
\frac{-1}{\sqrt{2}} \\
\frac{i}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>which is not correct. Could someone point out the obvious error?</p>
| 4,552 |
<p>I am considering the cathode ray tube of the set up, when the cathode rays were discovered</p>
<p>Voltage = Very High<br />
Gas = any<br />
Atmospheric Pressure = We change</p>
<p>(In the following example i am just changing the atmospheric pressure everything else is kept same)</p>
<p>At <br />
1 atmospheric pressure (atm) -> Tube Does not glow<br />
0.1 atm -> The whole tube lightens<br />
0.01 atm -> The tube glows at the anode end (Glowing is shown as there is a detector coating of ZnS)</p>
<p>[Note: I don't have this set-up this is just taken by me from theory]</p>
<p>My Question: why when i am just reducing the atm from 1 to 0.01 first it is not glowing then it glows completely and after that it glow just at one end. Why so?</p>
<p>[I am asking this question here because on chemistry forum i was suggested by someone to post it here too as it was related to plasma and people over here could help me better. <a href="http://chemistry.stackexchange.com/questions/8632/cathode-ray-tube">Link</a> to my question on chemistry forum]</p>
| 4,553 |
<p>On pp 103 - 105 of <em>The Character of Physical Law</em>, Feynman draws this diagram to demonstrate that invariance under spatial translation leads to conservation of momentum:</p>
<p><img src="http://i.stack.imgur.com/BrYgE.jpg" alt="enter image description here"></p>
<p>To paraphrase Feynman's argument (if I understand it correctly), a particle's trajectory is the path AB. Space is horizontal; time vertical. </p>
<p>Because of spatial translation symmetry, the path CD has the same action as AB. Because AB has stationary action, ACDB has the same action as well.</p>
<p>That means the action of AC and BD are the same. (Note that they are traversed in opposite directions on the path ACDB.) This is a conserved quantity, and it turns out to be the momentum.</p>
<p>My question is about the meaning of the action of AC and BD. These paths aren't physical trajectories; they represent infinite velocity. I tried thinking of the trajectory as if the velocity, as a function of time, has two delta functions in it. However, because the Lagrangian depends on $v^2$, I think this leads to infinite action for the horizontal segments.</p>
<p>Mathematically, I see that the symmetry here implies $\frac{\partial L}{\partial x} = 0$. Least action implies $\frac{\partial L}{\partial x} = \frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial \dot{x}}$. Combining these shows that the momentum $\frac{\partial L}{\partial \dot{x}}$ is constant, but I don't quite understand the connection to the picture.</p>
<p>Also, Feynman doesn't describe how he knows the conserved quantity is the momentum. Is there a way to get this from the picture? Finally, if momentum is being conserved, why isn't the trajectory a straight line?</p>
| 4,554 |
<p>Imagine a vertical pipe (both ends opened) in the water. Drop several ping-pong balls into pipe and cover them with a cylinder. When you have enough balls, the cylinder will float. Now start adding weight into the top of a cylinder, and simultaneously start adding ping-pong balls via the bottom of pipe, to compensate the increasing weight. </p>
<p><img src="http://i.stack.imgur.com/Y3ZOT.jpg" alt="enter image description here"></p>
<p>At the some weight (and balls columng height) the topmost row of balls start crunching due the buoyancy pressure. <a href="http://physics.stackexchange.com/questions/8846/how-deep-in-the-ocean-can-a-ping-pong-ball-go-before-it-collapses-due-to-pressur">In this question</a> @mms <a href="http://physics.stackexchange.com/questions/8846/how-deep-in-the-ocean-can-a-ping-pong-ball-go-before-it-collapses-due-to-pressur/8851#8851">answered</a> than one ping-pong ball can withstand 3 atmosphere pressure.</p>
<p>The question is: how to approximate the maximum heigh of ball column (or maximum weight is possible float) for the pipe radius "R" before the topmost row of balls start crunching?</p>
<p>Or, maybe will start crunching not the topmost row, but somewhere else because the sum of buoyancy pressure (from the balls bellow) and water pressure will be more the 3atm. How to determine?</p>
| 4,555 |
<p>My 8yo son is in the Cub Scouts.</p>
<p>He has a pinewood derby coming up next month and I would like to take this project and turn it into a fun, physics lesson for him. </p>
<p>For those not familiar, a pinewood derby is where you shape a block of wood into a car (or truck, or where ever your imagination leads you) and race it on a track against other cars.</p>
<p>The track looks something like this (not to scale):
<img src="http://i.stack.imgur.com/mo6UI.jpg" alt="Pinewood Derby"></p>
<p>The black curve represents the track. The peculiar, red triangle with wheels is the car. (<a href="http://scouting.org/scoutsource/CubScouts/Cub%20Scouts/ThingsToDo/PineDesign.aspx" rel="nofollow">Click this link</a> to see the various options for the block of wood.)</p>
<p>So, a few talking points that come to mind are as follows:</p>
<ol>
<li><strong>Gravity.</strong> Obviously w/o this the car would go nowhere when released. </li>
<li><strong>Friction.</strong> All wheels come with metal axles. We are allowed to use powered graphite to reduce the friction and make the car move quicker.</li>
<li><strong>Weight.</strong> The heaver it is, the faster it will move. However, there is a 5oz max weight the car can reach. Should the weight of the car be evenly distributed to maximize speed?</li>
<li><strong>Design.</strong> I imagine the design of the car is important to reduce drag...are there any designs from the previous link you would pick regarding that?</li>
</ol>
<p>Any thoughts on how to elaborate on the items above?</p>
<p>Is there anything I haven't listed that would be helpful to talk about?</p>
| 4,556 |
<p>When <code>taxpayers</code> pay <code>money</code> for expensive research (irrespective of the <code>partition-function</code> wheither a few projects worth <code>megabucks</code> [<code>M$</code>] or many smaller cheaper experiments), should the <code>raw data</code>/<code>designs</code>/... that result from it be <code>gratis</code> (as in linux), <code>opensource</code> (as in the source of beer) or even licensefree?</p>
<p>(the question is not intended as a binary one: it is more ethics of modern physics funding, assume it is possible)</p>
<p>this would also more easily allow people with or without diplomes to try processing the scientific data...</p>
<p>(<code>upvotes</code> if you can present your argument <code>completely formalized</code> in <code>deontologic</code> <code>Kripke semantics</code>)</p>
| 4,557 |
<p>A <a href="http://en.wikipedia.org/wiki/Vortex_tube">Vortex Tube</a> takes a pressurized input stream, most typically of a gas, and creates two output streams with a temperature differential. <a href="http://www.exair.com/Cultures/en-US/Primary+Navigation/Products/Vortex+Tubes+and+Spot+Cooling/Vortex+Tubes/A+Phenomenon+of+Physics">Apparently, it has been described as a Maxwell's Demon</a>.</p>
<p>Both linked sources are scarce with information about how and why this works. Now, I have two questions:</p>
<ul>
<li><p>Why does it work, specifically why should the situation in the vortex lead to a transfer of thermal energy from the inner stream to the outer one?</p></li>
<li><p>How efficient can it be? </p></li>
<li><p>How do you define the efficiency of a device that may be closer to Maxwell's Demon than to a heat pump? My feeling is that any analysis should not only take into account the sum of input energy (thermal and mechanical energy instream) and sum output (thermal energies and pressures of both gas streams), but also the Temperature differential that is created - since that contains an ability to create work.*</p></li>
<li><p>If course it's pointless to create heat from high grade 8mech.) energy to transform it back to mech. energy - but it gives an idea on the worth of the output.</p></li>
</ul>
| 316 |
<p>Ive read a few courses on <strong>statistical mechanics</strong>, and while their textual explanations and example choices differ, the flow of information from microscopy to macroscopy seems the same, and reading between the lines you can see some mathematical construct. Has statistical mechanics been formalized in the sense that say analysis has been formalized (<em>down to quantifiers, sets, functions,...</em>) more rigorously? Where can one find a <strong>formal axiomatic approach</strong> to statistical mechanics as opposed to an introductory descriptory approach?</p>
| 4,558 |
<p>Please move this if it's not in the right location.</p>
<p>I'm looking for the name of a device that I frequently see in many scenarios, specifically that of an office/library which can be described as having multiple rings that rotate in various directions. I was thinking it was a gyroscope or perhaps a celestial globe, but something tells me that it's not quite what I'm looking for. I recall that there is a movie production company which uses this device as their symbolic figure of their logo.</p>
| 4,559 |
