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<p>I get the front part, but why is the back curved too? I do not see a problem with the back being flat.</p>
| 8,981 |
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<p>I'm wonder what precisely is meant by the renormalizability of the standard model. I can imagine two possibilities:</p>
<ol>
<li><p>The renormalizability of all of the interaction described by the Lagrangian before <a href="http://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking" rel="nofollow">spontaneous symmetry breaking</a> (SSB) by the nonzero vacuum expectation value (VEV) of the Higgs field.</p></li>
<li><p>The renormalizability of the Lagrangian obtain from the initial one after SSB, expressed in terms of suitable new fields (which has direct physical interpretation contrary to the fields appearing in initial Lagrangian). </p></li>
</ol>
<p>It seems that in case (2) we obtain an effective (nonrenormalizable) theory only and this precisely was the reason to introduce the mechanism of generating mass by nonzero VEV of Higgs field. The original Lagrangian (case (1)) contains only power counting renormalizable vertices so if there are no anomalies then SM befor SSB is renormalizable. However, in physical prediction (actual computations being performed), as far as I know, Lagrangian after SSB is used. Does is require infinite number of counterterms (is it effective theory)?</p>
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<p>Let us choose to postulate (e.g. considering the analogy of the Hamiltonian being a generator of time evolution in classical mechanics)
$$
i\hbar \frac{d\hat{U}}{dt}=\hat{H}\hat{U}\tag{1}
$$
where $\hat{U}$ is the (unitary, linear) evolution operator and $\hat{H}$ the Hamiltonian (the most general version of which; i.e. time-dependent with instances at different times non-commuting).</p>
<p>In S-picture, one can easily show that (1) is <strong>equivalent</strong> to
$$
i\hbar \frac{d}{dt}|\psi_S(t)\rangle=\hat{H}_S|\psi_S(t)\rangle\tag{2}
$$
where $\psi$ is a state, $|\psi_S(t)\rangle = \hat{U}(t)|\psi_S(0)\rangle \equiv \hat{U}(t)|\psi_H\rangle$ and $\hat{H}_S:=\hat{H}$.</p>
<p>In H-picture, it is straightforward to show that (1) <strong>implies</strong>
$$
\frac{d\hat{A}_H}{dt} = \frac{\partial\hat{A}_H}{\partial t}+\frac{1}{i\hbar}[\hat{A}_H,\hat{H}_H]\tag{3}
$$
where $A$ is an observable and $\hat{A}_H(t)=\hat{U}(t)^\dagger \hat{A}_H(0)\hat{U}(t)\equiv\hat{U}(t)^\dagger \hat{A}_S\hat{U}(t)$ (and also $[\hat{H}_{H},\hat{H}_H]=0$ implying that the time dependence of $\hat{H}_H$ is purely explicit, i.e. $\hat{H}_H=\hat{H}_S\equiv \hat{H}$ with $[\hat{H},\hat{U}]=0$).</p>
<p><strong>My question:</strong> is it possible to obtain (1) from (3), i.e. to show that (1) is <strong>equivalent</strong> to (3)? </p>
<p>Some thoughts on this: it is extensively mentioned in literature that both pictures yield same answers. Therefore, it should be possible to obtain (1) from (3) since (1) and (2) are equivalent. Assuming (3), the best I can get is that given an observable $A$, the operator
$$
\hat{C}:= \hat{A}_S\left(\frac{d\hat{U}}{dt} \hat{U}^\dagger - \frac{\hat{H}}{i\hbar}\right)
$$
must be skew-Hermitian. </p>
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<p>Are all baryons from decuplet resonances?? Because all resonances decay by strong interaction; but omega minus baryon can't decay via strong, because any other bound state with strangeness -3 exists.
Thanks</p>
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<p><a href="http://en.wikipedia.org/wiki/Hopf_algebra" rel="nofollow">Hopf algebra</a> appears in recent papers that systematize renormalization of quantum field theory (QFT). For example see <a href="http://www.google.com/search?q=connes+hopf+site%3Aarxiv.org&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a" rel="nofollow">Connes' work and citing papers</a> or a paper referenced <a href="http://physics.stackexchange.com/questions/4068/formalizing-quantum-field-theory">here on PSE</a>:</p>
<p>R. E. Borcherds, "Renormalization and quantum field theory"<br>
<a href="http://arxiv.org/abs/1008.0129" rel="nofollow">http://arxiv.org/abs/1008.0129</a></p>
<p>This seems to be an effort that is separate from string theory, but I wonder if they are compatible. Since "compatible" is perhaps too loose of a term, I'm asking:</p>
<blockquote>
<p>Why do string theory and Hopf algebra renormalization seem to have no intersection?</p>
</blockquote>
<p>If the reader feels the question could be improved by rewriting, please so assist.</p>
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<p>I am currently taking a graduate level class on lasers. The primary focus of the class is on the design and engineering aspects of lasers, e.g. resonator design. However the first portion of the class is an overview of the quantum mechanics of laser processes in semi-classical terms: transition probabilities for a 2-level dipole atom in an external (classical) field, perturbation theory, and matrix QM.</p>
<p>I have an undergraduate degree in physics, so the basics of QM are familiar to me, but it has been years since I seriously applied any of that knowledge. In addition, the professor is moving through this material very rapidly, as it is not the primary focus of the class. I can follow well enough that I'm not worried about my grade, but I'm feeling a bit cheated out of a more thorough understanding of this topic, which I would really like to have. Not only is this subject matter an appropriate level of advancement over my existing knowledge, it is also the basis for something (lasers) which I will likely spend a career dealing with.</p>
<p>Can anybody recommend a text which covers this topic, and would be appropriate for somebody with my background? I would value a clearly written description over absolute rigor, but I am by no means looking for a laypersons description of QM. For example, I am quite comfortable already with the notation and concepts in the textbook "Quantum Mechanics of atoms, molecules, solids, nuclei, and particles" By R. Eisberg and R. Resnick. The ideal reference would be at a similar level of sophistication, but provide a more in-depth look at laser processes in particular.</p>
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<p>We tied a helium filled balloon to a counterweight and it floats aimlessly in the room. I asked if the balloon were to be outside the building (all things considered no wind same temperature) would the balloon float at the same level?</p>
| 8,987 |
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<p>In other question, Ron Maimon says that he thinks string theory is the <em>physical</em> regulator. I did not know that string theory regularize divergencies.</p>
<p>So, <strong>Q1</strong>: How does string theory regularize the ultra-violet divergencies of the "low-energy" (Standard Model) fields? And <strong>Q2</strong>: Why it doesn't regularize its own divergencies.</p>
<p>By regularization I mean that the theory is ultra-violet finite before removing the regulator. </p>
| 8,988 |
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<p><s>Proper orthochronous Loentz transform are Lorentz transforms that satisfy the conditions (sign convention of Minkowskian metric $+---$)
$$\det \Lambda=+1, \qquad \Lambda^0{}_0 \geq +1.$$
How to prove they form a subgroup of Lorentz group? All books I read only give this result, but no derivation.</s></p>
<p>Why is this condition $\det \Lambda=+1, \ \Lambda^0{}_0 \geq +1$ enough for a Lorentz transform to be proper orthochronous?</p>
<p>The temporal component of a transformed vector is
$$x'^0=\Lambda^0{}_0 x^0+\Lambda^0{}_1 x^1+\Lambda^0{}_2 x^2+\Lambda^0{}_3 x^3,$$
the positivity of $\Lambda^0{}_0$ alone does not seem at first glance sufficient for the preservation of the sign of temporal component.</p>
<p>And how to prove that all Lorentz transform satisfying such simple conditions can be generated from $J_i,\ K_i$?</p>
<hr>
<p>For those who think that closure and invertibility are obvious, keep in mind that
$$\left(\bar{\Lambda}\Lambda \right)^0{}_0\neq \bar{\Lambda}^0{}_0\Lambda^0{}_0,$$
but instead
$$\left(\bar{\Lambda}\Lambda \right)^0{}_0= \bar{\Lambda}^0{}_0\Lambda^0{}_0+\bar{\Lambda}^0{}_1\Lambda^1{}_0+\bar{\Lambda}^0{}_2\Lambda^2{}_0+\bar{\Lambda}^0{}_3\Lambda^3{}_0.$$</p>
<p>And I'm looking for a rigorous proof, not physical "intuition".</p>
| 8,989 |
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] |
<p>How did people determine the proton number for each element from experiment in each decade of 20th century?</p>
| 8,990 |
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<p>I'm starting to wonder if the description of Mass given to us when we hear physicists talk about Mass created by the Higgs field is the same type of mass we ordinarily think of, like inertial mass for example. I am wondering if they are talking about a field that stops the energy in "mass" from just flying apart and traveling at the speed of light, a field that in effect traps the energy and keeps it bundled up so that the energy stays as a particle? </p>
| 229 |
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<p>I've been wondering about microcausality for some time now (a <a href="http://physics.stackexchange.com/q/33225/955">recent question</a> of mine regarding the topic) and i'm wondering if its possible to devise an experiment to detect potential violations</p>
<p>I thought something like this: the hypothesis to test is that if two atoms A and B are close enough, and by close enough i mean that the cross-section of atom B and photons emitted in all/random directions from A is roughly of the order $\frac{4 \pi}{100}$, so statistically, and assuming no dipolar couplings affecting the orientation, if A is excited and B is on the base state, 1% of photons emitted from A will be absorbed by B if microcausality holds, and any deviations from this average will suggest a causality violation (i.e: that the atom B at time $t + \tau_0$ absorbs an advanced photon that "causes" A at time $t$ to emit it, where $\tau_0 = \frac{d}{c}$)</p>
