question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
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<p>In General Relativity is there a TE symmetry similar to CPT symmetry in the Standard Model ? It's pretty easy to understand that by flipping charge and parity you merely get a time reversed equivalent of your system, so flipping time as well would lead to an equivalent description. Similarly, since metric perturbations in GR are sourced by energy density, it seems to me that GR <em>is</em> invariant if we operate the transformation $(t,\rho) \rightarrow (-t,-\rho)$. Is this correct or am I missing something here ? Do the other $T_{\mu \nu}$ terms come into play in ways which I haven't considered here ? Is the symmetry actually $(g_{\mu \nu},T_{\mu \nu}) \rightarrow (-g_{\mu \nu},-T_{\mu \nu})$ ?</p>
<p>The reason I think this might work is if you make the energy density negative in the Friedmann equations expansion turns into contraction, then you time flip it and it turns back into expansion. Is this a ubiquitous behavior ? If this is indeed generally true can we say there is indeed an ET symmetry ?</p> | g6751 | [
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<p>Statistical mechanics is restricted to the postulate of the equal a priori probability, but this postulate does not need to be considered for thermodynamics, so the valid ranges of statistical mechanics and the second law of thermodynamics are different.</p>
<p>For example, consider a freely falling body, the potential energy of the body is converted into the kinetic energy of random motion in the process, the driving force of the process does not satisfy the condition of the postulate of the equal a priori probability, it is easy to calculate the change of the entropy of the process by thermodynamics. </p>
<p>The question is: Can anyone calculate the change of the entropy of the process by statistical mechanics?</p> | g232 | [
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<ol>
<li><p>What is the relation between entropy and mass of black hole?</p></li>
<li><p>And what is the relation between symmetry of physics operation and entropy?For instance,measuring or doing measure on state of quantum system especially pure state of a system has to lead to increase in entropy of the system,and the measuring is not symmetric operation,but it seems that the statement is tautologic,because that operations make processes symmetric,means nothing has been changed.</p></li>
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<p>What happens when You make a contact junction between normal metal with some fermi energy $E_{F}$ and superconductor with fermi level $E_{SC}$, but this levels are not necessarily the same ? </p>
<p>There is some analogy between p-n junction or contact potential in metals?</p> | g6753 | [
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<p>Simple question: as the title says, what makes a real Feynman diagram real, and what makes a virtual diagram virtual? Or in other words, how do I tell whether any given diagram is real or virtual? I've never gotten a really satisfying explanation of this. I would imagine it has something to do with virtual particles, but all internal propagators are virtual particles and I know for a fact that having internal lines doesn't make a diagram virtual.</p> | g6754 | [
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<p>When solving Schrödinger's equation for a 3D quantum well with infinite barriers, my reference states that: $$\psi(x,y,z) = \psi(x)\psi(y)\psi(z) \quad\text{when}\quad V(x,y,z) = V(x) + V(y) + V(z) = V(z).$$ However, I cannot find any rationale for this statement. It may be obvious, but I would appreciate any elucidation.</p> | g6755 | [
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<p>I saw <a href="https://www.youtube.com/watch?v=1Xp_imnO6WE">this video</a> by <a href="https://www.youtube.com/channel/UCHnyfMqiRRG1u-2MsSQLbXA">Varitasium</a> and I was not 100% sure about the third phenomena, a statically charged object attracting a stream of water, especially because he explicitly mentioned that it is not due to the <a href="http://en.wikipedia.org/wiki/Permittivity">permittivity</a> of the water. A week later he uploaded an <a href="https://www.youtube.com/watch?v=jIMihpDmBpY#t=228">video explaining</a> all five phenomena and he says it is because of repelled equally charged ions, back up the water flow, such that the water actually falling along the charged object would be oppositely charged and therefore attracted. Here is a still image from the video illustrating this:</p>
<p><img src="http://i.stack.imgur.com/EbW0h.jpg" alt="enter image description here"></p>
<p>However this explanation seems strange to me, since this would mean that this way you could build up a charge in the water which has exited the tap (as well as in the water inside the tap as well). Therefore it should get harder to push those ions back over time, and therefore there also would be a decrease in the attraction of the water (assuming there is no other way to discharge it). I have tried a simple similar experiment, where I catched the water leaving the tap in an insulated bowl, but I did not notice a decrease in attraction.</p>
<p>There a couple of reasons why my experiment does not rule out his theory:</p>
<ul>
<li>I was holding the charged (plastic) object by hand, which caused that its distance to the water stream varied, making it difficult to observe a decrease in attraction.</li>
<li>I only conducted my experiment for roughly 30 seconds, which might be enough time for a opposite charge to build up.</li>
</ul>
<p>The reason that he mentioned why permittivity can't cause this phenomena is because the electric field would be homogeneous and therefore the attractive and repulsive force of both dipoles of a water molecule would cancel out. However the electric field would only be homogeneous if the charged object would be an infinitely large plate, which it isn't. Thus water molecules would be attracted to the charged object. In order to make the permittivity theory more plausible I thought of maybe doing a order of magnitude calculation to see if it could generate a large enough force would be able the water stream by the observed amount. However I do not know what a good guess would be for variables such as the amount charge on the charged object and how the electric field would fall off over distance. </p>
<p>So, my question is whether his theory is really correct, or if the permittivity of the water can cause it. </p> | g6756 | [
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<p>Accounts of the "secret" of the hydrogen bomb describe Xrays from a primary fission explosion reflecting off of the bomb case (occasionally passing through polystyrene foam) and compressing and heating the fusion fuel. No mention is made of gamma rays doing the same thing. Is there a physical explanation for why X-rays are able to compress the secondary, but gamma rays are not? Does the primary fission reaction produce gamma rays as well as x-rays?</p> | g6757 | [
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<p>I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. </p>
<p>First of all I wrote down this Lagrangian: </p>
<p>$$S=\int dt ds \left[\frac{\rho}{2}(\dot{x}^2+\dot{y}^2)-\rho g y(s,t)+\frac{\lambda(s,t)}{2}\left(\left(\frac{\partial x}{\partial s}\right)^2+\left(\frac{\partial y}{\partial s}\right)^2-1\right)\right]$$</p>
<p>This Lagrangian describes heavy string with fixed ends in gravitational field. Where
$\rho$ is density, $g$ is <a href="http://en.wikipedia.org/wiki/Gravitational_acceleration">gravitational acceleration</a>, $s$ is <a href="http://en.wikipedia.org/wiki/Differential_geometry_of_curves#Length_and_natural_parametrization">natural parameter</a>.</p>
<p>So I have 3 equations from <a href="http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation">Euler-Lagrange equations</a>.</p>
<p>$$\rho\ddot{x}+\frac{d}{ds}\left(\lambda(s,t)\frac{\partial x}{\partial s }\right)=0$$
$$\rho\ddot{y}+\frac{d}{ds}\left(\lambda(s,t)\frac{\partial y}{\partial s }\right)+\rho g=0$$
$$\left(\frac{\partial x}{\partial s }\right)^2+\left(\frac{\partial y}{\partial s }\right)^2=1$$</p>
<p>After that I've found stationary solution ($\frac{\partial x}{\partial t}=\frac{\partial y}{\partial t}=\frac{\partial \lambda}{\partial t}=0$). (I just put $\ddot{x}=\ddot{y}=0$)</p>
<p>$$y_0(x)=-\frac{C_1}{\rho g}\cosh\left(\frac{\rho g x}{C_1}+C_2\right)$$</p>
<p>Where $C_1,C_2$ is integration constants (depends on positions of ends of string). And $\cosh(x)$ is <a href="http://mathworld.wolfram.com/HyperbolicCosine.html">hyperbolic cosine</a>.</p>
<p>To study small oscillations I've tried to use <a href="http://en.wikipedia.org/wiki/Perturbation_theory">pertrubation theory</a>. </p>
<p>So, I put
$$y(s,t)=y_0(s)+\bar{y}(s,t)$$
$$x(s,t)=x_0(s)+\bar{x}(s,t)$$
$$\lambda(s,t)=\lambda_0(s)+\bar{\lambda}(s,t)$$</p>
<p>But after that I get difficult differential equations, which I can't solve.</p>
<p><strong>Maybe someone know the more simplier aproach to solve this problem or know how to solve it in this way?</strong></p> | g6758 | [
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<p>QCD and confinement specify that hadrons must be color-neutral. My understanding is that this means you can have mesons (quark + antiquark) or baryons with 3 quarks, one of each color: Red+green+blue=neutral.
In a meson, does the color of the quark and antiquark matter? Must a red quark be paired with a red antiquark; or does the color change constantly due to the exchange of gluons which also carry color charg?</p> | g6759 | [
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<p>An explosion is a rapid increase in volume and release of energy in an extreme manner.
A blast wave in fluid dynamics is the pressure and flow resulting from the deposition of a large amount of energy in a small very localised volume.
The equation for a Friedlander waveform describes the pressure of the blast wave as a function of time:</p>
<p>$$P(t)=P_oe^{-\frac {t}{t^*}}(1-\frac {t}{t^*})$$
where P$_o$ is the peak pressure and t$^*$ is the time at which the pressure first crosses the horizontal axis (before the negative phase).</p>
<p>My <strong>Question:</strong>
Why does the pressure temporarily drop below ambient after the wave passes?</p> | g6760 | [
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<p>Going to as little details as possible, here is a statement from Wald's text on QFT in curved spacetimes(I am not quoting the book)</p>
<p>He considers two vector spaces ${\cal S}$ and ${\cal H}$.</p>
<blockquote>
<p>Note - For more details about ${\cal S}$ and ${\cal H}$, read this box. I believe for most part of the question, the following details are irrelevant, but I will provide them nonetheless. Otherwise, skip below.</p>
<p>He starts by considering the solution space of a classical system ${\cal S}$ with symplectic structure $\Omega$. This has a natural vector space structure. He complexifies it to ${\cal S}^{\mathbb C}$ and extends $\Omega$ to ${\cal S}^{\mathbb C}$ by complex linearity on each variable. He then defines the map $(\cdot, \cdot): {\cal S}^{\mathbb C} \times {\cal S}^{\mathbb C} \to {\mathbb C}$ on ${\cal S}^{\mathbb C}$ as
$$
(y_1, y_2) = - i \Omega( \overline{y_1}, y_2)
$$
This satisfies all the properties of an inner product except positive-definiteness. He then considers the subspace ${\cal H}$ of ${\cal S}^{\mathbb C}$ on which the inner product above is positive-definite. (There are of course many such choices of ${\cal H}$. Any one of them will do.)</p>
</blockquote>
<p>He then shows that there is a one-one onto map $K: {\cal S} \to {\cal H}$. He shows that one can define a real inner product $\mu: {\cal S} \times {\cal S} \to {\mathbb R}$ on ${\cal S}$. He then goes on to show that one can use this to define a complex inner product on $\cal H$ as
$$
\left( K y_1, K y_2 \right)_{\cal H} = \mu(y_1, y_2) - \frac{i}{2} \Omega(y_1, y_2)~\forall~y_1, y_2 \in {\cal S}
$$
where $\Omega: {\cal S} \times {\cal S} \to {\mathbb R}$ is an antisymmetric function on ${\cal S}$, i.e. $\Omega(y_1, y_2) = - \Omega(y_2, y_1)$.