<p>Suppose we view fluids classically, i.e., as a collection of molecules (with some finite size) interacting via e&m and gravitational forces. Presumably we model fluids as continuous objects that satisfy some differential equation. What mathematical result says that modeling fluids as continuous objects can accurately predict the discrete behavior of the particles? I don't know anything about fluid mechanics, so my initial assumption may in itself be wrong.</p>
| 187 |
<blockquote>
<p>If it takes work W to stretch a Hooke’s-law spring (F = kx) a distance d from its unstressed length, determine the extra work required to stretch it an additional distance d (Hint: draw a graph and give answer in terms of W!).</p>
</blockquote>
<p>I don't understand why the answer is not 2W since Force is proportional to x, or even how to begin using a graph to disprove why the answer is not 2W. Any help would be greatly appreciated.</p>
| 4,560 |
<p>Is it possible to reclaim nuclear waste from commercial reactors for useful purposes, if not necessarily energy production?</p>
| 4,561 |
<p>Case 1: two people wake up in spaceships accelerating at 1g. They can measure or observe anything inside the room but not outside. They couldn't determine if they were on a spaceship or on earth. If they ever communicated in the future they would be the same age. Is this correct?</p>
<p>Case 2: one person wakes up in a room on earth, another on a spaceship accelerating 1g. Same measuring restrictions. Again neither could determine if they were on a spaceship or earth. However now if they communicated in the future they would find they are different ages. Is this correct?</p>
<p>I've heard acceleration from a rocket or gravity are the same (e.g. time slows down near a black hole). But case 2 above seems there is a difference?</p>
| 4,562 |
<p>I just want a book on classical mechanics that covers the same ground as Goldstein's book but is more on the line of DJ Griffiths's Classical Electrodynamics. I mean less formal and more conversational. </p>
| 98 |
<p>In QFT we associate to each Gauge theory a continuous group of local transformations (a Gauge group), and then we require\define fermion fields to be irreducible representations belonging to the fundamental representation of this Gauge group.</p>
<ol>
<li><p>What is the <a href="http://en.wikipedia.org/wiki/Fundamental_representation" rel="nofollow">fundamental representation</a>, and why do we require fermions to be in it?</p></li>
<li><p>What does it mean for a field to <em>belong to a certain <a href="http://en.wikipedia.org/wiki/Group_representation" rel="nofollow">representation</a></em>? Is this just a way of stating that the fields are the "targets" of the Gauge transformations we introduced, meaning that they belong to the vector space where the representation of these transformations act?</p></li>
<li><p>A Gauge transformation must by definition not change the physics. This means that given any field $\psi$ we have to identify as a single physical entity all the fields that can be obtained by $\psi$ by means of any element of the Gauge group. Is the formalization of this concept the reason we require fields to belong to <a href="http://en.wikipedia.org/wiki/Irreducible_representation" rel="nofollow">irreducible</a> representations? Is there any other justification for it?</p></li>
</ol>
| 4,563 |
<p>How does one see it as obvious that</p>
<p>$$\int_S \frac{\partial A_i}{\partial x^j} dS^{ji} = \int_S\frac{1}{2}(\frac{\partial A_j}{\partial x^i} - \frac{\partial A_i}{\partial x^j})dS^{ij}$$</p>
<p>where $d S^{ij} = dx^i dx^{j*} - dx^j dx^{i*} $</p>
<p>From <a href="http://books.google.ie/books?id=X18PF4oKyrUC&lpg=PP1&pg=PA22#v=onepage&q&f=false" rel="nofollow">Landau's CToF</a>.</p>
| 4,564 |
<p>Suppose you have an 1-dimensional system with a charge distribution $\rho(x)$ (not given) moving with an speed $v(x)$ (not given), calculate the potential $\phi(x)$ and the charge distribution $\rho(x)$ in the quasistatic limit $\frac{d}{dt}=0$. </p>
<p>Hints:</p>
<p>$\frac{d^{2} \phi}{dx^{2}}=-\rho/ \varepsilon_{0}$ (Poisson equation)</p>
<p>$j=\rho v$</p>
<p>$\frac{d}{dx}(\rho v)=0$ (Continuity equation)</p>
<p>$\frac{1}{2} mv^{2}=q\phi$(Energy Conservation)</p>
<p>My attempt for solving it was:
From the energy conservation equation we get that
$$\frac{1}{v}=\sqrt{\frac{m}{2q}} \phi^{-1/2}$$
Continuity equation tells us that $j$ is constant, then
$$ \rho = \frac{j}{v}=j\sqrt{\frac{m}{2q}} \phi^{-1/2}$$
Using Laplace equation
$$-\varepsilon_{0}\frac{d^{2} \phi}{dx^{2}}=j\sqrt{\frac{m}{2q}} \phi^{-1/2}$$
Then
$$\frac{d^{2} \phi}{dx^{2}}+\frac{j}{\varepsilon_{0}}\sqrt{\frac{m}{2q}} \phi^{-1/2}=0$$
This is just an equation of the form
$$ f^{\prime\prime}+kf^{-1/2}=0$$
Multiplying by $f^{\prime}$ and integrating
$$ \int f^{\prime}f^{\prime\prime}dx+k\int f^{\prime}f^{-1/2}dx=0$$
$$ \frac{1}{2}(f^{\prime})^2+2k\sqrt{f}=0$$
$$ (f^{\prime})^2=-4k\sqrt{f}$$
$$ f^{\prime}=\sqrt{-4k} f^{1/4}$$
And here is my problem, i have the $\sqrt{-4k}$ term that in general is not real!
$$ \frac{df}{f^{1/4}}=\sqrt{-4k}dx $$
$$ \frac{4}{3} f^{3/4}=\sqrt{-4k}x +C $$
$$ f={\frac{3}{4}[\sqrt{-4k}x +C]}^{4/3} $$</p>
| 4,565 |
<p>Photons have no charge. Light is a form of electromagnetic energy.</p>
<p>All spectroscopic effects (to my knowledge) are due to changes in electron state, induced either through an interior or exterior EM (Electro-Magnetic) field. EM forces may affect that state, which in turn affects the light emitted during the change of state, e.g. the Zeeman effect, etc. </p>
<p>However, if we <strong><em>exclude</strong> all such spectroscopic phenomena</em>, and consider EM fields purely energetically on the one side, and light energy on the other, are there any know <strong>direct</strong> effects of EM fields on light itself? </p>
<p>(I'd really like to hear from physicists with hands on knowledge - and please keep all the Tags as is because I have reasons for selecting them, thx.)</p>
| 4,566 |
<p>For years I have been very fascinated by the "mystery" aspect of gravity. Functionally, we understand it perfectly for our all applications, but in my (limited to undergrad General Physics 3 quarters) understanding, we don't know WHY it exists or HOW the "pull" works. </p>
<p>I'm very sorry for what is surely trite pop-science term use, but, to provide an example of what I mean: there has to be SOME "measurable material" of gravity between say the earth and the moon -- some kind of 'graviton' (not that it needs to be a particle or anything, I have <em>zero</em> claims as to the nature of how gravity does what it does). The [butchered] saying of "pluck a flower and move the furthest moon," because gravity in theory, has an infinite range (?) and moving a flower on earth could maybe move an atom on jupiter ever so slightly (?)."</p>
<p>Anyway, similar to how we had "very good" hypotheses about the existence of higgs-boson that the LHC 99%+ confirmed, do we have any "very good" hypotheses in regards to the fundamental way how gravity does what we have long-known it to do?</p>
| 4,567 |
<p>Depending on the theories, the center of our galaxy is a super massive black hole, this is easy to accept as a truth, but what I couldn't simply devour is how the solar system is orbiting around it while not getting absorbed to the inside ? It's simple to understand how earth orbits the sun, but the black hole is something more energetic and at most pulls everything to it's center.
By looking to this image for example:
<img src="http://i.stack.imgur.com/MXn7W.jpg" alt="enter image description here"></p>
<p>If we follow the bright lines it looks like everything is really going to the true center like a vortex.
If you have any simple ways to enlighten me or any references to read I will be thankful, because sometimes I don't know what topic should I search for to find answers without posting questions like this one.</p>
<p>And also, would our galaxy run out of stars since the black hole devours them fast while they take too long to reproduce ?</p>
| 4,568 |
<p>Suppose I have plenty of food I want to heat (which will provide load) in the microwave, and one item I don't want to heat. What properties would make a material a a good shield, to reduce or prevent heating of that item? I know metal can work as a barrier in the form of a Faraday cage, but that there are also potential issues with arcing. Presumably some kind of smoothly flexible metal mesh would be a good candidate - what properties would it need to be effective? (For example, we might consider mesh spacing, wire diameter, and the choice of metal.)</p>
<p><sub>(Note: this is based on <a href="http://cooking.stackexchange.com/q/33871/1672">this question</a>, which was recently migrated over to Seasoned Advice (food and cooking), but I think that it could really use physics expertise, so this is a rephrased version, addressing the complaints I saw leading to that question's migration.)</sub></p>
| 4,569 |
<p>I'm trying to introduce myself to QFT following <a href="http://www.damtp.cam.ac.uk/user/tong/qft.html" rel="nofollow">these lectures</a> by David Tong. I've started with lecture 1 (Classical Field Theory) and I'm trying to prove that under an infinitesimal Lorentz transformation of the form</p>
<p>$$\tag{1.49} {\Lambda^\mu}_\nu={\delta^\mu}_\nu+{\omega^\mu}_\nu,$$</p>
<p>where $\omega$ is antisymmetric, the variation of the Lagrangian density $\mathcal{L}$ is</p>
<p>$$\tag{1.53} \delta\mathcal{L}=-\partial_\mu({\omega^\mu}_\nu{x}^\nu\mathcal{L}).$$</p>