<p>In order to detect when photons are emitted from each atom, actually we'll arrange so atom A favours a two-photon decay $\omega_0$ and $\omega_A$ from the excited state, and B, when in its base state, will accept $\omega_0$ but quickly decay to a metastable level sending a photon of $\omega_B$. We will use timings of $\omega_A$ and $\omega_B$ photons to roughly time the emission and absortion times of each atom</p>
<p>But there is still a problem with the above setup: is entirely time-symmetric, so there is no good reason to expect that the atom B at the future, even if emitting advanced photons, will be more likely to interact with the past A atom (because both atoms will see each-other cross sections to be symmetrical). So in order to fix this, we actually arrange not one, but many atoms like A surrounding the atom B, so there is a probability $p_R$ of all the atoms A emitting a photon that is absorbed by B in the future (if only retarded causes are allowed), but there is a higher probability $p_A$, say, very close to 1, that the atom B will absorb an advanced photon from some of the A atoms. Any experimental outcome between $p_R \le p \le p_A $ would imply a mixture between retarded and advanced causation.</p>
<p>Does this sounds like something that makes sense, and if it does, sounds like something that is doable? I've think about this from time to time, but never actually found a reason why it would not work.</p>
<p>Obviously, sayings stuff like "this is nonsense because microcausality holds and i know it because etc." its useful but <em>not the point of the question</em>, and with that i mean, if there are theory arguments against a positive result (beyond assuming causality holds ad hoc) it would be great to know them. But my question is regarding the experiment itself. For instance if you can sketch and argument about, say, $\Delta E \Delta t \ge \hbar $ implies that any correlations will be swamped by quantum noise, that is completely relevant to the question and you should write about that</p>
<p>thanks!!!</p>
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] |
<p>The following questions are based on these lectures, <a href="http://arxiv.org/abs/hep-th/9108028" rel="nofollow">http://arxiv.org/abs/hep-th/9108028</a></p>
<ul>
<li><p>I would like to know what is the relationship between the last equation on page 82 ($(L_0)_{cyl} = L_0 - \frac{c}{24}$) and the last 2 sets of equations on page 84 (where one has derived the zero-point energies of $\pm 1/24$, $\pm 1/48$ of periodic and anti-periodic Fermions on the cylinder) </p>
<p>Can the equations below 7.6 (on page 84) be derived from the last equation on page 82? </p></li>
<li><p>I can understand the derivation of the partition function in equation 7.5 at the top of page 84 where one gets that $Z = q^{-\frac{c}{24}}\bar{q}^{-\frac{\bar{c}}{24} } Tr q^{L_0}\bar{q}^{\bar{L}_0}$ </p>
<p>But from there how does one derive the statements in the first paragraph of page 92 where he states that (1) when the Fermion is anti-periodic along both time and space the partition function is $q^{-1/48}Tr_A q^{L_0}$, (2) when its periodic in time and anti-periodic in space the answer is $q^{-1/48}Tr_A (-1)^Fq^{L_0}$ (3) when its anti-periodic in time and periodic in space the answer is $(1/\sqrt{2})q^{-1/48}Tr_P q^{L_0}$ and (4) when its periodic along both its $(1/\sqrt{2})q^{-1/48}Tr_P (-1)^Fq^{L_0}$</p>
<p>These 4 answers above look very mysterious to me at various levels - (1) I don't see how they can be read off from the general answer of $Z = q^{-\frac{c}{24}}\bar{q}^{-\frac{\bar{c}}{24} } Tr q^{L_0}\bar{q}^{\bar{L}_0}$, (2) how is the (-1)^F operator seeing the boundary conditions? (3) why do these answers have only the $q^{L_0}$ part and not the full $q^{L_0}\bar{q}^{\bar{L}_0} $</p></li>
</ul>
| 8,992 |
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<p>According to my physics book, if an electron were accelerated with 15 MeV of (kinetic?) energy and collided into a 100g thermally insulated copper block (not sure if the fact it is thermally insulated is relevant) the energy would transfer into thermal energy on the copper block and the copper block would heat up by a few degrees.</p>
<p>However, if I were to collide into that same copper block with a bowling ball travelling with 15 MeV of kinetic energy then that energy would be transferred into kinetic energy on the copper block and the copper block would move.</p>
<p>It seems to me, that in both cases, there is a thing smashing into another thing with 15 MeV of energy. When the first thing is small (e.g. electron) the energy is transferred into thermal energy. When the first thing is large the energy is transferred into kinetic energy.</p>
<p>Why doesn't the electron's energy get transferred into kinetic energy as well?</p>
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<p>Why do different wavelength get impeded more or less when in different materials? Moving with the same speed, but a longer physical distance would imply that the fields oscillate less times in the material, but I don't know why a difference in the number of oscillations would impede the wave- I don't even know why things slow down in general. Why some electromagnetic wave would slow down just because it's entering other electromagnetic fields... It would seem to me that the only factor would be time taken to physically move some electron or something in the direction of the fields...
But that seems to simple of an explanation to me.</p>
| 298 |
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<p>I have a question after reading a section from Goldstein's Classical Mechanics. The question deals with equation 1.43 in the text (given below):</p>
<p>$$ \tag{1.43} \sum\limits_{i} {\bf F}_i^{(a)}\cdot \delta{\bf r}_i ~=~ 0.$$</p>
<p>Just below the equation in the text, Goldstein says </p>
<blockquote>
<p>[...] <em>in general ${\bf F}_i^{(a)} \neq 0$, since the $\delta {\bf r}_i$ are not completely independent but are connected by the constraints. In order to equate the coefficients to zero, we must transform the principle into a form involving the virtual displacements of the $q_i$, which are independent.</em></p>
</blockquote>
<p>I do not understand what the fact that the $\delta {\bf r}_i$ are not completely independent has to do with the applied force ${\bf F}_i^{(a)}$. Moreover, I'd like to see how transforming into generalized coordinates $q_i$ can send the applied forces to zero.</p>
| 8,994 |
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<p>I recently came across an article indicating that the half life of DNA in the most ideal situations is 521 years (<a href="http://www.nature.com/news/dna-has-a-521-year-half-life-1.11555" rel="nofollow">http://www.nature.com/news/dna-has-a-521-year-half-life-1.11555</a>). However, since human's DNA is 99.9% identical (and 98% identical to chimps), I can't quite understand how DNA evidence is often used in old samples. There has been DNA extracted from 100,000 year old Neanderthals, and DNA evidence has been used in cases over 50 years old. </p>
<p>However, with a 521 year half life, after only 0.75 years, there would only be 99.9% of the DNA left. Surely if 99.9% of a human's DNA is identical after only this short amount of time wouldn't it be impossible to distinguish any sample from any other? After 50 years only 93% would remain the same, meaning it would be much less similar to a human than just any chimp I would think.</p>
<p>And the 100,000 year old Neanderthal would only have 1.6*10^-57 % of the original sample left. How is there possibly any sort of useful information left?</p>
<p>All in all, how can DNA be distinguished from other samples when they are all so similar and the half life is so low?</p>
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<p>I came across a <a href="https://courses.physics.illinois.edu/phys598PTD/fa2013/L5.pdf" rel="nofollow">lecture note</a> on weak localisation by Prof. A. J. Leggett. In this note, he wrote down his first equation as follows: $$\sigma = \lim_{\omega\rightarrow 0} \lim_{q\rightarrow 0} \frac{1}{i\omega}\frac{\delta j(q\omega)}{\delta A(q\omega)} = \lim_{\omega\rightarrow 0} \lim_{q\rightarrow 0}\frac{1}{i\omega}\langle[j_q(t),j_q(0)]\rangle_{\omega}\\ = \int^{\infty}_0 dt\int\int\frac{dr dr'}{V}\langle[j(rt),j(r'0)]\rangle.$$ I understand the first two equalities. But how do I prove the third one? Your help is greatly appreciated.</p>
| 8,996 |
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<p>Specifically, I would like to know the general formula, in terms of $n$ and $l$, assuming the electron is in an orbital (i.e. simultaneous eigenstate of $H$, $L^2$, and $L_z$).</p>
<p>I understand that it involves integrating an associated Laguerre polynomial, but I wasn't able to find the formula for the integral. I looked on Wikipedia and in Abramowitz & Stegun, but no luck.</p>
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<p>Assuming you place an object so heavy on a table that it breaks it, then according to newtons third law the forces must cancel out (equal magnitude and opposite direction), but if this is true, then how can the object break the table in the first place?</p>
| 8,998 |
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<p>I have a question about how would seasons and the moon cycle be affected in a system where one planet orbits Sun #1, and Sun #1 orbits a second sun. Online I found this description:</p>
<blockquote>
<p>"Type II: "Close Stars" - The suns may occupy different parts of the sky, indicating that one sun orbits the other farther out than the planet."