He then uses the <a href="http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality" rel="nofollow">Cauchy-Schwarz Inequality</a> for ${\cal H}$. This reads
$$
\left( K y_1, K y_1 \right)_{\cal H} \left( K y_2, K y_2 \right)_{\cal H} \geq \left| \left( K y_1, K y_2 \right)_{\cal H} \right|^2 \geq \left| \text{Im} \left( K y_1, K y_2 \right)_{\cal H} \right|^2
$$
Expanding it out, he writes
$$
\mu(y_1, y_1) \mu(y_2, y_2) \geq \mu(y_1, y_2)^2 + \frac{1}{4} \Omega(y_1, y_2)^2 \geq \frac{1}{4} \Omega(y_1, y_2)^2
$$
More specifically
$$
\boxed{ \mu(y_1, y_1) \mu(y_2, y_2)\geq \frac{1}{4} \Omega(y_1, y_2)^2 }
$$</p>
<p>Now, here is the statement that confuses me</p>
<blockquote>
<p><strong>Indeed, since $K$ is one-to-one and onto and since the Schwarz inequality on ${\cal H}$ always can be ``saturated", we obtain the following stronger version of the last inequality: For each $y_1 \in {\cal S}$ we have</strong>
$$
\mu(y_1, y_1) = \frac{1}{4} \max_{y_2 \neq 0} \frac{ \Omega(y_1, y_2)^2}{\mu(y_2, y_2)}
$$
Here's my question
<strong>Q. Where did he get the above expression from?</strong></p>
</blockquote>
<p>He seems to be claiming that the boxed inequality is always saturated for some vector $y_2 \in {\cal S}$. Is that true? Why?</p>
<p>PS - I will understand if some people think that this question is more of a math question than a physics one. But, I thought that it might be possible that the answer relies on some of the assumptions we make in physics, so I asked it here. Any comments will be helpful</p> | g6761 | [
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<p>What does it mean by oscillating neutral for <a href="http://en.wikipedia.org/wiki/Three-phase_electric_power" rel="nofollow">3-phase electrical</a> system? Is it any effect of harmonic production due to magnetic core hysteresis nature?</p>
<p>I have been searched a lot about this through internet, but I failed. So, please tell me about it & also mention if this question is wrong. Cause this question makes me confused. </p> | g6762 | [
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<p>In the hydrogen atom, the energy does not depend on l. This degeneracy is sometimes called "accidental" (because it does not correspond to some symmetry?). However, there is l dependence in the energy multi-electron atoms. Since the original degeneracy was "accidental", is it no longer correct to talk about what breaks this degeneracy? Physically, I understand this is a result of the lower l-value states being concentrated closer to the nucleus, but is there a way to see that this would be the case in advance, without finding the eigenvalues of the Hamiltonian?</p> | g6763 | [
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<p>I have a small motor connected to DC source, and use the ampere meter to survey the current through the motor. While the motor is rotating, I hold the motor by hand so that it stop. I see the current through the motor increases. Could you help me explain this problem?</p>
<p><img src="http://i.stack.imgur.com/98Y8Q.jpg" alt="enter image description here"></p> | g233 | [
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<p>What determines the form of the intensity spectra of different particle species in Laser-Induced Fluorescence (LIF) measurements? See e.g. </p>
<p>I figure that bigger particles have more ways to get excited and so the intensities accumulate and make the curve wider? But how exactly do I derive an expected curve for a given molecule type? Why the steep rise and the slower fall?</p>
<p><img src="http://i.stack.imgur.com/5WEEM.gif" alt="enter image description here"></p> | g6764 | [
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<p>I was not able to find an answer for this question...</p>
<p>Some radioactive elements have half-life measured in thousands of years and some others even in millions, but over 4.5 billion years all the radioactive material that was part of the initial material that formed the planet earth should have decayed by now?</p>
<p>However, there is still radioactive material with short half-life to be found in nature. How is this possible and if the answer is that the new radioactive material is constantly being generated somehow, can you explain the mechanism of how this happens? </p>
<p>Thanks.</p> | g6765 | [
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<p>(c.f Conformal Field Theory by Di Francesco et al, p39)
From another source, I understand the mathematical derivation that leads to eqn (2.126) in Di Francesco et al, however conceptually I do not understand why the equation is the way it is. The equation is $$\Phi'(x) - \Phi(x) = -i\omega_a G_a \Phi(x)$$ G is defined to be the generator that transforms both the coordinates and the field as far as I understand (so it is the full generator of the symmetry transformation) and yet it seems there are no instances of the transformed coordinate system (the primed system) present on the LHS of the equation. </p>
<p>Another example is the equation $\Phi'(x') = D(g)\Phi(x)$, where the field transforms under a representation $D$ of some Lie group. $D$ is then decomposed infinitesimally as $1 + \omega \cdot S$ where $S$ is the spin matrix for the field $\Phi$. So, when $S$ acts on the field, should it not only transform the spin indices on the field? But it appears we are in the primed system of the coordinates on the LHS meaning that the coordinates have changed too?</p>
<p>Can someone provide some thoughts?</p>
<p>I was also wondering how Di Francesco obtained eqn (2.127). Here is what I was thinking: Expand $\Phi(x')$, keeping the 'shape' of the field (as Grenier puts it) the same, so $\Phi(x') \approx \Phi(x) + \omega_a \frac{\delta \Phi(x')}{\delta \omega_a}$. Now insert into (2.125) gives $$\Phi'(x') = \Phi(x') - \omega_a \frac{\delta x^{\mu}}{\delta \omega_a}\frac{\partial \Phi(x')}{\delta x^{\mu}} + \omega_a \frac{\delta F}{\delta \omega_a}(x)$$ which is nearly the right result except Di Francesco has a prime on the x at the final term. My thinking was he defined an equivalent function F in the primed system, i.e $F(\Phi(x)) \equiv F'(\Phi(x'))$. Are these arguments correct?</p> | g6766 | [
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<p>I'm trying to prove that, under the gauge transformation $$A_{\mu} \rightarrow A_{\mu}^{\prime} = g^{-1} A_{\mu} g + g^{-1} \partial_{\mu} g,$$ the non-abelian Chern-Simons Lagrangian density:</p>
<p>$$\mathcal{L}_{CS} = \kappa \epsilon^{\mu \nu \rho} tr \left( A_{\mu} \partial_{\nu}A_{\rho} + \dfrac{2}{3} A_{\mu}A_{\nu}A_{\rho} \right)$$</p>
<p>becomes:</p>
<p>$$\mathcal{L}_{CS} ~\longrightarrow~ \mathcal{L}_{CS} - \kappa \epsilon^{\mu \nu \rho} \partial_{\mu} tr \left( \partial_{\nu} g g^{-1} A_{\rho} \right) - \dfrac{\kappa}{3} \epsilon^{\mu \nu \rho} tr \left( g^{-1} \partial_{\mu} g g^{-1} \partial_{\nu} g g^{-1} \partial_{\rho} g \right)$$ </p>
<p>as stated in Gerald V. Dunne's lecture notes 'Aspects of Chern-Simons Theory' pages 15-16. </p>
<p>The second term in the last equation can be disregarded as it's a total derivative and the third term can be shown to be some integer multiple of $2\pi$ provided $\kappa$ is an integer.</p>
<p>Now I understand that gauge invariance of the CS-term can be proven using some clever reasoning (see: <a href="http://physics.stackexchange.com/q/19602/">Gauge invariant Chern-Simons Lagrangian</a>). However I want to show how we can arrive at the second equation above using the `brute force' method of plugging in the gauge transformed vector field into the Lagrangian. Unfortunately I get stuck with a large number of terms that I'm not sure how to combine or cancel. </p>
<p>Does anyone know of a source that goes through the above calculation in more detail, or does anyone have any tips for how to proceed. I've done a rather extensive search and can't find any sources that show some of the steps. I already tried using the cyclic properties of the trace and the cancelation of any symmetric term with the anti-symmetric $\epsilon^{\mu \nu \rho}$. </p>
<p>Thank you in advance for any suggestions.</p> | g6767 | [
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<p>According to Hubble's law, light and other kinds of electromagnetic radiation emitted from distant objects are redshifted. The more distant the source, the more intense is the redshift. Now, the expansion of the universe is expected to explain the redshift and its nearly linear dependence on distance between source and observer. But isn't there an other source influencing the redshift? We know that a light beam passing the Sun is deflected by the Sun's gravity in accordance with predictions made by Einstein's general theory of relativity. This deflection is dependant on a gravitational interaction between the Sun and the light beam. Thus, the position of the Sun is affected by the light beam, though by such a tiny amount that it is impossible to detect the disturbance of the Sun's position. Now, during its journey to the Earth a light beam, originating from a distant source in the Universe, is passing a certain amount of elementary particles and atoms. If the light beam interacts gravitationally with those elementary particles and atoms, affecting the microscopic mechanical properties of the individual elementary particles and atoms at issue, can this interaction be detected as a redshift of the light beam? If so, could we use this gravity redshift to measure the mean density of matter and energy in space? The beginning of the sentence "If the light beam interacts gravitationally with those elementary particles and atoms..." should be interpreted to say "If the light beam <em>interacts gravitationally</em> with those elementary particles and atoms by way of leaving them in a state of acceleration different from their initial state of acceleration...." This clarification seems to necessitate the additional question: "why would a gravitationally interacting object (a cluster of photons) passing another gravitationally interacting object (a mass) leave that mass in the same state as before the passage?" </p> | g6768 | [
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<p>This question seems to be naive, but I really want some intuitive way of understanding the reason.</p>
<p>Neglecting some trivial explanations, I have only one idea about this: the vacua state.</p>
<p>Consider the harmonic oscillator problem in quantum mechanics, there are the creator (operator) $a^\dagger$ and the annihilator (operator) $a$. The lower bound of energy exists due to the fact that there is a vacua state which is invariant under annihilator $\left|0\right>$:</p>
<p>$$ a \left|0\right> = 0$$</p>
<p>(while there is no such state for the creator) therefore the lowest energy state would be $\left|0\right>$ - a lower bound.</p>
<p>Is there a more general explanation or principle that demands the existence of lower bound of energy?</p>
<p>Is there any case there is a upper-vacua state (or should I say: saturated state)?</p> | g6769 | [
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<p>I thought for fun I might measure how my ceiling fan slows down when turned off, and maybe find out what forces act on it when it slows down. My problem is that for that I need to measure its rotational speed when it's turned on. When it's in the lowest speeds it's easy because you can see it rotate, but for higher speeds that's not an option.</p>
<p>I thought one way would be to use a strobe light and try to match up the frequency, but I don't have one of those. Can you think of any DIY way to measure the speed of a very fast ceiling fan?</p> | g6770 | [
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<p>Background Information:
I'm doing an experiment in which I place a bare tungsten wire in to various liqids, to measure a coefficient $\alpha $ in the equation
$$ Power Dissipated = \alpha * \Delta T $$
I was also given the equation:
$$R=R_0*(1+0.0045 \Delta T)$$
I decided to measure $R_0$ at a low voltage and current to stop the wire from heating up. Then I placed it in the liquid and measured the current going through the wire for a variety of voltages. </p>
<p>Originally I planed the substitute $Power Dissipated = V*I$ and obtain $R$ from the tangent of a V-I graph (can't use Ohms Law because the situation isn't ohmic)
Unfortunately once I have substituted the values into the formulae I got a different value for every data point (all in the same range 10^-7).