<p>Using $\mathcal{L}=\mathcal{L}(\phi,\partial_\mu\phi)$, I've tried computing $\delta\mathcal{L}$ directly using</p>
<p>$$\tag{1.52} \delta\phi=-{\omega^\mu}_\nu{x}^\nu\partial_\mu\phi$$</p>
<p>[which I obtained earlier computing explicitly $\phi(x)\to\phi(\Lambda^{-1}x)$], however, I get
$$\delta\mathcal{L}=-\partial_\mu({\omega^\mu}_\nu{x}^\nu\mathcal{L})-\frac{\partial\mathcal{L}}{\partial(\partial_\mu\phi)}{\omega^\sigma}_\mu\partial_\sigma\phi$$
The extra term arises when I compute
$$\partial_\mu(\delta\phi)=-{\omega^\sigma}_\nu\left[{\delta^\nu}_\mu\partial_\sigma\phi+x^\nu\partial_{\mu\sigma}\phi\right]=-{\omega^\sigma}_\mu\partial_{\sigma}\phi-{\omega^\sigma}_\nu{x}^\nu\partial_{\mu\sigma}\phi$$</p>
<p>[because I'm assuming $\partial_\mu(\delta\phi)=\delta(\partial_\mu\phi)$]; I thought I'd get rid of it just replacing $\phi$ with $\partial_\sigma\phi$ in $(1.52)$, however $\partial_\mu(\delta\phi)=\delta(\partial_\mu\phi)$ should still hold, ain't it? I also tried using (the previous expression to) 1.27 in the lectures, namely that the derivatives of the field transform as</p>
<p>$$\tag{1.26b} \partial_\mu\phi(x)\to{(\Lambda^{-1})^\nu}_\mu\partial_\nu\phi(\Lambda^{-1}x),$$</p>
<p>but I still get (to the first order in $\omega$),</p>
<p>\begin{align}{(\Lambda^{-1})^\nu}_\mu\partial_\nu\phi(\Lambda^{-1}x)&=({\delta^\nu}_\mu-{\omega^\nu}_\mu)\partial_\nu\phi(x^\sigma-{\omega^\sigma}_\rho{x}^\rho)\\&=({\delta^\nu}_\mu-{\omega^\nu}_\mu)\left[\partial_\nu\phi(x)-{\omega^\sigma}_\rho{x}^\rho\partial_{\sigma\nu}\phi(x)\right]\\&=\partial_\mu\phi-{\omega^\sigma}_\rho{x}^\rho\partial_{\sigma\mu}\phi-{\omega^\nu}_\mu\partial_\nu\phi\end{align} </p>
<p>I'm resisting the idea that ${\omega^\nu}_\mu\partial_\nu\phi=0$, but I don't understand what I'm doing wrong.</p>
| 4,570 |
<p>In proving that the action $$S\equiv \int^{t_2}_{t_1}L(x, x',t)dt$$ has a has a stationary point $x_0$ that satisfies the following:
$$\frac{d}{dt}(\frac{\partial L}{\partial x'_0})=\frac{\partial L}{\partial x_0}$$
My textbook finds the action of $$x_a(t)\equiv x_0(t)+a\beta (t)$$ differentiated with respect a to the first order to reach the expression:
$$\frac{\partial}{\partial a} S[x_a(t)]=\int^{t_2}_{t_1}(\frac{\partial L}{\partial x_a} - \frac{d}{dt}(\frac{\partial L}{\partial x'_a}))\beta dt$$
It then says that the only way this can be 0 for all $\beta$ is if the expression in the parentheses evaluated at $a=0$ is identically equal to zero. I don't understand why we can evaluate it at 0, please could someone explain? (I would understand if the thing in the parentheses had to be 0 for all $a$ but why does been it been 0 for $a=0$ imply it is 0 for all $a$?)</p>
| 4,571 |
<p>I am looking for a device to provide variable excitation voltage (30VDC to 200VDC) to a Transducer for a variable time (10 to 20 milliseconds).</p>
<p>Can someone please advise how I could achieve this using an off the shelf product? </p>
| 4,572 |
<p>I know that if the Helmholtz free energy, $A$, is expressed as a function $A\sim A(N,V,T)$, then this function contains all thermodynamic information about the system. For instance, the pressure of the system is given by:</p>
<p>$$P(N,V,T) = -\frac{\partial A}{\partial V}\Bigg|_{n,T}$$</p>
<p>Indeed, if we imagine $N$ and $T$ are fixed, then this in effect gives us pressure as a function of volume:</p>
<p>$$P\sim f(V).$$</p>
<p>My question relates to the inverse of this equation. If we are given $P$ rather than $V$ (still with $T$ and $N$ fixed and known) then either numerically or analytically we can solve this to find $V$. But if the equation is complicated enough, <em>there maybe multiple values of $V$ for a given $P$, $T$ and $N$</em>.</p>
<p>This didn't seem too unreasonable to me (perhaps physically this represents a gas and a liquid co-existing at the same $T$, $P$ and $N$ at equilibrium), until I realised that, if we worked with the Gibbs free energy instead, and found values of $G(T,P,N)$, then in that case</p>
<p>$$V(T,P,N) = \frac{\partial G}{\partial P} \Bigg|_{N,T}$$</p>
<p>and this gives us an explicit, <em>single-valued</em> equation for $V$ as a function of $P$, $T$ and $N$ (though perhaps the inverse $P(V)$ is now multi-valued?).</p>
<p>What's going on here? One formulation of thermodynamics gives me an EOS in which there can exist multiple values of $V$ for a given $P$, and the other says I can have multiple values of $P$ for a given $V$! </p>
| 4,573 |
<p>Eq (1.137) in Negele and Orland gives the following identity for a normal-ordered operator $A(a_i^\dagger,a_i)$:</p>
<p>$$\langle \phi|A(a_i^\dagger,a_i)|\phi'\rangle=A(\phi_i^*,\phi'_i)e^{\sum \phi_i^*\phi'_i}$$</p>
<p>For the coherent (boson) states $|\phi\rangle=e^{\sum\phi_ia^\dagger_i}|0\rangle $. When I try to prove this I get a factor of 1/2 in the exponent. I'm going to take a simple example $A=a_i^\dagger a_i$ to try and find my mistake. First I define $\eta'=\sum \phi'_ia_i^\dagger$, and use the identity</p>
<p>$$a_i\eta'^n=n\phi'_i\eta'^{n-1}+\eta'^n a_i.$$</p>
<p>Then I can show</p>
<p>$$a_i|\phi'\rangle=(e^{\eta'}a_i+\phi'_ie^{\eta'})|0\rangle$$</p>
<p>One term of which kills the vacuum so I have shown</p>
<p>$$\langle \phi |a^\dagger_i a_i|\phi'\rangle=\langle 0| \phi^*_i\phi'_ie^{\eta^*}e^{\eta'}|0\rangle$$</p>
<p>Then I want to use the Baker-Campbell-Hausdorf formula. The commutator </p>
<p>\begin{equation}
[\eta^*,\eta']=[\sum\phi^*_ia_i,\sum\phi_ja^\dagger_j]=\sum[\phi^*_ia_i,\phi_i'a_i^\dagger]+\sum_{i\neq j}[\phi^*_ia_i,\phi_ja^\dagger_j]=\sum\phi_i^*\phi'_i,\qquad (1)
\end{equation}
and when you commute everything through the second term and kill the vacuum. Since this is a scalar, the BCH formula gives</p>
<p>$$\ln(e^{\eta^*}e^{\eta'})=\eta^*+\eta'+\frac{1}{2}\sum\phi_i^*\phi_i'$$</p>
<p>Rearrange the sum, exponentiate, kill some more vacuum and I get the right expression but with a factor of 1/2!</p>
<p>What am I doing wrong? My first guess is in equation (1), maybe there is some dobule-counting I don't see but you can write things like</p>
<p>$$[\sum,\sum]=[1,\sum]+[2,\sum]+...=[1,1]+[1,\sum_{\neq 1}]+[2,2]+[2,\sum_{\neq 2}]+...$$
$$=\sum[i,i]+\sum_{i\neq j}[i,j].$$</p>
| 4,574 |
<p>Can we generate a pulse , transmit it and after that can we record it's response time ?</p>
<p>I am curious because I want to know that is it possible to make a mapping device (like SLAM) which uses this technique.
I have done a little search but didn't get the satisfying result .
If any one has any idea about this or where I can get more knowledge about it please share it.</p>
| 4,575 |
<p>In the book "A Briefer History of Time" Stephen Hawking wrote:</p>
<blockquote>
<p>The unpredictable, random element comes in only when we try to
interpret the wave in terms of the positions and velocities of
particles. But maybe that is our mistake: maybe there are no particle
positions and velocities, but only waves. It is just that we try to
fit the waves to our preconceived ideas of positions and velocities.
The resulting mismatch is the cause of the apparent unpredictability.</p>
</blockquote>
<p>Are there evidences that disprove this hypothesis? </p>
<p>If true, would it eliminate most of the apparent quantum paradoxes, and necessity to <a href="http://en.wikipedia.org/wiki/Copenhagen_interpretation#Alternatives" rel="nofollow">"Shut up and calculate!"</a> for those who attempt to interpret quantum physics with common sense?</p>
<p><strong>Edit:</strong> I assume that S. Hawking is aware of Standard Model, and he considers this statement as a legitimate hypothesis. Are there evidences that prove that it's not? In other words, is it a philosophical or scientific question?</p>
| 4,576 |
<p>What happens if I charged a capacitor then i touch the 2 poles in same time?</p>
| 4,577 |
<p>This question is a follow-up to <a href="http://physics.stackexchange.com/users/2190/david-bar-moshe">David Bar Moshe</a>'s answer to my earlier question on the <a href="http://physics.stackexchange.com/questions/34990/aharonov-bohm-effect-and-flux-quantization-in-superconductors">Aharonov-Bohm effect and flux-quantization</a>. What I forgot was that it is not the <em>wavefunction</em> that must be single-valued, but rather, the <em>probability density</em> (wavefunction-squared).</p>
<p>But if that is so, how do I justify the quantization condition $m=\{\ldots,-1,0,1\ldots\}$ based on the boundary condition on the azimuthal part of spherically symmetric wavefunctions $\psi(x,y,z)\sim R(r)\Theta(\theta)\Phi(\phi)$:</p>
<p>$$\Phi(\phi)\sim e^{im\phi}$$</p>
<p>whose square (probability density) is unity, independent of $m$?</p>
| 4,578 |
<p>I would like to point to the beautiful section 4.3 (page 42) of <a href="http://www.people.fas.harvard.edu/~xiyin/253b_Lectures.pdf">these lecture notes.</a> I think this is the most educative exposition I have ever seen anywhere about Yang-Mill's beta function. What I love best about it is that it does it without using diagramatics (and its confusing combinatorics)(..though of course these are equivalent..but I find this language most comfortable..) </p>
<p>I have the following questions in relation to the above, </p>
<ul>
<li><p>In the above the author has picked out the terms quadratic in the fluctuations in equation 4.40 and evaluated the determinant and that gives the 1-loop effective action. </p>
<p>What would one do in this method if one had to go to 2-loops or higher?