(I had a sketch, but didn't know how to upload it)</p>
</blockquote>
<p>To make it easier to explain I'm going to assume this system's Sun #1, planet, and moon are equal mass and size of Earth, it's moon and it's sun. The planet is in a habitable zone of Sun #1 but outside the gravitational pull of the second sun. So I guess my questions are:</p>
<ul>
<li><p>How would the moon cycle be affected when the planet orbits between both suns? Would there be times when it seemed like the sun never set or would days be twice as short, because there is a sun on both sides of the planet for 3-4 months out of the year?</p></li>
<li><p>Would the same situation described above cause a significant shift in seasons(summer, winter,spring) when the planet is between two suns?</p></li>
<li><p>Does the size of a sun, or it's mass more dictate it's gravitational pull? Is it even possible for a system such as this to survive or would it eventually get stuck in between both suns gravitational pull, or switch to a figure 8 orbit, and eventually be thrown out of both suns orbit.</p></li>
</ul>
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<p>What is the <a href="http://en.wikipedia.org/wiki/Land%C3%A9_g-factor" rel="nofollow">Landé g factor</a>?</p>
<p>I know that it gives the relation between magnetic moment and angular moment, but i wanted to know why are those magnitudes related to each other and why is the magnetic moment operator defined proportional to he angular moment and how is the gyromagnetic ratio calculated theoretically.</p>
| 9,000 |
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<p>I never understood the relationship between Infrared and Heat. Is IR emitted when heat is generated, is heat generated when IR is made, and how do the two relate?</p>
| 9,001 |
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<p>The Hamiltonian of an atom coupled to an EM field, both described quantum mechanically is:
$$H = \frac{1}{2m}(\hat{p}-q\hat{A})^2 = \frac{\hat{p}^2}{2m} -\frac{q}{m}\hat{p}\hat{A}+\frac{q^2}{2m}\hat{A}^2$$
Under the condition of transversality ($\hat{p}$ and $\hat{A}$ are vectors). I have only seen it treated in the dipole approximation where the last term becomes a constant and so unphysical; but what is its general interpretation? Is it shifting the energy of the free photons, it doesn't look diagonal in number of occupation basis.</p>
| 9,002 |
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<p>Always when we want to represent the magnetic field of the earth we see a similar image:</p>
<p><img src="http://i.stack.imgur.com/BRFM7.gif" alt="enter image description here"></p>
<p>My question is, what exactly does this show? What are the blue and orange lines, what do they represent? Why are they curved like that? I have a vague idea about field lines, but I do not fully comprehend this. An explanation would be appreciated</p>
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<p>With multipole expansions, we speak only of monopoles, dipoles, and $2^n$-poles. Why is there nothing like a tripole? So how would something like $rsin(3 \theta)$ be expressed with a multipole expansion? Is the reason for not having terms like this in a multipole expansion that it is redundant, or is there some more fundamental reason? </p>
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<p>There are several ways to make charges on an object evenly distributed. For example, if the surface of the object is infinite or the object is a sphere. There is one more way which I am not sure if it is a good way: if the object is made out of an insulating material. </p>
<p>I would like to know if there are other ways to make the charges on a finite charged plate evenly distributed over the surface? Also, how efficient is the idea of using an insulating material?</p>
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] |
<p>The photoelectric effect is the historic origin of the quantum particle description of light. From it we learn that when light is shone onto a metal single photons interact with single electrons in the metal which are ejected if the absorbed energy is larger than the binding energy of the metal. </p>
<p>The (free) process is:</p>
<p>$e^-+\gamma\rightarrow e^-.$</p>
<p>However, this process violates conservation of energy (all final states are real particles). Of course the reason the process occurs is because the electron is initially bound (not free), and some energy goes into releasing the electron from the metal potential.</p>
<p>The question is, is there anyway to do this calculation in QED, somehow incorporating the binding energy in the calculation?</p>
| 9,006 |
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<p>Considering $X$ and $Y$ such that $[X,Y]=\lambda$, which is complex, and $\mu$ is another complex number, prove: $$e^{\mu(X+Y)}=e^{\mu X} e^{\mu Y} e^{-\mu^2\lambda/2}$$
My attempt (so far) is: Expand the exponent. $$\mu(X+Y)=\mu X+ \mu Y$$ and then split it. How can I introduce $\lambda$?</p>
<hr>
<p>Taylor expansion:
$$e^{\mu(X+Y)}=\sum\limits_{n=0}^\infty \frac{(\mu X+\mu Y)^n}{n!}=1+\mu X+\mu Y+\ldots$$</p>
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<p>Australia's history has been littered with the problem of how to manage safety in bushfires. The local fire authority recommend consideration be given to preparing a bushfire management plan, deciding whether to stay and defend, or leave early.</p>
<p>A back- up plan is also suggested, which may include the use of a personal fire bunker.</p>
<p>Temperatures can be up to $935^\circ C$ in a bushfire, and above ground bunkers are marketed as being safe for one hour.</p>
<p>Fire loads can peak at $100kWm^{-2}$.</p>
<p>My question relates to the effectiveness of fire bunkers to provide safe shelter in a fire. Key aspects of this are the ability of the bunker to achieve the following criteria: 1. Non combustible construction 2. Limit heat flow through walls to $2.5kWm^{-2}$ 3. Limit max surface temperature on the inside walls to $75^\circ C$ 4. Limit air temperature on the inside walls to $40^\circ C$; 5. Fire rated door, with non-combustible seal;</p>
<p>Research into this topic has yielded the following: 1. English fire expert experienced in fire door testing and fire gasket seals says it can't be done; expect the people in the bunker to be microwaved; 2. USA makes tornado/hurricane safe refuges, nominally fire resistant, but Californian authority advice is: not to be used in a wildfire.</p>
<p>My question relates to the meeting of the nominated Aus standards. Some finite element studies I have done into items 1,2,3 says all three can be achieved.</p>
<p>Items 4 and 5 are problematic.</p>
<p>Item 4 is the internal air temp. Even with a heat flow reduction from $100kWm^{-2}$ to $2.5kWm^{-2}$, as nominated in the Aus guidelines, if there is a fire refuge in lockdown, with limited air mass, no ventilation, prelim studies into this show the temp will rise. Lots.</p>
<p>This is based on: $Q=mC_{p}\Delta T$</p>
<p>It is a one liner, but says the temp goes up. A lot. Not a lot of mass in the air. Lots of exposed area in the walls and roof.</p>
<p>With better insulation, we can get this heat input down to $0.5kWm^{-2}$. This is lower than sunlight.</p>
<p>But the Time to heat up above $40^\circ C$ from a base of $35^\circ C$ is still very low, based on this formula, much lower than 60 mins target.</p>
<p>As a structural engineer with many years in structures, who is doing this as a bit of a hobby, I am heading back to my Uni notes to help. No doubt I am missing something; or are the Brits/US authorities on the right track?</p>
<p>To complicate the issue, there are people in the bunker, all huffing and puffing as the temp rises. That complicates the physics a bit more.</p>
<p>Item 5 Heat seal; smoke seal; air seal. Again a bit problematic as fire doors distort and let air in. Break the seal. Also internal temperature rise also heats up the internal air pressure. Which would also break the seal.</p>
<hr>
<p>Trust this gives a bit of background into what is an interesting problem. Would appreciate people's feedback on possible ways to better evaluate the internal room temperature/pressure rise in the bunker.</p>
| 9,008 |
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<p>Temperature is related to average of particles kinetic energy.</p>
<p>I would like to ask about a singular state of a particle system of a little time interval.</p>
<p>The question is:</p>
<p>If all particles were going same direction, same speed, same mass, for that while they were avoiding external forces, internal colision, interaction, etc, then even within this interval they will have an average kinetic energy, so a definite temperature.</p>
<p>But, in this case, I think it's better to describe as a "movement of whole the system", instead of a "temperature of the system", because there is no relative shaking, then I see there is a kind of restriction about particle speeds, they have to be <em>diverse</em> to have a temperature.</p>
<p>I know in practice that's a very unusual process or even a ephemeral one, but I would like to think about theoretical meaning, <strong>How is this assumption of speed diversity defined within a gas model ?</strong> </p>
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<p>Questions about the temperature of something in space are often very hard to pin down (<a href="http://physics.stackexchange.com/questions/10449/what-are-the-temperatures-of-objects-in-leo">example</a>), since there is radiative transfer to/from many different regions in the field of view at dramatically different temperatures - leading to different answers depending on an object's position and radiative properties. I want to ask about the most simple case of an object in Low Earth Orbit (LEO) I can think of.</p>
<p>Let's ignore the fact that an object in orbit on the night side of Earth will eventually move to the sunny side. Let's say there is a black-body at an orbital altitude above Earth on the opposite side as the sun. No internal heat production. Completely steady state. What would the temperature of the object be?</p>
<p><strong>Some initial thinking:</strong></p>
<p>For simplicity, we'll make it a plate. From this point, I don't know where to go exactly. The Earth occupies an even $2 \pi$ solid angle of the field of view. We know $T$ of the Earth and space, but do we need more information? The answer would probably be a function of the emissivity of the Earth.</p>
<p>Alternatively, maybe we would find $\dot{Q}$ from the Earth and assume that all outgoing radiation from the satellite is lost. This last argument is certainly true, but is a source of my confusion.</p>
<p><strong>Why I ask, my confusion (not needed to answer the question):</strong></p>