It made me wonder is there an equivalent formula for non-ohmic power I'm missing or is it something else entirely?</p> | g6771 | [
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<p>I understood that quantum field theory is essentially based on a problematic mathematical basis. Can someone please explain what is the fundamental problem to formulate QFT as a rigorous mathematical theory? It's clear that it has to do with renormalization but similar techniques are already exist in analytically number theory (and are considered to be a mathematical theory).</p> | g234 | [
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<p>If I charge a capacitor and connect one lead to ground keeping the other lead floating, will the capacitor discharge ?</p>
<pre><code> G-------||------ open/floating
+q -q
</code></pre>
<p>(G for ground)</p> | g6772 | [
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<p><em>(This question is <strong>not</strong> about coding)</em></p>
<p>I have built a little code in Python that allows the user to plot the energy vs the wave number of particle in a 2D box, depending on what values for the integers $p$ and $q$ they desire. </p>
<p>The energy $E_{p q}$ is given by:</p>
<p>$E_{p q} = \frac{\hbar^2}{2m}[\frac{p^2\pi^2}{a^2} + \frac{q^2\pi^2}{b^2}]$</p>
<p>The wave numvber $k_{p q}$ is given by:</p>
<p>$k_{p q} = \frac{p^2\pi^2}{a^2} + \frac{q^2\pi^2}{b^2}$</p>
<p><strong>Should the user be allowed to enter any values for $p$ and $q$ or should they only be allowed to enter matching values?</strong> (e.g.: $p=3$, $q=3$ and not $p=3$, $q=1$)</p>
<p><strong>Which results are more interesting, or are they all equally significant (why?)</strong></p>
<p>This is the sort of graph you get when you plot matching values:</p>
<p><img src="http://i.stack.imgur.com/QbuLF.png" alt="enter image description here"></p> | g6773 | [
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<p>I'm sure I'm not the only person with this problem at the moment. I have been asked to give a public (not quite public, scientists, just not physicists) about 'this <a href="http://en.wikipedia.org/wiki/Higgs_boson" rel="nofollow">Higgs boson</a> thing'. I am trying to think of a good analogy because even my own rather limited knowledge of the <a href="http://en.wikipedia.org/wiki/Higgs_mechanism" rel="nofollow">Higgs mechanism</a> stretches to realising how bad the swimming through treacle metaphor is. I was wondering about refraction although I'm not sure how well understood that will be by a general audience? Superconductivity might be ok for physicsts but again probably rather specific for a more general audience.</p>
<p>Any other tips on how to pitch such a talk are appreciated but I'm aware I have to pose a specific question and describing the Higgs mechanism is the real conundrum.</p> | g6774 | [
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<p>Can fusion and fission happen at the same time, in the same place? I was talking with a friend, and he thinks that fission and fusion happen at the same time at the sun, is that true? I guess this would cause perpetual motion, then I speculated that they could happen, but in different proportions and I believed that fusion is happening in a higher proportion than fission. What do you think? </p>
<p>I've searched on wikipidia, and I still found no mention to fission happening in the sun. </p> | g6775 | [
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<p>If I define the vector as $V_i=V^T_i+V^L_i$ and the transverse part is defined by $$V^T_i=\Big(\delta_{ij}-\frac{\partial_i\partial_j}{\partial^2}\Big)V_j$$ then is is obvious that $\nabla.V^T=0$ as well as $\nabla \times V^L=0$. What happened if I took the the divergence of the cross product of two different vectors with only transverse component? Are they zero too?
For example is $\nabla.(A^T\times V^T)=0?$</p> | g6776 | [
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<p>After listening of some <a href="http://www.youtube.com/watch?v=2DIl3Hfh9tY#t=782s" rel="nofollow">lectures</a> of Leonard Susskind about black holes, he mentioned that conservation of information is one of the foundations of physics. After searching the web I cannot seem to find how we came up with this theory. Could someone explain how we know this is true and/or how did we come to this conclusion?</p> | g235 | [
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<p>We often hear that Higgs boson is a scalar boson, and that Higgs field is a scalar field. I was always thinking that this means "4-scalar". In other words, it is space-time invariant, .i.e. it's properties are not changing if move relative to it. Unlike photon which changes it's frequency, polarization and other properties, if we look at it from moving frame, Higgs is always the same.</p>
<p>Is above correct? If not then what is correct and what is not?</p> | g6777 | [
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<p><strong>Setup</strong></p>
<p>Imagine a two-body system of masses under a classical mechanics model. The separation and mass-ratio doesn't matter for this example. Presume they are initially stationary.</p>
<p>Now suppose that we hold one of the masses, m1, permanently stationary with an external force opposing the gravitational force due to the second mass. This external force changes over time such that it always balances the gravitational force on m1.</p>
<p>Take the frame-of-reference centred on m1 - the stationary mass.</p>
<p><strong>Problem</strong></p>
<ol>
<li>If we think of the two bodies as as system, then we would say that
the centre-of-mass will accelerate from stationary, and will be
displaced in the same direction as the external force. Therefore,
positive work is being done on the system by the external force
(energy is added to the system).</li>
<li>However, consider the bodies individually. For m1, it experiences no
net force. Nor is it displaced. Therefore, we must conclude that no
work is done on m1. m2 only experiences a gravitational force, and
so is accelerated from stationary in the direction of the force.
Therefore work is done on m2.</li>
</ol>
<p>But, if energy is transferred to the system from an external source (as suggested from 1), which of the two objects received this energy?</p>
<p>It can't have been m1, since it was stationary. But how m2 gain this external energy when the external force acted on m1?</p> | g6778 | [
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<p>Does a complete theory of quantum gravity require anthropic post-selection? Certainly the black hole complimentarity and causal patch conjectures highlights the essential role of observers, at least in the asymptotic future of their future timelike trajectories. Does the measure problem in quantum gravity cosmology suggest that a "global god's eye view" of the universe might be an incoherent fiction? However, if observers are essential, don't we have to post-select to those states containing the observer of interest?</p>
<p>It might be suggested the S-matrix of string theory in a superselection sector with only a finite energy difference from the vacuum over a BPS background provides a counterexample, but can an asymptotic future state of noninteracting Fock space particles really support the future trajectory of an observer?</p> | g6779 | [
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<p>Lately, there has been a war between physicists and philosophers. Some of the exchanges can be found at <a href="http://www.nytimes.com/2012/06/10/opinion/sunday/what-physics-learns-from-philosophy.html?bl" rel="nofollow">http://www.nytimes.com/2012/06/10/opinion/sunday/what-physics-learns-from-philosophy.html?bl</a>, <a href="http://opinionator.blogs.nytimes.com/2012/05/10/can-physics-and-philosophy-get-along/?ref=sunday" rel="nofollow">http://opinionator.blogs.nytimes.com/2012/05/10/can-physics-and-philosophy-get-along/?ref=sunday</a> and www.3ammagazine.com/3am/time-lord/. are physics and philosophy compatible? Does physics need philosophy?</p> | g6780 | [
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<p>According to Newtons second law: F = ma, if acceleration is zero then the force must be zero, but assuming you have an object moving with a constant velocity of say 2 m/s, and that object strikes you, then obviously some sort of 'force' would be felt by you, so my question is what do you call that 'force' since it actually is not a 'force' and is there an equation to calculate it?</p> | g6781 | [
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<p>let be the Schroedinguer equation</p>
<p>$$ - \frac{d^{2}}{dx^{2}}y(x)+ae^{cx}y(x)=E_{n} $$ (1)</p>
<p>here a and c are constants.</p>
<p>i know how to solve it from <a href="http://eqworld.ipmnet.ru/en/solutions/ode/ode0232.pdf" rel="nofollow">http://eqworld.ipmnet.ru/en/solutions/ode/ode0232.pdf</a></p>
<p>but what is the condtion to get the energies ?? on the interval $ [0. \infty) $ or in other interval if you wish</p>
<p>the solution to (1) i know that is given in terms of the Bessel function but i have problems to get the energy quatnizatio condition i have tried a get a nonsense like</p>
<p>$$ J_{\sqrt{E_{n}}}(b)=0 $$ for a certain real number b but is this true ??</p>
<p>of course i know that semiclassically the energies satisfy </p>
<p>$$ 2\pi n \sim \int_{0}^{\infty} \sqrt{E_{n}-ae^{cx}} $$</p> | g6782 | [
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<p>The idea of the material Maxwell equation is almost clear. But I'm curious about the idea that except for material equation the pure Maxwell equation should work, but in harder sense: more currents and charges.</p>
<p>There are plenty of vacuum in solid body, so, I think, that there should be some precursors of electro-magnetic waves that propagates through the body: $v = c/n$ the speed of wave in body, but part of wave propagates in vacuum with the speed of $c$. And for <strong>any</strong> frequency some part of amplitude would be observed much earlier.</p>
<p>Is there some theory behind this and does this phenomena is observed?</p> | g6783 | [
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<p>all Lorentz observers watching a particle move will compute the same value for the quantity</p>
<p>$$ds^2 = -(c \, dt)^2 + dx^2 + dy^2 + dz^2,$$
$$ds^2 = g_{\mu\nu}dx^{\mu}dx^{\nu},$$
and ''ds/c'' is then an infinitesimal proper time. For a point particle not subject to external forces (''i.e.,'' one undergoing inertial motion), the relativistic action is:</p>
<p>$$S = -m_oc \int ds.$$</p>
<p><strong>Remark:</strong> An edit to the comment.