What is the relationship between how many orders one keeps in the fluctuation field and how many loop result it translates into? (..if there a reference which shows going to higher loops in this method?..) </p></li>
<li><p>Can I use the method in these notes to evaluate the corrected gauge or the Fermion propagator? If someone could outline the steps.. </p>
<p>Here the author has chosen a constant and static background gauge (why?) and hence he has in 4.40 no term which is a derivative of the background gauge field left. I guess one would have to lift this restriction if one had to calculate the gauge field propagator correction. With this assumption about the background gauge field lifted I guess that one would have to then compute the $\Gamma^{1-loop}$ as defined in equation 4.41 and pick out the terms quadratic in the gauge field in it and invert that. </p></li>
<li><p>In the above the author has picked out from $\Gamma^{1-loop}$ only the terms quartic in the gauge field and and calculated the divergent contribution to it which is the shift in the gauge coupling constant. But the gauge coupling constant is also multiplying the term cubic in the gauge field and there is a 1-loop shift even there. What about that? Is there some theorem which guarantees that the beta-function derived by tacking the cubic term would have been the same? </p></li>
</ul>
<p>I guess that since even after choosing a constant and static gauge field one can track a change in the gauge coupling constant through a quartic term, it makes sense. But if one were in a theory (or in light-cone gauge!) where the gauge coupling constant were existing only in a term which has derivatives of the gauge field then I guess this choice of a background would not work. </p>
<p>I would like to know of a precise way of understanding the above. (...there is also the issue of whether the 1-loop effective action done this way can throw up terms that were removed by a gauge choice..and then what would one do..) </p>
| 4,579 |
<p>I've looked in and out the forum, and found no precise definition of the meaning of <a href="http://en.wikipedia.org/wiki/Fine-tuning" rel="nofollow">fine-tuning</a> in physics.</p>
<p><strong>QUESTION</strong></p>
<p>Is it possible to give a precise definition of fine-tuning?</p>
<p>Of course, I guess most of us understand the empirical meaning of the phrase... but it seem so ethereal, that's the reason behind my question.</p>
| 4,580 |
<p>I've come across a problem with finding the energy stored in time/frequency electric field. In space/time we have (taking $\epsilon = 1$)</p>
<p>$$ Energy = \frac{1}{2} \int_V |\mathbf{E}(\mathbf{x},t)|^2 \;d^3x $$ </p>
<p>But, I presume that the formula is different for a frequency-dependent electric field. I've searched Griffiths and Jackson but can't quite find what I'm looking for...</p>
<p>I've also tried to Fourier transform my expression for the electric field back to space/time, but my electric field is a fairly gruesome expression - I couldn't FT it easily. I was hoping to compute the energy from $E(\mathbf{x},\omega)$ via computational integral, once I find an expression for the energy.</p>
| 4,581 |
<p>I was watching a youtube video the other day where an economist said that he challenged his physics professor on this question back when he was in school. His professor said each scenario is the same, while he said that they are different, and he said he supplied a proof showing otherwise.</p>
<p>He didn't say whether or not the cars are the same mass, but I assumed they were. To state it more clearly, in the first instance each car is traveling at 50mph in the opposite direction and they collide with each other. In the second scenario, a car travels at 100 mph and crashes into a brick wall. Which one is "worse"?</p>
<p>When I first heard it, I thought, "of course they're the same!" But then I took a step back and thought about it again. It seems like in the first scenario the total energy of the system is the KE of the two cars, or $\frac{1}{2}mv^2 + \frac{1}{2}mv^2 = mv^2$. In the second scenario, it's the KE of the car plus wall, which is $\frac{1}{2}m(2v)^2 + 0 = 2mv^2$. So the car crashing into the wall has to absorb (and dissipate via heat) twice as much energy, so crashing into the wall is in fact worse.</p>
<p>Is this correct?</p>
<p>To clarify, I'm not concerned with the difference between a wall and a car, and I don't think that's what the question is getting at. Imagine instead that in the second scenario, a car is crashing at 100mph into the same car sitting there at 0mph (with it's brakes on of course). First scenario is the same, two of the same cars going 50mph in opposite directions collide. Are those two situations identical?</p>
| 58 |
<p>Are all <a href="http://en.wikipedia.org/wiki/Wave" rel="nofollow">waves</a> in the universe the same as <a href="http://en.wikipedia.org/wiki/Electromagnetic_waves" rel="nofollow">electromagnetic waves</a>?</p>
<p>Basically, my question arises from an equation I found in my chemistry textbook:</p>
<p>$$\lambda \nu ~=~ c.$$</p>
<p>This states that the wavelength (distance from crest to crest) times the frequency (amount of times the wave passes the center point) equals the speed of light. Now, I know this applies in a vacuum and that the speed of light changes based on density. However, does this apply to all waves? If so, does this apply to a wave in water?</p>
<p>It seems as though it should. You have a high frequency of light that is incredibly high compared to water, but you have a incredibly small wavelength which causes that value to be lower. In the case of water, if you considered only the wavelength, the value would be too high, but if you also consider that the frequency is going to be orders of magnitude lower than light, you can see where I might arrive at this conclusion.</p>
<p>If we measure the crest of a <a href="http://en.wikipedia.org/wiki/Surface_wave" rel="nofollow">wave</a> of water and the frequency of that wave (I assume from the surface of the body of water) and consider the density of the water in our calculation (as some other variable that is normally used when calculating this), would the result also be the speed of light? In addition, if water was within a vacuum and we were to create a wave, how would this react? If we could create a wave in water in this vacuum, would our values reflect $c$ or a variation of $c$ based on the density of the water?</p>
<p>If $\lambda \nu ~=~ c$ is valid for all waves, what other attributes must be supplied within the equation to make the math work out to give the correct answer of $c$?</p>
| 4,582 |
<p>I'm creating a simple astronomy simulator that should use Newtonian physics to simulate movement of plants in a system (or any objects, for that matter). All the bodies are circles in an Euclidean plane, that have properties such as position, velocity, mass, radius and the resultant force.</p>
<p>I want to update the universe in small time steps, usually a few milliseconds, but I'm not sure how to correctly calculate the changes in position.</p>
<p>The force is simple: <code>fr = sum(G * body.m * bodyi.m / dist(body, bodyi)^2)</code>.</p>
<p>But how do I go on from there?</p>
<p>I could do this:</p>
<pre><code>a = Fr/body.m
v += a*dt
position += v*dt
</code></pre>
<p>But that would, of course, be false. Maybe if I added <code>0.5</code> as a factor in position calculation?</p>
| 4,583 |
<p>We know that space-time dimensions are 3+1 macroscopically, but what if 2+2?
Obviously it is tough to imagine two time dimensions, but mathematically we can always imagine as either having two parameters $t_1$ and $t_2$ or else in Lorentz matrix
$$\eta_{00} = \eta_{11} = -1$$ and, $$\eta_{22} = \eta_{33} = 1.$$</p>
<p>Is there any physical reason for not taking this, like the norms become negative or something else? </p>
| 4,584 |
<p>Suppose there are two electrons in an atom with $s_1 = \frac{1}{2}$, $l_1 = 1$ and $s_2 = \frac{1}{2}$, $l_2 = 1$. Hence the total $S$ (of the atom) may be +1 or 0. And total $L$ is either $+2$, $+1$ or $0$.</p>
<p>Now If we consider </p>
<p>$$\begin{align}
S=1,L=2 &\to 2S+1=3; J=3,2,1\\
S=0,L=2 &\to 2S+1=1; J=2\\
S=1,L=1 &\to 2S+1=3; J=2,1,0\\
S=0,L=1 &\to 2S+1=1; J=1\\
S=1,L=0 &\to 2S+1=3; J=1\end{align}$$</p>
<p>But the last one does not show that $2S+1$ is multiplicity as it has only one $J$ value. Where am I making a mistake?</p>
| 4,585 |
<p>The question I have in mind is: <strong>If we place a conductor (arbitrary shape) of total charge zero in a uniform external electric field $\textbf{E}_0$, does it experience any net force? Why (not)?</strong></p>
<p>Now I will discuss the context of the question. I am working on Griffiths <em>Introduction to Electrodynamics, Fourth Edition</em>, p.112 Problem 2.59 (<strong>not homework problem</strong>, though). it says,</p>
<blockquote>
<p>Prove or disprove (with a counterexample) the following</p>
<p>Theorem: Suppose a conductor carrying a net charge $Q$, when placed in
an external electric field $\textbf{E}_e$, experiences a force
$\textbf{F}$; if the external field is now reversed ($\textbf{E}_e \to
- \textbf{E}_e$), the force also reverses ($\textbf{F} \to -\textbf{F}$).</p>
<p>What if we stipulate that the external field is <em>uniform</em>?</p>
</blockquote>
<p>In general this is obviously not true. I will first <strong>limit myself to the case of $Q=0$</strong>.</p>
<p>One approach: when $\textbf{E}$ is reversed, the surface charged distribution $\sigma$ is also reversed (to cancel $\textbf{E}$), so the electrostatic pressure at every point, $\frac{1}{2\epsilon_0} \sigma^2\, \hat{\textbf{n}}$ stays the same. Consequently, $\textbf{F}$ stays the same rather than flips sign.</p>
<p>Another approach: there is an intuitive counterexample. A conductor is generally attracted to a point charge nearby; if the sign of the point charge is flipped, the conductor is still attracted rather than repulsed.</p>
<p>So the first question is easy, and the interesting one is "<strong>What if we stipulate that the external field is <em>uniform</em>?</strong>" I suspect that in a uniform external field the net force is zero, so that $\textbf{F} = 0 = -\textbf{F}$, but I can't think of a way to prove or disprove it.</p>
| 4,586 |
<p><a href="http://physics.stackexchange.com/q/27939/2451">Here</a> and <a href="http://physics.stackexchange.com/q/28181/2451">here</a> it states that water is at its highest density around $4^\circ$ Celsius. I know very little physics and a Google search has left me without an answer. I am teaching an <a href="http://en.wikipedia.org/wiki/Ordinary_differential_equation" rel="nofollow">ODE</a> class in the math department. I have a student that heard the above stated in a physics course. She is wondering whether this is an appropriate project for my class. So, does this fact come from some differential equations? </p>
| 4,587 |
<blockquote>
<p>I have a pot with water of mass $m$ and it is heated by a stove
element of temperature $T_E$ and with a surface area of $A$. The
water starts at temperature $T_W > 0^\circ\, C$.</p>
<p>How long would it take to heat up this water to a final temperature of
$T_F$ ($T_W<T_F < 100^\circ \, C$)? Metal of the pot is negligible.</p>
</blockquote>
<p>The heat travels with convection in the water, presumably. I was trying to figure out a solution to this problem, but I am unsure as to what formula to use. </p>
<p>Would the answer change if someone is constantly stirring?</p>
| 4,588 |
<p>$$E_{\mathrm{ms}} = \frac{1}{2}\mu_0 \int_V \mathbf{M} \cdot \mathbf{H}_{\mathrm{ms}} d^3 r$$</p>
<p>I can't understand this formula, what is the magnetostatic stored potential energy?! What does it show?
Does it explain anything relative to magnetization?</p>
| 4,589 |
<p>I try to understand constructing of Hamiltonian mechanics with constraints. I decided to start with the simple case: free relativistic particle. I've constructed hamiltonian with constraint:</p>
<p>$$S=-m\int d\tau \sqrt{\dot x_{\nu}\dot x^{\nu}}$$</p>
<p>$\phi=p_{\mu}p^{\mu}-m^2=0$ $-$ <a href="http://en.wikipedia.org/wiki/First_class_constraint" rel="nofollow">first class constraint</a>.</p>
<p>Then $$H=H_{0}+\lambda \phi=\lambda \phi.$$ </p>
<p><strong>So, I want to show that I can obtain from this Hamiltonian the same equation of motion, as obtained from Lagrangian.</strong></p>
<p>But the problem is that I'm not sure what to do with $\lambda=\lambda(q,p)$. I tried the following thing:</p>
<p>$\dot x_{\mu}=\{x_{\mu},\lambda \phi\}=\{x_{\mu},\lambda p^2\}-m^2\{x_{\mu},\lambda\}=\lambda\{x_{\mu},p^2\}+p^2\{x_{\mu},\lambda\}-m^2\{x_{\mu},\lambda\}=2\lambda \eta_{\mu b} p^b+p^2\{x_{\mu},\lambda\}-m^2\{x_{\mu},\lambda\}=2\lambda \eta_{\mu b} p^b+p^2\frac{\partial \lambda}{\partial p^{\mu}}-m^2\frac{\partial \lambda}{\partial p^{\mu}}$</p>
<p>$\dot \lambda=\{\lambda, \lambda \phi \}=\{\lambda,\lambda p^2\}-m^2\{\lambda,\lambda\}=\lambda\{\lambda,p^2\}+p^2\{\lambda,p^2\}=2\lambda\eta_{ak}p^{a}\frac{\partial \lambda}{\partial x^{k}}$</p>
<p>$\dot p_{\mu}=\{p_{\mu},\lambda p^{2}-m^2\lambda \}=p^{2}\{p_{\mu},\lambda\}-m^2\{p_{\mu},\lambda\}=-p^{2}\frac{\partial \lambda}{\partial x^{\mu}}+m^2\frac{\partial \lambda}{\partial x^{\mu}}$</p>
<p>If we recall that $p^2-m^2=0$, then we get from the third equation: $\dot p=0$, and from the first: $\dot x_{\mu}=2\lambda\eta_{ak}p^{a}$.</p>
<p>So we have </p>
<p>1) $\dot x_{\mu}=2\lambda\eta_{\mu b}p^{b}$</p>
<p>2) $\dot \lambda=2\lambda\eta_{ak}p^{a}\frac{\partial \lambda}{\partial x^{k}}$</p>
<p>3) $\dot p=0$</p>
<p><em>But I dont know what to do next.</em> Can you help me?</p>
| 4,590 |
<p>Let's have potential
$$
U(r) = -U_{0}e^{-\frac{r}{a}}.