<p>What does it <em>mean</em> that the greenhouse effect <em>insulates</em> the earth radiatively? We have the surface at a given $T$, then some of the outgoing thermal radiation is blocked. What does that mean? Is the outgoing radiation then the $T$ of the colder upper atmosphere? Is that how it reduces the thermal radiation? Or is the thermal radiation the same average $T$, but at a lower intensity? This last explanation would seem to violate the 2nd law. If we consider the plate above the night side of Earth, and the far side of the plate is perfectly insulated from the rest of space... then it <em>must</em> reach equilibrium at the $T$ of Earth (be it the surface or upper atmosphere $T$, either is possible). Or did I interpret the law wrong? This is a common contradiction I run into with thinking about radiative heat transfer, and any correct solution to this problem should clear it up.</p>
<p>The concept of emissivity $<1$ makes sense to me. But that's only allowed because the surface will also proportionally reflect more light. Thus, a neighboring object absorbs less light from it, but it will then absorb more of its own reflection, leading to thermal equilibrium again, with the two objects at the same $T$. But that approach doesn't work for the Earth. As far as a satellite is concerned, any radiation it emits is gone, because the Earth is very very big. Would insulation via the greenhouse effect then just cause greater coupling between the satellite and the vacuum of space? You can imagine a $T$ of Earth and a temperature of space, with the object falling in-between them. Is the correct conclusion then that the object's temperature then lies closer to the temperature of space?</p>
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<p>I have a (possibly) fundamental question, which is driving me crazy.</p>
<p><strong>Notation</strong></p>
<p>When considering the Dirac action (say reading Peskin's book), one have</p>
<p>$\int dV\;\bar{\psi}\left(\imath\not\partial-m\right)\psi,$</p>
<p>or (following Weinberg)</p>
<p>$\int dV\;\bar{\psi}\left(-\not\partial-m\right)\psi.$</p>
<p>Where Dirac conjugation is defined according to the metric signature.</p>
<p><strong>Question</strong></p>
<p>Is there a reason why the kinetic term in those actions have that particular sign choice?</p>
<p>Are these actions:
$\int dV\;\bar{\psi}\left(-\imath\not\partial-m\right)\psi$ and
$\int dV\;\bar{\psi}\left(\not\partial-m\right)\psi$ ill-possed?</p>
<p><strong>Personal Thoughts</strong></p>
<ul>
<li><p>Elements of Clifford algebra are well defined up to a sign, therefore, I would say the second set of actions is Ok.</p></li>
<li><p>I'm afraid that the different sign would spoil the positivity of energy. However, I'm not sure how to prove that statement.</p></li>
</ul>
<p>Any help or thoughts are welcome! Thank you.</p>
| 9,011 |
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<p>Can someone help me or guide me how the <a href="http://en.wikipedia.org/wiki/Lens_%28optics%29" rel="nofollow">thin lens formula</a>:</p>
<p>$$\frac{1}{s_1}+\frac{1}{s_0}=\frac{1}{f}$$</p>
<p>can be proven?</p>
<p>I was trying to prove it on my own using similar triangles, only to fail.</p>
| 9,012 |
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<p>I'm looking at a solution in my book that says $[xp_{y},x]$ commutes.<br>
Does bracket notation imply:</p>
<p>$[A,B]=AB-BA$</p>
<p>so that </p>
<p>$[xp_{y},x]=xp_{y}x-xxp_{y}$ </p>
<hr>
<p>Taking the comment from Max Graves and solving a slightly different commutation relation:</p>
<p>\begin{align}
-[yp_{x},x]f &= yi\hbar\frac{\partial}{\partial x}(xf)-xyi\hbar \\
&=i\hbar y \bigg( (x\frac{\partial f}{\partial x} -\frac{\partial x}{\partial x}f)-x\frac{\partial f}{\partial x} \bigg) \notag\\
&=yi\hbar \bigg( x\frac{\partial f}{\partial x}+ f-x\frac{\partial f}{\partial x} \bigg) \notag\\
&=yi\hbar f\ \Rightarrow -[yp_{x},x] = yi\hbar
\end{align}
Does this look correct? Do the first and last terms cancel even though the order is not exactly the same? </p>
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<p>I am trying to learn about optics and I am having a hard time understanding the meaning of "real" vs "virtual" image.</p>
<p>My understanding is that for a concave mirror, the image focuses on the same side as the object so it is a real image.</p>
<p>For a convex mirror, the image focuses on the opposite side of the object from the mirror so it is a virtual image.</p>
<p>However, we can both see either real or virtual images, so how are we seeing something that focuses on the other side of the mirror in the convex case ?</p>
<p>I am very confused.</p>
| 209 |
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<p>I have read that the mass term appearing in the electroweak Lagrangian stops it (the Lagrangian) from becoming gauge invariance. Can someone explain where and why this term is creating the problem?</p>
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<p>I have a following optical system: 3 cams (left and top, which is orthogonal to the left, and right, which is parallel to the left and orthogonal to the top) and the 2 cubes in the 3D-space with following coordinate system:
<img src="http://i.stack.imgur.com/ox5l0.png" alt="optical system">
Each of the points $P_t$, $P_l$, $P_r$ lies in the middle point of the appropriated side on the cube. The length of the each cube's side (left and right) is $c$ (in mm). The cubes are parallel to each other. The distance between the points $P_lP_r = w$</p>
<p>From the optical recognition (matching) I know the 2D-coordinates of these points on the projections in px: $P'_l = (P'_lx, P'_ly)$, $P'_t = (P'_tx, P'_ty)$, $P'_r = (P'_rx, P'_ry)$. The distances from the origin to the projection are also defined: $OO_l = d_l$, $OO_l = d_l$, $OO_r = d_r$ in mm.</p>
<p>The focal lengths $f_l$, $f_t$ and $f_r$ can be also defined and used if needed.</p>
<p>In order to calculate the 3D-coordinates of the cube I need to calculate the scale factor that allows to covert the projections 2D-coordinate in px to the real coordinate in mm.</p>
<p>So how is can I calculate the $P_lx$, $P_lz$ in mm (from the left projection), $P_tx$, $P_ty$ in mm (from the top projection), $P_rx$, $P_rz$ in mm (from the left projection)?</p>
<p>Can someone please help me to solve this problem?</p>
| 9,015 |
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] |
<p>Interaction of particle with Higgs field provides mass to the particles, then why still some particles are massless?</p>
| 9,016 |
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<p>Can someone help me understand my mistake here?
I'm thinking of a photon travelling with momentum $p=h/\lambda$ which reflects off a solar sail of mass $m$ travelling with momentum $p_0$ in the same direction. Before the reflection, the total momentum is $p+p_0$ and after it is $-p'+p_1$ where $p'$ is the magnitude of the reflected photon's momentum and $p_1$ is the sail's new momentum. Conservation of momentum and energy then requires
$$p+p_0 = -p'+p_1$$ and
$$pc + \frac{p_0^2}{2m} = p'c + \frac{p_1^2}{2m}$$
if the sail is travelling at much less than relativistic speeds. But then solving the resulting quadratic for $p_1$ I get the entirely unreasonable
$$p_1 = 4m\left\{-c \pm \sqrt{c^2+\frac{2}{m}\left(\frac{p_0^2}{2m}+p_0c+2pc\right)}\right\}$$
What have I done wrong? </p>
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] |
<p>In the photoelectric effect the electrons are supposed to be removed from the plate if light of appropriate wavelength hits the plate. </p>
<p>If electrons are removed, the plate should get ionized (positively). If this is true, does the plate change its properties?</p>
| 9,018 |
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<p>The cross product $\vec{a} \times \vec{b}$ can be written as the determinant of the matrix:</p>
<p>$$\left| \begin{matrix}
\vec{i} & \vec{j} & \vec{k} \\
a_i & a_j & a_k \\
b_i & b_j & b_k
\end{matrix}\right|$$</p>
<p>Is there any physical significance to this matrix, or is it just some mathematical trick?</p>
| 9,019 |
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] |
<p>The definition of current is flow of electric charge. But recently I have heard that the electrons cannot move, that they just transmit energy to the other electrons and so on.</p>
| 9,020 |
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] |
<p>I've tried to find an answer for this but couldn't find one. Whats the problem with matter being created with little or no antimatter</p>
| 9,021 |
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] |
<ul>
<li>Are photons units of energy?</li>
<li>What is the relation between EM force, EM energy and the photon?</li>
<li>Do EM forces carry energy, do they carry the photon (as unit of energy)?</li>
</ul>
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<p>[This question was inspired by a identical question asked on a other forum]</p>
<p>Note that we may morally include general relativity in the gauge theories. </p>
<p>We may have several (some are deliberately contradictory) remarks : </p>
<p>1) Gauge invariance is only a mathematical redundancy, which is unphysical. In fact, we are not using the correct mathematical tools, and/or we have to give up the standard view of space-time (and action). </p>
<p>2) We can't avoid the gauge formalism, because it corresponds to something fundamental, it is not only more pratical for calculus.</p>
<p>3) For massless particles, it is interesting to consider the helicity formalism (the masslessness derives automatically from the formalism). </p>
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<p>I know that on the smallest scales, general relativity predicts that space-time is flat. But I've also read that space-time can be described as a sort of "quantum foam" for distances smaller than the Planck length. Isn't this something of a contradiction (one more way in which quantum mechanics and general relativity disagree)? To make matters worse, theories about quantized space-time means that space-time could be "discrete", and not smooth at all. </p>
<p>So which principle does the physics community think is right? The idea of smooth, locally flat space-time, or the idea of "block-like", discrete space-time?</p>
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<p>In the book (Supergravity - Daniel Z.Freedman & Antoine Van Proeyen - Cambridge), there are (Chapters 16-17) a presentation of pure supergravity or supergravity with matter, from a SuperConformal approach.</p>
<p>The "simplest" link, is to begin with a Superconformal gauge multiplet coupled to a chiral multiplet, then gauge fix which will break the scale and special conformal transformation symmetries, and finally get a pure supergravity (in the same dimensional space-time). Here one speaks about $\mathcal N=1$ supersymmetry in a $D=3+1$ space-time.</p>
<p>I have some questions about this approach.</p>
<p>1) Is it only a mathematical approach, or it is also a physical approach, that is, is it possible to associate some physical quantities of the $2$ theories in some way ?</p>