we can write a Lagrangian for a relativistic particle, which will be valid even if the particle is traveling close to the speed of light. To preserve Lorentz invariance, the action should only depend upon quantities that are the same for all (Lorentz) observers.</p> | g6784 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/9415/why-do-electrons-occupy-the-space-around-nuclei-and-not-collide-with-them">Why do electrons occupy the space around nuclei, and not collide with them?</a><br>
<a href="http://physics.stackexchange.com/questions/20003/why-dont-electrons-crash-into-the-nuclei-they-orbit">Why don’t electrons crash into the nuclei they “orbit”?</a> </p>
</blockquote>
<p>From what I learned in chemistry, the protons in the nucleus pull the electrons in and push on each other through electromagnetic forces, but are held in place by the strong nuclear forces in its gluons. Not much was said, however, about what keeps the electrons orbiting. I've always just assumed it was other electrons that prevented an electron from becoming part of the nucleus. In the form of Hydrogen that only has one electron, what keeps that electron from being pulled completely into the nucleus? </p> | g132 | [
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<p>Everybody knows you can produce electrostatic charge rubbing two different materials together. But have you ever smelt e.g. at the plastic after charging it? There actually is a distinct electrostatic charge smell :-) While normally smelling involves the transport of molecules, what you are smelling here, is the electric field itself, or do you? What is happening?</p> | g6785 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/13170/particle-physics-plots">Particle physics plots</a> </p>
</blockquote>
<p>I have seen graphs like this in lots of talks by phenomenologists talking about the Higgs search (see for example <a href="http://prl.aps.org.proxy.uchicago.edu/abstract/PRL/v104/i6/e061802" rel="nofollow">FIG 3 in this paper</a> or <a href="http://resonaances.blogspot.com/2010/07/higgs-still-at-large.html" rel="nofollow">this blog post</a> or <a href="http://quark.phy.bnl.gov/~dawson/chicago1.pdf" rel="nofollow">slide 38 of this presentation</a>). I believe the y-axis is some sort of scaling, $R_{lim}$, applied to the expected Standard model signal, but I don't understand what is the source of this in the experiment and why it is different from $1$. It appears to be some sort of a <a href="http://en.wikipedia.org/wiki/Bayesian_probability" rel="nofollow">Bayesian</a> calculation but I do not understand what exactly is being calculated.</p>
<p><img src="http://i.stack.imgur.com/7bhbn.png" alt="enter image description here"></p>
<p>Thanks!</p> | g236 | [
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<p>I have learned (the basics) of how one can incorporate the principles of special relativity to quantum mechanics to obtain quantum field theory. Can the same be done with GR and QM to obtain a new theory? If not, what happends if one tries, what exactly goes wrong? Is there a mathematical inconsistency in any theory that combines them, such that either current GR or QM must be modified, or is it just that we dont know how to yet?</p> | g6786 | [
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<p>I need to draw a graph of measurements of time for a ball to drop on an inclined plane, with error bars, along with lines of best and worst fit. The problem is that I need to do this on the computer and I am unsure about what graphing package I can use to do this and how to go about doing it. I have access to Wolfram Mathematica 7, but I'm unsure about graphing points with uncertainties.</p> | g6787 | [
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<p>I've consulted several books for the explanation of why </p>
<p>$$\nabla _{\mu}g_{\alpha \beta} = 0,$$</p>
<p>and hence derive the relation between metric tensor and affine connection $\Gamma ^{\sigma}_{\mu \beta} $</p>
<p>$$\Gamma ^{\lambda } _{\beta \mu} = \frac{1}{2} g^{\alpha \gamma}(\partial _{\mu}g_{\alpha \beta} + \partial _{\beta} g_{\alpha \mu} - \partial _{\alpha}g_{\beta \mu}).$$</p>
<p>But I'm getting nowhere. May be I've to go through the concepts of manifold much deeper. </p> | g6788 | [
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<p>Basically I wonder what happens to emitted radiation by douubling a light e.g. twice the surface area of the sun will emit how much more radiation? 4 times more? Is there a formula?</p> | g6789 | [
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<p>Particularly in the case of Majorana neutrinos, it seems a little odd that the particle and antiparticle would have differing cross sections.</p>
<p>Perhaps the answer is in here, but I've missed it:
<a href="http://pdg.lbl.gov/2013/reviews/rpp2013-rev-nu-cross-sections.pdf" rel="nofollow">http://pdg.lbl.gov/2013/reviews/rpp2013-rev-nu-cross-sections.pdf</a></p>
<p>In the caption of figure 48.1 of the PDG excerpt linked above, it says "Neutrino cross sections are typically twice as large as their corresponding antineutrino counterparts, although this difference can be larger at lower energies."</p>
<p>Is it common for particles to have different cross sections from their corresponding antiparticle?</p>
<p>Is there a reason for this difference? Can we theoretically predict the magnitude of this difference?</p> | g6790 | [
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<p>I have learned that a torque on an object due to the gravity can be calculated as if the gravity acts on the center of mass of the object when the object is near the surface of the earth.</p>
<p>Now I want to prove it...</p>
<p>So, I have $$\tau=\int d\tau=\int r(dmg)sin\theta=g\int rsin\theta dm.$$</p>
<p>Then, how do you obtain $$\int rsin\theta dm= mr_{cm}sin(\theta_{cm}),$$ where $r_{cm}$ is the distance between an axis of rotation and the center of mass, and $\theta_{cm}$ is the angle between the two vectors $\vec{r_{cm}}$ and $m\vec{g}$ at the center of mass??? Would $$\int r dm=mr_{cm}$$ be helpful to prove this?</p>
<p>Would the integral be dependent on the object I use, or would there be a general way to prove this?</p> | g6791 | [
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<p>To quote from Wikipedia on elastic scattering, "In this scattering process, the energy (and therefore the wavelength) of the incident photon is conserved and only its direction is changed."</p>
<p>How does this work? The impacted particle will also start moving to conserve momentum. So it'll also carry some energy. How can the photon not lose any energy during the collision?</p>
<p>Another possibly unrelated question: how exactly can the photon and the particle interact? The photon essentially carries information about a changing electromagnetic field. How can it influence a particle that carries neither charge nor magnetism?</p> | g6792 | [
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<p>Can someone explain to me how to solve $6.6738410\times 10^{-11}\ \text{m}^3\ \text{kg}^{-1}\ \text{s}^{-2}$, the formula to find the <a href="http://en.wikipedia.org/wiki/Gravitational_constant" rel="nofollow">gravitational constant</a>?</p>
<p>I'm writing a bunch of reports about the scientific perspective about the video game Minecraft, and I'm trying to find the gravitational constant of Minecraft. I'm having a little bit of trouble solving $6.6738410\times10^{-11}\ \text{m}^3\ \text{kg}^{-1}\ \text{s}^{-2}$, as I don't know what many of the variables are. Some I get, like $\text{m}$ is the mass of something, $\text{kg}$ is something's weight in kilograms, and $\text{s}$ [for seconds] is the time it takes an object to fall in seconds.</p>
<p>It would be really helpful if someone could explain to me what some of these variables mean, and help guide me through the equation. </p> | g6793 | [
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<p>I am working on some radiative transfer equations, and struggling as I'm fairly new to this field. I have read about the Rayleigh Phase Function which is:</p>
<p>$P(\theta) = \frac{3}{4}(1 + cos^2 \theta)$</p>
<p>I can plot this function, and generate values from this function in my computer program (which is what I need to do) - but what is it actually telling me? If I know I have a ray of incident light at a certain angle, will this function tell me what angle it will scatter at? Or is it more of a statistical generalisation where the areas where the function is higher are the angles at which the scattering is more likely to happen?</p>
<p>Furthermore, when I see the function plotted it is always from 0-180, rather than 0-360 as I would expect for the scattering. This makes me think that the function may be giving the difference between the incoming angle and the outgoing angle rather than the absolute angle it is scattered at. Is that correct?</p> | g6794 | [
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<p>This remark from Lubos puzzles me</p>
<blockquote>
<p>Ramond's string - and Neveu-Schwarz string - wasn't really an "origin of string theory". String theory had "origin" as bosonic string theory which has no fermions. All SUSY/fermioncs strings are "new".</p>
</blockquote>