$$
I need to find energy levels for particles moving in this field (for an arbitrary values of orbital number $l$). This task isn't exactly solvable, so I need some method which can help to find approximate energy levels.</p>
<p>What to do?</p>
<p>I reduced the Schrodinger equation to the form (with normalized $r \to \frac{r}{a}$ and $\Psi (r, \varphi , \theta ) = \kappa e^{-\beta r}r^{l}\kappa (r) Y_{lm}(\theta , \varphi )$)
$$
r\kappa '' + \kappa {'}(2l + 2 - 2\beta r) + \kappa (\alpha^{2}r e^{-r} - 2\beta (l + 1)) = 0,
$$
where
$$
\alpha^{2} = \frac{2mU_{0}a^{2}}{\hbar^{2}}, \quad \beta^{2} = \frac{2m |E|a^{2}}{\hbar^{2}}.
$$
It would be tempting to use the approximation
$$
r \approx \frac{1 - e^{-r}}{e^{-r}},
$$
but $r e^{-r}$ didn't reduce to the normal form.</p>
<p>The exact solution for $l = 0$ is existed.</p>
| 4,591 |
<p>With relativistic aberration, a sky full of stars gets concentrated in the direction of motion. As a rough measure of the degree of concentration, one could use the radius of a small circle, centered on the direction of motion, which contains the objects which, when you are at rest, are in half the sky (if you take my meaning).</p>
<p>Using the formula for relativistic aberration:</p>
<p>beta=0: half-sky radius=90 deg</p>
<p>beta=0.8: half-sky radius= 36.87 deg (this is just arcos(beta))</p>
<p>When I compare this calculation with diagrams created both by others and myself, there seems to be a difference of a few degrees, and I can't figure out why. I seem to be missing something.</p>
<p>For the case of beta=0.80, I measure the half-sky radius as 39 degrees. The difference is small, but it's large enough that I'm pretty sure it's not a measurement error.</p>
<p>You can measure this for yourself, using this diagram (created by someone else), with the 90 deg lines:
<a href="http://erkdemon.blogspot.ca/2009/11/relativistic-ellipse.html" rel="nofollow">http://erkdemon.blogspot.ca/2009/11/relativistic-ellipse.html</a></p>
| 4,592 |
<p>I would like to buy a good book on Variational Calculus. Most of the books that I find seem to be rather formal in a mathematical sense, which is not necessarily bad, but makes the studying a bit cumbersome.</p>
<p>Could you provide me with advice on a good variational calculus books which focuses on physics problems and has plenty of examples, preferably in the field of mechanics.</p>
| 150 |
<p>The equation of motion for the harmonic oscillator (mass on spring model)</p>
<p>$$\frac{d^2x}{dt^2} + \omega_0^2 x = 0$$</p>
<p>with $\omega_0^2 = D/m$, $D$ and $m$ being the force constant of the spring and the mass, has the solution</p>
<p>$$x=ce^{\lambda t}$$</p>
<p>where $c$ and $\lambda$ are a constant and a parameter.
Inserting $x$ leads to</p>
<p>$$\lambda_1 = +i\omega_0$$</p>
<p>and</p>
<p>$$\lambda_2 = -i\omega_0$$</p>
<p>and so the solutions are</p>
<p>$$x_1(t) = c_1 e^{i \omega_0 t}$$</p>
<p>and</p>
<p>$$x_2(t) = c_2 e^{-i \omega_0 t}.$$</p>
<p>In my book, I now read "...these solutions are linearly independent for $\omega_0 \neq 0$."</p>
<p>What does this mean (i.e. how can I see this) and why is it important?</p>
| 4,593 |
<p>We know that in an isolated system, the density matrix is the microcanonical distribution matrix. That this the possibility for all the states with energy in a certain interval is a constant?
But how can I deduce this from the postulate of equal probability? </p>
| 4,594 |
<p>I am trying to the calculate the link budget for link between a ground station on Earth (with a particular latitude and longitude) and a rover at a particular location on the surface of Mars, either directly or through a satellite on Mars. Now, if I need to determine the link availability between the rover and the ground station, the first step is to determine weather I have a line of sight between the ground station and the rover.</p>
<p>For this, the first step is to determine whether Mars is above our horizon or not and if so, for how long. This can be easily done using packages such as PyEphem or Novas.</p>
<p>The next step would be to determine if the rover is actually facing Earth or is on the other side of Mars. It is this second step that I need to determine with reasonable accuracy, but have not been able to figure out how to so far.</p>
<p>Later on I would need to include the satellites in the link path as well, but for now, I need to determine if I can get a straight line of sight communication between the rover on Mars and ground station on Earth.</p>
<p>Any sort of help will be appreciated.</p>
| 4,595 |
<p>When working with Bose-Einstein condensates trapped in potentials, how can one tell what the density of state of a system of identical bosons given the Hamiltonian, $H$? (I have been told that it is possible.)</p>
<p>Suppose the Hamiltonian is some 2D harmonic oscillator -- so $$H=p^2/2m+(1/2)(a^2x^2+b^2y^2) \quad ?$$</p>
<p>I think there is some general formula, something like $$\rho(E)=[gV_dS_dp^{d-1}/(2\pi\hbar)^{d}] (dp/dE) \quad ,$$ where $d$ is the dimension of the space we are working in, $g=2s+1$ where $s$ is the spin of the particles and $V_d$ is the $d-$dimensional "volume", so for a fixed volume box, this is the volume of the box.</p>
<p>But what is $V_d$ in this case? And is $p$ simply $$p^2=2m[E-(1/2)(a^2x^2+b^2y^2)] \quad ?$$</p>
| 4,596 |
<p>I've been wondering exactly why the elements are distributed the way they are on Earth. The heavier elements have their origins in the centers of stars, or in supernovae. After the death of the stars, you end up with a dust cloud containing the heavier elements. Later, planets form out of these along with new stars.</p>
<p>If the heavier elements were randomly distributed in these explosions, how do we end up with special deposits of minerals on Earth? We have mines and special areas where the concentrations of different materials are higher. For example, we have iron, gold, nickel and uranium mines. Why aren't these materials uniformly distributed? Why isn't the Earth composed of a substance which is a uniform mixture of all the heavy elements? Why does it seem there is sometimes a preference for like materials to clump together?</p>
<p>The nickel and iron mostly make up the Earth's core, which I guess makes sense in terms of them being fairly heavy while comparatively abundant relative to heavier elements, but what about everything near the surface that we observe?</p>
| 4,597 |
<blockquote>
<p><em>A) Explain how Kepler's $2^{nd}$ law - "The radius vector from the Sun to a planet sweeps out equal areas in equal time intervals" - can be understood in terms of angular momentum conservation.</em></p>
</blockquote>
<p>I know that:</p>
<p>Angular momentum is conserved and therefore $\vec{L}=\vec{r} \times \vec{p}=\vec{r} \times m\vec{v}=constant$ and $L=mrv\sin\theta$.</p>
<p>Kepler's $2^{nd}$ law means $\frac{dA}{dt}=constant$</p>
<p>Somehow this comes out to be $dA=(\frac{1}{2})(\frac{L}{m})dt$ but I'm having a hard time getting there.</p>
<blockquote>
<p><em>B) Explain how circular motion can be described as simple harmonic motion.</em></p>
</blockquote>
<p>I know that:</p>
<p>For circular motion
$m\vec{a}=\vec{F}_{c}=-m\frac{v^2}{R}\vec{r}=-m\omega^2R\vec{r}$</p>
<p>However, I'm fairly lost on this equation. Where does the negative sign come from, and where does the $\vec{r}$ come from?</p>
| 4,598 |
<p>Suppose there's some satellite orbiting the earth in circular motion. Suppose there's an asteroid that hits the satellite in the same direction as the instant velocity vector of the satellite. The collision causes the satellite to move faster. And here are my 2 questions:</p>
<p>1) Why will the satellite start moving in an elliptical orbit? Is it because its speed has increased, but the centripetal acceleration hasn't? It seems intuitively right for me, because then the satellite covers larger path before the centripetal acceleration causes the change in the velocity vector direction.</p>
<p>2) However, what confuses me is the fact that the centripetal acceleration is dependent on the velocity ($v^2/r$). On the other hand, since the force of gravity exerted on the satellite by the earth, hasn't changed after the hit (if we neglect asteroid's mass or suppose it just fell down after the hit), because there was no change in the radius (i suppose) of the circular path, there was no change in the centripetal acceleration. So these two arguments contradict each other. Where am I wrong? What I miss here? </p>
<p>Thanks in advance.</p>
| 4,599 |
<p>This question is about cosmology and general relativity.</p>
<p>I understand the difference between the universe and the observable universe. What I am not really clear about is what is meant when I read that the universe is infinite.</p>
<ul>
<li>Does it have infinite mass or is it
dishomogeneous? </li>
<li>How can the universe
transition from being finite near the
big bang and infinite 14 billion
years later? Or would an infinite
universe not necessarily have a big
bang at all?</li>
</ul>
| 922 |
<p>Here's something that I've found difficult to wrap my head around. The relationship between the Schwarzschild radius and mass is linear. It's generally known that if you take an object in the universe and squeeze it down to it's Schwarzschild radius, that radius will always be smaller than smaller than the original object's radius. E.x, the sun has 1 solar radius, which is much larger than it's Schwarzschild radius of 3 km.</p>
<p>But if you started calculating Schwarzschild radius for an object with really high mass, things seem to get a bit funky. Take an object that has a mass of $10^{100}$ kilograms. The corresponding Schwarzschild radius for that is $1.48513 \times 10^{73}$ meters. But if we took an object that has the density of the Sun (1410 $kg/m^{-3}$) and tried to find it's radius normally, we end up with a radius of $1.19244 \times 10^{32}$ meters which is smaller than the Schwarzchild radius. How is this possible? I understand that you won't be able to have an object that large enough to even consider this to be "possible", but this still is confusing to me. Are my calculations off?</p>
| 4,600 |
<p>I think we all heard general statements like "once big enough star burns out there is nothing to prevent the gravitational collapse ending in a black hole". But I can't remember even seeing the process described precisely.</p>
<p>Here's the deal: at first there is a nice object, a star. Stars can be nicely modeled by general relativity, nuclear physics and statistical physics combined and very much is known about these models and it can be observed whether they agree with things like light and neutrino fluxes, surface temperature and probably also lot of other stuff I know nothing about.</p>
<p>After the collapse we are left with another nice object, a black hole. We know that <a href="http://en.wikipedia.org/wiki/No-hair_theorem">black holes have no hair</a>.</p>