<p>2) Thinking about AdS (4)/CFT(3), there is some regime, where supergravity is trustable. In this regime, with the above approach, we have $2$ sides of a triangle, so it may be tempting to look at the 3rd side of the triangle, that is a link between a superconformal theory in $3+1$ dimensions, with a superconformal theory in $2+1$ dimensions, or maybe a step further, that is looking at the superconformal theory in $3+1$ as a "mother" theory, as a united point of view of AdS (4)/CFT(3), at least in the supergravity regime. Does all this makes sense ? </p>
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<p>If we look at the Einstein vacuum equations, that is without matter (there is the possibility or curvature without matter), for instance we may consider gravitational waves. The question is: Is there some link between the Riemann curvature tensor, and/or the Weyl tensor, and some gravitational "physical" quantities (as stress-energy tensor or total energy) (one may take the example of gravitational waves). Of course, at first glance, there is no covariant gravitational stress-energy tensor, so it seems there is no relation, but maybe things are more subtle?</p>
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<p>I came across some notation that I can't quite understand:</p>
<p>$$ \hat{r}\hat{r} - \textbf{1}_3$$</p>
<p>where $\textbf{1}_3$ is the 3$\times$3 identity matrix, $\hat{r}$ is a unit 1$\times$3 vector, and the result is supposed to be a 3$\times$3 matrix. What is the operation (implied) in the juxtaposition $\hat{r}\hat{r}$?</p>
<p>The source of this notation is equations (6) and (10) in <a href="http://www.opticsinfobase.org/view_article.cfm?gotourl=http%3A%2F%2Fwww.opticsinfobase.org%2FDirectPDFAccess%2F60A7A4D6-9AAF-CD33-34BDA8670C0CBCE1_709%2Fjosaa-11-4-1491.pdf%3Fda%3D1%26id%3D709%26seq%3D0%26mobile%3Dno&org=" rel="nofollow">this paper</a>.</p>
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<p>Is there an intuitive geometrical picture behind the <a href="http://en.wikipedia.org/wiki/Dirac_equation">Dirac equation</a>, and the gamma matrices that it uses? I know the <a href="http://en.wikipedia.org/wiki/Geometric_algebra">geometric algebra</a> is a Clifford algebra. Can the properties of geometric algebra, be used to paint a picture of the Dirac equation? I searched the web for this, but I couldn't find a credible source, that explains everything properly. </p>
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<p>Wikipedia has this to say about the discovery of the aberration of light:</p>
<blockquote>
<p>In 1728, while unsuccessfully attempting to measure the parallax of Eltanin, James Bradley discovered the aberration of light resulting from the movement of the Earth. Bradley's discovery confirmed Copernicus' theory that the Earth revolved around the Sun.</p>
</blockquote>
<p><a href="http://en.wikipedia.org/wiki/Gamma_Draconis" rel="nofollow">http://en.wikipedia.org/wiki/Gamma_Draconis</a></p>
<p>If parallax was a known phenomenon at the time, what was the theory at the time that caused parallax? Other than the motion of Earth around the Sun, what else could account for parallax?</p>
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<blockquote>
<p>"Optical lattice requires a very low temperature scale to enter magnetism regime." </p>
</blockquote>
<p><em>Why is that?</em></p>
<p>What I know:</p>
<ol>
<li>optical lattice systems suppress kinetic energy (hopping parameter: $t$ small);</li>
<li>superexchange is a second order process;</li>
<li>Therefore, the energy gap due to exchange will be small ($\Delta E\propto t^2$)</li>
</ol>
<p><em>Is that the reason?</em></p>
| 9,030 |
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<p>Please consider the publication</p>
<blockquote>
<p><a href="http://arxiv.org/abs/1104.0699" rel="nofollow">Invariant Mass Distribution of Jet Pairs Produced in Association with a W boson in $p\bar{p}$ Collisions at $\sqrt{s} = 1.96$ TeV</a></p>
</blockquote>
<p>by the <a href="http://en.wikipedia.org/wiki/Collider_Detector_at_Fermilab" rel="nofollow">CDF-Collaboration</a>, already with <a href="http://www.google.de/search?q=fermilab%20new%20force" rel="nofollow">huge media attention</a>. I must admit that I am puzzled, astonished and excited at the same time. Not being an expert, it would be really nice if someone could shed light on the following question they posed:</p>
<blockquote>
<h3>Did we find a fifth fundamental force that cannot be explained by the standard model?</h3>
</blockquote>
<p>What do you think? </p>
<p>PS.: A part of figure 1 in the publication that is re-printed over and over again:</p>
<p><img src="http://i.stack.imgur.com/JOgV1.jpg" alt="Fig 1"></p>
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<p>Very basic question: When to use $s=vt$, $s=\frac{1}{2}vt$, $s=at$ and $s=\frac{a}{t^2}$?
What was the difference between those?</p>
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<p>In the classic (and morbid) <em>Schrodinger's Cat</em> thought experiment, we imagine putting a cat into a box with a vial of poison which will be triggered by a quantum detectors. We set up a radioactive nucleus or an excited ion, and set up a detector to look for radiation resulting from radioactive decay or drop to the ground state. When we detect this radiation, we break a vial of cyanide, which would kill the cat. If the box is sealed away from external influence, it is commonly said that the cat is in a superposition of life or death, as a result of the uncertain time of the radiation occurring: with no-one to observe the cat, the state of its health life itself becomes uncertain in a quantum mechanical way.</p>
<p>Add a twist. Don't ever open the box. Explode it with a bomb instead and destroy all evidence. Did the wave function ever collapse?</p>
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<p>The Coleman-Mandula theorem states that under certain seemingly-mild assumptions on the properties of the S matrix (roughly: one particle states are left invariant and the amplitudes are analytic in external momenta) the largest possible Lie algebra of symmetries of a (non-trivial) S matrix is given by Poincaré times an internal symmetry.<br>
On the other hand, there are (interacting) field theories whose Lagrangians are symmetric under the conformal extension of the Poincaré group, and in some rare case this property is retained even at the quantum level.<br>
Why (interacting) conformal invariant QFTs do not contradict the theorem? Is it possible to define an S matrix in these theories? I have read somewhere that they do not admit a particle interpretation, what does it mean exactly?</p>
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<p>Some background info on what an evaporator is:
It is a system of metal pans set over a heat source. Sap constantly enters the first pan controlled by a float valve to keep a constant depth. The pans have channels which are open to each other at alternating ends, so that the sap flows back and forth in a serpentine pattern. At the end of the pan system there is a manual valve where you periodically draw off finished syrup. From the beginning of the pan system to the end there is a ever-increasing concentration of sugar. </p>
<p><strong>My question is, how does the sap get more concentrated towards the end of the pan? Or conversely, how is it that the sap doesn't maintain a homogenous sugar concentration throughout? (If you let the fire go out, once the sap cools it will redistribute itself until it is homogenous.)</strong> </p>
<p>I think somebody will probably tell me it has to do with the distance the sap has flowed through the pan by the time it gets to the other end (it would be a linear distance of about 24 feet in my system) but I don't think that answers the question because when you first start a batch, you flood the whole system with cold, fresh sap, all of uniform sugar content, and then you start the fire. It doesn't take long before there is a visible color difference between each channel of the final pan, with the darkest one being next to the draw-off valve. </p>
<p>And no, it's not flow caused by the pans being angled downwards either (a BS answer posted on yahoo!answers to a similar question). The pans are perfectly level. And as far as I can tell the heat intensity from the fire below is uniform at least for the final four channels, which are where you really begin to see visible color graduation as it becomes syrup.</p>
<p><img src="http://i.stack.imgur.com/4NVQS.jpg" alt="here is a quick drawing of the setup that may help with visualization"></p>
<p>There is one detail that I didn't describe at first because I couldn't figure out how to without a drawing, so now that I've added the drawing I'll elaborate on that. The first pan, where the sap goes in, has flues, which are deep, narrow vertical pockets in the bottom of the pan, which reach all the way down into the stove itself. The flames actually pass between the flues on their way to the stovepipe. This (obviously) greatly increases the surface area being heated. I don't know if this changes anything but I thought I should add it. </p>
<p><img src="http://i.stack.imgur.com/klCOD.jpg" alt="evaporator (cold)"> </p>
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<p>Apologies if too specific.</p>
<p>Watched a documentary <a href="http://natgeotv.com/nl/mega-factories-2/videos/bugatti-veyron" rel="nofollow">National Geographic Megafactories Bugatti Veyron</a></p>
<p>I told an colleague (engineer) about the need to warm the car up and then unleash it on the long stretch to be able to make it to 405km/h and mused that the curve before the straight probably had to be taken at 250km/h to do so. He immediately replied that the G-force of going around a(ny) curve at 250km/h would kill the driver... I find that very hard to believe but do not have the skills nor knowledge to refute it. It would be cool to get him this app <a href="http://www.dynolicious.com/" rel="nofollow">http://www.dynolicious.com/</a> and a trip in a Veyron ;)</p>
<p>Here is the <a href="http://googlesightseeing.com/2007/03/super-secret-volkswagen-test-track/" rel="nofollow">Ehra-Lessien track </a> and here is the <a href="http://googlesightseeing.com/maps?p=&c=&t=k&hl=en&ll=52.595202,10.787587&z=16" rel="nofollow">actual curve</a> where some of the clever people here could glean the radius - I think 350m</p>
<p>Can someone show some math and a graph or so?</p>
<p>I have been looking at <a href="http://en.wikipedia.org/wiki/Formula_One_car#Lateral_force" rel="nofollow">http://en.wikipedia.org/wiki/Formula_One_car#Lateral_force</a></p>
<blockquote>
<p>Turn 8 at the Istanbul Park circuit, a
190° relatively tight 4-apex corner,
in which the cars maintain speeds
between 265 and 285 km/h (165 and 177
mph) (in 2006) and experience between
4.5g and 5.5g for 7 seconds—the longest sustained hard cornering in
Formula 1.</p>
</blockquote>
<p>which supports my claim - but would love some more information on this specific matter</p>
<p>Here is a link on what an <a href="http://www.drivingfast.net/techniques/racing-line.htm" rel="nofollow">Apex means in motoring</a><br>
And here are some <a href="http://forums.autosport.com/lofiversion/index.php/t53791.html" rel="nofollow">formulas</a></p>