<p>How to fit this view, which seems to be the common one, with the fact that the R and NS papers date from 1971, before the concept of supersymmetry, long before superstrings themselves, and only three years later than the Veneziano model, and almost simultaneous (less than two years) with the idea of a String interpretation of the model? </p>
<p>Were the R-NS models just a hep-th proposal, without any link to, nor motivation from, phenomenology? It could be so. I can not find any clear reference to baryonic regge trajectories in the early literature, and I can not find any duality diagram involving fermions, before 1971. But on other hand, Susskind 1970 abstracts keep speaking of "model of hadrons", not just "mesons", when exposing the idea of strings. So perhaps I am just being sloppy in my spires searches. </p> | g6795 | [
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<p>So as part of a video I'm working on, I'm trying to launch a 10kg table about 8m into the air. A machinist friend of mine has provided a solution that involves pneumatic cylinders and a pump to generate the force needed to propel the table. </p>
<p>What we're trying to calculate is the amount of PSI needed to lift the table. All these calculations don't need to be exact (if it only goes 16m up, then there's no issue)</p>
<p>I don't know where to even start to figure it out. Once gravity gets involved, it throws me off.</p>
<p>Any real help would be appreciated, thanks!</p> | g6796 | [
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<p>Below is a picture of a simple pendulum clock. Suppose that the bob (a rigid disk) on the end of the pendulum can spin without friction about its geometrical axis and is spinning at an angular velocity $\omega=const$. Will the clock gain or lose time compared to the ordinary pendulum clock. Or it does not have any effect on the time? If it does then what is the percentage? Ignore air drag.</p>
<p><img src="http://i.stack.imgur.com/ZSwHI.jpg" alt="enter image description here"></p> | g240 | [
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<p>What I mean is could it turn out that the world is not described by string theory / M-Theory, but that nevertheless some version of one of these extra-dimensional theories is true?</p>
<p>I have no real background in this area. I just read Randall and Sundrum's 1999 paper "A Large Mass Hierarchy from a Small Extra Dimension" (http://arxiv.org/PS_cache/hep-ph/pdf/9905/9905221v1.pdf). Other than the use of the term "brane" and a couple of references to string excitations at TeV scale, I don't see much about string theory, and I notice their theory only requires 1 extra dimension, not 6 or 7.</p> | g6797 | [
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<p>When a lambda particle decays into proton and a pion, I am told it does not conserve parity. Why?</p> | g6798 | [
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<p>Show that: $$\int _v \vec{J} dV = \frac{d \vec{p}}{dt}$$</p>
<p>Here's my attempt: $$\vec{p} = \int _v \rho r dV \rightarrow \frac{d}{dt} \int _v \rho r dV = \int _v \vec{J} dV = \int _v \frac{\partial p}{\partial t}r = \int _V \vec{J} dV$$ </p>
<p>Because of the fact that $\nabla \cdot \vec{J} = - \frac{\partial p}{dt}$ we have $$ \int _v (\nabla \cdot \vec{J})rdV$$</p>
<p>I'm not exactly sure how to turn this divergence of the current density per unit volume into the original $\int _v \vec{J} dV$ </p>
<p>The last expression is very close to equaling the current, maybe we could use that? </p> | g6799 | [
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<p>I've been reading an introduction to quantum mechanics online, and while constructing the Schrodinger equation for a free particle, the equation $i\hbar \frac{d \Psi}{dt}=\hbar\omega\Psi$ is obtained. </p>
<p>It is then explained that if $i\hbar \frac{d}{dt}$ is considered as an operator, then the equation means "that when it operates on $\Psi$, the result we get back is the energy eigenvalue of the wave." </p>
<p>It's clear to me that $\Psi$ is an eigenfunction of $i\hbar\frac{d}{dt}$, with the eigenvalue being $\hbar\omega$, but I don't understand why they say that $\hbar\omega\Psi$ is the "energy eigenvalue of the wave." </p>
<p>As far as my understanding goes, $\hbar\omega$ gives the energy of a photon with angular frequency $\omega$, and so it's unclear to me why the energy of a photon multiplied by $\Psi$ would be of particular significance. </p>
<p>Furthermore, I don't think I understand what is meant by the statement "the energy eigenvalue of the wave". </p>
<p>If anyone could help explain these concepts (preferably without presupposing too much knowledge of QM) that would be great.</p> | g6800 | [
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<p>Consider a real scalar field operator $\varphi$. It can be written in terms of creation and anihilation operators as
$$\varphi(\textbf{x})=\int \tilde{dk}[ a(k)e^{i\textbf{kx}}+a(k)^{\dagger}e^{-i\textbf{kx}}]$$
where $\tilde{dk}$ is a Lorenz-invariant measure.
If $\varphi$ is interpreted as creating a particle at $\textbf{x}$ when acting on the vacuum, what is its action on a generic state? It seems to be creating a superposition of a state with one added quantum of energy through the creation operator, and a state with one less quanta of energy through the annihilation operator.</p> | g6801 | [
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<p>I am taking an introductory course on quantum mechanics and would like to understand this.
Do forces act in quantum mechanics?
In orbitals, is the charge of an electron dispersed, with a higher charge at places with a higher probability of finding an electron?
Is there any centripetal force/acceleration at the quantum mechanical level?
Thank you.</p> | g6802 | [
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<p>I read that the reason solids emit continuous spectra is that they don't have time to let their electrons decay-they are too close together. Given that electrons decay on the order of 100 nanoseconds I find this difficult to believe. Also, do electromagnetic waves move the electrons, or the atom, or both? If it is simply exciting the electrons, I don't know why is should also give way to the vibration of the atoms. If it does give way to vibration, then shouldn't gases <em>also</em> give way to continuous spectra?</p> | g6803 | [
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<p>For some reason I am suddenly confused over something which should be quit elementary.</p>
<p>In two-dimensional CFT's the two-point functions of quasi-primary fields are fixed by global $SL(2,\mathbb C)/\mathbb Z_2$ invariance to have the form</p>
<p>$$\langle \phi_i(z)\phi_j(w)\rangle = \frac{d_{ij}}{(z-w)^{2h_i}}\delta_{h_i,h_j}.$$
So a necessary requirement for a non-vanishing two-point function is $h_i = h_j$. Now consider the Ghost System which contains the two primary fields $b(z)$ and $c(z)$ with the OPE's</p>
<p>$$T(z)b(w)\sim \frac{\lambda}{(z-w)^2}b(w) + \frac 1{z-w}\partial b(w),$$
$$T(z)c(w)\sim \frac{1-\lambda}{(z-w)^2}c(w) + \frac 1{z-w}\partial c(w).$$
These primary fields clearly don't have the same conformal weight for generic $\lambda$, $h_b\neq h_c$. However their two-point function is</p>
<p>$$\langle c(z)b(w)\rangle = \frac 1{z-w}.$$</p>
<p>Why isn't this forced to be zero? Am I missing something very trivial, or are there any subtleties here?</p> | g6804 | [
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<p>I know (from Kinematics) that for an object moving linearly with an acceleration and without air resistance the following equations can be used to determine v(velocity) or x(position of the object) at any time:</p>
<p>$v=v_0+at$</p>
<p>$x=x_0+v_0t+\frac{1}{2}at^2$</p>
<p>Where $x_0$ is the position of the object at the start of accelerated movement, $v_0$ is the velocity at the start of the motion and a is the acceleration.</p>
<p>Now if I want to add air drag, say we take the formula for air drag as:</p>
<p>$D=0.5CA\rho v^2$</p>
<p>$C$ is a coefficent, $A$ is the reference Area, $\rho$ is the density and $v$ the velocity.
Since $D$ is a force the air drag results in an acceleration, so in other words: The resulting acceleration is $a-D/m$, however $D$ depends on $v$, which depends on the acceleration. And that's where my problem is, I simply can't wrap my mind around that.</p>
<p>How would I go about getting the Equations for $x$ and $v$ including air drag (and don't forget there's acceleration too)?</p> | g6805 | [
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<p>I tried to solve the following problem:
There are 2 objects . The object m1 with charge q and the object m2 with charge q.(same charge).The object m2 is connected with a rope to the ceiling. </p>
<p>at the initial state , m1 and m2 were on the same height.
When the object m2 is placed in distance d from the object m1, the following situation occurs:
<img src="http://i.stack.imgur.com/KhKjc.png" alt="enter image description here"></p>
<p>Please ignore the force of gravity between the masses and ignore any kind of friction.
just consider the tension , electrical force and mg.</p>
<pre><code>m2 : ΣFx,y=0
</code></pre>
<p>You have to find x.</p>
<p>You can use the parameters k(Coulomb's constant), q , L , d , mg.</p>
<p>I was able to find only 2 equations that would help to solve the problem but one is still missing.</p>
<p>I wasn't able to calculate the components of the electrical force.