<p>The question is: what happens in-between? More precisely, between the time when all of the nuclear material has been burned out (and if possible ignore effects like reheating of the star after big enough compression) and the time where there is nothing more than just a black hole.</p>
<blockquote>
<ul>
<li><p>Give a description of what happens during the collapse?</p></li>
<li><p>How does the star "lose its hair"?</p></li>
<li><p>Can the actual collapse be solved analytically?</p></li>
<li><p>At what point is singularity created?</p></li>
</ul>
</blockquote>
<p><strong>Update:</strong> <em>I don't want to know what an outside observer will see. Instead, I'd like to find out what an individual part of the dead star will "feel" when a black hole is about to form near it. In other words, I want a complete solution (ideally analytical, but numerical would be also completely fine)</em></p>
<p>Feel free to assume anything that makes your life easier. Spherical symmetry is definitely fine. Also, if for any reason the questions don't make sense (like Cauchy problem is ill-defined in the presence of the singularity) feel free to interpret them in a way that make them sensible (e.g. assume that black hole is built from D-branes).</p>
<hr>
<p>Also, I have a feeling that what I intended as a simple question at first ended up being pretty complex. If you think it should be split into smaller (and therefore more manageable and answerable) parts, let me know.</p>
| 4,601 |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/14074/what-are-the-prerequisites-to-studying-general-relativity">What are the prerequisites to studying general relativity?</a> </p>
</blockquote>
<p>I'am 27 now and i have a burning desire to study math and physics from the ground up and I strongly prefer doing a self study.I want to be a self tutor till i reach certain level.</p>
<p>My question is what is the minimum knowledge needed to read and completely understand the General and Special Theory of Relativity.</p>
<p>As of now my level of math knowledge is basic differential calculus.I also have a basic understanding of Kinematics {One dimensional motion with constant acceleration}</p>
<p>I welcome all possible sugessions,advices and recomendations.</p>
<p>Thank's in Advance</p>
| 108 |
<p>Consider an point particle moving on a frictionless semicircular hill (curve). The particle's initial kinetic energy is equal to the potential energy on the top of the hill, i.e it has the necessary energy to climb the hill. </p>
<p>Will it reach the top of the hill in infinite or finite time? </p>
<p>In my proof it needs infinite time and this is quite non-intuitive because, though the particle has the necessary energy to climb the hill, it needs an infinite time. Also if we reverse the time, when the particle is in equilibrium on the top of the hill, it will never go down, therefore this process is time irreversible.</p>
| 4,602 |
<p>I am making a comparation between the photon gas and the ideal classic gas for my Thermodynamics class. The photon gas is defined by the equations:</p>
<p>$$U=aVT^4 $$
$$P=\dfrac{1}{3}aT^4$$</p>
<p>I found this document: <a href="http://www.csupomona.edu/~hsleff/PhotonGasAJP.pdf" rel="nofollow">http://www.csupomona.edu/~hsleff/PhotonGasAJP.pdf</a> which explain how to find some basic things, like enthalpy and entropy. It says that a great exercise is to compare the Carnot cycle of the photon gas with the Carnot cycle of the ideal gas. According to it, the efficiency is $\eta=1-\frac{T_2}{T_1}$ the same as the ideal gas. I think that this is really interesting for my comparation, so I'm trying to calculate the Carnot cycle efficiency for this gas.</p>
<p>I have no problem with the isothermal process, which is solved in that document:
$$W_{ab}=-\dfrac{1}{3}aT^4\Delta V$$</p>
<p>However, I'm not sure if my result of the adiabatic process is correct. Work is $W=\int PdV$. Now, I can use the photon gas adiabatic equation (see the document) $PV^{4/3}=k$, where $k$ is a constant, to substitute $P$ in work equation, and integrate to obtain:</p>
<p>$$W_{bc} =\dfrac{3}{4}k\left( \dfrac{1}{V_b^3} - \dfrac{1}{V_c^3} \right)$$</p>
<p>I'm not sure if this result is correct. When I try to calculate the efficiency of the cycle, I have:
$$\eta=\dfrac{|W_T|}{|Q_{ab}|}=\dfrac{|W_{ab}+W_{bc}+W_{cd}+W_{da}|}{|Q_{ab}|}$$</p>
<p>where $W_{ab}$,$W_{cd}$ are isothermal and $W_{bc}$,$W_{da}$ are adiabatic. The heat is also defined in the document as:</p>
<p>$$Q_{ab}=\dfrac{4}{3}aT^4\Delta V$$</p>
<p>But with these values I can't obtain the correct expression for the efficiency, or I don't know how to reduce the efficiency expression to obtain what I want. Which is the correct way to calculate adiabatic work in a photon gas? And the Carnot cycle efficiency?</p>
<p>Thank you all for your answers :D</p>
| 4,603 |
<p>What is the molecular level reason behind the pattern (sine function) of the waves?</p>
<p><img src="http://i.stack.imgur.com/wAoQL.jpg" alt="enter image description here"></p>
| 4,604 |
<p>Let a wire be shaped according to some even function $y=f(x)$, with $f'(0)=0$ and $f''(0)>0$, and let a bead of negligible size slide frictionlessly on the wire. Let the bead oscillate under the influence of gravity about $x=0$ with amplitude $A$ (i.e., between $x=-A$ and $x=+A$) and frequency $\omega(A)$. Clearly $\omega$ is nearly constant for small $A$; it differs from the frequency $\omega_o$ of simple harmonic motion by at most $O(A^2)$. By choosing $f$ to be a fourth-order polynomial, we could presumably adjust the wire's shape so as to eliminate the errors of order $A^2$ and make $\omega(A)$ constant up to $O(A^4)$. Possibly we could continue this process of approximation and make all the derivatives $d^n\omega/dA^n$ vanish up to some finite $n$, or maybe for all $n$.</p>
<p>If the derivatives can be made to vanish for all $n$, then I think $\omega$ would have to be nonanalytic at $x=0$. It seems impossible that there is any $f$ such that isochrony holds for arbitrarily large $A$. No matter how steep you make the sides, the bead can't do any better than accelerating downward with acceleration $g$. Therefore I think the best $f$ you can find is probably one that blows up to infinity at $|x|$ equal to some $x_{max}$. On dimensional grounds, we would have to have $x_{max}=cL$, where $c$ is a unitless constant and $L=g/\omega_0^2$.</p>
<p>So my multipart question is: (1) Is there a function $f$ that gives $d^n\omega/dA^n=0$ for all $n$? If so, ... (2) How is $f$ characterized, and what is $c$? (3) Is $\omega(A)$ analytic at $x=0$, and if so, what is its radius of convergence to its Taylor series in units of $L$?</p>
| 4,605 |
<p>When a ray of ordinary light is passed on the surface of the water the reflected light will be completely polarized( vibrations in one plane).</p>
<p>My question is what will be <strong>plane of vibration in the partially polarized light</strong> that undergoes refraction? <strong>How many planes of vibration</strong> will be there? Deep explanation focusing on the <strong>planes of vibration</strong> of the partially polarized light would be appreciated.</p>
| 4,606 |
<p>If a future astronaut travelled to Alpha Centauri at a significant percentage of light-speed?
Apart from increased blue shifted radiation from their direction of travel - how would they experience other cosmic radiation? </p>
<p>If the trip took a subject several times faster than an observer on earth. Would the astronaut get less or more time / exposure to cosmic radiation?</p>
| 4,607 |
<p>Wikipedia says:</p>
<blockquote>
<p>It is believed that, due to the extraordinarily small scale of the
universe at the time, quantum effects of gravity dominated physical
interactions.</p>
</blockquote>
<p>But I wonder whether there is any indication that the dimensions of the universe were small at the time rather than being infinite?</p>
<p>Undoubtedly it was very dense but very dense does not necessary mean "small".</p>
<p>Is Wikipedia wrong on this point?</p>
| 4,608 |
<p>The media are reporting the commercially sold 128-bit quantum computer from D-Wave</p>
<blockquote>
<p><a href="http://news.google.com/news?ned=us&hl=us&q=d-wave+quantum&cf=all&scoring=n">http://news.google.com/news?ned=us&hl=us&q=d-wave+quantum&cf=all&scoring=n</a></p>
</blockquote>
<p>which of course sounds amazing. The gadget is described as something capable of doing quantum annealing</p>
<blockquote>
<p><a href="http://en.wikipedia.org/wiki/Quantum_annealing">http://en.wikipedia.org/wiki/Quantum_annealing</a></p>
</blockquote>
<p>which looks less convincing. I want to ask you what classes of problems the D-Wave computer can actually solve or perform. It can't run Shor's algorithm on 128 qubits, can it?</p>
| 528 |
<p>String theory - for example - requires extra spatial dimension. Say for example in 10 dimensional string theory, what theoretically prevents clustering of the extra 6 dimensions in 2 timeless 3 dimensional (infinite) spaces? </p>
| 4,609 |
<p>Some time far into the future, humans have made the technology breakthroughs to construct decoherence-proof reversible quantum computers with quantum fault tolerance. They have also solved the hard AI problem. They program a quantum conscious being on such a computer and also a two state quantum system. The quantum conscious being is programmed to entangle with the quantum system, measuring it. The rules of the Copenhagen interpretation tell us the state of the quantum system happened. The programmers reverse the program, undoing the measurement, with all the memory wiped clean. Did the quantum system unhappen?</p>
| 4,610 |
<p>I can find equations to give the force of an electromagnet on a piece of iron when the iron touches the electromagnet. </p>
<p>But what about when the iron is some distance from the electromagnet? Presumably the force depends on the shape/size of the iron piece as well as the location of the piece away from the magnet. </p>
<p>If anybody can tell me how to calculate this, even if I have to write a numerical calculation routine, I would appreciate any direction on this. </p>
| 4,611 |
<p>How to estimate the amount of water condensing from air on a surface, given the air's temperature and relative humidity and how they change over time, the surface temperature, material's thermal properites, roughness and whatever else needs to be given about the air and surface?</p>
<p>For my purpose, we may assume the surface starts off dry, but the more general situation would be as interesting. If enough water condenses, it'll form drops and run off - can we account for that? </p>
<p>Are there some fairly simple formulas or rules of thumb? High accuracy is not needed; I'll be happy to get grams per sq meter per second (or whatever) to within a factor of two. (What if we wanted higher accuracy?)</p>
| 4,612 |
<p>Also the side question is how many Joules is one photon (any between 450-660nm).