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<p>The Metropolis-Hastings algorithm is an efficient way of simulating classical ensembles using the Monte Carlo method. Is there a generalization of this algorithm to quantum systems? What I DON'T have in mind is Wick rotation to a classical Euclidean system.</p>
| 9,036 |
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] |
<p>I have readings of colors from a spectrophotometer that records across the human visible color spectrum 390nm to 790nm intervals. I'd like to convert this into any color space, could be CIE XYZ, HSL, CIE-Lab, etc. Any color temperature is okay.</p>
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] |
<p>A sonar continuously emits x(t), a general but known waveform that is reflected by a target and received by the sonar. Both the sonar and the target move in the 3-dimensional space in a general but known manner. That is the positions of the sonar and the target are known. What would be the relation between and the transmitted and received signasl? What would happen if the sound speed, sonar speed and the target speed are all comparable? Is it possible that the received signal contains something like multipath? that is some past signal points of different times are received at the same time? Like receiving multiple balls thrown at different times being received at the same time.</p>
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] |
<p>How exactly can you measure the atomic radius of a noble gas such as Neon or Helium accurately? Would liquefaction help? I also heard that the aforementioned gases are the only common elements which have not been measured accurately as they don't bond with anything.</p>
| 9,039 |
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<p>I have been recently reading a paper on dust removal and I have a few basic questions regarding it. </p>
<p>First off, I am citing this paper - "<a href="http://www.slideshare.net/sauravdhar1/electrostatic-dust-removal" rel="nofollow">Dust removal system with static electricity</a>" </p>
<p>Basically, an electric field is applied, like so:</p>
<p><img src="http://i.stack.imgur.com/zPKTN.jpg" alt="enter image description here"></p>
<p>Since, the particle is initially grounded, the positive charge gets neutralized. </p>
<p>The polarized charge q of the particle is then given by </p>
<p>$$q = 3 \epsilon _{o} {\epsilon_{s}-1 \over \epsilon_{s}+2} E$$</p>
<p>where $\epsilon _{o}$ and $\epsilon _{s}$ are permittivity of free space and relative permittivity of the particle respectively. </p>
<p><strong>First Question</strong> : How did the author get this expression? there is not much explanation in the paper. I have tried to derive it on my own, without much luck.</p>
<p>The particle is then collected by the electrode and the trajectory is governed by the following equation. </p>
<p>$$ m{du \over dt} = qE + mg $$</p>
<p>which makes sense.
<img src="http://i.stack.imgur.com/Ns44X.jpg" alt="enter image description here"></p>
<p><strong>Second question</strong> : What if the surface on which the dust was initially resting on was not conductive surface</p>
<p>Say, a situation like this -</p>
<p><img src="http://i.stack.imgur.com/HSTHz.jpg" alt="enter image description here"></p>
<p>The electric field, will then be constant $ E = {V \over d}$, where $ V $ is is the potential difference between two plates and the $d$ is the distance between them. </p>
<p>The positive charge, here will not be neutralized in this case, and the particle will remain as a induced dipole. Which I can treat as two point charges $q_{+}$ and $q_{-}$ which has the same magnitude. The total electrostatic force on the particle due to the electric field will be </p>
<p>$$ F = q_{+}E - q_{-}E $$ </p>
<p>but since $E$ is constant, $F= 0$, and the particle will not be collected by the top plate.</p>
<p>Am I thinking it right? A second opinion will help.</p>
<p>I have asked a similar question here : <a href="http://physics.stackexchange.com/questions/39502/calculating-dust-attraction-to-a-charged-surface">Calculating dust attraction to a charged surface</a></p>
<p>And the attraction between charge and the dipole seems to exist only because of changing E.</p>
<p><strong>Third Question</strong> : The paper models the entire thing inside a vacuum chamber, will it make any difference if it is not? The same equations will apply right? except may be a slight change in $\epsilon_{o}$</p>
| 9,040 |
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<p>In doing second order time-independent perturbation theory in non-relativistic quantum mechanics one has to calculate the overlap between states </p>
<p>$$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' | n \rangle|^2}{E_n^{(0)}-E_m^{(0)}}$$ </p>
<p>(where $E^{(k)}_n$ represents the kth order correction to the nth energy level).</p>
<p>For the Hydrogenic atom the spectrum of the Hamiltonian consists of a discrete set corresponding to "bound states" (the negative energy states) and a continuum of "scattering states" (the positive energy states).</p>
<p>Is there an example where the overlap between a bound state and the scattering states makes a measurable contribution to the energy in the perturbative regime? Should the scattering states be included in the perturbative calculations? Are there experimental results that backs this up? (For example, perhaps the electron-electron interaction in highly excited states of Helium).</p>
<p>As an aside, what "is" the Hilbert space of the Hydrogen atom in the position representation? I've often read the basis of eigenstates of the Hydrogen atom Hamiltonian isn't complete without the scattering states, but I've not seen any convincing argument of this. I've read that the radial bound states are dense in $L^2((0, \infty))$ (e.g. <a href="http://www.ams.org/journals/ert/2000-004-08/S1088-4165-00-00096-0/" rel="nofollow">here</a>), so including the scattering states the Hilbert space must strictly contain this.</p>
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] |
<p>What are some important examples of paradoxes in physics which are still currently unresolved?</p>
| 9,042 |
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<p>I am taking an introductory lab course in which we've done an experiment on the physical pendulum.</p>
<p><img src="http://i.stack.imgur.com/PkD3g.jpg" alt="drawing of physical pendulum"></p>
<p>We've seen that for small oscillations, the period is </p>
<p>$$T=2\pi\sqrt{\dfrac{I_S}{Mgd_{cm}}}\tag{1}$$</p>
<p>where $S$ is the pivot point, $M$ is the total mass of the object, and $d_{cm}$ is the distance between $S$ and the pendulum's center of mass. </p>
<p>Now, varying $d_{cm}$, I've obtained seven different periods. I've calculated $g$ in terms of $T$ and $d_{cm}$ for those seven distinct values of $T$ and $d_{cm}$. So, $g$ can be expressed as </p>
<p>$$g=4\pi^2\dfrac{I_S}{T^2Md_{cm}}.\tag{2}$$ </p>
<p>All the periods I've obtained were always greater than $1$, and the values of $g$ where between $10.15$ and $10.3$. I am trying to understand why is it that $g$ gave me always greater than $9.8$, the expected value, and not less than $9.8$. If I consider the air friction, I would expect the period to be greater; from what I've said and from equation (2), I would say that the values of $g$ should be less than $9.8$, contrary to the values I got.</p>
<p>Note that that $T$ is in seconds, $[g]=\dfrac{m}{s^2}$ and the angle from which the pendulum was released is of $25$ degrees approximately.</p>
<p>I would appreciate if someone could help me to understand the reason why I've obtained these values for $g$.</p>
| 9,043 |
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<p>The Chinook Helicopter has 2 rotors to counteract the torque generated by spinning the blade. </p>
<p>Theoretically, could you use a smaller "back" rotor that is farther away from the main rotor to achieve the same result, ie no twisting?</p>
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<p>let be the problem </p>
<p>$$ -\frac{d^{2}}{dx^{2}}y(x)+f(x)y(x)=E_{n}y(x)$$</p>
<p>however we have a problem, we do not know the potential but its inverse</p>
<p>$$ f^{-1}(x)=g(x) $$</p>
<p>we know $ g(x) $ but not $ f(x) $ what happense then since</p>
<p>a) the function $ f(x) $ may be multi-valued</p>
<p>b) the function $ f(x) $ may not exists even if we know $ g(x)$</p>
<p>howe can we analytically solve $ f^{-1}(x)=g(x)$ so we get $ f(x) $ ?? in the case $ f(x)=f(-x) $ is even.</p>
| 9,045 |
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] |
<p>After September,I will be a sophomore.During the vocation, I am learning optics by myself. And I learn it by reading Ajoy Ghatak's <strong><em>Optics</em></strong>(<a href="http://books.google.de/books/about/Optics.html?id=jStDc2LmU5IC&redir_esc=y" rel="nofollow">http://books.google.de/books/about/Optics.html?id=jStDc2LmU5IC&redir_esc=y</a>). But I find it difficult for me. <strong>So,I hope that someone can introduce a good textbook to me.</strong> </p>
| 299 |
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<p>In Dirac's The Principle of Quantum Mechanics he makes the general assumption that "if the measurement of the observable $\xi$ for the system in the state corresponding to $|x\rangle$ is made a large number of times, the average of all the results obtained will be $\langle x|\xi|x\rangle$, provided $|x\rangle$ is normalized." </p>
<p>Then he states that the average value of any function of $\xi$, $f(\xi)$ is $\langle x|f(\xi)|x\rangle$. Now, taking $f(\xi)$ to be the function that is equal to unity when $\xi=a$ and to be zero otherwise, noted by $\delta_{\xi a}$, the average value of this function is the probability $P_a$ of obtaining the result $a$ when we perform a single measurement of the observable $\xi$. </p>
<p>Now I know that this really gives the probability, because $\langle x|\delta_{\xi a}|x\rangle=|c_a|^2$, where $c_a$ is the coefficient of the eigenstate of $\xi$ corresponding to the eigenvalue $a$ in the expansion of $|x\rangle$. But Dirac seems to "know" that this is the probability without "knowing" that $|c_a|^2$ is the probability of obtaining a certain result. So my question is: how do we know that this expression $\langle x|\delta_{\xi a}|x\rangle$ is really the probability $P_a$ without using the expansion coefficients?</p>
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<p>What's the evidence, if any, for some local concentration(s) of dark matter in some region(s) smaller than a galaxy?</p>
<p>Galactic-sized--or larger--gravitating halos seem to get all the attention. I'm just wondering about the status of smaller halos/concentrations; if any.</p>
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<p>Suppose there is one rod and a force F is applied in two cases:<br>
<strong>Case 1:</strong> exactly at the middle on center of mass<br>
<strong>Case 2:</strong> at one end of rod
<img src="http://i.stack.imgur.com/3w7Mt.png" alt="enter image description here"></p>
<p>In which case would the center of mass of rod be accelerated more? Or would acceleration of its center of mass be the same in each case?