The equations that I found are :</p>
<p>1) r ^ 2 = (L-Lcos a) ^ 2 + (x+d) ^ 2
(r is the distance between the two objects)</p>
<p>2) sin a = x / L</p>
<p>3) as you can see ΣFx = 0 and ΣFy = 0 (The object m2),
but without the components of the electrical force I wansen't able to calculate anything.</p> | g6806 | [
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] |
<p>Just curious ... </p>
<p>Known facts:</p>
<ul>
<li>When outside the atmosphere levels of radiation are higher</li>
<li>Typically such radiation is CBR, Solar Radiation</li>
</ul>
<p>Question:</p>
<p>If the matter of the atmosphere and magnetosphere as shields is kept aside for a moment, does gravity affect radiation incident on the planet?</p> | g6807 | [
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<p>I have a differential equation of the form </p>
<p>$ \frac{d^2 y}{dt^2} + f(t) \frac{dy}{dt} + g(t) y = 0 $</p>
<p>where $f$ and $g$ are known functions of time. </p>
<p>Is there a systematic (or otherwise) way of finding the conserved quantities, if there are any?</p>
<p>I've been trying to google this topic, but haven't had much success yet. Perhaps someone with more mathematical knowledge than myself (i.e. almost everyone) can point me in the right direction. Even phrases to search for would help.</p> | g6808 | [
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<ol>
<li>Is there a simple intuitive way to understand the difference between left-handed and right-handed fermions (electrons say)? </li>
<li>How to experimentally distinguish between them?</li>
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<p>[sorry, this way below the level of this forum -- flames are most welcome]</p>
<p>When a photon is absorbed by a piece of matter that does not reflect it -- where does the photon "go"? Eg, one shines light at a black object -- clearly the photon arrives at the object and then, well, vanishes. Or does it?</p>
<p>Thanks very much.</p> | g6810 | [
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<p>According to the equation $V = E-Ir$, the gradient of a graph of $V$ against $I$ should be $-r$ (internal resistance) and the Y intercept should be the EMF. Am I right?</p>
<p>In an experiment I used a constant wind speed to drive a small motor, keeping everything constant and changing the resistance in the circuit using a variable resistor, measuring the output in volts. How is it that the graph shows a positive gradient (and therefore a negative internal resistance ?).</p>
<p>The equation of the line is $0.0732934 + 0.0396359x$.</p>
<p><a href="http://cl.ly/image/0b3i393E0E0G" rel="nofollow">http://cl.ly/image/0b3i393E0E0G</a></p> | g6811 | [
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<p>The world <em>A Song of Fire and Ice</em> series is set on is characterized by seasons that last several years (how years are measured on this planet is not specified to my knowledge). However, they are of unpredictable, variable lengths, though seemingly in balance (long summers are followed by long winters). Rather than some sort of massive El Niño, it seems to be a result of something astrophysical, as winter can be forecast by the shortening of days.</p>
<p>Is there some possible mechanic for this or is it outside the realm of possibility?</p> | g6812 | [
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<p>Consider the Newtonian gravitational potential at a distance of Sun:</p>
<p>$$\varphi \left ( r \right )~=~-\frac{GM}{r}.$$</p>
<p>I write the classical Lagrangian in spherical coordinates for a planet with mass $m$:</p>
<p>$$L ~=~ \frac{1}{2}m (\dot{r}^{2} + r^{2}\dot{\theta ^{2}} + r^{2}\dot{\phi ^{2}}\sin^{2}\theta ) + \frac{GM}{r},$$</p>
<p>and find that the canonical momentum $p_{\phi }$ is a constant of motion, because:</p>
<p>$$\dot{p_{\phi }}~=~ \frac{\partial L}{\partial \phi} ~=~ 0.$$</p>
<ol>
<li><p>What is the physical interpretation of the canonical momentum?</p></li>
<li><p>How can we from the Lagrangian see that it is a constant of motion?</p></li>
</ol> | g6813 | [
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<p>Today I had a discussion with a colleague who teaches electricity and magnetism to 2nd year undergraduate physics students. He is seeking the best way to explain how is the <a href="http://en.wikipedia.org/wiki/Electromotive_force#Chemical_sources" rel="nofollow">emf generated inside a battery</a> with a minimal appeal to physics beyond classical. We have lamented that some textbooks refer to "non-electromagnetic chemical forces" since all of chemistry is essentially electrostatics+quantum mechanics. </p>
<p>Our proposal is to draw the students' attention to the existence of atoms which can not be explained by classical mechanics + classical electromagnetism. In the same vein the forces on charge carriers in galvanic cells are electromagnetic but the response is not classical. Thus a battery "amplifies" non-classicality to the level macroscopic electricity. It is not that forces are non electrostatic but the systems response is not classical. Can you recommend textbooks or online sources that use/expand this idea?</p>
<p>(the main tag for this question should be "teaching" but I'm too much of a rookie here to create one)</p> | g6814 | [
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<p>The conclusion of <a href="http://lenr-canr.org/acrobat/KarabutABanalysisof.pdf" rel="nofollow">this paper</a> (p. 6) discusses some hypothetical Pd(d,f) yields as a possible explanation for anomalous results that the author observed. Suspending disbelief in the data reported in the paper for a moment, what are some good ways to go about exploring the feasibility of a set of fission chains along these lines, given an arbitrary amount of energy? Here is one that was mentioned as a possibility:</p>
<blockquote>
<p>${{}^{104}Pd} + 2D \rightarrow [Pd;2D]* \rightarrow {{}^{44}Ca} + {{}^{64}Ni} + 45.44 MeV$</p>
</blockquote>
<p>The proposed [Pd;2D]* intermediate step is an "intermediate short-lived neutron excessive compound-nucleus," according to the paper.</p>
<p>I was able to find <a href="http://www-nds.iaea.org/exfor/exfor.htm" rel="nofollow">an interface</a> to the EXFOR database, and using a query with the the parameters [Target="Pd-104", Reaction="d,*"], the results seem to indicate that there are only nine known or hypothesized Pd-104 + D reactions, and none of them involve fission.</p>
<p>My questions:</p>
<ol>
<li>Am I missing a basic detail here? Have I done something wrong?</li>
<li>Are there better ways to go about exploring the feasibility of the proposed chains? For example, would a simple back-of-the-envelope calculation have gotten me this far (aside from an objection about Coulomb repulsion)?</li>
<li>How likely is it that an actual Pd+D chain would not be available in EXFOR? What conclusions can I draw about the presence or absence of a chain in EXFOR? (I understand that some of the entries are hypothetical.)</li>
</ol>
<p>These questions are methodological ones, about how to look into the merits of the paper's proposal about palladium fission chains, rather than ones about the actual merits of the proposal (which I assume takes the author into left field).</p>
<p><strong>EDITS:</strong> Changed example reaction from one of deuteron absorption to an actual fission chain (also from the paper), modified details to relate to the new reaction. Mentioned an important assumption regarding input energy.</p> | g6815 | [
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<p>Say Silicon and boron doped silicon. Would the doping affect the binding energy? Could I see this in an XPS spectra?</p> | g6816 | [
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<p>Is there any facet of the energy emitted by a human body that is consistent and unique - like a fingerprint, but a signal that could be detected by a remote device?</p> | g6817 | [
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<p>Adiabatic approximation or the Born-Oppenheimer approximation is used whenever the electronic motion is too fast that the electrons effectively see static nuclei and the nuclei, in turn, see an averaged electronic cloud. My question is: </p>
<ol>
<li><p>As the word 'adiabatic' suggests no heat/energy transfer, does this mean that the energies associated with nuclear and electronic motions are non-transferable?</p></li>
<li><p>If my understanding is right, the limiting criterion of the approximation is when transfer can no longer be neglected. My other question is how to judge when the transfer is significant?</p></li>
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<p>I am facing some problems in understanding what is the importance of a <a href="http://en.wikipedia.org/wiki/Killing_vector_field" rel="nofollow">Killing vector field</a>? I will be grateful if anybody provides an answer, or, refer me to some review or books. </p> | g6819 | [
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<p>When doing perturbation theory in quantum mechanics, if the perturbation hamiltonian is made of three terms :
$$W = W_1 +W_2 + W_3,$$
can I treat each term separately and performing perturbation theory for each one of them, then adding the perturbed energies together to get the total energy ?</p>
<p>$$ E \stackrel{?}{=} E^0 + E_1^1 +E_2^1 +E_3^1 $$
where $E^0$ is the energy of the unperturbed hamiltonian, and $E^1_j$'s are energies at first order of $W_j$'s.</p>
<p>Edit : What about degenerate perturbation theory ?</p> | g6820 | [
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<p>When one drops a pebble in a body of water, one can observe multiple waves emanating from the point the pebble came in contact with water. Be it because the water "jumps" up and comes back down, creating more waves or because the water does "up and down" motion, there are definitely many waves.</p>
<p>But when one snaps ones fingers, thus creating a wave in the air, there is only one clear sound, no multiple, diminishing snaps (unless there is echoes, but this is not a concern), unlike one would expect just by observing waves in water. Why is this?</p> | g6821 | [
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<p>I am working a problem concerning a 3 axis gryoscope, the spinning mass is a magnet (dipole). This is part of a optical sensing device. The inner gimbal is for pitch rotation, and the outer gimbal is for yaw precession. The outer gimbal is fixed in the sensor casing. The whole assembly is well balanced and not affected by gravity. The casing contains 4 electrical coils located at 90 degree intervals. These coils are pulsed to make the magnetic rotor spin as in a motor. There is another coil that is wrapped around the casing and it is pulsed to precess the gyro in pitch and yaw. The spinning mass is on a bearing through which extends a non spinning axis (forward). On the end of that axis is an optical sensor (which does not spin). The outer casing clearly will limit the range of pitch and yaw motion. And technically, it is desirable to not come into contact with it. The part that would come into contact is the optical sensor. There are other sensors that keep up with spin speed, pitch and yaw gimbal angle, and dipole location. This is needed to be able to send proper spin and precession commands.</p>