Thank you</p>
<p>P.S. I am asking because I want to estimate how much thermal energy should be dissipated by LED when part of known energy is emitted as light.</p>
<p>P.S. Got an answer from Robert. Thank you.
So those 6500 Lumen 100Watt white LED arrays emit about 9 watt of energy in photons alone and rest 91W goes into heat. Not bad.</p>
| 4,613 |
<p>Cellular automata provide interesting models of physics: Google Scholar gives more than 25,000 results when searching for <a href="http://scholar.google.com/scholar?q=%22cellular+automata%22+physics&hl=en&btnG=Search&as_sdt=2001&as_sdtp=on">"cellular automata" physics</a>.</p>
<p>Google Scholar still gives more than 2.000 results when searching for <a href="http://scholar.google.com/scholar?hl=en&q=%22quantum+cellular+automata%22&btnG=Search&as_sdt=2000&as_ylo=&as_vis=0">"quantum cellular automata"</a>.</p>
<p>But it gives only <a href="http://books.google.com/books?hl=en&lr=&id=sab-9fGPCEcC&oi=fnd&pg=PA1&dq=%22relativistic+cellular+automata%22&ots=rG9eoNgPYh&sig=ZNQpI-0B-0S2358zX9To-h4NtdI#v=onepage&q=%22relativistic%20cellular%20automata%22&f=false">1</a> (one!) result when searching for <a href="http://scholar.google.com/scholar?hl=en&q=%22relativistic+cellular+automata%22&btnG=Search&as_sdt=2000&as_ylo=&as_vis=0">"relativistic cellular automata"</a>, i.e. cellular automata with a (discrete) Minkoswki space-time instead of an Euclidean one.</p>
<blockquote>
<p>How can this be understood? </p>
<p>Why does the concept of QCA seem more
promising than that of RCA?</p>
<p>Are there conceptual or technical barriers for a thorough treatment of RCA?</p>
</blockquote>
| 4,614 |
<blockquote>
<p><strong>Possible Duplicates:</strong><br>
<a href="http://physics.stackexchange.com/questions/14973/what-would-be-the-immediate-effects-if-light-does-not-go-at-the-maximum-speed-pos">What would be the immediate effects if light does not go at the maximum speed possible?</a><br>
<a href="http://physics.stackexchange.com/questions/14968/superluminal-neutrinos">Superluminal neutrinos</a></p>
</blockquote>
<p>I was reading this <a href="http://hosted.ap.org/dynamic/stories/E/EU_BREAKING_LIGHT_SPEED?SITE=AP&SECTION=HOME&TEMPLATE=DEFAULT" rel="nofollow">article</a> about a group of scientist thinking that they might have surpassed the speed of light with neutrinos, and are wanting other groups to check their work.</p>
<p>If their research is proven true, what impact would this finding have on the world of physics?</p>
| 83 |
<p>How does it make sense to vary the position and the velocity independently?</p>
<p><strong>Edit:</strong></p>
<p>Velocity is the derivative of position, so how can you treat them as independent variables? Doesn't every physics student ask this question when he learns calculus of variations? Does anybody ever answer this question? Ever? If so, please educate me.</p>
| 505 |
<p>Inspired by <a href="http://physics.stackexchange.com/questions/234/how-should-a-physics-student-study-mathematics">How should a physics student study mathematics?</a> and in the same vein as <a href="http://physics.stackexchange.com/questions/193/best-books-for-mathematical-background">Best books for mathematical background?</a>, although in a more general fashion, I'd like to know if anyone is interested in doing a list of the books 'par excellence' for a physicist.</p>
<p>In spite of the frivolous nature of this post, I think it can be a valuable resource.</p>
<p>For example:</p>
<hr>
<p><a href="http://rads.stackoverflow.com/amzn/click/0750628960">Course of Theoretical Physics</a> - <strong>L.D. Landau, E.M. Lifshitz.</strong></p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0805370021">Mathematical Methods of Physics</a> - <strong>Mathews, Walker</strong>. Very nice chapter on complex variables and evaluation of integrals, presenting must-know tricks to solve non-trivial problems. Also contains an introduction to groups and group representations with physical applications.</p>
<p><a href="http://rads.stackoverflow.com/amzn/click/048667164X">Mathematics of Classical and Quantum Physics</a> - <strong>Byron and Fuller.</strong></p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0471010901">Topics in Algebra</a> - <strong>I. N. Herstein</strong>. Extremely well written, introduce basic concepts in groups, rings, vector spaces, fields and linear transformations. Concepts are motivated and a nice set of problems accompany each chapter (some of them quite challenging).</p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0126546568">Partial Differential Equations in Physics</a> - <strong>Arnold Sommerfeld</strong>. Although a bit dated, very clear explanations. First chapter on Fourier Series is enlightening. The ratio interesting information/page is extremely large. Contains discussions on types of differential equations, integral equations, boundary value problems, special functions and eigenfunctions.</p>
<hr>
| 4,615 |
<p>If a rectangular pan has a constant and uniform temperature $T$ first, then put it in a vacuum. Considering the effect of thermal radiation, the temperature distribution of the rectangular blackbody will change. My question is, will the temperature of the corner be higher than the edge?</p>
| 4,616 |
<p>As the air molecules are environment for carrying sound waves, could stream of photons be environment for carrying electromagnetic waves? What contradictions cause this assumption in the existing theories?</p>
| 4,617 |
<p>All around I read that buoyancy is numerically equal to the weight of fluid <strong>displaced</strong> by a submerged object, the volume of displaced fluid being equal to that of the <strong>submerged portion</strong> <a href="https://en.wikipedia.org/wiki/Archimedes%27_principle" rel="nofollow" title="Wikipedia - Archimedes' principle">(Wikipedia)</a>. However, thinking about it brought me to believe that such wording is not very good.</p>
<p>Consider the 2D example below of a box being sunk into water.</p>
<p><img src="http://i.stack.imgur.com/gJ5MV.png" alt="Archimedes 1"></p>
<p>In this example, it is clear that the buoyancy is equal to the weight of 4 cm² of water, which is the volume of the submerged box. However, closer inspection reveals that this does not match the displaced volume.</p>
<p><img src="http://i.stack.imgur.com/pBWhx.png" alt="Archimedes 2"></p>
<p>I concluded that the common definition works well when the body of fluid is large compared to the object, such that its surface level does not change significantly upon submersion. In this case, <em>displaced volume</em> matches <em>volume of submerged portion</em>. However, for the more general case (including example above), it would be more accurate to forgo <em>displaced volume</em> and hang on to <em>volume of submerged portion</em> only.</p>
<p>Am I missing something here? Is the original, ubiquitous wording indeed accurate?</p>
| 151 |
<p>What are the physics of wind (or any gas flow really) bouncing off surfaces?</p>
<p>If a wind hits a wall directly (in a 90 degree angle) does any of it bounce back? </p>
<p>Are there any similarities with, say, light rays hitting a mirror?</p>
<p>I understand, that the other extreme case is a 0 degree angle in gas pipes, for example, where the surface guides the flow further.</p>
| 4,618 |
<p>In a Leyden jar, I have read that a charged object is brought in contact with the conductor in contact with the metal inside the jar, thus giving the inner metal a similar charge. And the metal outside the jar then gets an opposite charge.</p>
<p>My question is simply how does the metal outside the jar get the opposite charge, given that there is an insulator in-between?</p>
<p>I hope that someone can give me a clear reply, explaining exactly what happens with the outer metal.</p>
| 4,619 |
<p>Earlier today, I saw <a href="http://www.orlandosentinel.com/business/nationworld/sns-bc-eu--breakinglightspeed,0,5266439.story">this link</a> on Facebook about neutrinos going faster than the speed of light, and of course, re-posted. Since then, a couple of my friends have gotten into a discussion about what this means (mostly about time-travel), but I don't really know what this really implies. This made me wonder...</p>
<p>What are the biggest and most immediate implications of this potential discovery?</p>
<p><strong>Related:</strong> <a href="http://physics.stackexchange.com/q/14968/3454">Superluminal neutrinos</a></p>
| 83 |
<p>A teacher of mine told me once that there were no ninth gluon because such a one should be white and interact infinitely far, and no one has been observed. Is there also a theoretical reason?</p>
| 4,620 |
<p>The derivation for Heat Equation I am reading starts by stating </p>
<p>Net change of heat inside $[x,x+\Delta x]$ = Net flux of heat across boundaries + Total heat generated inside $[x,x+\Delta x]$ and writes the conservation equation</p>
<p>$$\textit{Total Heat Inside} [x,x+\Delta x]=
cpA \int _{ x}^{x+\Delta x}u(s,t) ds
$$</p>
<p>and later equates net flux across the boundary with</p>
<p>$u_x(x+\Delta x,t) - u_x(x,t)$,</p>
<p>so the heat flow is proportional to the spatial gradient of temperature at both ends. What I dont understand is why is net flux proportional to the spatial gradient, why cant we use the temparature variable $u$ itself to measure the difference? If the temparature difference at both ends is high, then we would expect higher flow from high temparature to low, right? What would be the physical intuition behind this? Was this model arrived at by experimentation?</p>
<p><img src="http://i.stack.imgur.com/d5On3.png" alt="enter image description here"></p>
| 4,621 |
<p>I am still struggling with C being a constant and what that implies.
So can an experiment be done to find the resting state for the universe?