I have worked towards this and found case 2 would impart a greater acceleration. I just want to check my answer and see if I am making a mistake here.(The question just came into my head and I don't have any source to check the answer from)
<strong>$$My$$</strong> <strong>$$solution:$$</strong>
In case 1 the rod would undergo a translational motion and C.O.M. would get an acceleration of <strong>$F/M$</strong>. In case 2 the rod would rotate about its other end and a torque would act which would be equal to <strong>$Fl$</strong>. Equating this to <strong>$I\alpha$</strong> we get <strong>$\alpha$ = $3F/Ml$</strong> and since C.O.M. is at <strong>$l/2$</strong>(rod is of uniform density) acceleration would be equal to <strong>$3F/2M$</strong>.
Is my solution and thinking correct?</p>
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<p>In nonrelativistic quantum mechanics the state of a system is characterized by a vector of a Hilbert space. </p>
<p>To characterize a state we need a complete set of commuting observables, and once we have that we label the state using some set of quantum numbers.</p>
<p>Now, in field theory I have been told that the Hilbert space of possible states is the space of all field configurations. I see that, but nothing has yet been mentioned to me of something analogous to quantum numbers.</p>
<p>So, my question is, how is a possible field configuration labeled in QFT? Do we have something analogous to a complete set of commuting observables? do we have quantum numbers? </p>
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<p>I ask this because it occurred to me that the inertial property of mass only actually arises in the context of forces (such as the EM force) as a resistance to their accelerating effect. Inertia plays no role in gravity (which as per General Relativity is not really a force, though does resemble a force in certain respects). Under gravity all bodies of whatever mass are accelerated in proportion to the mass of all the other bodies in the universe, in inverse proportion to the square of the distance that stands between them. The role of mass therefore is not to resist acceleration but to warp space-time (and thus induce acceleration, or rather the apparent acceleration of movement in warped space-time). </p>
<p>Under the EM force, and other forces, however, the amount of acceleration that a body experiences depends on its own mass. This relation is generally taken to be an intrinsic property of mass, a resistance to acceleration. But should it not be better conceived as a feature of the force itself, as an action per unit mass, and thus as an acceleration in inverse proportion to mass? In other words, is what appears to be a resistance to acceleration not actually better understood simply as a consequence of the fact that forces act per unit mass? (Mass here is understood as the “bound energy” of General Relativity which warps space-time.) </p>
<p>This re-conceptualisation of the relation between mass and inertia doesn’t have any physical implications of course. But it does perhaps enable us to understand the origin of the equivalence principle (between inertial and active gravitational mass) in that the inertial properties of mass are re-conceived as a property of the forces that interact with it rather than a kind of bolt-on property of the mass itself. The equivalence principle therefore becomes essentially the observation that forces accelerate mass inversely proportionally, on a per unit basis. They could conceivably follow some other rule, some other relation to mass (like gravity does) - though if they did then physics would be quite different of course.</p>
<p>So my question is, is this right? And if it is, does it tell us anything interesting or useful? </p>
| 9,049 |
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] |
<p>Does anyone know where I could find and purchase the book "Statistical Mechanics" by R. Pathria, in 1st edition (the 2nd and the 3rd are readily available, but I really need the first). I believe the first edition was published in 1972. I have searched high and low for it, but can't seem to find it even on Amazon.</p>
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<p>When presenting the stress tensor (say in a non-relativistic context), it is shown to be a tensor in the sense that it is a linear vector transformation: it operates on a vector $n$ (the normal to a surface), and returns a vector $t_n$ which is the traction vector. It is then shown that conservation of angular momentum leads to symmetry of the matrix.</p>
<p>However, tensors are more more naturally presented a multilinear functions. I wonder:</p>
<ul>
<li>What type of tensor is the stress tensor? Is $n$ a vector or a co-vector? What about $t_n$?</li>
<li>Is there a way to understand the symmetry when thinking of the stress tensor as a function of two vectors (or two co-vectors), under which it will seems intuitive why $\sigma(A,B) = \sigma(B,A)$?</li>
</ul>
<p><em>Edit</em>: To clarify, let's look, for example, at the 1st coordinate of the traction vector $t_n$ of an arbitrary normal $n$: This is $\left<e_1, \sigma(n)\right>$. From symmetry, this is equivalent to $\left<n, \sigma(e_1)\right>$ - the inner product of $n$ with the traction vector of a surface orthogonal to $e_1$. Mathematically, I understand why this is correct. But is there any intuitive meaning as to why these two quantities are the same?</p>
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] |
<p>I am working with a rotary damper (paddle hanging off a shaft attached to the bottom of a rotary table and into a vat of fluid). I know the viscosity of the current Newtonian fluid, I know the flow is laminar, and I know the Q-factor of the damping in this fluid. I need to find a way to get a relation between them to figure out how viscous of a liquid I need to replace the current stuff with to get critical damping.</p>
<p>Is there a simple relationship between Q-Factor and viscosity for a Newtonian fluid based rotary damper in laminar flow?</p>
| 9,052 |
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] |
<p>Does a quark, for example a up-quark has a fixed energy? The <a href="https://commons.m.wikimedia.org/wiki/File:Standard_Model_of_Elementary_Particles.svg" rel="nofollow">standard model</a> gives well defined masses in MeV which is energy too.</p>
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<p>This is probably a simple question: I see this claims in many books, but I can't figure a reason why this is true. </p>
<p>So my question is why this claim is true:
"If we know that the system is in the ground state, then the temperature is zero".
So I wonder how this follows from the statistical definition of temperature. </p>
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<p>If you were able to ride along a photon and a second photon passed you in the opposite direction, would what you observe be twice the speed of light?