<p>I have built a very good simulink model using Euler's torque equations, and all of the primary suff works. I even have a good idea of how to model the impact of the rotor precessing INTO the casing wall (reflect the pitch and yaw rotor velocities). But I cannot seem to figure out how to do the other case: Casing rotating into the rotor, where rotor precessions are essentially zero. How do I trasfer the casing momentum to the rotor and still keep the solution physically bounded by the casing itself?</p>
<p>Since the casing is mounted in a moving platform with 6 DOF, it can clearly rotate into the rotor. But remember, only the non-spinning part of the sensor will touch the casing, so the angular momentum of the rotor is not DIRECTLY involved with contact.</p>
<p>Thank you, and sorry for the long description, MikeO</p>
<p>Here is a graphic, certainly not scale. And the design is such that the optical sensor would contact the encasement before the rotor could. Two spin coils are not depicted. This drawing is purely conceptual. In the actual device, the gimbals are quite small and hidden inside a hollow spot within the center of the rotating gyro mass. You cannot see the gimbals. </p>
<p><img src="http://i.stack.imgur.com/6sYwH.jpg" alt="Precession Commanded Gyro"></p>
<p>The inertia tensors for the case and the rotor are known. The gimbals are taken as inconsequential. The intertia tensor of the case is much larger than that of the gyro and can be seen to be unaffected by the gyro. Whether the case rotates about the rotor, or the rotor rotates does not matter (by rotate, I mean pitch and yaw, not spin). The only parts of the entire assembly that can come into contact are the non-rotating optical sensor assembly and the case wall. Therefore the rotor will not touch the case. I am looking to write a conservation of angular momentum equation that would describe the initial rotations (pitch and yaw) of the rotor assuming the rotor was not pitching or yawing at the time of contact, in other words, the case rotated into the optical sensor which in turn transmits torques about the gimbal axes.</p>
<p>In the equations v1=u1*(m1-m2)/(m1+m2) + u2*(2*m2/(m1+m2)) and
v2=u2*(m2-m1)/(m1+m2) + u1*(2*m1/(m1+m2))</p>
<p>May I subsitute the inertia tensors for mass and the body rates for velocities?</p>
<p><img src="http://i.stack.imgur.com/yHh2X.jpg" alt="enter image description here">
<img src="http://i.stack.imgur.com/zY9jK.jpg" alt="enter image description here">
<img src="http://i.stack.imgur.com/ULXOk.jpg" alt="enter image description here"></p>
<p>The problem I am trying to solve is how to compute the reactions at the the boundry (the cylinder that blocks motion). I think I have solved the problem of what to do when the gyro is driven into the wall... I am reflecting the precession values (pitch and yaw). But the other problem is harder... what to do when the cylinder is driven into the gyro. Remember, the rotating mass never comes into contact with the wall, just the non-rotating mass at the end of the axle (spin axis). At first glance, it might seem that the answer is the same, but it does not work. I need to be able to calculate the "imparted torque" from the collision, and confine computed location within the cylindrical boundary.</p> | g6822 | [
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<p>We can derive Lagrange equations supposing that the virtual work of a system is zero.</p>
<p>$$\delta W=\sum_i (\mathbf{F}_i-\dot {\mathbf{p}_i})\delta \mathbf{r}_i=\sum_i (\mathbf{F}^{(a)}_i+\mathbf{f}_i-\dot {\mathbf{p}_i})\delta \mathbf{r}_i=0$$</p>
<p>Where $\mathbf{f}_i$ are the constrainded forces and are supposed to do no work, which it's true in most cases. Quoting Goldstein:</p>
<blockquote>
<p>[The principle of virtual work] is no longer true if sliding friction forces are present [in the tally of constraint forces], ...</p>
</blockquote>
<p>So I understand that we should <strong>exclude friction forces</strong> of our treatmeant. After some manipulations we arrive to:</p>
<p>$$\frac{d}{dt}\frac {\partial T}{\partial \dot q_i}-\frac{\partial T}{\partial q_i}=Q_i$$</p>
<p>Further in the book, the <a href="http://en.wikipedia.org/wiki/Rayleigh_dissipation_function" rel="nofollow">Rayleigh dissipation function</a> is introduced to <strong>include friction forces</strong>. So given that $Q_i=-\frac {\partial \mathcal{F}}{\partial \dot q_i}$ and $L=T-U$, we get:</p>
<p>$$\frac{d}{dt}\frac {\partial L}{\partial \dot q_i}-\frac{\partial L}{\partial q_i}+\frac {\partial \mathcal{F}}{\partial \dot q_i}=0$$</p>
<p><strong>Question:</strong> Isn't this an inconsistency of our proof, how do we know the equation holds? Or is it just an educated guess which turns out to be true?</p> | g6823 | [
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<p>It is written in Jackson (page 3) :</p>
<blockquote>
<p>In fact, though there are <strong>recurring attempts</strong> to eliminate explicit reference to the fields in favor of action-at-a-distance descriptions of the interaction of charged particles, the concept of the electromagnetic field is one of the most fruitful ideas of physics, both classically and quantum mechanically.</p>
</blockquote>
<p>What does he mean?</p>
<p><strong>What advantages can a action-at-a-distance description have over the field view of forces, that makes (at least some) people try toward that description?</strong></p> | g6824 | [
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<p>I am confused as to how a particular equation in Thornton & Marion's 'Classical Dynamics of Particles and Systems' was derived. It is equation 9.88, on page 354 of the fifth edition.
<br/>
An incoming particle, $m_1$, is fired with kinetic energy $T_0$ at a stationary particle, $m_2$. After the collision, the incident particle $m_1$ deflects at an angle $\psi$ with kinetic energy $T_1$, while the target particle $m_2$ deflects at an angle $\zeta$ with kinetic energy $T_2$. All quantities are measured in the lab frame.
<br/>
The equation in question is
$$
\frac{T_2}{T_0} = 1 - \frac{T_1}{T_0} = \frac{4m_1m_2}{(m_1+m_2)^2}\cos^2(\zeta).
$$
The only seemingly relevant equation given immediately before this equation is the following:
$$
\frac{T_1}{T_0} = \frac{m_1^2}{(m_1+m_2)^2} \left[ \cos{\psi} \pm \sqrt{ (\frac{m_2}{m_1})^2 - \sin^2{\psi}} \right]^2.
$$
I am sure that the second equation must somehow lead to the first, but I don't see how. If I could find a relation between $\zeta$ and $\psi$, I am sure that would help.</p> | g6825 | [
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<p>I think about a rotating torus (simplified tire) filled with ideal gas. Mass of gas is $m$ and molar mass is $M$. Pressure in non rotating torus is $p_0$. Temperature is constant $T$. Inner radius of torus is $r$ and outer radius is $R$.</p>
<p>Then the cylinder begins to rotate with angular velocity $\omega$</p>
<p>How can I derive difference of pressures near the wall between inner wall and outer wall? Do I need more data (for a simple model)?</p>
<p>If someone knows how to make it numerically, It would be also interesting for me.</p>
<p>I would also appreciate if someone could tell which book should I read to know more about solving such problems.</p> | g6826 | [
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<p>When a domain is aligned to an exterior uniform magnetic field.
There are no forces acting on it?
Magnetization force = 0, and all other force?</p> | g6827 | [
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<p>I am a student who is interested in scientific facts. I want a simple definition for <a href="http://en.wikipedia.org/wiki/Radiation" rel="nofollow">radiation</a>. Neither too scientific, nor too simple.</p> | g6828 | [
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<p>Whilst studying for my physics courses, I like to drink tea. Today, I noticed that if you pull a bag of tea out of a hot cup of water, it gradually starts to rotate, picking up speed as time progresses and reaching a asymptotic speed after a while. My first question is: why does it start rotating? Of course it has something to do with the liquid water entering the gas phase just above the cup of tea, but how does that give the bag of tea a directed motion to one side? I presume that the momentum of the gaseous water is quite randomly directed vertically, so I don't see a reason for a horizontal rotation. Second question, how is the direction determined? I haven't tried, but might the direction of rotation be equally probable to be left-handed and right-handed? Third question: might the shape of a tea bag have an influence on what we observe? If we take a pyramid tea bag, for example, does the behavior change?
I will perform some of these experiments while making my cup of teas and report back to you :)</p> | g6829 | [
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<p>How does one go about accurately modeling sound propagation in a room (with reflections, absorption, and diffusion characteristics) from the motion of a loud speaker? More specifically what are the governing equations that are needed? Obviously Naiver-Stokes but this is too general? Is there an easier way?</p> | g6830 | [
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<p>Lets say we have a complex vector $\vec{z} \!=\!(1\!+\!2i~~2\!+\!3i~~3\!+\!4i)^T$. Its scalar product $\vec{z}^T\!\! \cdot \vec{z}$ with itself will be a complex number, but if we conjugate the transposed vector we get $\overline{\vec{z}^T}\!\! \cdot \vec{z}$ <em>(this is a inner product right?)</em> and a positive real number as a result:</p>
<p>\begin{align*}
\overline{\vec{z}\,^{T}}\! \cdot \vec{z}&=\begin{pmatrix}1-2i&2-3i&3-4i\end{pmatrix} \begin{pmatrix}1+2i\\2+3i\\3+4i\end{pmatrix} =\\
&=\begin{pmatrix}(1-2i)(1+2i) + (2-3i)(2+3i) + (3-4i)(3+4i)\end{pmatrix} = \\
&= \begin{pmatrix}(1-2i+2i+4) + (4+6i-6i+9) + (9-12i+12i+16)\end{pmatrix} = \\
&= (5 + 13 + 25) = 43
\end{align*}</p>
<hr>
<p><strong>1st question:</strong></p>
<p>I know that ket $\left|z\right\rangle$ is a vector of a Hilbert space and i know that $\vec{z}$ is the same as $\left|z\right\rangle$. But what about $\overline{\vec{z}^T}$? Is it equal to a bra $\left\langle z\right|$ ?</p>
<hr>
<p><strong>2nd question</strong></p>
<p>Notation $\overline{\vec{z}^T}$ means we have to conjugate & transposethe a vector $\vec{z}$. Can this notation be swapped with a dagger $\dagger$ <em>(afterall this is an operation named <a href="http://en.wikipedia.org/wiki/Conjugate_transpose" rel="nofollow">conjugate transpose</a>)</em>? </p>
<hr>
<p><strong>3rd question:</strong></p>
<p>From all of the above it seems logical to ask if this equality holds $\left|z\right\rangle^\dagger = \left \langle z \right|$ ?</p> | g6831 | [
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<p>I am studying quantum physics and I would like to know a bit more in detail about <a href="http://en.wikipedia.org/wiki/Group_velocity" rel="nofollow">group velocity</a>, particle velocity and <a href="http://en.wikipedia.org/wiki/Phase_velocity" rel="nofollow">phase velocity</a>.</p>
<p>Can you guys suggest some books/online resources where I can learn the same. </p> | g98 | [