Take a device with an observer and a light source and two mirrors, one 10 meters in front and the other 10 meters behind the light source. Now move this through space at some speed. Can’t you determine your speed by using the red/blue shift from the light reflected by the mirrors? Will this allow you to find the resting reference for the entire universe?</p>
| 4,622 |
<p>I know it is hard , but can we transfer the charge on a capacitor plate elsewhere? </p>
| 4,623 |
<p>The usual "proof" entropy is a state property is like that:</p>
<p>"Consider a system which undergoes a reversible process from state 1 to state 2 along path A, and let cycle be completed along path B, which is also reversible. Since the cycle is reversible we can write: </p>
<p>$$\int_1^2 \delta Q / T + \int_2^1 \delta Q / T = 0 $$</p>
<p>Now let cycle be completed along path C, but paths B and C represent arbitrary reversible processes. So $\int_2^1 \delta Q / T $ is the same for all reversible paths between states 2 and 1."</p>
<p>My question is, isn't the equation above already assume entropy is a state property? Only if it is a state property it can go around a cycle without changes. How can it be valid to prove entropy is state property if it is already assumed from the beginning?</p>
| 4,624 |
<p>I was doing some simple harmonic motion problems and I came across this <a href="http://i.imgur.com/W2zi40o.jpg" rel="nofollow">picture</a> describing the position, velocity and acceleration of a linear oscillator. At the moment in time when v is 0 the linear oscillator should not be moving, only changing directions. I'm having a hard time understanding why the acceleration is the greatest at that time (according to these graphs), since there is no velocity change. Is it because acceleration is only the difference in velocity at two different points in time and not one? How exactly does the change in direction affect acceleration?</p>
<p>edit: I found another <a href="http://physics.stackexchange.com/questions/34178/how-can-an-objects-instantaneous-speed-be-zero-and-its-instantaneous-accelerat?rq=1">question</a> that answered my question. haha.</p>
| 152 |
<p>Isn't speed a relative thing in space? If so, why would the speed of a propellant matter? Why can't a space ship accelerate infinitely?</p>
| 4,625 |
<p>I'm current developing cargo loader software, but i have a little challenge with calculating load for each axle when a cargo is placed on container. I know that all axles will be affected (the nearest ones are the most affected ones of course), and I want to find approximately the value of each load. Here's example scenario in pictures:</p>
<p><img src="http://i.stack.imgur.com/LCqjF.jpg" alt="enter image description here"> </p>
<p>I tried to find loads using balance rules taking each point as a pivot and calculating equation based on that position as below (EDIT: on the following figure in case 4 the 5th axle is pivot, I forgot to show it on figure):</p>
<p><img src="http://i.stack.imgur.com/3AP9g.jpg" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/v0D88.jpg" alt="enter image description here"></p>
<p>But I think I have problem with above solution as I could not find F3, F4, F5 in special examples (putting "d" distance values from pivot - P.S in this last picture all "d"s are different distances from pivot in that case - so d3 in the first equation is not equal to d3 in second equation as these both have different distances to different pivots) - for easy calculation you can use Cramer's rule online calculator <a href="http://matrix.reshish.com/cramer.php" rel="nofollow">here</a>.</p>
<p>I tried to solve this problem with moment but I could not done as I'm not good in physics :( I could not find relations between different forces in that case, I had only F1*d1 + F2*d2 + F3*d3 = F4*d4 + F5*d5 and F1 + F2 + F3 + F4 + F5 = mg ===> i got 5 unknowns but only 2 equations :(</p>
<p>So, i need your help! Any suggestions will be appreciated! </p>
| 4,626 |
<p>The question I am working on is, "Two blocks are free to slide along the friction-less wooden track shown below. The block of mass $m_1 = 4.98~kg$ is released from the position shown, at height $h = 5.00~m$ above the flat part of the track. Protruding from its front end is the north pole of a strong magnet, which repels the north pole of an identical magnet embedded in the back end of the block of mass $m_2 = 9.40~kg$, initially at rest. The two blocks never touch. Calculate the maximum height to which $m_1$ rises after the elastic collision."</p>
<p><img src="http://i.stack.imgur.com/Uz4To.gif" alt="enter image description here"></p>
<p>This question comes from webassign. On webassign they have a feature called "Watch It;" this feature allows you to see a person solve a problem nearly similar to this one. I feel as though there is an error in what the person says in the video. The person says that the mechanical energy of the block-earth system is conserved, but that wouldn't be true; if we were looking at the block-block system--that is, $m_1$ and $m_2$--the mechanical energy would be conserved. By looking at just the block-earth system, there would be a loss in kinetic energy, because when the two blocks "collide," they apply a force over a distance(work), causing a change in kinetic energy of each block, because the kinetic energy of the moving block is transferred into the other block, which is why the first block doesn't return to its initial height. Is this correct? If not, what am I misunderstanding?</p>
<p>As a result of this contention with what the person said in the video, I am not very certain on how to solve this problem.
EDIT (attempt to solve): </p>
<p>Energy analysis:</p>
<p>$m_1:$ $PE_i=mgh=KE_f$, where $h$ is the height from which it drops.</p>
<p>$KE_i=0~J$; $PE_f=mgh_0$, where $h_0$ is the height is rises to after the collision</p>
<p>$m_2:$ $KE_i=PE_i=PE_f=0~j$; $KE_f=\frac{1}{2}m_2v^2_{f,2}$</p>
<p>Momentum Analysis:</p>
<p>$m_1:$ $\vec{p}_{i,1}=m_1\vec{v}_{i,1}$; $\vec{p}_{f,1}=m_1\vec{v}_{f,1}$</p>
<p>$m_2:$ $\vec{p}_{i,2}=m_2\vec{v}_{i,1}$; $\vec{p}_{f,2}=m_2\vec{v}_{f,2}$</p>
<p>When I set up an equation for change in mechanical energy, and an equation for conservation of momentum, I get two equations, with a lot of unknowns. What did I do wrong?</p>
| 44 |
<p>Ok, so I remember reading that every conservation law has a corresponding symmetry (i.e. conservation of momentum is translational symmetry, conservation of angular momentum is rotational symmetry).</p>
<p>Now conservation of energy is temporal symmetry (you can rewind the tape and it looks exactly the same, but in reverse--you don't get a different "movie" running the tape in reverse).</p>
<p>But I just saw an article here...</p>
<p><a href="http://arstechnica.com/science/2012/11/finding-a-direction-of-time-in-exotic-particle-transformations/" rel="nofollow">http://arstechnica.com/science/2012/11/finding-a-direction-of-time-in-exotic-particle-transformations/</a></p>
<p>...where researchers found violations of time-reversal symmetry.</p>
<p>Now wouldn't that therefore mean that they found processes that create or destroy energy?? Does T-Symmetry violation mean that energy is not being conserved?</p>
| 4,627 |
<p>What is the orbital motion where both foci are located at one point? I know that an ellipse orbit is motion with two distinct foci.</p>
| 4,628 |
<p>I have this problem:</p>
<p>A 4.0 kg block is given an initial speed of 8.0 m/s at the bottom of a 20° incline. The
frictional force that retards its motion is 15.0 N. (a) If the block is directed up the
incline, how far does it move before stopping? (b)Will it slide back down the incline? </p>
<p>I've managed to get part (a) which was 4.51m but I'm not sure how to start part (b)..</p>
<p>The coefficient of Kinetic Friction was 0.407</p>
<p>Any ideas?</p>
| 4,629 |
<p>I have been told that trasverse wave propogates by the oscillation of medium particles in direction perpendicular to propogation.</p>
<p>Consider a wave on a taught string (x-y plane).
What is the mechanism of movement of the same sinosudial function along the string?</p>
<p>Suppose we start moving the particle on one end sinosudialy the how come the next particle also moves sinosudialy? How does elastic force between them does this work?
If we displace the particle, there is some elastic force developed which is at some angle with horizontal so the next particle should move at some angle and its vertical displacement should be less than the previous one. </p>
<p>So how come in a propogating wave all particle rise to the same height?</p>
| 4,630 |
<p>When we send an electromagnetic short wave to the sky, it reflects due to the ionosphere effects. But if we send it horizontally, is it correct that it moves around the surface of the earth, and if it has enough energy, it can return to its first position?</p>
<p>If yes, then how could that happen?</p>
| 4,631 |
<p>Thermodynamic buoyancy. I have an air intake for combustion air entering into a basement furnace room. During cold weather, the air enters unchecked (no damper on pipe is allowed). I have this 5 foot vertical pipe, suspended downwards within a 2 foot high box, terminating 12" from the bottom. The cold air spills over the top of the box (combustion appliances are off at this point). How do I create a "cold air trap" like a p-trap (thermal equilibrium)? Would raising the height of the box help?</p>
| 4,632 |
<p>How is spacetime depicted in quantum field theory?
Is space and time completely separate, and time is just nature of law as in Newtonian mechanics?</p>
| 4,633 |
<p>This is an ultra-soft question about relatively recent history. While reading some of Mandelstam's papers, I noticed that he cites David John Candlin consistenly whenever he does anything with Grassman path-integral. Everyone else cites Berezin.</p>
<p>So I read Candlin's 1956 paper, and I was stunned to find a complete and correct description of anticommuting variables, presented more lucidly than anywhere else, with a clear definition of Grassman integration, and a proof that it reproduces the Fermionic quantum field. This is clearly the original source of all the Grassman methods. I was stunned that the inventor of this method is quietly buried away.</p>
<p>I wrote the <a href="http://en.wikipedia.org/wiki/David_John_Candlin">Wikipedia page on the guy</a>, but I couldn't find out anything beyond the sketchy stuff I found on an old Princeton staff listing. The fellow doesn't google very well at all.</p>
<p>Here are the questions:</p>
<ul>
<li>Is he still alive? (Hello? Are you there?)</li>
<li>Did he become the experimental physicist David John Candlin in the late 1970s/early 1980s? Or is this someone else with the same name?</li>
<li>Did he get any credit for his discovery?</li>
</ul>
<p>I mean, this is one of the central tools of modern physics, it is used every day by every theorist, and the inventor is never mentioned. It's 50% of the path integral. Why the silence?</p>
| 4,634 |
<p>I live in Ireland where serving food on hot plates is considered “good cooking practice” to ensure the food remains warm – I come from France where I have rarely seen it done.</p>
<p>I am wondering if this practice really is useful. I assume it depends on the difference of temperature between the food and the plate, as heat won’t transfer as fast to the plate. But wouldn’t the extra time the food remains above an “acceptable” temperature threshold just be marginal?</p>
| 4,635 |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/29805/richtmyer-meshkov-instability-in-mhd">Richtmyer Meshkov instability in MHD</a> </p>
</blockquote>
<p>The Richtmyer Meshkov instability in Hydrodynamics:-
1) When shock wave interacts with the contact discontinuity, it accumulates the vorticity on the CD
2) This causes the density discontinuity to curl up, and form series of vortices</p>
<p>In application of the longitudinal magnetic field with conducting fluid as the working medium,</p>
<p>1) The RM instability is suppressed
2) Series of new shocks is formed and it carries away the vorticity</p>
<p>My question is ,
what exactly happens in Magneto-Hydrodynamic system?
Why the RM instability is supressed?
How can one get the physical intuition of what is happening at the interface?</p>
| 462 |
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