And would that change what you would see of the second source of light?</p>
| 109 |
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<p>If a pipe extended from just above the ocean floor to outside the atmosphere, would water be sucked up it by the vacuum beyond the atmosphere? If a hole was made in the pipe, above sea level, how would that affect the flow of water? Would it stop it completely?</p>
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<p>The title explains it all. Do objects suspended in ice sink over time? You may remember the story of World War 2 planes that were found 260 ft under the ice which would be anachronistic with seasonal ice layering alone. I'm trying to establish other possible mechanisms. I know that ice flows up and down in glaciers, but will an object actually sink in ice over time? </p>
<p>Also, in what way would they sink? Would heavier parts sink faster than the lighter. Does buoyancy play a role.</p>
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<p>I was doing some physics homework involving direct current circuits and resistors in series, and I started to question the accuracy of the following property of resistors in series, namely that the voltage across the battery is equal to voltage drop across the resistors. But what about the resistance in the wire itself. I wouldn't think that you could just ignore that, especially for very long wires or wires with a significant amount of resistivity. So my question is, why don't text books write</p>
<p>$\Delta V=IR_{1} + IR_{2}+...+IR_{n} + IR_{w}$ where $R_{w}=$ The resistance in the wire </p>
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<p>I need to get rid of water excess in my vacuum chamber, and for that there is the procedure of baking. In order to do that there are several things that one needs to consider, the power, heat load, type of heat tape to use etc. Since I've never done this before, I hope that some of you could share their advice on that subject.</p>
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] |
<p>Which of the following were the intentions of M&M?</p>
<ol>
<li>to disprove the existence of aether.</li>
<li>to show that the aether has no effect on matter and energy and therefore is as good as non-existent.</li>
</ol>
<p>Feel free to insert more reasons/intentions.</p>
<p>Which of the following were the corollaries/conclusions?</p>
<ol>
<li>Aether indeed does not exist</li>
<li>M&M does not prove or disprove the existence of aether.</li>
<li>M&M was a pointless experiment.</li>
</ol>
<p>Feel free to add more corollaries/conclusions.</p>
| 883 |
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<p>This question is kind of inspired in this one:</p>
<p><a href="http://physics.stackexchange.com/questions/4359/diffm-as-a-gauge-group-and-local-observables-in-theories-with-gravity">Diff(M) as a gauge group and local observables in theories with gravity</a></p>
<p>The conundrum i'm trying to understand is how is derived the (quite) extraordinary statement that in GR there are no local observables. I just want to stress that this is indeed an extraordinarily counter-intuitive assertion (with extraordinarily dramatic consequences for any compatible theory of quantum reality), and it deserves an extraordinarily robust explanation. </p>
<p>Among the statements i see are mostly involved in this argument are:</p>
<ul>
<li><p><em><strong>It is usually argued that Diff(M) is a gauge transformation.</em></strong> This point i don't have any sort of issue; the atlas of reference frames we use to describe space-time are indeed a human convention and physical laws should not depend on such conventions</p></li>
<li><p><em><strong>A physical observable should be invariant under any gauge transformation.</em></strong> whaaa? i mean, this is clearly preposterous non-sense; actually i think this is more dangerous than simple non-sense, is just circular self-justification. This is actually saying that observables should be scalars?</p>
<p>I can provide you a proof that this is non-sense by saying that the momentum of a particle is an observable in my reference-frame, and in other Diff(M) gauge (that is, another reference frame) i will see a different momentum of the same observable. All eigenvalues and eigenvectors transform according to the vector representation of the Poincare group. You are now of course free of dismiss such 'proof' as non-sense because my assumption that the momentum of a local particle is an observable is non-sense, but then, how are you sustaining that part of the argument, without actually saying again that Diff(M) is a gauge transformation? how do you avoid the circularity in this argument?</p>
<p>U(1) gauge is a bad example because this is an internal symmetry; Diff(M) are space-time symmetries and i don't think that what is true in there (A eletromagnetic vector potential being unobservable, but B and E being observable, hence observables are invariant under U(1) )</p></li>
<li><p><em><strong>It is usually argued that observables in GR formally exists in the asymptotic boundary of the space-time.</em></strong> Is there an argument for this that is unrelated/independent to the previous point?</p></li>
</ul>
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] |
<p>What is the full text (and possibly the source) of the summary of the 3 laws of thermodynamics that goes something along the lines of "Can't break even, can't win and can't even stop playing the game"?</p>
| 9,060 |
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] |
<p>the values $ \zeta (-1)= -1/12 $ and $ \zeta (-3)= 1/120 $ give accurate results for casimir and to evaluate the dimension in bosonic string theory</p>
<p>so is there a physcial JUSTIFICATION to justify that in phsyics (not mahthematics) every time we see a divergent series like $ 1+2^{s}+3^{s}+......... $</p>
<p>otherwise how it would be possible that zeta regularization gave only correct results for the series $1+2+3+4+5+..... $ and $1+8+27+64+.. $ but not for example for $ 1+4+9+16+25+..=0 $</p>
<p>why a matheamtical fucntion would be useful only for certain values but not for others :(</p>
| 9,061 |
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<p>In theory do wormholes have a side to their path through space?</p>
<p>What is there at a point in line with the entry and exit, would anything look different at that point in space?</p>
<p>Could a space ant get in through the side of a wormhole?</p>
<p>Update: The wormhole would be an einstein-rosen bridge from GR. I also wonder if it's torus would radiate Hawking radiation?</p>
| 9,062 |
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<p>Suppose we have a chemical reaction of the form</p>
<p>$$n_1 A_1 + \cdots + n_r A_r \leftrightarrow m_1 B_1 + \cdots + m_s B_s$$</p>
<p>where $A_i$ and $B_i$ are molecules, and the $n_i$ and $m_i$ are the integer coefficients of the equation. Let $[X]$ be the concentration of $X$, that is, the amount of moles per unit volume. The law of mass action says that at chemical equilibrium, the following holds:</p>
<p>$$
\frac{[A_1]^{n_1}\cdots[A_r]^{n_r}}{[B_1]^{m_1}\cdots[B_s]^{m_s}} = K(T)
$$</p>
<p>In Fermi's <em>Thermodynamics</em>, he gives a proof that uses kinetic theory (slight edition and emphasis by me):</p>
<blockquote>
<p>A reaction from left to right can occur as a result of a multiple collision involving $n_1$ molecules $A_1$, $n_2$ molecules $A_2$, ..., $n_r$ molecules $A_r$. The frequency of such multiple collisions is <strong><em>obviously</em></strong> proportional to the $n_i$th power of $[A_i]$, that is, to the product:</p>
<p>$$ [A_1]^{n_1}\cdots[A_r]^{n_r}$$</p>
</blockquote>
<p>That is not obvious at all for me. Could someone go into a little more detail explaining why the frequency of collisions should be proportional to $[A_i]^{n_i}$?</p>
| 9,063 |
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<p>First question: Does anyone know of any low permeability, low coercivity magnetic compounds? A physics professor told me that I should dig deep in the literature, but that I should look for materials with a Curie temperature ~100K and that I should avoid cubic structures. I haven't had much luck finding anything though. </p>
<p>In terms of compounds with low permeability, I have found Gd75Co25, and TcC, but I haven't found any permeability information about them.</p>
<p>Thanks for anyone who gives this question a second thought. </p>
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<blockquote>
<p>A rock is thrown towards a window, and hits it. The window does not break and the rock reverses its direction and falls under the window.</p>
</blockquote>
<p>My question is, under this circumstance since the rock reversed it's direction of movement I want to say that the force exerted by the window was larger than that of the rock because if they were equal, the rock would simply stick to the window and slide down until it reaches the bottom.</p>
<p>However, the answer to this problem claims that the window and the rock had the same force. Can someone explain me what is going on?</p>
| 9,065 |
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] |
<p>It is quite easy to compute the first derivative of vapor pressure with respect to temperature from a cubic equation of state at least at the critical point since there is a continuity with the critical isochore. But, is there any way to establish the second derivative or at least its value at the critical point? For simplicity, Van der Waals or Redlich-Kwong, Soave-Redlich-Kwong or Peng-Robinson equations of state are in my mind.</p>
| 9,066 |
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] |
<p>When looking at the pressure-temperature diagram along the critical isochore (up to quite high reduced temperatures) a very linear trend can be observed. From a theoretical point of view, is the critical isochore linear or just almost linear ?</p>
| 9,067 |
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<p>I've been looking for problems to practice on this topic and found a problem asking to use the Maxwell-Boltzmann distribution function to calculate the fraction of Argon gas molecules with a speed of 305 m/s at 500 K. I thought the distribution function could only be used to find the fraction of molecules moving between two given speeds not at a specific speed. Can someone explain how to do this?</p>
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<blockquote>
<p>In an artificial satellite, a space traveler tries to fill a pen by
dipping it in ink. The amount of ink filled in the pen as compared to
the amount of ink filled on the Earth's surface will be:</p>
<p>A) less</p>
<p>B) more</p>
<p>C) same</p>
<p>D) nil</p>
</blockquote>
<hr>
<p>The answer is B) more but I can't understand why?<br>
Is it because the acceleration due to gravity, $g$, is less there, so the ink rises faster?</p>
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] |
<p>What is highest known value been achieved for single atom (artificial atom) cooperativity ($C=\frac{g^2}{\kappa\gamma}$) factor in the strong coupling regime for Cavity and Curciut QED? </p>
| 9,070 |
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<p>I am referring to this recent "news feature" by Zeeya Merali from Nature magazine <a href="http://www.nature.com/uidfinder/10.1038/478302a">www.nature.com/uidfinder/10.1038/478302a</a>. Here is the specific quote:</p>
<p>"To make matters worse, some of the testable predictions from string theory look a tad bizarre from the condensed-matter viewpoint. For example, the calculations suggest that when some crystalline materials are cooled towards absolute zero, they will end up in one of many lowest-energy ground states. But that violates the third law of thermodynamics, which insists that these materials should have just one ground state."</p>
<p>What crystalline materials are predicted to have this degeneracy? How was string theory used to arrive at this prediction, and can it be arrived at without string theory?</p>
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<p>I am studying the piezoelectricity in Gallium arsenide (GaAs), $[110]$ and $[\bar{1}10]$ oriented. Piezoelectricity is usually described microscopically by a 3 index tensor, $d_{ijk}$ where
i,j and k equal to x,y and z.</p>
<p>$[110]$ and $[\bar{1}10]$ have different piezoelectric behaviour but they are linked by a parity operation on the x-axis: $$x\rightarrow -x$$
Can I assume the following identity:$$d^{[110]}_{ijk}=(-)^{\delta_{xi}+\delta_{xj}+\delta_{xk}}d^{[\bar110]}_{ijk}$$
Derived by applying the same transformation.</p>
| 9,072 |
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