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<p>WMAP/Planck results confirm than we live in a de Sitter-like phase, i.e., a Universe with positive acceleration or positive cosmological constant! Therefore, I believe that a way to solve the cosmological constant problem could be to extend QFT from Minkowski to de Sitter space. I would not be surprised if our "mistake" to get the theoretical "wrong" value of the cosmological constant is associated to the fact of calculating the vacuum energy in a Minkowskian QFT setting. </p>
<p>My question is: what are the problems that a QFT on de Sitter space faces in order to explain the observed vacuum energy? Could it work? </p>
<p>PS: Does someone know good references about QFT in de Sitter space?</p> | g6832 | [
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<p>What is the fundamental basis of resolution of vector. Suppose we have a vector $\vec{mg}$, now we resolve it into two components, horizontal and vertical. My question is what is the basis for telling that this is the horizontal and this is the vertical component since the Cartesian plane can be drawn on any direction.</p> | g6833 | [
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<p>Lets say we have a potential step as in the picture: </p>
<p><img src="http://i.stack.imgur.com/HB3XI.png" alt="enter image description here"></p>
<p>In the region <strong>I</strong> there is a free particle with a wavefunction $\psi_I$ while in the region <strong>II</strong> the wave function will be $\psi_{II}$.</p>
<p>Let me take now the schrödinger equation and try to derive $\psi_I$: </p>
<p>\begin{align}
&~~W \psi = -\frac{\hbar^2}{2m}\, \frac{d^2 \Psi}{d\, x^2} + W_p \psi ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\nonumber \\
&~~W \psi = -\frac{\hbar^2}{2m}\, \frac{d^2 \Psi}{d\, x^2}\nonumber \\
&\frac{d^2 \Psi}{d\, x^2} = -\frac{2m W}{\hbar^2}\,\psi \nonumber\\
{\scriptsize \text{DE: }} &\boxed{\frac{d^2 \Psi}{d\, x^2} = -\mathcal L\,\psi}~\boxed{\mathcal{L} \equiv \sqrt{\tfrac{2mW}{\hbar^2}}} \nonumber\\
&~\phantom{\line(1,0){18.3}}\Downarrow \nonumber\\
{\scriptsize \text{general solution of DE: }} &\boxed{\psi_{I} = C \sin\left(\mathcal{L}\, x \right) + D \cos \left(\mathcal{L}\, x \right)}\nonumber
\end{align}</p>
<p>I got the general solution for the interval <strong>I</strong>, but this is nothing like the solution they use in all the books: $\psi_{I} = C e^{i\mathcal L x} + D e^{-i \mathcal L x} $ where $\mathcal L \equiv \sqrt{{\scriptsize 2mW/\hbar^2}}$. I have a personal issue with this because if $x= -\infty$ part $De^{-i \mathcal L x}$ would become infinite and this is impossible for a wavefunction! I know that i would get exponential form if i defined constant $\mathcal L$ a bit differently as i did above: </p>
<p>\begin{align}
{\scriptsize \text{DE: }} &\boxed{\frac{d^2 \Psi}{d\, x^2} = \mathcal L\,\psi}~\boxed{\mathcal{L} \equiv -\sqrt{\tfrac{2mW}{\hbar^2}}} \nonumber\\
&~\phantom{\line(1,0){18.3}}\Downarrow \nonumber\\
{\scriptsize \text{general solution of DE: }} &\boxed{ \psi_{I} = C e^{\mathcal L x } + D^{-\mathcal L x} }\nonumber
\end{align}</p>
<p>This general solution looks more like the one they use in the books but it lacks an imaginary $i$ and $\mathcal L$ is defined with a - while in all the books it is positive. Could anyone tell me what am i missing here so i could understand this? </p> | g6834 | [
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<p>Today, at the Brazilian news, I heard that a men fell from a cruise into the sea, from a height of 50m, and decided to see if he could have survived. I took his weight for being 80kg. </p>
<p>I did $V^2=V0^2 + 2 G H$, this resulted $V = 31.3 m/s$ or $112.69 km/h$.
Also $F = m a=784 N$. </p>
<p>My question is:</p>
<p>How to relate this to the surface tension of water to get the actual strength of the impact? Assuming he fell standing and the area of contact was $700cm^2$, two foot side by side.</p> | g6835 | [
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<p>In pictures taken from the summit of Mount Everest (<a href="http://www.peakfreaks.com/images/Everest_summit_view_north.JPG">such as this one</a>), the colour of the sky is a very dark blue or even black in some pictures. I remember from my own experiences of hiking in the Himalayas that the sky appeared to be darker blue as I climbed higher. In shots looking outward from the summit there's a very interesting effect of having a black sky above with a blue sky lower down near the horizon. (<a href="http://apod.nasa.gov/apod/ap050306.html">one example here</a>) I believed that this happens because there is less atmosphere above the climbers to scatter the blue wavelengths.</p>
<p>However, this same black sky effect does not occur when looking out the window of a plane. As the plane climbs, the sky does not appear to "change colour" at all as the plane ascends. The cruising altitude of commercial airliners on an international flight is slightly higher than Everest, so one would expect the sky to appear quite similar.</p>
<p>What explains these two observations?</p> | g6836 | [
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<p>I have some difficulties designing my experimental apparatus:</p>
<p>The goal is creating a Solenoid in air (or iron powdered core) able to produce at least 50G of peak B field on his axis at a distance of 1".</p>
<p>I would like to drive this solenoid in such a way that the B field varies sinusoidally from 0G to 50G (hopefully even higher) with a frequency ranging from DC to 30kHz.</p>
<p>Probably the easiest way is to use a function generator as an input for a power amplifier (I have trouble choosing it, I don't know if I need a four quadrant amplifier or a traditional one)</p>
<p>Since I need a fast varying B field I suppose that I have to try to keep inductance as low as possible -> so maybe I'll put not so many turns but more current..inductance will probably also create problem in the correct impedance matching with the power amplifier (I don't have a strong background on this topic.)</p> | g6837 | [
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<p>I was recently reading about NASA Faster than Light proposed spaceship, it supposedly will bend spacetime behind the spacecraft, so technically instead of bringing the ship to the destination, "it will bring the destination to you." now, I have an understanding of calculus-based physics, and a basic understanding of relativity. </p>
<p>From my lackluster knowledge of relativity, by conventional means achieving the speed of light is nearly impossible if not impossible, according to Special Relativity. if I am not mistaken if we try using a spaceship, as we approach the speed of light because of relativity, wouldn't the mass of the spaceship go to infinity? and if we have infinite mass doesn't it mean we need an infinite amount of energy to push it? </p>
<p>Even so, if we travel to say alpha centauri, which is 4.4 light-years away it will probably take around a month to go there at the speed of light, which is not bad. It will take a month for the traveler to go there, what about those outside? </p>
<p>to put it simpler, if someone goes to Alpha Centauri at the speed of light and he comes back, how much time would have passed in Earth? </p>
<p>(I would have used, calculations to illustrate better, but I do not know how to use equations in Stack-Exchange yet.) </p> | g6838 | [
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<p><strong>Question</strong> Measuring the number of decays per minute $N(t)$ of a radioactive source every four days we have that: $N(t=0):=N_0=200$, $N(t=4)=141$, $N(t=8)=100$, $N(t=12)=71$, where $t$ is measured in days ($d$). ¿Which radioactive isotope is it?</p>
<p><strong>Answer</strong> From the decay law we have that $N(t)=N_{0}e^{-\lambda t}$, then $\lambda=\frac{1}{t}\ln\frac{N_{0}}{N}$, and</p>
<p>$$T_{1/2}=\frac{\ln2}{\lambda}=\frac{t\,\ln2}{\ln\left(N_{0}/N\right)}$$</p>
<p>Inserting the values for $N(t=4)$ , I find that</p>
<p>$$T_{1/2}=7.93171\ d$$
Inserting the values for $N(t=8)$ , I find that</p>
<p>$$T_{1/2}=8.00000\ d$$
And inserting the values for $N(t=12)$ , I find that</p>
<p>$$T_{1/2}=8.03154\ d$$</p>
<p>**</p>
<blockquote>
<p><strong>My question is</strong> which one of these half-lives is the correct? And knowing the right value for $T_{1/2}$, how can I know the isotope?</p>
</blockquote>
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<p>I am designing a <a href="http://externalcombustion.org/thermionic-converters-problems-and-solutions/" rel="nofollow">thermionic converter</a> and one of the biggest inefficiencies is the thermal conductivity and limited electrical conductivity of the leads. I'm trying to mitigate the loss of heat besides finding other materials that conduct heat poorer and electricity better than Tungsten. One option open is the shape of the lead. Although I don't know if changing the shape of the lead will make any appreciable difference. I am considering a spherical shaped lead in between two flat electrodes. The point of contact of the sphere should be flattened somewhat to allow a better connection. I don't have the mathematical skill to apply Fourier's law to a semi-sphere. I also need to know its overall resistance and I don't have the skills for this either. </p>
<p>If you think it would be worth calculating please share your answer and formulas. Or if not, please explain your reasoning.</p>
<p>update 6/29/14</p>
<p>It seems to me that if you had a sphere with 2 opposing contact areas (Ca) it would not conduct heat any faster or slower than a straight cylinder with the same contact area (Ca). The cooling part and the heating part are the same size in area. </p>
<p>Calculating the resistance was fairly easy to do in slices in javascript. And the resistance reduction from a straight cylinder with contact areas (Ca) on either side to a sphere with a limited contact areas (Ca) was considerable.</p>
<p>How far is my reasoning now?</p> | g6840 | [
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<p>I'm trying to do my prelab for an E&M course, and am asked if, for plotting $V$ vs $I$ with a varying temperature, I should expect a linear slope. I know that both $V$ and $I$ depend on $R$, and since $R$ is proportional to $T$ that I shouldn't.</p>
<p>Trying to show this, I'm having some problems -- probably because my differential equations skills are a bit rusty.</p>
<p>Simplely, if $V = I \,R(T)$, how do I take $\mathrm{d}V/\mathrm{d}I$?</p>
<p>I can find $\mathrm{d}V/\mathrm{d}T$ by chain rule, but i'm just drawing a blank with $\mathrm{d}V/\mathrm{d}I$ since $I = V/R(T)$</p>
<p>Excuse my ineptitude, and thanks in advanced for helping me out. </p> | g6841 | [
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<p>The solution to the Dirac equation (in the Dirac basis) are 4 coupled fields. The first 2 of them represent a particle (spin up/down), the other 2 fields are the antiparticle (spin up/down). When the particle is observed from its rest reference frame, the antiparticle solutions are zero. However once the particle is moving, all the 4 fields become coupled.</p>
<p>Does it mean that a moving electron is a little bit of a positron at the same time (in the given reference frame)?</p> | g6842 | [
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